The Star Cluster Population of M51 III. Cluster disruption and formation history

合集下载

tpo32三篇托福阅读TOEFL原文译文题目答案译文背景知识

tpo32三篇托福阅读TOEFL原文译文题目答案译文背景知识阅读-1 (2)原文 (2)译文 (5)题目 (7)答案 (16)背景知识 (16)阅读-2 (25)原文 (25)译文 (28)题目 (31)答案 (40)背景知识 (41)阅读-3 (49)原文 (49)译文 (53)题目 (55)答案 (63)背景知识 (64)阅读-1原文Plant Colonization①Colonization is one way in which plants can change the ecology of a site.Colonization is a process with two components:invasion and survival.The rate at which a site is colonized by plants depends on both the rate at which individual organisms(seeds,spores,immature or mature individuals)arrive at the site and their success at becoming established and surviving.Success in colonization depends to a great extent on there being a site available for colonization–a safe site where disturbance by fire or by cutting down of trees has either removed competing species or reduced levels of competition and other negative interactions to a level at which the invading species can become established.For a given rate of invasion,colonization of a moist,fertile site is likely to be much more rapid than that of a dry, infertile site because of poor survival on the latter.A fertile,plowed field is rapidly invaded by a large variety of weeds,whereas a neighboring construction site from which the soil has been compacted or removed to expose a coarse,infertile parent material may remain virtually free of vegetation for many months or even years despite receiving the same input of seeds as the plowed field.②Both the rate of invasion and the rate of extinction vary greatly among different plant species.Pioneer species-those that occur only in the earliest stages of colonization-tend to have high rates of invasion because they produce very large numbers of reproductive propagules(seeds,spores,and so on)and because they have an efficient means of dispersal(normally,wind).③If colonizers produce short-lived reproductive propagules,they must produce very large numbers unless they have an efficient means of dispersal to suitable new habitats.Many plants depend on wind for dispersal and produce abundant quantities of small,relatively short-lived seeds to compensate for the fact that wind is not always a reliable means If reaching the appropriate type of habitat.Alternative strategies have evolved in some plants,such as those that produce fewer but larger seeds that are dispersed to suitable sites by birds or small mammals or those that produce long-lived seeds.Many forest plants seem to exhibit the latter adaptation,and viable seeds of pioneer species can be found in large numbers on some forest floors. For example,as many as1,125viable seeds per square meter were found in a100-year-old Douglas fir/western hemlock forest in coastal British Columbia.Nearly all the seeds that had germinated from this seed bank were from pioneer species.The rapid colonization of such sites after disturbance is undoubtedly in part a reflection of the largeseed band on the forest floor.④An adaptation that is well developed in colonizing species is a high degree of variation in germination(the beginning of a seed’s growth). Seeds of a given species exhibit a wide range of germination dates, increasing the probability that at least some of the seeds will germinate during a period of favorable environmental conditions.This is particularly important for species that colonize an environment where there is no existing vegetation to ameliorate climatic extremes and in which there may be great climatic diversity.⑤Species succession in plant communities,i.e.,the temporal sequence of appearance and disappearance of species is dependent on events occurring at different stages in the life history of a species. Variation in rates of invasion and growth plays an important role in determining patterns of succession,especially secondary succession. The species that are first to colonize a site are those that produce abundant seed that is distributed successfully to new sites.Such species generally grow rapidly and quickly dominate new sites, excluding other species with lower invasion and growth rates.The first community that occupies a disturbed area therefore may be composed of specie with the highest rate of invasion,whereas the community of the subsequent stage may consist of plants with similar survival ratesbut lower invasion rates.译文植物定居①定居是植物改变一个地点生态环境的一种方式。

Ionized gas kinematics and massive star formation in NGC 1530

a r X i v :a s t r o -p h /0307234v 1 11 J u l 2003Astronomy &Astrophysics manuscript no.ms4084February 2,2008(DOI:will be inserted by hand later)Ionized gas kinematics and massive star formation in NGC 1530A.Zurita 1,M.Rela˜n o 2,J.E.Beckman 2,3,and J.H.Knapen 41Isaac Newton Group of Telescopes,38700,Santa Cruz de La Palma,Canarias,Spaine-mail:azurita@ing.iac.es 2Instituto de Astrof ´ısica de Canarias,C.V´ıa L´a ctea s/n,38200,La Laguna,Tenerife,Spain e-mail:mpastor@ll.iac.es,jeb@ll.iac.es 3Consejo Superior de Investigaciones Cient´ıﬁcas (CSIC),Spain 4University of Hertfordshire,Hatﬁeld,Herts.AL109AB,UK e-mail:knapen@Abstract.We present emission line mapping of the strongly barred galaxy NGC 1530obtained using Fabry–P´e rot interferometry in H α,at signiﬁcantly enhanced angular resolution compared with previously published studies.The main point of the work is to examine in detail the non–circular components of the velocity ﬁeld of the gas,presumably induced by the strongly non–axisymmetric gravitational potential of the bar.To do this we ﬁrst derive a model rotation curve making minimum assumptions about kinematic symmetry,and go on to measure the non–circular component of the full radial velocity ﬁeld.This clearly reveals the streaming motions associated with the spiral density wave producing the arms,and the quasi–elliptical motions with speeds of order 100km s −1aligned with the bar.It also shows in some detail how these ﬂows swing in towards and around the nucleus as they cross a circumnuclear resonance,from the dominant “x 1orbits”outside the resonance to “x 2orbits”within paring cross–sections of this residual velocity map along and across the bar with the surface brightness map in H αindicates a systematic oﬀset between regions of high non–circular velocity and massive star formation.To investigate further we produce maps of velocity gradient along and across the bar.These illustrate very nicely the shear compression of the gas,revealed by the location of the dust lanes along loci of maximum velocity gradient perpendicular to the bar.They also show clearly how shear,seen in our data as velocity gradient perpendicular to the ﬂow,acts to inhibit massive star formation,whereas shocks,seen as strong velocity gradients along the ﬂow vector,act to enhance it.Although the inhibiting eﬀect of gas shear ﬂow on star formation has long been predicted,this is the clearest observational illustration so far of the eﬀect,thanks to the strong shock–induced counterﬂow system in the bar.It is also the clearest evidence that dust picks out shock–induced inﬂow along bars.These observations should be of considerable interest to those modelling massive star formation in general.Key words.Galaxies:general –Galaxies:individual (NGC 1530)–Galaxies:ISM –Galaxies:spiral–Galaxies:kinematics and dynamics –ISM:kinematics and dynamics1.IntroductionThe interactive relation between dynamics and morpholo-gy is a well known aspect of barred galaxies.It has been invoked to throw light on one of the more interesting ques-tions in galactic evolution:by what mechanism or mecha-nisms is material driven in to regions close to the nucleus where it can participate in star formation,or contribute to the mass of the central supermassive black hole,and to the activity around it (Shlosman et al.1989).As an archetypal barred galaxy NGC 1530has received conside-rable attention both morphologically and kinematically.These studies have been facilitated observationally by the strength and length of the main bar,which compensate for its distance.The latter is 36.6Mpc (Tully &Fisher 1988),2Zurita et al.:Ionized gas kinematics and massive star formation in NGC1530of their work on velocity and surface luminosity mapping in CO with some additional stellar information presented in Greve et al.(1999),while Regan et al.’s most important contributions come from their velocity and surface bright-ness mapping in Hαwith a useful contribution from CO supplemented by near–IR mapping in the initial paper of their published series.NGC1530is a dramatic twin-armed spiral galaxy,with arms breaking away sharply from the ends of the long primary bar.It is notable that these arms,though trail-ing,have shorter opposing lengths,curving inward from the tips of the bar as prolongations of the main arms. They are well brought out in Hαas seen in Regan et al. (1995)or in Fig.1a of the present paper.The bar ima-ged in broad band is wide and contains prominent dust lanes which,as the publications by Regan et al.and by Downes&Reynaud listed above well point out,pick out shocked gas following trajectories generally aligned with the bar.These are almost straight along the bar but begin to curve inwards from a galactocentric distance of some 2kpc,bending sharply in towards the nucleus.They link the prominent star–forming regions at the ends of the bar, seen very well here in Hαin Fig.1a,with the even more prominent star–forming ring feature with radius∼2kpc noted in blue images by Buta(1984)and by Wray(1988) and also clearly picked out in Hαin bining near–IR with optical data to give colour maps,Regan et al.(1995)explored the stellar and dust morphology in the bar and in the central zone following the lanes right into the nucleus.One of the aims of the present paper is to elucidate further the relation between gasﬂows and star formation which are implied in these morphological data described above.However,this aim has been pursued with conside-rable achievement previously by the two groups men-tioned above.Regan et al.(1996)combined atomic hy-drogen21cm measurements with ionized hydrogen HαFabry–P´e rot spectroscopy to derive a rotation curve for NGC1530.From this they derived a bar pattern speed of 20km s−1kpc−1and used it to predict resonances at radii coinciding with prominent morphological features,inclu-ding an outer gaseous ring seen in H i,an inner ring seen in H i and Hα,and the nuclear star–forming ring men-tioned above.Downes et al.(1996)mapped the galaxy in CO and identiﬁed the major concentrations of potentially star forming molecular gas;these are located over the cen-tral prominent inner disc zone of radius∼2kpc and extend out more weakly over the bar to less prominent concentra-tions over the ends of the bar.They added interferometric mapping of the central zone,ﬁnding a circumnuclear ring structure with gas in orbits apparently perpendicular to the elongated orbits in the outer parts of the bar.They re-late these patterns to the predictions of resonance models (Athanassoula1984;Jenkins&Binney1994)in which gas within corotation moves along x1orbits along the bar un-til it reaches an inner Lindblad resonance(ILR)where it moves into the x2orbits perpendicular to the bar.A neat schematic diagram inﬁg.10of Downes et al.(1996)illus-trates the predicted behaviour of the gas under these cir-cumstances.Although the stars follow quasi–elliptical x1 orbits,in the case of gas,the shocks are produced along the bar and specially at the ends of the bar,where orbit crowd-ing occurs,as was well predicted in Roberts et al.(1979). However,as the gas reaches the outer limit of the zone dominated by x2dynamics,it suﬀers another shock,and is pulled through a right–angle,falling in again towards the nucleus.Gas on x1orbits with an impact parameter a little larger with respect to the nucleus is less aﬀected by the eﬀects of the resonance,and proceeds along the out-going edge of the bar,albeit with declining velocities.It is just this kind of arrangement for allowing gas to fall to the centres of barred galaxies which was invoked by Shlosman et al.(1989)in their“bars within bars”scenario as a fu-eling mechanism for the diﬀerent types of circumnuclear activity:starbursts and AGN.Using Fabry–P´e rot Hαmapping of NGC1530,Regan et al.(1997)demonstrated that the two–dimensional Hαvelocityﬁeld in the bar region shows the skew pattern predicted for x1orbits superposed on the general galac-tic rotation.They went on to combine hydrodynamical models with their observations to compute a net inﬂow rate to the nuclear zone of∼1M⊙per year,with the re-maining gas spraying back outwards along the major bar axis before coupling into a new inﬂow ing molecu-lar emission from CO and HCN,the former at angular res-olution of1.8′′and the latter at3.6′′,Reynaud&Downes (1997)detected steep velocity gradients spatially conﬁned to two arcs coupling into a ring.These arcs represent shock fronts where the inﬂow along the bar is being constrained to change direction and assume the x2orbital conﬁgura-tion along the nucleus.These arcs correspond to two small arm features picked out in Hαto the north and south of the circumnuclear zone of enhanced star formation(see Fig.1a of the present paper).The points where the arcs couple to the circumnuclear ring are the main emitters in HCN,suggesting points of maximum molecular density. Reynaud&Downes postulate the presence of two ILR’s: one at1.2kpc from the nucleus where the shock arcs are rooted,and one very close to the nucleus,at the inner edge of the molecular ring.They support these inferences using resonance theory and their rotation curve,which is de-rived kinematically but supported by a dynamical model. In a subsequent article Reynaud&Downes(1999)map the same area in two emission lines each of12CO and13CO, showing that the molecular gas density is highest in the circumnuclear ring and not so high in the arcs referred to above.Perhaps of most interest and relevance for the study we present here is that of Reynaud&Downes(1998),who use their CO kinematics of the whole bar region in NGC1530 to explore the relation between velocity changes and star formation.They conclude that strong velocity changes, which represent shocks and shear,are negatively corre-lated with star formation and that the distribution of star formation does not correspond fully to the distribution of available molecular gas,as traced by CO.Although itZurita et al.:Ionized gas kinematics and massive star formation in NGC15303is true that the major concentration is found in the cen-tral circumnuclear zone where star formation is most en-hanced,there is considerable CO measured along the bar as well as at its ends,while the star formation is clearly weak along of the bar.Reynaud&Downesﬁnd veloci-ty jumps across the dust lanes from velocities of order 100km s−1along the bar in one direction,to similar velo-cities in the reverse direction.These jumps maximize half way out along the bar from the nucleus on both sides. They conclude that steep velocity gradients,both shear and shock,prevent molecular clouds from condensing to form stars.One of the main aims of the present paper is to examine this hypothesis in a little more detail using an Hαvelocityﬁeld.We present new high resolution velocity and inten-sity maps of NGC1530,obtained in Hαemission using a Fabry–P´e rot interferometer.The instrument provides a three–dimensional“data cube”,akin to a conventional ra-diastronomical set of line maps,in which the emission in-tensity is given as a function of three coordinates:two positional coordinates and the velocity.From this“data cube”one goes on to compute maps in integrated line intensity,line peak velocity,and velocity dispersion.The next step is to obtain the rotation curve of the galaxy and to subtract it oﬀtwo–dimensionally from the com-plete observed velocityﬁeld.This allows us to obtain the non-circular motions due to non-axisymmetric elements of the galaxy.For NGC1530the dominant source of non–axisymmetry is the strong bar of length almost28kpc, which dominates the appearance of the galactic disk.We alsoﬁnd kinematic signatures of the streaming motions in the sharply deﬁned spiral arms.Besides we also see,in the central5kpc,evidence for a distinct kinematic structure predicted by classical resonance theory,and already care-fully observed and characterised in the studies by Regan and coworkers,and by Reynaud&Downes in the referen-ces given above.As a further step we have prepared plots of the velocity gradients in the whole of the bar and arm structure as ima-ged in Hαemission.We have related the velocity gradient morphology to the distribution of the massive star forma-tion in arms,bar,and the central zone.Our main steps forward compared with previous studies are due to the uniformly high angular resolution we could obtain over the full image.This has enabled us to make a more precise de-ﬁnition of the rotation curve,and hence an improved map of the non-circular velocityﬁeld,both around the main bar,and in the central zone.From the two–dimensional display of the non-circular velocities we have gone on to derive a map of the velocity gradients,with a resolution better than2′′over the wholeﬁeld of the galaxy.Such a map has not been previously produced,so we are able to make progress here in characterising the geometrical and physical relationships between velocity gradients and star formation.2.Observations and data reductionThe Fabry–P´e rot observations of NGC1530were taken at the Roque de los Muchachos Observatory with the 4.2m William Herschel Telescope(WHT)on the night of September2nd,1998.The TAURUS-II instrument, equipped with a TEK CCD camera was used to observe the galaxy in the Hαemission line,with a plate scale of0.292′′per pixel,which corresponds to a pixel scale 179pc arcsec−1at the distance of the galaxy(37Mpc). The observations consisted of exposures of150s at equally spaced positions of the etalon,at intervals of0.407˚A,co-rresponding to18.62km s−1.The total number of steps was55,allowing us to scan the full wavelength range of the Hαline in the galaxy.We used the appropriately red-shifted narrow band Hαﬁlter as an order-sortingﬁlter (λc=6613˚A,∆λ=15˚A,corresponding to the galaxy’s sys-temic velocity v sys=2461km s−1;de Vaucouleurs et al. 1991;hereinafter RC3).Wavelength and phase calibration were performed using observations of a calibration lamp (taken before and after the observations of the galaxy),u-sing the TAUCAL package in the FIGARO environment. The spatial resolution of the resulting data set is∼1′′.The data set was placed on a correctly oriented spatial grid by comparing positions of point–like features in the HαFabry–P´e rot intensity map with those in the narrow-band Hαimage from Rela˜n o et.al(2003b),yielding maximum uncertainties in positions of0.3′′.Theﬁnal calibrated data cube has941×941pixels×55‘planes’in wavelength,se-parated by18.62km s−1.We examined plane by plane the data cube and found that it had a considerable number of cosmic ray events.We eliminated them with the task imedit in IRAF,which allowed us to replace the anoma-lous pixels by a mean background value.We determined which channels of the data set were free of Hαline emission after smoothing the data to a resolution of2.5′′×2.5′′.We found10channels free of line emission on the low-velocity side,and13channels on the high–velocity side.The con-tinuum was determined byﬁtting a linear relation to the line–free channels,and was then subtracted from the line emission channels.In order to study the kinematics on diﬀerent scales,the data–cube was convolved down from the original resolu-tion of1′′×1′′to resolutions of2′′×2′′,3′′×3′′,6′′×6′′and 10′′×10′′.For each data set we obtained the total Hαintensity(zeroth moment),velocity(ﬁrst moment)and velocity dispersion(second moment)maps.The proce-dure to obtain the moment maps is equivalent for each smoothed data cube so we describe the procedure followed for the full resolution data set only.A reader wanting a fuller description of the procedure canﬁnd it in Knapen (1998).The points with low signal were eliminated pro-ducing a conditionally transferred data cube,in which values were retained only at positions where the inten-sity in the smoothed data cube of3′′×3′′was larger than 2.5times the rms noise of the smoothed cube;pixel va-lues at all other positions were set to undeﬁned.We then removed noise peaks outside the area where Hαemission4Zurita et al.:Ionized gas kinematics and massive star formation in NGC1530Fig.1.a)Intensity map(zeroth order moment)of the Hαemission in NGC1530.The map was obtained from the 2′′resolution data cube.The kinematic centre is marked with a black cross.b)Velocity map(ﬁrst moment)of the Hαemission in NGC1530,derived from the2′′resolution data cube.c)Model velocity map of NGC1530,obtained from the Hαrotation curve of the galaxy shown in Fig.3,with Hαisointensity contours overlaid.We can clearly see“wiggles”at the radii of the spiral arms,due to the density wave streaming motions not subtracted oﬀfrom the rotation curve.d)Map of the residual velocities of NGC1530,obtained by subtracting the model velocityﬁeld (Fig.1c,after taking out the ripples due to the streaming motions in the spiral arms,see text for details)from theZurita et al.:Ionized gas kinematics and massive star formation in NGC15305 is expected by setting the pixel values there to undeﬁnedtoo.This was done interactively by inspecting the highresolution channel maps one by one and comparing themwith the corresponding and adjacent channel maps in the3′′×3′′data set.The resulting data cube was then used tocalculate the moment maps using the moments task inthe GIPSY package.moments obtains the zeroth,ﬁrst and second mo-ments of the emission at each spatial pixel in the galaxy and produces a corresponding map for each moment.In the procedure,moments takes into account the signal only when two conditions are met:the signal is higher than2.5times the rms noise of the high-resolution cube, in at least three adjacent channels.Theintensity map for the2′′resolution data cube is shown in Fig.1a and the ﬁrst moment(velocity)map is shown in Fig.1b.Although the moments procedure is a more useful tech-nique for studying the global kinematics in the galaxy,it must be treated with caution when it is used for a detailed description of the kinematics of individual H ii regions. The moments procedure gives an underestimate of the ve-locity dispersion of the proﬁle(van der Kruit&Shostak 1982),thus,if a precision measurement of this quantity is required,a betterﬁt to the line proﬁles,using Gaussian functions,is needed.3.Kinematics3.1.Rotation curveThe rotation curve of the galaxy can be derived from the velocity map,which gives the projected velocity along the line of sight in each position of the galaxy.Assuming that the measurements refer to a position on a single inclined plane,the projected velocity can be related to the rotation velocity in the plane of the galaxy by this expression:v(x,y)=v sys+v rot(r)cos(θ)sin(i)(1) where v(x,y)denotes the radial velocity at the sky coor-dinates x and y,v sys the systemic velocity,v rot the ro-tational velocity,i the inclination angle of the normal to the galaxy plane to the line of sight,andθthe azimuthal distance from the major axis in the plane of the galaxy,re-lated to the rotation centre(x0,y0)and the position angle of the galaxy,PA.We derived the rotation curve following the procedure described by Begeman(1989),where the rotation curve is determined byﬁtting tilted rings to the observed velocityﬁeld.For each ring independently,the parameters v sys,v rot,i and x0,y0and PA are obtained making a least–squaresﬁt to Eq.1using the observed velocityﬁeld v(x,y).We discarded the points within a certain free–angle θmax around the minor axis since they carry less informa-tion about the underlying circular velocity of the galaxy and the values obtained in this zone are less accurate due to projection eﬀects.In the case of NGC1530a value of θmax=45◦was used to avoid the non-circular motions along the bar.Besides,we give more weight to positionsRadius (arcsec)020*********100200300Radius (kpc)Fig.2.Hαrotation curve of the disc of NGC1530,for the receding and the approaching sides of the galaxy separately.The agreement between the two sides shows the symmetry of the velocityﬁeld and the reliability of the rotation centre.close to the major axis using a weighting function pro-portional to|cosθ|in theﬁt.The procedure used to ob-tain each of the parameters which characterise the rotation curve is the following.The parameters v sys,x0and y0depend on the symme-try of the velocityﬁeld and are the same for each ring. We obtained the position of the kinematic centre(x0,y0) using the velocity map of6′′resolution.We took annuli of 3′′width,ﬁxed values for the heliocentric systemic velo-city at2461km s−1(RC3),inclination angle at i=50◦(a mean between the values of Downes et al.1996and Regan et al.1996)and position angle at188◦(the value found by Regan et al.1996)and obtained(x0,y0)using Eq.1.We found a large scatter in the values of the kinematic centre for annuli far from the centre of the galaxy.This is due to the paucity of Hαemission in the disc of the galaxy outside the arms and to the fact that lower resolution data cubes are more spatially aﬀected by the smoothed non-circular motions along the bar in the data cubes.The mean value of(x0,y0)for the rings inside12′′corresponds to the coor-dinates4h23m26.94s(±0.02s)75◦17′44.0′′(±0.1′′),J2000. We checked this value using the same procedure for the velocity maps of lower and higher(10′′and2′′)resolution, and found that the diﬀerences in the rotation centre from the value adopted were inside the error bars.The systemic velocity was obtained from the10′′reso-lution velocity map with rings of width5′′.The centre po-sition wasﬁxed to the value found previously,and the in-clination and position angle wereﬁxed to the same values used to derive the rotation centre.The mean value for v sys in all the rings is2466±4km s−1,where the error is the6Zurita et al.:Ionized gas kinematics and massive star formation in NGC1530 standard deviation from the mean.This value is in agree-ment with the value found by Reynaud et al.(1997)ofv sys=2466km s−1for CO data,but diﬀers from that ob-tained by Regan et al.1996in Hα,v sys=2447±2km s−1.A way to test whether the rotation centre and thesys-temic velocity are well determined is shown in Fig.2, where we have plotted rotation curves for the receding and approaching halves of the galaxy derived separately u-sing the rotation centre and systemic velocity found above. The coincidence of the velocity points for both sides,espe-cially in the central zone of the galaxy,provides evidence of the symmetry of the velocityﬁeld and the validity of the values for the rotation centre and systemic velocity. We also derived the rotation curves for the receding and a-pproaching halves with the rotation centre found in Regan et al.(1996),but in that case we found discrepancies which appeared unphysically large.It is the better resolution of our data(1′′,while Regan et al.(1996)has a net resolution of4′′)which allows us to obtain a more accurate positionfor the rotation centre.Finally,we obtained the rotation curve using the ve-locity map at2′′resolution in Fig1b.For the internal part of the galaxy,out to12.5′′,we used rings of width1′′,and rings of width6′′for larger radii.The rotation curve ob-tained in this way is shown in Fig.3,where the PA and the inclination wereﬁxed at188◦and50◦respectively.Fig.3 also displays the rotation curve from Regan et al.1996, which is similar to that found here,but we obtain higher values of the rotation velocity in the inner part,10′′–15′′, and also in the70′′–90′′radial range.In order to check the PA adopted,we left it as a free parameter in theﬁt,ﬁnd-ing that the values given by the program for most of the annuli are close to188◦and that the rotation curve did not change signiﬁcantly from the curve with aﬁxed PA.The adopted inclination angle i=50◦was also checked.We ﬁtted v rot and i with Eq.1,keeping the other kinematic parametersﬁxed,and found a mean value of i=(53±8)◦, in good agreement with the value adopted.To test the importance of a careful deﬁnition of the the free–angle we reduced its value to20◦and rederived the rotation curve.As seen in Fig.4this produced“ro-tational velocities”rising to values of over500km s−1,as there is an obvious contribution from the non–rotational motion along the bar projected into the line of sight.As we will see below the amplitude of the gas motion along the bar is over100km s−1,and it is easy to see that this will yield the unrealistically high velocities shown in Fig.4. Fortunately,the bar orientation in NGC1530does not make it too diﬃcult to isolate and avoid the emission from gas which contains a signiﬁcant non–circular velocity com-ponent,but Fig.4oﬀers a warning to those using maps of much lower resolution in similar circumstances.3.2.The residual velocity mapAfter deriving the mean rotation curve,an easy way to explore non–circular motions within the galactic disc isRadius (arcsec)020*********100200300Radius (kpc)051015Fig.3.Hαrotation curve of the disc of NGC1530,up to18kpc from the galactic centre.The rotation curve was obtained byﬁtting tilted rings to the observed ve-locityﬁeld in Fig.1b.Also shown is the rotation curve obtained by Regan et al.(1996).to make a two–dimensional projection of this curve and subtract it from the observed velocityﬁeld.The two–dimensional projection of the initial rotation curve is seen in Fig.1c,where we have superposed an isophote map of intensities to show the positions of the emitting compo-nents.The projection has classical symmetry,but shows a few small features:“wiggles”which occur at some three quarters of the radial distance from the centre to the edge of theﬁeld.These can be explained as eﬀects of stream-ing motions in the spiral arms,which have not been sub-tracted adequately from the mean rotation curve.While it is diﬃcult to get an exact separation of ro-tation and streaming motions,we have made aﬁrst a-pproximation by assuming that the true rotation curve is smooth.Applying a second order polynomialﬁt to the part that is observed as smooth,i.e.between27′′and63′′from the centre,we then extrapolate this to cover the range between63′′and the edge of theﬁeld at99′′from the centre,and go on to combine it with the original curve out to63′′radius,to give theﬁnal“true”rotation curve. The result of this procedure is shown in Fig.5,where we have compared our original rotation curve with the new curve and also with the curve by Regan et al.(1996).Our procedure has isolated the wiggles between63′′and93′′.We can then proceed to produce a new two–dimensional projected model for the rotation in which the wiggles are no longer present,and to subtract oﬀthis new rotation model from the original velocityﬁeld,yielding a resulting map of residuals as shown in Fig.1d.There areZurita et al.:Ionized gas kinematics and massive star formation in NGC 15307Radius (arcsec)204060801000200400600Radius (kpc)51015freeangle 20 degfreeangle 45 deg Fig.4.H αrotation curves of the disc of NGC 1530ob-tained with diﬀerent “free–angles”and with rings of 1′′width.For free–angles less than ∼30◦there is an obvi-ous contribution from the non–rotational motion along the bar in the mean calculated rotational velocity that can “contaminate”the rotation curve of the galaxy.clearly ordered ﬁelds of non–circular velocity both around the bar,and in the arms,but we can check on the mo-del subtraction by examining the residuals of the regions which are in the disc outside the arms and bar.These in general show,as they should if the rotation curve sub-traction is valid,net residual velocities close to zero:less than ∼10km s −1,which is close to the precision limit of the observations.We can nowsee clearly the streaming motions across the arms in Fig.1d.These have projected values between 10and 30km s −1,with similar amplitudes in both arms.3.2.1.The residual velocities along the barOf most striking interest is the fairly complex non–circular velocity ﬁeld associated with the bar.Approaching veloc-ities of up to 120km s −1are observed along the north side of the bar,and receding velocities of the same am-plitude along the south side.These values,and the im-plied vectorial direction in elongated quasi–elliptical or-bits around the bar with long axis parallel to the bar axis,are in line with classical predictions of the dynamical ef-fects of a stellar bar on the rotating gas which date back to Huntley et al.(1978)and Roberts et al.(1979)as well as to more recent studies by Athanassoula (1992).Most of the observational work has been performed either in H i or more recently in CO emission.There have been relatively few H αstudies of this phenomenon,for two probable rea-sons:slit spectroscopy is costly in time if more than a couple of position angles are taken (one good early studyRadius (arcsec)204060801000100200300Radius (kpc)Fig.5.H αrotation curve of the disc of NGC 1530.This rotation curve has been obtained by subtracting the ef-fect of the streaming motions in the spiral arms of the galaxy from the mean rotation curve shown in Fig.3(see text for further details).in this mode using six slit positions on NGC 1512was published by Lindblad &Jorsater 1981);and H αemis-sion is much patchier than either H i or CO.However,as we can see from the data in the present article,the use of a scanning Fabry–P´e rot for this work permits full two–dimensional coverage at an angular resolution better than that of essentially all H i or CO measurements,which can compensate to an interesting degree for the intrinsic patchiness of the observed ﬁeld.In Fig.1d there are several complexities in the non–circular velocity ﬁeld which are worth pointing out.Taking the north side of the bar we can see a zone with high bar–streaming velocities,of order 120km s −1in a direction approaching us to the east of the centre,and another re-gion,more restricted in size and velocity range,with simi-lar velocities to the west.To the south of the bar we can see a diametrically symmetric ﬂow,with high receding ve-locities,again of order 120km s −1receding on west side,and two smaller zones with similar velocities to the east.It is tempting to consider these ﬂows as direct evidence for motion aligned with the bar and terminating in zones of shock towards the ends of the bar.We will see later that there is considerable evidence in favour of this,and of the direct causal links between properties of these ﬂows,and both the stimulation and inhibition of massive star forma-tion.Examining Fig.1d,the question arises as to how the ﬂow can apparently be stopped half way along the bar,yet continue on beyond the central zones as described above.This appearance does not give a true picture of the ve-locity ﬁeld and is essentially due to the patchiness of the。

玉米籽粒皱缩突变体sh2021_的表型分析和基因定位

任文闯, 王欣, 张亚辉, 等. 玉米籽粒皱缩突变体sh2021的表型分析和基因定位[J]. 华南农业大学学报, 2023, 44(5): 750-759.REN Wenchuang, WANG Xin, ZHANG Yahui, et al. Morphological characterization and genetic mapping of shrunken endosperm mutant sh2021 in maize[J].Journal of South China Agricultural University, 2023, 44(5): 750-759.玉米籽粒皱缩突变体sh2021的表型分析和基因定位任文闯，王　欣，张亚辉，汤蕴琦，黄　君(华南农业大学农学院, 广东广州 510642)摘要: 【目的】分析玉米籽粒皱缩突变体的表型特征并进行籽粒相关基因的精细定位，为揭示该基因调控玉米籽粒发育的分子机制奠定基础。

【方法】以玉米自交系‘B73’种植过程中籽粒自发突变个体为材料，命名为shank2021(sh2021)，对其形态学和细胞学特征进行观察；构建分离群体，通过混合群体分离分析法(Bulked segregant analysis ，BSA)对基因进行初步定位，筛选交换单株进一步缩小定位区间，最后结合转录组测序及基因功能注释推测控制籽粒缺陷性状的候选基因。

【结果】与野生型相比，sh2021籽粒凹陷皱缩、颜色加深、籽粒排列不规则，且百粒质量降低。

扫描电镜观察发现，与野生型相比，sh2021胚乳细胞和淀粉粒均显著变小，且淀粉粒大小不均匀。

遗传分析结果表明，sh2021是由单个隐性基因突变所致。

利用BSA 分析方法将目的基因定位在3号染色体末端约13.25 Mb 区域。

进一步扩大分离群体筛选交换单株，将目的基因定位在标记ID5与I D 9之间的529.60 k b 范围。

Three clusters of the SMC from ACSWFC HST archive data NGC 265, K~29 and NGC 290 and their

a r X i v :a s t r o -p h /0702281v 1 10 F eb 2007Astronomy &Astrophysics manuscript no.vallenari˙6834cESO 2008February 5,2008Three clusters of the SMC from ACS/WFC HST archive data:NGC 265,K 29and NGC 290and their ﬁelds populationEmanuela Chiosi 1,Antonella Vallenari 21Astronomy Department,Padova University,Vicolo dell’Osservatorio 2,35122Padova,Italy 2INAF,Padova Observatory,Vicolo dell’Osservatorio 5,35122Padova,Italye-mail:emanuela.chiosi@oapd.inaf.it;antonella.vallenari@oapd.inaf.itReceived:December 2006/Accepted:January 2007ABSTRACTAims.We determine the age,metallicity and initial mass function of three clusters,namely NGC 265,K 29,NGC 290,located in the main body of the Small Magellanic Cloud.In addition,we derive the history of star formation in the companion ﬁelds.Methods.We make use of ACS/WFC HST archive data.For the clusters,the age and metallicity are derived ﬁtting the integrated luminosity function with single synthetic stellar population by means of the χ2minimization.For the companion ﬁelds,the history of star formation is derived using the χ2minimization together with the downhill-simplex method.Results.For the clusters we ﬁnd the following ages and metallicities:NGC 265has log(Age)=8.5±0.3yr and metallicity 0.004±0.003(or [Fe/H]=-0.62);K 29has log(Age)=8.2±0.2yr and metallicity Z=0.003±0.002(or [Fe/H]=-0.75);NGC 290has log(Age)=7.8±0.5yr and metallicity 0.003±0.002(or [Fe/H]=-0.75).The superior quality of the data allows the study of the initial mass function down to M ∼0.7M ⊙.The initial mass function turns out to be in agreement with the standard Kroupa model.The comparison of the NGC 265luminosity function with the theoretical ones from stellar models both taking overshoot from the convective core into account and neglecting it,seems to suggest that a certain amount of convective overshoot is required.However,this conclusion is not a strong one because this cluster has a certain amount of mass segregation which makes it diﬃcult to choose a suitable area for this comparison.The star formation rate of the ﬁeld population presents periods of enhancements at 300-400Myr,3-4Gyr and ﬁnally 6Gyr.However it is relatively quiescent at ages older than 6Gyr.This result suggests that at older ages,the tidal interaction between the Magellanic Clouds and the Milky Way was not able to trigger signiﬁcant star formation events.Key words.Galaxies:Magellanic Clouds,star clusters,stellar content,luminosity function,mass function1.IntroductionIt is well known that the rich cluster system of the Magellanic Clouds (MCs)is quite diﬀerent from that of our own Galaxy where a dichotomy is found between young sparse open clusters and old compact objects.The MCs present a wide distribution of rich cluster ages and constitute an ideal laboratory for testing the star and clus-ter formation process,either due to global eﬀects,such as gravitational triggers because of tidal interactions,or to internal processes.In fact,the star formation (SF)process depends on the cooling and the heating of the interstel-lar gas which in turn,depend on the presence of met-als (Lisenfeld &Ferrara 1998;Wolﬁre et al.1995).The Large and Small Magellanic Clouds (LMC and SMC,re-spectively)are particularly important as they allow us to2 E.Chiosi&A.Vallenari:Three clusters of the SMC Table1.Equatorial coordinates of the SMC regions containingthe three clusters.NGC2650:47:12-73:28:38K290:51:53-72:57:14 NGC2900:51:14-73:09:41Cluster∆m F555WP SF−AP(3pix)∆m F814WP SF−AP(3pix)-0.14±0.02-0.15±0.02-0.14±0.02-0.15±0.02-0.14±0.02-0.13±0.02the aperture photometry is calculated with an aperture of3pixels,the point spread function(PSF)is derived for each colour and each CCD,and the PSF photome-try is performed.Data areﬁnally corrected for the charge transfer eﬃciency(CTE)using the Riess&Mack(2004) transformations.This correction goes from0.01mag for the brightest magnitudes to0.1mag for the faintest mag-nitudes.Calibration.The transformation from the instrumen-tal magnitudes to the ACS/WFC-Vega system,taken from Bedin et al.(2005),is given bym filter≡−2.5log10I e−E.Chiosi &A.Vallenari:Three clusters of the SMC318202224260.10.080.060.040.02magF555WF814WFig.1.Mean photometric errors σas function of the magni-tude for the F555W and F814W pass-bands for the studiedﬁelds.of the saturated stars in the ACS photometry from the OGLE II catalog (see the sections below for more detail).We estimate the photometric errors in the two pass-bands by means of the artiﬁcial stars experiments as the diﬀerence between the assigned and recovered magnitude for any simulated star.The results are shown in Fig.1as a mean of all the studied ﬁelds.This is justiﬁed by the fact that diﬀerences from ﬁeld to ﬁeld are not relevant.The observational CMDs of the three clusters are pre-sented in the top left panels of the Figs.2,3,and 4.They will be examined in detail below.They refer to a circular area having 22–25”of radius (depending on the cluster)inside which the vast majority of the cluster stars falls as shown by the surface brightness proﬁles in the top right panels of the Figs.2,3,and 4(see the discussion below).Incompleteness .Correction for incompleteness is de-rived as usual by means of artiﬁcial star experiments where artiﬁcial stars of known magnitude are added to the original image and data are re-reduced.The ratio between the number of recovered stars and the original number of added stars gives the completeness correction Λ.The re-sults are shown in the bottom right panels of the Figs.2,3,and 4which present Λas function of the magnitude for the inner radius of the clusters.and for the external regions.More details can be found in the sections below.3.Distance modulus,reddening and metallicityThe distance modulus (m −M )0=18.9is assumed for the SMC,in agreement with recent determinations by Storm et al.(2004),Weldrake et al.(2004),Caputo et al.(1999)and Sandage et al.(1999).No assumptions are made for the reddening and metal-licity of each cluster.They are derived together with the age from the analysis of the CMD by means of the χ2minimization technique to be discussed below.In the study of the ﬁeld population,assumptions have to be made for the SMC depth along the line of sight,inter-stellar extinction and age-metallicity relation.We proceed as follows:(1)We adopt the SMC depth along the line of sight of 4kpc,which implies a diﬀerence in the distance modulus of about 0.14mag (Welch et al.1987;Zaritsky et al.2002).(2)The extinction map across the SMC derived by Zaritsky et al.(2002)shows that the interstellar redden-ing is spatially varying,i.e.increasing along the SMC ridge from North-East to South-West.A mean reddening E (B −V )=0.08mag is derived by Rachford et al.(2002)and Hunter et al.(2003).However,we prefer to use for the ﬁeld population the same extinction we have obtained for the study of the CMD of the companion cluster using the minimization procedure.(3)Our knowledge of the age-metallicity relation in the SMC is mainly based on clusters.The interpretation of the existing SMC age-metallicity relation widely varies from author to author.It goes from continuous enrichment from the oldest to the youngest objects as found by Da Costa &Hatzidimitriou (1998)and by Dolphin (2000b)to a burst-mode of star formation and enrichment as derived by Olszewski et al.(1996),Pagel &Tautvaiˇs ien˙e (1999),Piatti et al.(2001),Harris &Zaritsky (2004).To study the star formation history in the ﬁelds,we assume the enrichment history by Pagel &Tautvaiˇs ien˙e (1999).4.Method to derive ages,metallicities,and IMFsAge,metal content,and IMF are estimated by comparing theoretical luminosity functions (LF)that depend on the three parameters under examination to the observational one and by plotting the corresponding isochrones on the CMD to check the mutual consistency of the results.The determination is ﬁrst made by visual inspection of the CMD and it is reﬁned with the aid of the χ2minimization.Theoretical luminosity functions and isochrones are taken from the library of Girardi et al.(2002).Corrections for completeness and ﬁeld subtraction are the preliminary step to be undertaken to derive good ex-perimental luminosity functions.The analysis articulates as follows:1.Equal areas are considered for each cluster and com-panion ﬁeld.2.The luminosity interval spanned by the cluster and ﬁeld stars in each pass-band is divided in number of intervals of 0.5mag width.In each interval,and separately for the cluster and ﬁeld,we count the stars and apply the correc-tion for incompleteness (the cluster and ﬁeld completeness4 E.Chiosi&A.Vallenari:Three clusters of the SMC factors are used as appropriate)andﬁnally we calculatethe ratio1N true=E.Chiosi &A.Vallenari:Three clusters of the SMC5-112325201510F555W-F814W0.511.5-5-4.8-4.6-4.4-4.2log(r(arcsec))-1012325201510F555W-F814WmagnitudeF555W clusterF814W cluster 20222426283000.511.5F555W field F814W fieldFig.2.Summary panels for NGC 265.In the top left panel is the CM diagram (inner 22”)with a superposed isochrone of log(age)=8.5,Z=0.004and E(F555W-F814W)=0.08.The brightest stars settle at F555W=16.In the top right panel the surface brightness proﬁle (in arbitrary units)is ﬁtted by one of the King functions (dashed line)and by Elson proﬁle (continuous line).From this distribution we can determine core and tidal radius.Vast majority of the stars sets within a radius of 22”corresponding to log(r)=1.3.In the bottom left panel the CMD of ﬁeld stars is shown.The ﬁeld population is taken at about 1.6’from the cluster center and the area is comparable to the area of the cluster (see text for details).The bottom right panel shows the completeness factors for the cluster and ﬁeld regions as indicatedcoordinates αand δusing the task IRAF STSDAS ”xy2rd”.Then,the center of a cluster is determined calculating the luminosity weighted centroid at increas-ing radii.The photometric data of the stars that are saturated in the ACS/WFC observations are taken from OGLE II data,converted to the F555W pass-band,andﬁnally used to construct the surface brightness proﬁle.We are conﬁdent that this does not introduce errors in the derived proﬁles as we have already checked the consistency between the OGLE II photometry in the V magnitude and the ACS/WFC HST V calibration.6E.Chiosi &A.Vallenari:Three clusters of the SMC-112325201510F555W-F814W0.511.5-4.8-4.6-4.4-4.2-4log(r(arcsec))-1012325201510F555W-F814W0magnitudeF555W clusterF814W cluster 2022242628300.511.5F555W field F814W fieldFig.3.Summary panels for K 29.In the top left panel is the CM diagram (inner 22”)with a superposed isochrone of log(age)=8.2,Z=0.003and E(F555W-F814W)=0.14.The OGLE bright stars are indicated by the triangles.The brightest stars settle at F555W=15.In top right is the brightness proﬁle (in arbitrary units)ﬁtted with one of the King (dashed line)and with the Elson functions (solid line).From this distribution we can determine core and tidal radius.Vast majority of the stars sets within a radius of 22”(or log(r)=1.3).In the bottom left panel the CMD of ﬁeld stars is shown.The ﬁeld population is taken at about 1.6’from the cluster center and the area is comparable to the area of the cluster (22”).The bottom right panel shows the completeness factors for the cluster and ﬁeld regions as indicatedMany SMC clusters have elliptical isophotes.This is not the case of the objects studied in this paper,which have only moderate ellipticity,1−b/a ∼0.13−−0.3(Hill &Zaritsky 2006).Thanks to this,we can use circular aper-tures to calculate the proﬁle.Because of the high resolu-tion of our images,the surface brightness given as log (f )inside the i-th circle having radius b i is obtained simply by adding up the ﬂux of the stars falling inside the circle itself:log (f )=1/(πb 2i )×jΛj F jE.Chiosi &A.Vallenari:Three clusters of the SMC7-1012325201510F555W-F814W0.511.5-4.5-4-3.5log(r(arcsec))-1012325201510F555W-F814W0magnitudeF555W clusterF814W cluster 2022242628300.511.5F555W field F814W fieldFig.4.Summary panels for NGC 290.In the top left panel is the CM diagram (inner radius of 25”)with a superposed isochrone of log(age)=7.8,Z=0.003,E(F555W-F814W)=0.15.The OGLE bright stars are indicated by the triangles.The brightest stars settle at F555W=14.In top right is surface brightness proﬁle (in arbitrary units)ﬁtted with the King proﬁle (dashed line)and with the Elson function (solid line).From this distribution we can determine the core and tidal radius.Vast majority of the stars sets within a radius of 25”.In the bottom left panel the CMD of ﬁeld stars is shown (see text for details).The ﬁeld population is taken at about 1.6’from the cluster center and the area is comparable to the area of the cluster (25”).The bottom right panel shows the completeness factors for the cluster and ﬁeld regions as indicatedwhere Λj is the completeness factor inside the ring and F j the stellar ﬂux.Crowding can cause a signiﬁcant number of stars to be missed by ALLSTAR.Their ﬂux can af-fect the surface brightness proﬁle and must be accounted for.This is the reason why the completeness correction is applied to the ﬂux determination.We restrict the de-termination of the surface proﬁle to the area completely falling inside the small ﬁeld of view of the ACS/WFC cam-era.In all the cases,the proﬁles have maximum radii of log(r)∼1.5arcsec.The sky background subtraction is a critical step in the determination of the surface proﬁle especially in the8E.Chiosi &A.Vallenari:Three clusters of the SMC141618202004006008001000magNGC 265141618202004006008001000magK 29141618202004006008001000magNGC 290Fig.5.The luminosity functions of HST (solid line)data and OGLE II (dashed line)data for the ﬁeld area are compared.OGLE II ﬁeld areas are taken at a distance of 1deg from the clusters.The number of objects is normalized to an area of 22′′outer regions of a cluster.The ﬁeld population is sampled as discussed in the previous section,the contamination is calculated as the mean ﬂux in a ﬁeld area of about 22′′,and is ﬁnally subtracted.Two families of models are ﬁtted on the brightness proﬁles.The ﬁrst one is the tidally truncated functions of King (1962):f (x )=πr 2c kln (1+x )−4(1+x )1/2−11+x t(4)with x =(r/r c )2and x t =(r t /r c )2where k is a constant and r t and r c are the searched parameters,speciﬁcally r t is the tidal radius and r c the core radius.The second one is the Elson et al.(1987)family of functions:f (r )=2πµ0a 2a 21−γ/2(5)where a is a scale length and γthe power law index.These models are essentially the same as the King (1962)models,but they do not assume tidal truncation.The parameter a is related to the King (1962)core radius r c by:r c =a (22/γ−1)1/2The proﬁle ﬁt is made using the χ2minimization.The un-certainties on the proﬁles are calculated as Poisson errors.5.2.1.Results and comparison with previous workFigs.2,3,4present the surface brightness proﬁles of each cluster and Table 3gives the derived parameters.The core radii obtained using Elson et al.(1987)and King (1962)proﬁles are substantially in agreement,as expected be-cause the main diﬀerences between the models arise at larger radii.The tidal radius is quite uncertain,ﬁrst be-cause it strongly depends on the sky subtraction and sec-ond,because our photometry does not extend to large enough radii.Table 4compares our results on cluster pa-rameters with those by Hill &Zaritsky (2006).In compar-ison with our results,their values of r c are in agreement for NGC 265,but they tend to be overestimated for the other two clusters,especially concerning the ﬁt with Elson et al.(1987)proﬁles.The values of γby Hill &Zaritsky (2006)are overestimated for all the clusters.The question whether MC clusters are tidally limited or not is a long lasting one.The King (1962)models are expected to describe bound systems that have isothermal and isotropic stellar distribution functions and are lim-ited by a strong tidal ﬁeld.The Elson et al.(1987)models are empirically derived in order to reproduce the proﬁles of young MC clusters.The lack of tidal cut-oﬀwas origi-nally explained with the dynamical youth of those clusters having extra-tidal stars.In this view,it is possible for a cluster to evolve or not from an Elson et al.(1987)pro-ﬁle to a King (1962)one,depending on the environment and on the cluster’s characteristics.However,on an ob-servational ground,no clear correlation is found between the age of the clusters and the presence of tidal cut-oﬀ.Hill &Zaritsky (2006)ﬁnd that the SMC clusters are ﬁt-ted in a satisfactory way by both models,although the King (1962)proﬁles provide a slightly superior ﬁt in ∼90%of the cases.McLaughlin &van der Marel (2005)compare the King (1962)models,the Elson et al.(1987)proﬁles,and the modiﬁed isothermal spheres based on the Wilson (1975)models.These latter are spatially more ex-tended than the King (1962)functions,but still include a ﬁnite,tidal cut-oﬀin the density.The authors come to the conclusion that the un-truncated power-law distri-butions,Wilson (1975)models,and King (1962)proﬁles yield comparable good ﬁts of MC clusters.McLaughlin &van der Marel (2005)conclude that extended star en-velopes around MC clusters may not be transient features due to the age,but more probably halos of self-gravitating objects.For the LMC clusters,Elson et al.(1987)ﬁnd a clear trend that the spread in core radius is an increasing function of the cluster age.The observed trend probably represents a real structural evolution of the clusters:all clusters form with a relatively small radius and subse-quently some of them experience a core expansion,while others do not.This result is conﬁrmed by other authors (we quote as the most recent Mackey &Gilmore 2003).To check whether the trend found for the LMC is a property of SMC clusters as well,we combine the cluster age deter-minations derived from isochrone ﬁtting by Chiosi et al.(2006)with the values of the King (1962)core r c obtainedE.Chiosi&A.Vallenari:Three clusters of the SMC9 Table3.Core and tidal radius as determined by theﬁt with the King(1962)and Elson et al.(1987)functions.King(1962)r c aγχ2(pc)(pc)2.610.75 1.062.40 2.50 1.270.87 1.50 1.55Table4.Structural parameters of the clusters as determinedby Hill&Zaritsky(2006).Elson et al.(1987)r c r90(pc)(pc)NGC265 3.51 3.20K29 5.63 6.00NGC290 1.83 3.25Cluster log(Age)(yr)Z E(F555W−F814W)NGC2658.5±0.30.004±0.0030.08±0.06K298.2±0.20.003±0.0020.14±0.08NGC2907.8±0.50.003±0.0020.15±0.05NGC2658.7±0.20.004±0.0030.08±0.06K298.3±0.20.003±0.0020.14±0.08NGC2908.0±0.30.003±0.0020.15±0.0510 E.Chiosi&A.Vallenari:Three clusters of the SMCstatistically subtracted from the LF and the CMD.Inside the radius of22′′about1000cluster stars are detected down to F555W=25where the incompleteness reaches the50%level.Starting from an initial guess obtained from visual inspection of the CMD,and using the CMD and LF simulator,by means of theχ2minimization we derive:log(Age)=8.5±0.3yr,interstellar redden-ing E(F555W-F814W)=0.08±0.06,corresponding to A F555W=0.21(Bedin et al.2005),andﬁnally metallicity Z=0.004±0.003.All the errors on the determinations of the parameters are given at the68%conﬁdence level.The top left panel of Fig.2presents the CMD where the isochrone for the age and metallicity we have determined is superposed.The isochrone gives a good ﬁt of the observational CMD.Diﬀerent combinations of extinction,metallicity and age(inside the quoted errors) give reasonableﬁts of the CMD.For instance,when log(Age)=8.4yr,E(F555W-F814W)=0.1,and Z=0.007, the main sequence color,the turnoﬀmagnitude,and the luminosity of the loop of the core He-burning stars are well reproduced,while the theoretical loop is too red in comparison with the data.When log(Age)=8.6yr, E(F555W-F814W)=0.15,and Z=0.001,then the turnoﬀand the loop magnitudes and colors are well reproduced, but the colour of the unevolved part of the main sequence, two magnitudes about below the turnoﬀis poorlyﬁtted. On the other hand,it is clear that these features of the CMD depend on the details of the stellar models (treatment of convection,mixing length,bolometric corrections,adopted chemical mixture...).For this reason, at some extent,the derived set of bestﬁtting parameters is depending on the adopted stellar models.The turn-oﬀmass is about4M⊙.The IMF slope in the mass range M>1M⊙turns out to beα2=2.5±0.5,while in the mass range(0.7<M<1M⊙)isα1=2.4±0.4, substantially in agreement with the Kroupa(2000)IMF. We recall that the Kroupa(2000)IMF hasα1=2.2for 0.5M⊙<M<1M⊙,α2=2.7for M>1M⊙.When binary stars are included a slightly older age is found.We add a percentage of binaries amounting to 30%of the stars.Instead of an age of log(Age(yr))=8.5 weﬁnd the bestﬁt at an age of log(Age(yr))=8.7±0.2. As a consequence,the determination of the exponents of the IMF changes.For all the studied clusters,the summary of the IMF determination is presented in Table 6.The quality of theﬁt is shown in Fig.7where the observational LF is compared with the bestﬁt simulation.5.3.2.K29We sample the cluster population inside a radius of22”where about700stars are detected down to F555W=25 mag.As for NGC265,this radius is larger than the core radius.Theﬁeld population of K29is located outside the core radius.Table6.The bestﬁt IMF coeﬃcient in the range of low masses α1(0.7M⊙<M<1M⊙)and in the range of high massesα2 (M>1M⊙)is given for the three diﬀerent clusters.The68% conﬁdence interval is also given(σ1andσ2).No binariesBinariesFig.3(top left panel)presents the CMD of the cluster (inside the22′′radius),where bright stars that are sat-urated in the ACS/WFC photometry are taken from the OGLE II data,analogously to the procedure adopted in the determination of the brightness.The age derived by χ2minimization is log(Age)=8.2±0.2yr,the metallicity Z=0.003±0.002,and the reddening E(F555W-F814W) =0.14±0.08.The turn-oﬀmass is about4.5M⊙.The slope of the IMF in the mass interval from4M⊙to1M⊙is α2=2.7±0.5,while in the mass range(0.7<M<1M⊙) isα1=1.8±0.2in marginal agreement with the Kroupa law.The LF of the observational data is compared with the bestﬁt model in Fig.8.When binaries are included, the age of the cluster becomes log(Age)=8.3±0.2yr.See the entries of Table6for the eﬀect of binaries.5.3.3.NGC290Inside a radius of∼25′′about660stars are found.Once more this radius is larger than the cluster core.Evolved stars brighter than F555W=17.3mag are beyond the satu-ration level of the photometry.To cope with this we inte-grate our data for the red giants with those by OGLE II,whose photometry is converted in the F555W and F814W pass-bands,as described in the previous sections. Mounting the two sets of data has been made using equal areas in the two frames.No stars are missing in the HST photometry at the turnoﬀlevel F555W=18.This ensures that no spurious eﬀects due to the use of ground-based and HST photometry inﬂuences the age determination. The top left panel of Fig.4presents the composite CMD.As for the other two clusters,the preliminary inspec-tion of the CMD provides estimates of age and metallicity which is then reﬁned by the Monte Carlo technique.The automaticﬁt gives log(Age)=7.8±0.5yr withχ2=1.5, metallicity Z=0.003±0.002,and E(F555W-F814W) =0.15±0.05.The IMF slope givesα1=2.2±0.2in the mass range0.7M⊙≤M≤1M⊙,andα2=2.7±0.4 in the mass range M≥1M⊙.Fig.4presents the CMD of NGC290compared with our bestﬁt isochrone.Fig9 presents the observational LF compared with the bestﬁt model.An older age is found when30%of binary stars16182022240500100015002000F555WNGC 265simulated population log(age(yr))=8.5observational dataFig.7.LF of the cluster NGC 265.The best ﬁt is done with a population of log(Age)=8.5yr 1618202224050010001500F555WK 29simulated population log(age(yr))=8.2observational dataFig.8.LF of K 29ﬁtted with a population of log(Age)=8.2yrare included:log(Age)=8.0±0.3yr.Once again see the entries of Table 6for the eﬀect of binaries on the IMF parameters.5.4.Revisiting an old question:convective overshootBecker &Mathews (1983),comparing observational and synthetic CMDs of NGC 1866,ﬁrst noticed that classical stellar models they used predicted a number of red gi-161820222402004006008001000F555WNGC 290simulated population log(age(yr))=7.8observational dataFig.9.LF of the cluster NGC 290ﬁtted with a simulated population having log(Age)=7.8yrants larger than observed,and a smaller number of main sequence stars in turn as compared to the observations.The same authors suggested that a more careful treat-ment of core convection (rger convective cores)could remove the discrepancy.A number of subsequent studies conﬁrmed this idea and demonstrated that the inclusion of overshooting in the description of convective motions could reproduce the correct ratio of the number of evolved stars N R over the number of main sequence stars,N MS .Chiosi et al.(1989a),in particular,clearly showed that the overshooting scheme,by reducing the ratio between the lifetime of the stars in the He-burning and the H-burning phase,t He /t H ,oﬀers a good and simple solution to the problem.This conclusion was also reinforced by Lattanzio et al.(1991),who analysed the CMD of NGC 1866by means of overshooting and classical models.The classical theory of stellar structure predicts that in a star whenever the condition ∇r ≤∇a(6)is violated the region becomes unstable to convective mo-tions and fully mixed.This region is surrounded by sta-ble radiative layers.This is only an approximation:what happens physically at the border region passing from un-stable to stable conditions?If we deﬁne the Schwarzschild core as the region at border of which the acceleration of convective bubbles vanishes there is still a shell above in which the velocity is not zero (the so-called overshoot re-gion).The thickness,the thermal properties,and mixing eﬃciency in the overshooting region are still a matter of discussion.In any case,it is worth recalling that ﬁrst con-vective overshoot is a consequence of the inertia principle,so that neglecting its existence would not be physicallysound,second it is quite common in Nature(Deardorﬀet al.1969).As demonstrated in a number of studies,in-cluding numerical simulations(Freytag et al.1996),the penetration depth of convective elements into a formally stable region represents a non-negligible fraction of the size of the unstable zone.In addition to this,there is a number of astrophysical situations in which the hypoth-esis of substantial convective overshoot has been found to oﬀer better and more elegant solutions than other ex-planations(see Bertelli et al.1986a;Chiosi et al.1992). Among others,suﬃce it to recall here the so-called mass discrepancy of Cepheid stars(Bertelli et al.1986b;Chiosi et al.1992).Theﬁrst studies of this subject were by Shaviv &Salpeter(1973);Prather&Demarque(1974);Maeder (1975);Cloutman&Whitaker(1980b);Bressan et al. (1981);Stothers&Chin(1981),followed over the years by more sophisticated formulations standing on turbulence theories(Cloutman&Whitaker1980a;Xiong1980)and ﬂuid hydro-dynamics(Canuto&Mazzitelli1991;Canuto et al.1996;Unno&Kondo1989;Canuto2000).The ballis-tic description long ago proposed by Bressan et al.(1981) is particularly suitable for the calculation of stellar models. It has been proved to best reproduce the numerical results of laboratoryﬂuid-dynamics simulations(Zahn1991).The Bressan et al.(1981)procedure will be shortly summarized below.Despite all this,it has been often argued that unre-solved binaries could mimic the eﬀects of convective over-shoot and easily account for the low ratio of evolved stars to main sequence stars observed in the young LMC clus-ters.This hypothesis has been investigated by many au-thors,both in open clusters of the Milky Way(see Carraro et al.1994)and young clusters of the LMC(Chiosi et al. 1989a,b;Vallenari et al.1992)with somewhat contrast-ing results.Worth of mention is the study by Testa et al. (1999)of NGC1866,who introducing about30%of binary and using the classical models of Dominguez et al.(1999) came to the conclusion that convective overshooting is not required.The subsequent analysis of Barmina et al.(2002) of the same cluster carried out on the Testa et al.(1999) data,discovered that the correction for completeness ap-plied by Testa et al.(1999)was not correct thus invalidat-ing their conclusions.In addition to this,they performed a systematic analysis of the eﬀects of binary and stochastic ﬂuctuations in the IMF,and came to the opposite conclu-sion:convective overshoot in unavoidable.Here we have three clusters whose turn-oﬀmass is about4M⊙so it might be worth of interest to contribute further to this subject.In order to check which model bet-ter reproduces the data we need to have diﬀerent sets of stellar populations.They are the two sets with convective overshoot,i.e.the models by Girardi et al.(2002)and those by Pietrinferni et al.(2004)with a diﬀerent pre-scription so that comparison is possible.As already recalled,the ballistic description of con-vective overshoot by(Bressan et al.1981)is particularly suited to stellar models.The algorithm adopts a non-local treatment of convection in the context of the mixing-length theory(MLT)by B¨o hm-Vitense(1958):it looks for the layers where the velocity of convective elements (accelerated by the buoyancy force in the formally unsta-ble regions)gets zero into the surrounding stable regions, then adopts a suitable temperature stratiﬁcation in the overshoot regions,andﬁnally assumes straight mixing over-there.Since the Bressan et al.(1981)formalism makes use of the MLT,it expresses the mean free path of the convective elements as l=Λc×H p where H p is the local pressure scale height.According to this deﬁnition adopted by Bressan et al.(1981)Λc represents the overshoot distance across the Schwarzschild radius in units of the pressure scale height.In Bressan et al. (1981)Λc was assumed to be the same for all stellar masses.Over the years,this was slightly modiﬁed to treat overshoot in that particular range of mass which sees the transition from radiative core H-burning to convective core H-burning and during this phase the convective core starts small,grows to a maximum and then decreases.In this mass intervalΛc is not kept constant but let vary with mass according to the recipe in Girardi et al.(2000):1)Λc=0for M≤1.0M⊙(when the core is radiative)2)Λc=M/M⊙−1.0for1M⊙<M≤1.5M⊙3)Λc=0.5for M>1.5M⊙The last value stands also for the whole He-burning phase.Pietrinferni et al.(2004)adopt a similar prescription:1)Λc=0for M≤1.1M⊙(when the core is radiative)2)Λc=(M/M⊙−0.9)/4for1M⊙<M≤1.5M⊙3)Λc=0.2for M≥1.7M⊙where we have to keep in mind thatΛc is”measured”from the Schwarzschild border.Therefore it corresponds to about half of the Girardi et al.(2000)deﬁnition. Considered these premises,the two sets of tracks are prac-tically coincident.Thisﬁnding also ensures that using the classical models by Pietrinferni et al.(2004)is safe as the input physics adopted by the two groups is nearly the same.The analysis is made comparing the integrated lumi-nosity function of main sequence stars normalized to the number of evolved stars(thereinafter NILF)ﬁrst intro-duced by Chiosi et al.(1989a),which has been proved to be the only way to eﬀectively discriminate between the two diﬀerent evolutionary schemes.It is worth reminding the reader that the NILF is by deﬁnition proportional to the lifetime ratio t H/t He(Chiosi et al.1989a).The NILF requires that the number of evolved stars truly belonging to the cluster is known.The task is not trivial because it requires an accurate decontamination by ﬁeld stars.The procedure is as follows.First of all,we ap-ply to the CMD of the cluster andﬁeld the correction for completeness and area coverage.Second in the area of the cluster andﬁeld CMD we perform star counts.We statistically subtract from the cluster counts a number of。

On the massive stellar population of the Super Star Cluster Westerlund 1

a r X i v :a s t r o -p h /0504342v 2 21 A p r 2005Astronomy &Astrophysics manuscript no.2413clark February 2,2008(DOI:will be inserted by hand later)On the massive stellar population of the Super Star ClusterWesterlund 1⋆J.S.Clark 1,I.Negueruela 2,P.A.Crowther 3,and S.P.Goodwin 41Department of Physics and Astronomy,University College London,Gower Street,London,WC1E 6BT,England,UK 2Dpto.de F ´ısica,Ingenier ´ıa de Sistemas y Teor ´ıa de la Se˜n al,Universidad de Alicante,Apdo.99,E03080Alicante,Spain3Department of Physics &Astronomy,University of Sheﬃeld,Sheﬃeld,S37RH,England,UK 4Department of Physics and Astronomy,University of Wales,Cardiﬀ,CF243YB,Wales,UK.Received /AcceptedAbstract.We present new spectroscopic and photometric observations of the young Galactic open cluster Westerlund 1(Wd 1)that reveal a unique population of massive evolved stars.We identify ∼200cluster members and present spectroscopic classiﬁcations for ∼25%of these.We ﬁnd that all stars so classiﬁed are unambiguously post-Main Sequence objects,consistent with an apparent lack of an identiﬁable Main Sequence in our photo-metric data to V ∼20.We are able to identify rich populations of Wolf Rayet stars,OB supergiants and short lived transitional objects.Of these,the latter group consists of both hot (Luminous Blue Variable and extreme B supergiants)and cool (Yellow Hypergiant and Red Supergiant)objects -we ﬁnd that half the known Galactic population of YHGs resides within Wd1.We obtain a mean V −M V ∼25mag from the cluster Yellow Hypergiants,implying a Main Sequence turnoﬀat or below M V =−5(O7V or later).Based solely on the masses inferred for the 53spectroscopically classiﬁed stars,we determine an absolute minimum mass of ∼1.5×103M ⊙for Wd 1.However,considering the complete photometrically and spectroscopically selected cluster population and adopt-ing a Kroupa IMF we infer a likely mass for Wd 1of ∼105M ⊙,noting that inevitable source confusion and incompleteness are likely to render this an underestimate.As such,Wd 1is the most massive compact young cluster yet identiﬁed in the Local Group,with a mass exceeding that of Galactic Centre clusters such as the Arches and Quintuplet.Indeed,the luminosity,inferred mass and compact nature of Wd 1are comparable with those of Super Star Clusters -previously identiﬁed only in external galaxies -and is consistent with expectations for a Globular Cluster progenitor.Key words.stars:evolution -open clusters and associations:individual:Westerlund 1-galaxies:starbursts1.IntroductionMassive stars play an important role in the ecology of galaxies,providing a major source of ionising UV radia-tion,mechanical energy and chemical enrichment (Smith 2004).However,serious gaps in our understanding of mas-sive stars exist throughout their lifecycle,in large part due to the rapid evolution -and hence rarity -of such objects.For example,the lack of accurate observational constraints on the metallicity dependant mass loss rates of such stars -particularly for short lived phases such as Luminous Blue Variables (LBVs)and Yellow Hypergiants (YHGs)-restricts our ability to follow their post-Main Sequence (MS)evolution.In particular,currently we can-2J.S.Clark et al.:The stellar content of Wd1massive than galactic open clusters.Such objects may have very diﬀerent basic properties from their smaller rela-tives,with many authors arguing for diﬀerent kinds of top-heavy mass distributions(e.g.M82-F;Smith&Gallagher 2001).The relevance of such a possibility is clear when one considers that a large fraction of the stellar popula-tion of galaxies may have formed in starburst episodes in the distant past.If such episodes,in which very large num-bers of stars form,are in any way fundamentally diﬀerent from the much more modest star formation episodes that we observe in the present Milky Way,our modelling of the history and evolution of galaxies could be profoundly biased.Unfortunately,dense clusters of massive stars are rare in the galaxy.The Arches&Quintuplet Galactic Centre clusters(with masses of∼1×104M⊙;Figer2004)are the most massive known;however,observations are hampered by their extreme reddening.Recently,observations of the apparently unremarkable cluster Westerlund1(henceforth Wd1)have demonstrated that for over4decades the as-tronomical community has possibly overlooked the pres-ence of a SSC in our own galaxy.Discovered by Westerlund(1961),photometric (Borgman et al.1970,Lockwood1974and Koornneef 1977)and spectroscopic(Westerlund1987;West87) surveys suggested the presence of a population of highly luminous early and late type supergiants.However, despite these observations Wd1languished in relative obscurity throughout the past decade,due in large part to the signiﬁcant reddening(A v∼12.9mag.Piatti et al.1998)which made high resolution spectroscopic observations diﬃcult.Motivated by the unusual radio and mid-IR properties of two cluster members(Clark et al.1998),we have un-dertaken an extensive program of spectroscopic and pho-tometric observations of Wd1.Theﬁrst results of this program-the discovery of an unexpected large popula-tion of WRs and a new LBV-have already been reported in Clark&Negueruela(2002,2004).Here we report on the remainder of the observations,speciﬁcally their use in constraining the properties of the population of massive post MS objects within Wd1.The paper is therefore structured as follows.In Sect. 2we brieﬂy describe the observations and the data reduc-tion techniques employed.Sections3&4are dedicated to the presentation and analysis of both spectroscopic and photometric datasets.Finally,we present an analysis of the global properties of the cluster in Sect.5and sum-marise the results in Sect.6.2.Observations&Data ReductionLow resolution spectroscopy of cluster members over the red/near-IR spectral region(∼6000to11000˚A)was taken on2001June23rd to25th from the ESO1.52m tele-scope at La Silla Observatory,Chile.The telescope was equipped with the Boller&Chivens spectrograph,the Loral#38camera and the#1(night1)and#13(nights 2and3)gratings,giving dispersions of∼5˚A/pixel and ∼7˚A/pixel-leading to resolutions of≈11˚A and≈16˚A -respectively.Intermediate-resolution spectroscopy of the brighter cluster members was carried out on2002June7th,us-ing the ESO Multi-Mode Instrument(EMMI)on the3.6 m New Technology Telescope(NTT)at La Silla.The Red Medium Resolution mode was used.The instrument was equipped with gratings#6and#7in the red arm and the new2048×4096MIT CCD mosaic(in the2×2binning mode).Grating#7covered theλλ6310–7835˚A region at a dispersion of∼0.8˚A/pixel,while grating#6covered the λλ8225–8900˚A range at∼0.4˚A/pixel.Data pre-reduction was carried out with MIDAS soft-ware,while image processing and reduction were ac-complished with the Starlink packages ccdpack(Draper 2000)and figaro(Shortridge1997).Finally photometric observations of theﬁeld contain-ing Wd1were made with the SUperb-Seeing Imager2 (SuSI2)direct imaging camera on the NTT;the2mo-saiced2k×4k CCDs providing a5.5×5.5arcminﬁeld of view.Broadband UBVRI1images were obtained in ser-vice time on2001August21,with integration times for individual frames ranging from1200s(U band)to2s(R &I bands).Given the signiﬁcant interstellar reddening an-ticipated for Wd1a selection of nearby red Landolt(1992) standards was observed.Debiasing andﬂatﬁelding(both dome and twilightﬂatﬁeld frames were obtained)were accomplished with the Starlink package kappa.Final photometry was kindly extracted for us by Peter Stetson, using the daophot package in IRAF2(Stetson1991). 3.Spectroscopic classiﬁcation.In total,27stars were observed at intermediate resolution between6500and7900˚A and8200and8900˚A,and an additional26stars-including the11WRs identiﬁed in Clark&Negueruela(2002)-were observed at low resolu-tion between6500and8900˚A.Aﬁnding chart for all spec-troscopically observed stars is presented in Fig.1.Spectra are presented in Figs.2(new WR candidates;Sect.3.1), 3-7(Super-and Hyper-giants;Sect.3.2-3.5)and8(the unusual sgB[e]star W9;Sect.3.3.1).The6500to9000˚A window oﬀers the prospect of spectral classiﬁcation of moderately reddened objects for which traditional optical criteria are unavailable.Given the presence of transitions from H i,He i and numerous low-e.g.Fe i,Ca ii and N i-and high-e.g.He ii,C iii and N iv-ionisation species it would appear possible to construct an accurate classiﬁcation scheme.While au-thors have recognised the importance of this window(e.g.J.S.Clark et al.:The stellar content of Wd134J.S.Clark et al.:The stellar content of Wd1Andrillat etal.1995),comparatively few observations ex-ist within the literature,particularly of high luminosity and/or early type stars.We were therefore forced to adopt a twin approach for spectral classiﬁcation of our spectra -comparison to observational data where possible(spec-tral type mid-B→G)supplemented by construction of a grid of synthetic spectra where required(OB supergiants; Appendix A).The results of the spectral classiﬁcation are presented in Table1,along with the original classiﬁcation by West87. Where possible we have adopted the nomenclature of West87;if an individual object is resolved into two or more stars in our data we adopt the convention of retaining the designation of West87,with the addition of the suﬃx a for the brightest component,b for the second brightest etc.We further present the J2000co-ordinates and the BVRI broadband photometry for each object if available.Note that while we have utilised a grid of synthetic spectra for the classiﬁcation of the OB star population of Wd1we do not claim that these represent tailored analyses of individual stars.Given the breadth and com-plexity of the spectra presented,quantitative analysis is clearly beyond the scope of the current work,which aims to provide coarse spectral classiﬁcations for the objects presented.3.1.The candidate Wolf Rayet StarsClark&Negueruela(2002)reported the serendipitous dis-covery of11WR stars within Wd1in the low resolution2001ESO1.52m dataset,comprising6WN and5WC stars.Analysis of the2002intermediate resolution NTT data reveals a further two candidates within the cluster. These are W44and W66(=Candidates L&M respec-tively,following the notation of Clark&Negueruela2002); 6500to7900˚A spectra for both stars are presented in Fig 2.Turningﬁrst to W66,Fig.2reveals prominent blended emission in He ii6560+C ii6578˚A,C ii6725-42+C iii 6727-73˚A,C iii7037+He i7065+C iv7064˚A and C ii 7236+C iii7210-12˚A.Diﬃculty in deﬁning a continuum shortwards of7000˚A prevents the accurate measurement of line strengths for theﬁrst3blends,but we measure an EW∼−130±15˚A for the C ii7236+C iii7210-12˚A blend. For the lowest excitation WC8star(WR53),the C iv 7065˚A and C ii7236˚A lines are of similar strength,while all WC9stars have C ii7236˚A>>C iv7065˚A,indicating a classiﬁcation of WC9for W66.W44demonstrates emission in the comparatively low ionisation lines of Hα(∼−30˚A),He i6678(∼−8˚A)and 7065(∼−14˚A),with no emission from either higher(e.g. He ii,N iii-iv or C iii-iv)or lower ionisation species(e.g. Fe ii).The spectrum in the8200to8900˚A range appears completely featureless(to a limit of EW±0.5˚A)and hence is not presented.Given the apparent magnitude of W44,combined with the strength of the emission lines, the lack of Paschen lines(emission and absorption)and Fig.2.R band spectra of the2newly discovered WR stars in the cluster;Candidate L(=W44),a probable WN9star and Candidate M(=W66),a sixth WCL star(WC9). low ionisation species,we exclude a B emission line star classiﬁcation-such as classical Be or sgB[e]star-and in-stead suggest a WN identiﬁcation.The lack of N iv7116˚A precludes a classiﬁcation earlier than WN9,with a clas-siﬁcation of WN9rather than WN9ha more likely due to the comparative strength of the He i lines.This is theﬁrst such star identiﬁed within Wd1,although we note that the low resolution spectrum of W5is possibly indicative of an even later WNL classiﬁcation-this is detailed in Sect.3.3.3.3.2.The late O&early-B supergiantsIntermediate resolution spectra of all13stars in Fig.4 and W7,33,70&71in Fig.5fulﬁll the criteria for OB spectral types deﬁned in Appendix A and individual clas-siﬁcations are listed in Table1.The FWHM of the Paschen lines clearly satisfy the criterion of Caron et al.(2003)for supergiants,forming a continuous sequence with the later A-F stars in Fig.5,which we demonstrate in Sect.3.4to also be super-or hyper-giants.J.S.Clark et al.:The stellar content of Wd15 Table1.Summary of the53cluster members with spectroscopic classiﬁcations.Column1provides the notation of West87,while Column2provides our additional notation if required.Columns3&4provide the Equ J2000co-ordinates,while broadband BVRI photometric values are presented in Columns5-8where available.Columns9& 10list spectral classiﬁcations from West87and this work,respectively.Classiﬁcations listed in italics were derived from low resolution spectra.In general weﬁnd an encouraging correspondence between the two works,although our classiﬁcations appear to be systematically earlier for those stars classiﬁed as late B-early G by West87.Importantly we conﬁrm of the classiﬁcation of West87’s four YHG candidates,while identifying a further2candidates.Finally,we highlight one important diﬀerence;we are unable to identify any Main Sequence or giant stars,with all the OB stars in our study being classiﬁed as Supergiants(W6,10,11,28,33,70&71receiving revised luminosity classes).(new)W87New6J.S.Clark et al.:The stellar content of Wd 1Fig.3.Intermediate resolution R band(6400to7800˚A)spectroscopy of O-F supergiant and hypergiant members of Wd1.Prominent transitions of H i,He i and O i are indicated.Left panel:O and mid B supergiants;weﬁnd no evidence for He ii absorption in the spectra.Right panel:mid-B to F supergiants in Wd1.Weak C ii6578/82˚A absorption is visible in the red wing of the Hαline in the mid-B supergiants.We tentatively identify the three prominent absorption features between7420-7450˚A in W243and W16a as N i7423.6,7442.3&7468.3˚A.Weak Fe i lines at7112.2and 6999.9˚A also appear to be present in the spectrum of W12a(A5Ia+)and later objects.Possible identiﬁcations of the absorption features in the mid-A and later spectral types at∼7711˚A and∼7748˚A are Fe ii7712and Fe i7748.3˚A respectively.Weﬁnd W57a,70&71to have the latest spectral type -B3Ia-of the continuous sequence of OB supergiants present in the sample.This classiﬁcation may be assigned on the basis of the presence and strength of weak N i and O i8446˚A absorption.While W7&33apparently are of later spectral type,their spectra demonstrate several un-usual properties that suggest they have more in common with the transitional objects such as the LBV W243and the YHGs;hence we defer discussion until Sect.3.3.The remaining spectra display solely H i and He i pho-tospheric absorption lines,implying subtypes of B1.5Ia or earlier(T eff≥20kK).In addition,weﬁnd no signature of the He ii8238˚A line in any object,suggesting subtypes no earlier than O9.5Ia.Further subclassiﬁcation is ham-pered by the poor S/N of most spectra,which precludes the use of the Pa16+C iii/Pa15line ratio.Consequently,we may only attempt additional clas-siﬁcation based on the strengths of the Paschen lines. Measuring the strengths of the Paschen lines in the ob-served(and synthetic)spectra relative to W70&71(B3 Ia model)suggests an approximate range of spectral types for W61a,60,43a,19,23a,11,2a&28(earliest→latest) of O9.5Ia→B0.5Ia(30kK→24kK).While the system-atic weakening in line strength-resulting in the absence of higher Paschen series lines-of stars such as W61a& 60compared to W2a&28is clearly indicative of gradu-ations in spectral type within this group,we refrain from attempting any further subclassiﬁcation based on current data.Finally,while the spectra of W30,13,61b&24are almost completely devoid of photospheric features and hence suggest spectral types of O9Ia or earlier,the ab-sence of He ii8238˚A apparently precludes such a possi-bility.Instead we consider it likely that possible binarity or blending of2nearby objects leads to the featureless spectra and hence refrain from a classiﬁcation other than generic early OB supergiant for these4objects.Although the S/N for many spectra is rather poor, weﬁnd no evidence for a photospheric Hαproﬁle as pre-dicted by our synthetic spectra in the temperature range 10-34kK.A montage of the region containing the Hαline for those spectra with the largest S/N is presented in Fig. 6;weﬁnd evidence for either inﬁlling(W19,23a,24,43a, 57a60,61b&70)or emission(W11,13,28,30,61a& 71)in all spectra.Preempting the results of Sect.4,in the absence of an accurate photometric determination of bolo-metric luminosity,we may use the presence of Hαemission to infer a large luminosity and initial mass for the OB su-J.S.Clark et al.:The stellar content of Wd178J.S.Clark et al.:The stellar content of Wd1J.S.Clark et al.:The stellar content of Wd19Fig.6.Montage of the region of the spectrum containing Hαfor a selection of the OB supergiants.The left panel shows sample spectra for the O9.5Ia to B3Ia stars,the presence of either inﬁlling or Hαemission indicating a Ia luminosity classiﬁcation.The right panel shows the Hαproﬁles for the two highly luminous mid-B hypergiants W7&33,note the narrow line superimposed on a broader plinth of emission.pergiants.Speciﬁcally,McErlean et al.(1999)demonstrate that of their sample all the most luminous(M∼30-40M⊙) B supergiants demonstrate Hαemission.Fig.7presents a montage of the low resolution spec-tra of OB star candidates;where intermediate resolution spectra exist,these have been overplotted.Given both the lower resolution and S/N of the spectra,detailed classiﬁca-tion is diﬃcult.Hence we simply choose to divide the spec-tra into three morphological groups based on the presence of various photospheric features.Group1contains those stars without an obvious Paschen series and consists of W13,14a,15&44.Group2contains those stars with the Paschen series in absorption and consists of W2a,5,6,10, 11,23a,24,29,43a,55,56&238.Finally,group3consists of those stars with both Paschen and the O i7774˚A blend in absorption,and consists of W7,33,41,42,70&71.Of the group1objects W44and W13have already been discussed.With an essentially featureless spectrum we suspect that W15is likely a binary or blend of one or more OB SGs.The strong N iv emission seen in W14a is unexpected since this would imply an early O supergiant classiﬁcation,at odds with the expected age of the cluster (Sect.5).However,we note that W14a appears to be com-posed of2or more stars;hence an alternative explanation would be a blend containing at least one hitherto unde-tected WNE star.Clearly,future observations are required to resolve this apparent inconsistency.With a lack of O i7774˚A absorption,the group2ob-jects appear to have earlier spectral types than∼B3Ia. Indeed all those objects for which intermediate resolution observations are available are of spectral type O9.5Ia to B0.5Ia-hence we assume a late O/early B supergiant classiﬁcation for the remaining objects,with the sole ex-ception of W5,which,together with W7and33,we discuss in Sect.3.3.3.Of the group3spectra W41&42have only been ob-served at low resolution.W41apparently shows weak O i absorption,although it is coupled with an unexpectedly weak Paschen series.Hαis clearly seen in absorption;the only such object in our dataset.Given the rather unusual nature of the spectrum we tentatively suggest the spec-trum may be a blend of two or more stars.By contrast W42a has pronounced Hαemission and appears similar to the mid B supergiants W7&33(Sect.3.3.3)and is discussed therein.Finally,comparison of the two epochs of observations of W23a and43a are suggestive of variability,with Hαemission conspicuous in2001,but apparently absent in 2002.3.3.Anomalous B supergiantsAmongst the observations of the OB supergiants within the cluster weﬁnd a signiﬁcant number of objects with spectra demonstrating unusual properties.In this subsec-tion we detail these individually.3.3.1.The sgB[e]star W9The spectrum of W9is presented in Fig.8and is dom-inated by H i,He i and low ionisation metallic emis-sion(Fe ii,Ca i,N i and O i),with narrow,single peaked emission lines(FWHM(Hα)=125kms−1)and is notable for the complete lack of any photospheric features and the strength of certain emission features(e.g.Wλ(Hα)=-520±30˚A,Wλ(OI)=-48±2˚A).To the best of our knowledge such an equivalent width for Hαis completely unprece-dented for an early type emission line star,with the ex-ception of the extreme systems SS433(X-ray binary;e.g. Falomo et al.1987)andηCar(LBV;e.g.Davidson et al. 1999).Radio observations(Clark et al.1998,Dougherty et al.2004)reveal a strong,compact radio source to be associated with W9,while mid IR observations likewise10J.S.Clark et al.:The stellar content of Wd 1Fig.7.Low resolution spectra of cluster OB supergiants(solid black lines).Where available high resolution spectra (from Figs.4-6)are smoothed and overplotted(dotted red lines)on the corresponding low resolution spectra for comparison.Due to the low resolution an accurate determination of spectral type is impossible;hence we simply divide the spectra into3morphological classes based on the presence or otherwise of the Paschen lines and the O i 7774˚A feature;see Sect.3.2for further details.show strong emission(F10µm=50Jy),although the emis-sion mechanism(thermal dust or f-f/b-f)is still uncer-tain.Finally,an ISO-SWS spectrum reveals the presence of[O iv]emission,implying an exciting source with a tem-perature in excess of∼80kK must be present(Clark et al. 1998).While a quantitative analysis of the combined dataset is beyond the scope of this work,we note that the ob-servational properties of W9are unique within Wd1,and apparently amongst the wider galactic population of early OB stars.While it fulﬁlls the classiﬁcation criteria for su-pergiant B[e]stars of Lamers et al.(1998)we suspect that the emission line spectrum arises at least partially in the compact circumstellar envelope rather than in a stellar wind(Clark et al.1998).As such it could closely resem-ble the unusual object NaSt1,which Crowther&Smith (1999)propose to consist of a compact ejection nebula sur-rounding-and obscuring-an exciting WNE object.Such an hypothesis would naturally explain the[O iv]emission present in W9,although one might question the compact nature-and hence implied youth-of the radio nebula when contrasted to other LBV nebulae,given the require-ment for the central star to evolve through both the LBV and WNL phases.Clearly,while such an objection could be overcome by proposing a compact WR+LBV binary system,we also suggest an alternative possibility,namely that W9is the result of a recent merger event.Given the severely crowded nature of the central regions of the cluster(Sect.5.4) stellar collisions and interactions appear likely.A recent (∼103yr)interaction in which the outer H mantle of one or both objects were lifted oﬀto form the compact radio nebula would reveal the hot interior layers of the star(s)so aﬀected.This would then naturally explain the high exci-tation emission-until the remnant relaxed to a new equi-librium structure on a thermal timescale(∼104yrs);a sce-nario proposed by Clark et al.(2000)to explain the stellar and nebular morphology of the candidate LBV G25.5+0.2.3.3.2.The Luminous Blue Variable W243Clark&Negueruela(2004)present multi-epoch data that clearly demonstrate that W243-initially classiﬁed as an early B supergiant by West87-has evolved in the inter-vening decades to demonstrate a much cooler,A super-giant spectrum,albeit with anomalous emission features. The overall spectrum closely resembles that of the lumi-nous A supergiant IRC+10420(e.g.Oudmaijer1998), with the notable exception of emission in the He i6678 and7065˚A lines.Clark&Negueruela(2004)advanced the suggestion that W243was an LBV,with the unusual com-posite spectrum resulting from the formation of a pseudo-photosphere in a dense stellar wind.Fig.8.R and I band spectra of the sgB[e]star W9.Note that we are unable to identify the narrow emission features at7134,7233&7280˚A.Subsequently,de Koter(2004,m.)suggested that as presented such an hypothesis would predict sig-niﬁcantly stronger Hαemission(EW∼−100˚A)than ob-served.However,the presence of He i emission and strong electron scattering wings(extending to±103kms−1)in the Hαemission proﬁle apparently excludes a simple alterna-tive explanation that W243now has the physical proper-ties-and in particular a rather low mass loss rate-of a bonaﬁde A supergiant.Consequently,we suspect that a hybrid model may provide the correct explanation-viz.a cooling of the un-derlying star to a late B spectral type-still suﬃcient to produce He i emission-coupled with an increase in mass loss rate to simulate a later spectral type.3.3.3.Extreme B supergiants W5,7,33&42aBased on the strength of the O i8446˚A and N i features present in the intermediate resolution spectra(Fig.5),W7 &33appear to be B5supergiants.However,closer exami-nation shows a weak P Cygni proﬁle in the O i8446˚A line of both stars-to the best of our knowledge absent from any other mid-B supergiant,with the notable exception of the2002spectrum of the LBV W243.Examination of the Hαproﬁles also shows that they diﬀer from the weak P Cygni proﬁles expected for B su-pergiants,being composed of a single narrow peak super-imposed on a broad emission base(Fig.6).In this re-spect they again resemble the LBV W243(Fig.3),while the broad emission component is observed for the clus-ter member YHG W16a(Sect.3.4).Moreover,similar composite Balmer line proﬁles are also obtained for the ‘B-supergiant LBVs’studied by Walborn&Fitzpatrick (2000).Consequently,we propose that both objects are to be found in a shortlived,transitional evolutionary state more closely related to the LBV and YHG population of Wd1than the late O/early B supergiant population. Indeed,both stars are a magnitude more luminous than any other OB supergiant within the cluster,with an ob-served V band magnitude directly comparable to the YHG population.Comparable objects might therefore be the highly lu-minous B1.5a+hypergiants HD80077(Carpay et al. 1991)and HD152236(Van Genderen et al.1984),which are also characterised by strong Hαemission due to mass loss rates an∼order of magnitude greater than Ia and Ib supergiants of similar spectral type(e.g.Leitherer et al. 1995).Of the stars for which only low resolution spectra exist, weﬁnd that W42a has a comparable morphology to both W7&33,suggesting a similar classiﬁcation.W5demon-strates both dramatic Hαand also C ii∼7236˚A emis-sion,previously only identiﬁed in the WCL population. However,the lack of C iii9705˚A emision(not shown in Fig.7)precludes an identiﬁcation as a binary/blend con-taining a WCL star.Recent high resolution spectra ob-tained by us(Negueruela&Clark2004,in prep)conﬁrm the identiﬁcation of C ii emission,while also revealing the presence of weak He i P Cygni emission proﬁles.Such a morphology,with a lack of N iv7116emission,is indica-tive of either a very late WN star(WN9or later)or an extreme early BIa+supergiant,the lack of a He ii transi-tion in the current data precluding a further classiﬁcation.3.4.The Yellow HypergiantsThe remaining6spectra in Figs.3&5are seen to be dom-inated by low ionisation metallic photospheric lines,sug-gesting spectral types later than prehensive classi-ﬁcation criteria and standard spectra for cool supergiants are provided by Munari&Tomasella(1999).Comparison to their data,employing the relative strengths of the Ca ii lines and adjacent Paschen series lines-providing the same diagnostic as the Ca ii H&K versus the Balmer line strength in the optical region-achieves a broad clas-siﬁcation for B8-F8supergiants.This may then be further reﬁned by consideration of the presence and strength of the N i transitions between8650to8750˚A for A super-giants and the appearance of Fe i and Si i lines for the F supergiants in our sample.When combined with the (lower resolution)observations of Cenarro et al.(2001) we estimate a classiﬁcation accuracy of±2spectral sub-types for our current observations,from which we identify two A and four F stars(Tables1&2).The narrow line widths,forming a smooth progres-sion from the OB supergiants,together with the pro-nounced N i absorption features(c.f.Figs.17-25of Munari &Tomasella1999)clearly justiﬁes at least a supergiant classiﬁcation for the6stars in question.However,deter-mination of the bolometric luminosity of A-G stars may be made directly via the strength of the O i7774˚A blend;a re-lationshipﬁrst identiﬁed by Merrill(1925).We make use of the most recent calibration of this relationship by Arellano Ferro et al.(2003;their Eqn.2);which is calibrated from M V=+0.35to−9.5mag.The results are presented in Table2,with four stars(W4,12a,16a&265)apparently demonstrating absolute visual magnitudes in excess of the current calibration for the relationship.Consequently,we simply limit ourselves to the conservative statement that these stars have M V∼−9.5(log(L∗/L⊙)∼5.7);placing them at the empirical Humphreys-Davidson limit for cool hypergiants(under the assumption of negligible bolomet-ric correction).We further note that both the presence of chemically processed material at the stellar surface and/or inﬁlling of the blend due to emission from a stellar wind will only cause a systematic underestimate of the true luminosity;such an eﬀect is apparently observed for the YHGρCas.Therefore,we conclude the six A-F stars in Wd1have luminosities that are at least directly compa-rable to those of theﬁeld populations of YHGs found in both the galaxy and the Magellanic Clouds.However,as described by de Jager(1998)a high lumi-nosity(M V>-7)is not suﬃcient to designate a star as a bonaﬁde YHG.Rather,he deﬁnes the‘Keenan-Smolinski’criteria for the spectroscopic classiﬁcation of hypergiants;(i)the presence of one or more broad components of Hαand(ii)absorption lines that are signiﬁcantly broader than Table2.Equivalent widths for the O i∼7774˚A blend for the six yellow hypergiants in Wd1,with absolute visual magnitude and resultant luminosity determined directly from the relationship of Arellano Ferro et al.(2003;formal error of±0.4mag.).4F2Ia+ 3.0-10.18F5Ia+ 2.1-8.712a A5Ia+ 2.8-9.916a A2Ia+ 2.7-9.832F5Ia+ 2.3-9.1265F5Ia+ 2.6-9.7。

The Globular Cluster System of NGC 1316 (Fornax A)

a r X i v :a s t r o -p h /0103501v 1 29 M a r 2001Astronomy &Astrophysics manuscript no.(will be inserted by hand later)The Globular Cluster System of NGC 1316(Fornax A)M.G´o mez 1,2,T.Richtler 3,L.Infante 1,and G.Drenkhahn 41Departamento de Astronom ´ıa y Astrof ´ısica,P.Universidad Cat´o lica de Chile.Casilla 306,Santiago,Chilee-mail:mgomez@astro.puc.cl,linfante@astro.puc.cl 2Sternwarte der Universit¨a t Bonn,Auf dem H¨u gel 71,D-53121Bonn,Germany 3Departamento de F ´ısica,Universidad de Concepci´o n.Casilla 4009,Concepci´o n,Chile e-mail:tom@coma.cfm.udec.cl 4Max-Planck-Institut f¨u r Astrophysik,Postfach 1317,D-85741Garching bei M¨u nchen,Germany e-mail:georg@mpa-garching.mpg.deReceived .../Accepted ...Abstract.We have studied the Globular Cluster System of the merger galaxy NGC 1316in Fornax,using CCD BV I photometry.A clear bimodality is not detected from the broadband colours.However,dividing the sample into red (presumably metal-rich)and blue (metal-poor)subpopulations at B −I =1.75,we ﬁnd that they follow strikingly diﬀerent angular distributions.The red clusters show a strong correlation with the galaxy elongation,but the blue ones are circularly distributed.No systematic diﬀerence is seen in their radial proﬁle and both are equally concentrated.We derive an astonishingly low Speciﬁc Frequency for NGC 1316of only S N =0.9,which conﬁrms with a larger ﬁeld a previous ﬁnding by Grillmair et al.(1999).Assuming a “normal”S N of ∼4for early-type galaxies,we use stellar population synthesis models to estimate in 2Gyr the age of this galaxy,if an intermediate-age population were to explain the low S N we observe.This value agrees with the luminosity-weighted mean age of NGC 1316derived by Kuntschner &Davies (1998)and Mackie &Fabbiano (1998).By ﬁtting t 5functions to the Globular Cluster Luminosity Function (GCLF),we derived the following turnover magnitudes:B =24.69±0.15,V =23.87±0.20and I =22.72±0.14.They conﬁrm that NGC 1316,in spite of its outlying location,is at the same distance as the core of the Fornax cluster.Key words.galaxies:distances and redshifts –galaxies:elliptical and lenticular,cD –galaxies:individual:NGC 1316–galaxies:interactions1.IntroductionThe analysis of globular cluster systems (GCSs)in ellipti-cal galaxies can have diﬀerent motivations.One of them is to investigate the variety of GCS morphologies in relation to their host galaxy properties in order to gain insight into the formation of cluster systems (see Ashman &Zepf 1997and Harris 2000for reviews).On the other hand,GCSs have been successfully em-ployed as distance indicators (Whitmore et al.1995,Harris 2000).This is particularly interesting if the host galaxy is simultaneously host for a type Ia supernova whose ab-solute luminosity can accordingly be determined,as has been the case for SN 1992A in NGC 1380(Della Valle et al.1998)and SN 1994D in NGC 4526(Drenkhahn &Richtler 1999).However,it can happen that both aspects are equally interesting as with the target of the present contribution,NGC 1316.2M.G´o mez et al.:The Globular Cluster System of NGC1316(Fornax A)during a merger event.But despite the strong evidence for a previous merger in NGC1316,the only indication for cluster formation is that Grillmair et al.(1999,here-after Gr99),could not see a turnover in the GCLF at the expected magnitude.They interpreted thisﬁnding as an indication for an enhanced formation of many less massive clusters,perhaps in connection with the merger.However, their HST study was restricted to the innermost region of the galaxy.In contrast to other galaxy mergers,where,presum-ably caused by the high star-formation rate(Larsen& Richtler1999,2000),the speciﬁc frequency of GCs in-creases,Gr99found an unusually small total number of clusters relative to the luminosity of NGC1316(M V∼−22.8,adopting a distance modulus to Fornax ofµ= 31.35,Richtler et al.2000).There is also evidence from stellar population synthesis of integrated spectra that NGC1316hosts younger popu-lations(Kuntschner&Davies1998,Kuntschner2000)and thus the question arises,whether the surprisingly low spe-ciﬁc frequency is caused by a high luminosity rather than by a small number of clusters.Goudfrooij et al.(2000, hereafter Go00)obtained spectra of27globular clusters and reported that the3brightest clusters have an age of about3Gyr,indicating a high star-formation activity 3Gyr ago,presumably caused by the merger event.Theseﬁndings and the hope for a good distance via the GCLF were the main motivation to do the present study of the GCS of NGC1316in a larger area than that of the HST study.As we will show,this galaxy resembles in many aspects the“old”merger galaxy NGC5018,whose GCS has been investigated by Hilker&Kissler-Patig(1996).The paper is organized as follows:in Sect.2we dis-cuss the observations,the reduction procedure and the selection of cluster candidates.The photometric and mor-phological properties of the GCS are discussed in Sect.3. Sect.4contains ourﬁndings concerning the Speciﬁc Frequency.We conclude this work with a general discus-sion in Sect.5.2.Observations and ReductionThe B,V and I images were obtained at the3.6m tele-scope at La Silla during the nights29th and30th of December,1997(dark moon),using the ESO Faint Object Spectrograph and Camera,EFOSC2.Theﬁeld of view was 5.′6×5.′6with a scale of0.′′32/pixel.During theﬁrst night, short-and long-exposures in eachﬁlter were centred on the galaxy.In the second night,a backgroundﬁeld located about5′away from the centre of NGC1316was observed, overlapping by1′the observations of theﬁrst night.In addition,severalﬁelds containing standard stars from the Landolt catalog(Landolt1992)were acquired in eachﬁl-ter,as well as some short exposures of NGC1316.Fig.1 shows the combined frames from both nights and Table1 summarises the observations.Table1.Summary of the observations.Dec.29,1997B4×6001.′′1Dec.29,1997V5×3001.′′0Dec.29,1997I6×3001.′′0Dec.30,1997B4×6001.′′3Dec.30,1997V3×6001.′′3Dec.30,1997I3×6001.′′2M.G´o mez et al.:The Globular Cluster System of NGC1316(Fornax A)3 Table2.General parameters of the target galaxy,from de Vaucouleurs et al.(1991)and Poulain(1988).NGC131603h22m41.s6−37◦06′10′′240.◦16−56.◦69(R’)SAB(s)08.53±0.080.861793±12ﬁlter A j1A j2rms of theﬁtture radii between22.′′9and86.′′6are: ∆V =0.013,∆B−V =0.007and ∆V−I =0.006mag,well below therms of theﬁt(see Table3).We then deﬁned5local stan-dard stars in theﬁeld of NGC1316to set the photometryof both nights in a consistent way.2.3.Selection criteriaSeveral criteria have been applied to select cluster can-didates,according to colours,magnitude,photometric er-rors,stellarity index and projected position around thegalaxy.We assume that the clusters are similar to theMilky Way clusters.Adopting an absolute turnover mag-nitude(TOM)of V=−7.60for the galactic clusters(Drenkhahn&Richtler1999,Ferrarese et al.2000)andµ=31.35(Richtler et al.2000),the TOM of NGC1316isexpected to be V∼23.7mag,and the brightest clustersabout V∼20.Although no reddening corrections are normally ap-plied when looking towards Fornax(Burstein&Heiles1982),we cannot restrict the colours of the clusters inNGC1316to match exactly the galactic ones.One pointis the smaller sample of galactic clusters.Besides,we mustallow for signiﬁcant photometric errors of faint cluster can-didates.Fig.2shows a colour-magnitude diagram for allobjects detected simultaneously in B,V and I in bothnights(before the selection),together with the cut-oﬀval-ues adopted as criterium for this colour.As can be seen,the majority of objects have colours around V−I=1.0.Objects bluer than0.5mag are very probably foregroundstars.A fraction of the data points redder than V−I=1.6are background galaxies.We also tested in our images the robustness of the“stellarity index”computed by SExtractor.This indexranges from0.0(galaxy)to1.0(star)and varies for thesame object by about0.2when classifying under diﬀerentseeing conditions,except for the brightest objects,whichare clearly classiﬁed.By visual inspection of the images,we are quite conﬁdent that bright galaxies are always givenindices near to zero.However,this classiﬁcation becomesprogressively more diﬃcult with fainter sources.4M.G´o mez et al.:The Globular Cluster System of NGC 1316(Fornax A)−0.50.51 1.522.5V−I161820222426V Fig.2.A colour-magnitude diagram for all objects de-tected in B ,V and I in both nights before the selection criteria (911points).The dashedlines indicates the selection criterium in the V −I colour (see Sect.2.3.)V0.00.20.40.60.81.0s t e l l a r i t y i n d e xFig.3.The stellarity index computed by SExtractor as function of the V magnitude.The dashed lined indicates the cut value adopted in the selection criteria to reject background galaxies.Fig.3shows the “stellarity index”for the 911objects in our sample (before the selection criteria)as a function of the magnitude.Two groups of objects having indices of ∼0.0and ∼1.0can be seen,but it is apparent that faint clusters cannot be unambiguously distinguished from background galaxies due to the uncertainty of the stellar-ity index in the case of faint sources.Very similar results were obtained with our “artiﬁcial stars”(see Sect.2.5),where indices down to 0.2were measured for faint objects that are constructed using the PSF model and,therefore,are expected to have a stellarity index of ∼1.0.Guided by our experience with artiﬁcial stars,we de-ﬁned the cut-oﬀvalue for the stellarity index to be 0.35.Remaining galaxies will be statistically subtracted be-cause the same criteria are applied to the background ﬁeld (see Sect.2.4).Finally,we rejected objects with photometric errorlarger than 0.15mag.To summarise,the following criteria were applied to our sample of 911sources detected in B ,V and I :i)V >19.5ii)0.4<B −V <1.4iii)0.3<V −I <1.8iv)stellarity index >0.35v)error(V ),error(B −V ),error(V −I )<0.15375objects met this set of criteria and are our globular cluster candidates.2.4.Background correctionAfter the selection,there might still be some contamina-tion by foreground stars and background galaxies in our sample.To subtract them statistically,one needs to ob-serve a nearby ﬁeld,where no clusters are expected,and to apply the same detection and selection criteria as with the galaxy frame.However,the analysis of our background ﬁeld still shows a concentration towards the galaxy centre,which means that only part of the ﬁeld can be considered as background.We used the radial proﬁle of the GC surface densi-ties (see Sect.3.3)to select all objects on the ﬂat part of the proﬁle,i.e.,where the number of globular cluster can-didates per area unit exhibits no gradient.Fig.11(top)shows that this occurs at r ≈300′′,where r is the distance from the optical centre.Thus,all objects with galactocen-tric distances larger than 300′′and matching the above criteria,constitute our background sample.We constructed a semi-empirical luminosity function of the background clusters with a technique described by Secker &Harris (1993),where a Gaussian is set over each data point,centred at the corresponding observed magni-tude.The sum of all Gaussians gives a good representation of the background,without introducing an artiﬁcial undu-lation or loss of information due to the binning process.Fig.4shows the histogram of the background objects,us-ing a bin size of 0.4mag,and the adopted semi-empirical function,which we use as background in the calculation of the luminosity function (see Sect.3.4)and the speciﬁc frequency.Admittedly,the numbers are small.The dip at V =23may be simply a result of bad statistics.On the other hand,as Table 6shows,the background counts are small compared to the clusters counts.Therefore,errors of the order of the statistically expected uncertainty do not signiﬁcantly inﬂuence our results and are accounted for in the uncertainties of the total counts in Table 6.pleteness correctionTo correct statistically for completeness,one needs to de-termine which fraction of objects are actually detected by the photometry routines.These ‘artiﬁcial stars ex-periments’were performed using the task addstar inM.G´o mez et al.:The Globular Cluster System of NGC 1316(Fornax A)52021222324V05101520N Fig.4.The semi-empirical luminosity function for the background ﬁeld (dashed line).A histogram with a bin size of 0.4mag is over-plotted for comparison.DAOPHOT.In one step,100stars were added in the sci-ence frames from V =20to V =25in steps of 0.1mag,distributed randomly to preserve the aspect of the image and not to introduce crowding as an additional param-eter,but with the same coordinates in the B ,V and I frames every loop.The colours of the stars were forced to be constant B −V =0.7and V −I =1.0,close to the mean colours of the globular clusters in NGC 1316(see Sect.3.1).The object detection,photometry,classi-ﬁcation and selection criteria were applied in exactly the same way as for the globular cluster candidates.To get suﬃciently good statistics,we repeated the whole proce-dure 10times,using diﬀerent random positions in each of them and averaging the results.In all,50000stars were added.However,the completeness is not only a function of the magnitude.Due to the remaining noise after galaxy subtraction,the probability of detecting an object near the centre of the galaxy is smaller than in the outer parts.We divided our sample of artiﬁcial stars into elliptical rings,in the same way as we did in deriving the radial proﬁle (see Sect.3.3).The results of the completeness tests are summarised in Fig.5.It can be seen that the 50%limit goes deeper with increasing galactocentric distance.3.Photometric and morphological properties 3.1.Colour distributionIn this section we discuss the colours of our GC candidates.No interstellar reddening is assumed (Burstein &Heiles 1982)and therefore,only internal reddening might aﬀect the colours.The histograms in Fig.6show the colour distribution of the cluster candidates.A ﬁt of a Gaussian function with free dispersions returned the values listed in Table 4and is overplotted for comparison.As can be seen,the dispersion in the B −V and V −I histograms is completely explained by the photometric er-rors alone.This is not the case for the B −I histogram,due probably to the greater metallicity sensitivity of thisV0.00.20.40.60.81.0c o m p l e t e n e s spleteness factors in four elliptical annuli.The probability of detection strongly decreases near the centre of NGC 1316.Table 4.Fit of a Gaussian function to the colour his-tograms of the GC candidates.B −V 0.80±0.020.13±0.04V −I 0.95±0.010.17±0.02B −I 1.77±0.020.35±0.036M.G´o mez et al.:The Globular Cluster System of NGC 1316(Fornax A)0.00.51.0 1.52.0B−V0204060N0.00.51.0 1.52.0V−I0204060N0.81.31.82.3 2.8B−I010203040N Fig.6.Colour histograms of the cluster candidates.The bin size is 0.05mag in each colour.A Gaussian function has been ﬁt to the histograms (dashed line,see text).The dot-dashed line is a Gaussian with σ=0.15.The long-dashed line at B −I =1.75(lower panel)was set to divide the sample in red and blue clusters.the clusters are on average ∼0.2mag bluer than the un-derlying galaxy light.This is a property commonly found also in normal early-type galaxies,where the blue and presumably metal-poor clusters indicate the existence of−3.0−2.0−1.00.0 1.0[Fe/H]1020304050NFig.7.Metallicity histogram of the GCS of NGC 1316,from its B −I broadband colour.The galactic system (dashed line)is overplotted for comparison.The long-dashed line near [Fe /H]=−1.0divides the sample in metal-rich and metal-poor clusters,using the calibration from Couture et al (1990)and B −I =1.75(see text and Fig.6.)a faint metal-poor stellar (halo?)population,as the case of NGC 1380suggests (Kissler-Patig et.al 1997).However,the non-existence of a colour gradient is consistent with the ﬁnding that blue and red clusters have similar surface density proﬁles (Sect.3.3).Diﬀerential reddening caused by the irregular dust structure might aﬀect the width of the colour distribution,but apparently does not produce any colour gradient.3.2.Angular distributionFor all objects in our sample of clusters,a transformation from cartesian (x,y )coordinates to polar (r,θ)was done,with origin in the optical centre of NGC 1316.An oﬀset of 50◦in θwas applied to match the PA of the galaxy quoted by RC3.In this way,θ=0represents the direction of the semi-major axis (sma)of the galaxy,a ,and θ=90◦the direction of b ,the semi-minor axis.To analyse the angular distribution,we rejected ob-jects inside a radius of 150pixels (corresponding to 4.3kpc with µ=31.35),where the completeness is signiﬁcantly lower (see Fig.5)and some clusters appear over ripples and dust structures.Objects outside of 450pixels were also rejected,as one needs equally-sized sectors to do this analysis,and r =450is roughly the radius of the largest circle fully covered by our frame (see dotted line in Fig.10).Only candidates brighter than V =23.8(the 50%completeness level in the entire frame)were considered.The data were then binned in θ.Several bin sizes from 18◦to 30◦were tested,and Fig.9shows the histogram for a bin size of 22.◦5,which corresponds to dividing the sample into 16sectors.The bins were taken modulo πfor a better statistics,that is,we assume that the distribution of clusters is symmetric along the semi-mayor axis of the galaxy.Due to the substructures present in NGC 1316,andM.G´o mez et al.:The Globular Cluster System of NGC 1316(Fornax A)71.21.4 1.61.82.0 2.2 2.4log r (arcsec)1.02.03.0B −I1.02.03.0B −IFig.8.The B −I colour gradient along the projected galactic radius.Top:the cluster candidates and a least-square ﬁt(solid line).The crosses indicate the B −I colour of the galaxy.Bottom:the mean colour in several rings,with the error bars indicating the σof the mean at that ring.090180270360θ [deg]10203040N Fig.9.The angular distribution of globular clusters for a radius from 150to 450pixels (48′′to 144′′)down to V =23.8.The bin size is 22.◦5and the data were taken mod π.The histogram from 0◦to 180◦is repeated from 180◦to 360◦for a better visualisation.The dashed line indicates the best ﬁt of a double-cosine function.from the fact that it is a merger galaxy,one could expect some systematic diﬀerences in the azimuthal distribution of the clusters between both halves.Although this is not observed at any bin size,the small number of counts does not allow us to address this question clearly.The histogram shown in Fig.9demonstrates the strong correlation of the globular clusters with the galaxy light.By ﬁtting isophotes to the galaxy,we obtained ellipticities ranging from 0.27to 0.32and position angles from 49◦to53◦,between semi-major axes of 150to 450pixels (thesame used with the clusters).From the least-square ﬁt to this histogram (with ﬁxed period π),we derived PA =63◦±9◦and an ellipticity of 0.38±0.06.There are,however,some problems that cannot be eas-ily resolved with our ground-based data.As indicated,the detection of cluster candidates near the centre of the galaxy is quite poor.This is,unfortunately,the most in-teresting region to search for young clusters which might be related to a merger event.3.3.Radial proﬁleTo derive the radial surface density of GCs,we divide our sample into elliptical annuli,as shown in Fig.10.The annuli have a width of 100pixels along the major axis (a )and start from a =50pixels.Due to the small number of objects in the periphery of NGC 1316,rings beyond a =900were given a width of 300pixels.The ellipticity,position angle and centre of these rings were taken from the ﬁt of the galaxy light (see Sect.3.2)and ﬁxed for all annuli.In particular,the ellipticity e ,deﬁned as 1−(b/a ),where a and b are the semi-major and semi-minor axis respectively,was set to 0.3and the PA to 50◦.We then counted the number of globular cluster can-didates per unit area in each ring,down to V =23.8,and corrected them with the corresponding completeness function.The results are presented in Table 5.The ﬁrst column lists the mean semi-major axis of the ring.Column 2gives the raw number of clusters down to V =23.8,without correction for completeness.Column 3lists the corrected data with their errors.Column 4lists the visible area of the rings,in ⊓⊔′.Column 5gives the number of candidates per unit area.Column 6,7and 8are used to compute the Speciﬁc Frequency (see Sect.4).Fig.11shows the radial proﬁle of the clusters’surface density,before and after the subtraction of the background counts.A ﬁt of a power-law ρ(r )=A ·r α,where ρis the surface density and r the projected distance along the semi-major axis,gives αgcs =−2.04±0.20and αgal =−2.03±0.02for the clusters and the galaxy light,respectively.We are well aware that a King proﬁle may be more adequate than a power function,but our purpose is to compare our result with previous work in other GCSs in Fornax,which quote only power functions.The similarity between both slopes indicates that the GCS of NGC 1316is not more extended than the galaxy light.Moreover,αGCS =−2.04is in good agreement with other GCS of “normal”early-type galaxies in Fornax (Kissler-Patig et al.1997).We divided the system at B −I =1.75mag into blue (presumably metal-poor)and red (metal-rich)clusters,and searched for systematic diﬀerences in the morpholog-ical properties between both subgroups.Again,only clus-8M.G´o mez et al.:The Globular Cluster System of NGC1316(Fornax A)Table5.This table gives the result of the radial proﬁle of the cluster candidate surface density.Theﬁrst column lists the centre of each annulus(in pixels).Then follows the raw number counts down to V=23.8,before and after the correction for completeness.The fourth column gives the visible area of the annulus in⊓⊔′.Column5lists the mean density of GC per⊓⊔′.Columns6and7give the number of clusters down to the TOM in V,before and after the correction for completeness.The applied geometrical corrections are listed in column8.Finally,the number of the clusters in each annulus,after doubling the counts around the TOM.Note that the corrected and total number of clusters for the innermost annulus(sma=100)are NOT derived using the completeness correction.Instead,they were estimated by extrapolating the radial proﬁle towards the centre(see text in Sect.4).1002058.6±18.1 1.25146.86±14.4720200.2±37.5 1.400±7520053100.3±17.9 2.50240.09±7.1553100.7±18.0 1.201±3630068104.4±15.2 3.75127.84±4.0569109.4±15.8 1.219±324005465.4±10.7 5.00613.06±2.135668.9±11.0 1.134±225004858.2±10.0 6.2349.34±1.605162.0±10.40.997124±216003742.9±8.5 6.1596.96±1.223744.5±8.80.821108±217001922.4±6.2 5.1454.35±1.211922.8±6.30.58878±219001923.2±6.49.4402.45±0.68————12001112.7±4.67.1591.77±0.64————150045.3±3.2 2.8801.84±1.11————M.G´o mez et al.:The Globular Cluster System of NGC 1316(Fornax A)9Fig.10.The elliptical annuli used in the calculation of the globular cluster density and speciﬁc frequency.The open circles indicate the position of all GC candidates brighter than V =23.8.Objects outside the annulus deﬁned by r =150and r =450pixels (dotted line)were rejected for the analysis of the angular distribution (see Sect.3.2).Objects outside the dashed ellipse are considered as background.The scale and orientation is the same as in the Fig.1.There are two additional columns,namely the number of blue and red clusters.They were calculated in the same way and will be discussed in Sect.5.Bin sizes of 0.3,0.4and 0.5mag were tested,and the results were always in good agreement with each other.Finally,we have chosen 0.5mag as our bin size from the appearance of the ﬁt histogram,and the absence of undu-lations which are present for the other cases.We note,however,that our derived TOM is close to the limit of the observations,and the last bins are strongly aﬀected by the completeness correction.Nevertheless,the similarity of the results using diﬀerent bin sizes and cen-ters,and the robustness of the ﬁt against skipping the last bin,is encouraging.100110100G C /a r c m i n2100r (arcsec)110100G C /a r c m i n2Fig.11.Top:the radial proﬁle of the density of glob-ular cluster candidates.The dashed line indicates thevalue adopted for the background,corresponding to 2.0objects /⊓⊔′.Bottom:the radial proﬁle after subtrac-tion of the background counts.The crosses represent the proﬁle of the galaxy light,arbitrarily shifted.1.61.82.02.2 2.4log r (arcsec)−0.50.00.51.01.52.0l o g (G C /a r c m i n2)Fig.12.The radial proﬁle of the GC surface density for the red (triangles)and blue population (squares).No sys-tematic diﬀerence is seen and both are equally concen-trated.Fig.14shows the three luminosity functions in B ,V ,I .For ﬁtting the LF we chose t 5functions,which are of the form:t 5(m )=85πσt1+(m −m 0)210M.G´o mez et al.:The Globular Cluster System of NGC1316(Fornax A)Table6.The counts(in bins of0.5mag)used in the determination of the GCLF.Given are the V-magnitudes(or B,I,respectively)of the bin centers.Then follow the raw counts of the four elliptical annuli N i(see text)together with the corresponding completeness factors f i.The background counts are then listed as deﬁned in Sect.2.4.The completeness factors of the fourth annulus have been used for the background as well.The total number of clusters is the sum of the four annuli minus the background,normalised to the same area(see text).Also given is the number of clusters for the blue and the red population separately,where the separating colour was B−I=1.75.19.500.7110.981 1.002 1.000.04.0±2.01.0±1.03.0±1.720.010.7110.983 1.001 1.000.06.4±2.72.4±1.74.0±2.020.510.6700.984 1.002 1.000.26.9±3.13.9±2.63.0±1.721.020.6260.983 1.003 1.00 1.012.6±5.01.4±3.311.2±3.821.520.5830.94120.9970.99 2.518.8±7.07.8±4.611.3±5.222.020.5650.84140.97110.98 4.622.2±8.814.4±6.98.0±5.422.570.40110.68320.95140.95 4.269.8±12.536.6±9.033.3±8.623.030.35180.54390.93140.90 1.794.2±12.944.3±8.749.9±9.523.520.1480.28520.71190.79 3.7127.2±19.965.5±15.661.7±12.124.000.0720.20320.2280.25 3.8145.1±38.848.8±24.896.5±28.124.500.0000.0040.0310.030.5———B N B1f1N B2f2N B3f3N B4f4N B bkg.N B total N B blue N B red18.500.7110.980 1.002 1.000.03.0±1.70.0±0.03.0±1.719.000.7110.984 1.001 1.000.06.0±2.51.0±1.05.0±2.219.530.6710.983 1.000 1.000.08.5±3.34.0±2.34.5±2.320.000.6350.983 1.005 1.000.511.7±4.13.2±2.58.5±3.320.540.5840.94110.9950.99 2.819.8±7.49.5±4.910.3±5.521.020.5660.84160.97100.98 3.826.7±8.59.3±5.417.4±6.621.540.4090.68350.95170.95 5.163.1±12.133.0±9.030.1±8.022.050.35180.54370.93120.90 1.994.9±13.539.0±9.255.9±9.822.510.1490.28460.71150.79 2.3115.0±17.962.0±13.953.4±10.923.010.0700.20380.22150.25 4.3199.4±45.4130.6±36.468.8±24.623.500.0210.0030.0300.03 1.4———。

Stellar Populations and Variable Stars in the Core of the Globular Cluster M5

a rXiv:as tr o-ph/9711152v113Nov1997STELLAR POPULATIONS AND V ARIABLE STARS IN THE CORE OF THE GLOBULAR CLUSTER M51Laurent Drissen D´e partement de Physique and Observatoire du Mont M´e gantic,Universit´e Laval,Qu´e bec,QC,G1K 7P4Electronic mail:ldrissen@phy.ulaval.ca and Michael M.Shara Space Telescope Science Institute,3700San Martin Drive,Baltimore,Maryland 21218Electronic mail:mshara@ ABSTRACT We report the discovery of a variable blue straggler in the core of the globular cluster M5,based on a 12-hour long series of images obtained with the Planetary Camera aboard the Hubble Space Telescope .In addition,we present the light curves of 28previously unknown or poorly studied large-amplitude variable stars (all but one are RR Lyrae)in the cluster core.A (V,U-I)color-magnitude diagram shows 24blue stragglers within 2core radii of the cluster center.The blue straggler population is signiﬁcantly more centrally concentrated than the horizontal branch and red giant stars.1.IntroductionGlobular cluster cores are being imaged intensively with the Hubble Space Telescope, and continue to yield surprises.The realizations that blue stragglers are commonplace,red giants are depleted,and that horizontal branch populations may depend on core properties has spurred on observers in the pastﬁve years.As part of our program to study the dis-tributions of blue stragglers and variable stars in globular cores,we have now imaged NGC 5904=M5.The globular cluster M5harbors one of the richest collections of RR Lyrae stars in the Galaxy.It is also home to one of only two known dwarf novae in Galactic globular clusters. Until now,however,not a single blue straggler candidate has been identiﬁed in M5.Is this because none exist,or because blue stragglers reside only in the(until now unobservable) core of M5?In section2we describe the observations and reductions;the CMD of the core of M5is presented in section3.The variable stars weﬁnd are described in section4while our results are summarized in section5.2.Observations and reductions2.1.Search for variable starsA series of twenty-two600-second exposures of M5’s central(r≤50′′)region,spanning11.5hours,was obtained on March21,1993with the Planetary Camera(PC)aboard the Hubble Space Telescope(HST)before the repair mission.The F336Wﬁlter,similar to the Johnson U bandpass(Harris et al.al.1991),was used for the observations.Standard cali-bration(bias and dark subtraction,ﬂatﬁeld correction)was performed with STScI software within IRAF/STSDAS.The detection of variable stars was performed as follows.First,the22individual images were combined with IRAF’s combine task(with the crreject option)to create a deep image. This image is shown in Figure1.The individual images were remarkably well aligned with each other,so no shift was necessary.DAOPHOT’s Daoﬁnd algorithm(Stetson1987)was then used to build a masterlist of3144stars visible in the deep image.In order to eliminate the numerous cosmic rays,which are very diﬃcult to remove on single frames,the22individual images were combined two by two(again with the combine task and the crreject option),with an overlap of1(image1+image2,image2+image3,...).Aperture photometry with an aperture radius of4pixels(0.17′′),and a sky annulus with inner and outer radii of10and15pixels was then performed on the21resulting images, using the masterlist of stars previously found.The standard deviation from the mean in the 21frames was then computed for all stars;this resulted in the discovery(or re-discovery)of 29variable stars,which will be discussed in section4.Note that since for any given star the conditions(PSF,ﬂatﬁeld,star location,aperture, background)are virtually identical from frame to frame(with the exception of faint stars near bright,large amplitude variables),the relative photometry from frame to frame is expected to be much more precise than the relative photometry among stars within the same frame (mostly because of PSF variations which induce position-dependent aperture corrections and overlapping PSFs in a crowdedﬁeld).While the relative error from one star to the next within a single frame can be as large as0.2mag(if simple aperture photometry is used), even for bright stars,the typical standard deviation from the mean of the21frames for a given non-variable star is less than0.05mag at U=17.5,and reaches0.1mag at the cluster main sequence turnoﬀ.2.2.The color-magnitude diagramIn order to study the stellar populations in M5,a70second F555W(equivalent of Johnson Vﬁlter;Harris et al.1991)and a70second F785LP(comparable to I)PC images were retrieved from the HST archives.Both images were obtained on December27,1991. Fortunately,the center of these frames is only∼8′′away from the center of our images (the totalﬁeld of view of the4PC CCDs is70′′),so most stars detected in our F336W images are also located in the archive frames;the area common to all three sets of images is∼1.1arcmin2.Stellar photometry was performed in the most simple way on these frames:aperture photometry(with the same parameters as above)was performed on the deep,combined F336W frame using the masterlist.After proper shift and rotation of the coordinates,the same masterlist was used to obtain aperture photometry of the stars in the F555W and F785LP images.Although PSF-ﬁtting techniques are known to improve the photometric accuracy(especially at the faint end of the luminosity function and near bright stars;see Guhathakurta et al.1992for a detailed discussion),simple core aperture photometry gives results which are reliable enough(typicallyσ∼0.2mag above the turnoﬀ) for our purpose.A total of2153stars have been included in the color-magnitude diagram discussed below.Aperture corrections and photometric zero-points determined by Hunter et al.(1992) were used to calibrate the magnitudes and colors of the stars.Moreover,the absolute sen-sitivity of the CCDs is known to decrease slowly with time following each decontamination (Ritchie&MacKenty1993);this eﬀect was taken into account.As a consistency check,the photometric calibration was compared with ground-based data.The average F555W and F336W magnitudes of the RR Lyrae stars are F555W RR= 15.2and F336W RR=15.55,while Buonanno et al(1981)ﬁnd V RR=15.13and Richer& Fahlman(1987)obtained U HB=15.6.The agreement is excellent.3.Stellar PopulationsThe color-magnitude diagram for the2153stars located in the area common to the F336W(U),F555W(V)and F785LP(I)frames is shown in Figure2.In this plot,variable stars(see next section)are identiﬁed with special symbols;seven of29variables found in the F336W frames are located outside the F555W and F785LPﬁeld of view,and are therefore not included in Figure2.Photometry is fairly complete down to∼0.5magnitude below the turnoﬀ.The large wavelength diﬀerence between the U and Iﬁlters compensates for the relatively poor photometric accuracy,and allows us to clearly deﬁne the stellar populations. Two characteristics of the CMD are worth noting:the signiﬁcant blue straggler population and the morphology of the horizontal branch.3.1.Blue StragglersThe boundaries of the BS region of the CMD have often been arbitrarily deﬁned,vary from author to author,and also depend on theﬁlters used.As emphasized by Guhathakurta et al.(1994),the(V,U-I)CMD is well suited to deﬁne the blue straggler population.As a working deﬁnition,we decided to include in the BS region of the(V,U-I)CMD all stars signiﬁcantly brighter(0.4mag)than the turnoﬀand bluer than the average main sequence at the turnoﬀlevel;twenty-four stars are included in this region of the CMD(surrounded by dotted lines in Figure2)and can be considered as blue stragglers.Such a signiﬁcant blue straggler population in the core of M5is in striking contrast to the outer regions of the cluster, where none have been found(Buonanno et al.1981,for2′≤r obs≤5.6′;Richer&Fahlman 1987,for3′≤r obs≤25′).Recent CCD observations of the central regions of M5(Brocato et al.(1995);Sandquist et al.(1996))also reveal some blue stragglers.The two-dimensional distribution of red giants,horizontal branch stars and blue stragglers is shown in Figures 3a-c.It is obvious from these plots that the BS population is preferentially concentrated in the very core of the cluster.This is quantiﬁed in Figure4a,which shows the cumulativedistribution of the diﬀerent stellar populations within the inner50′′,and in Figure4b,within one core radius(24′′).A simple K-S test showed that there is a99.5%probability that the blue stragglers in the core of M5are more centrally concentrated than the horizontal branch stars,and a97.5%probability that they are more centrally concentrated than the red giants.This tendency for blue stragglers to be more centrally concentrated than other cluster members has been noted for most globular clusters observed to date(see Sarajedini(1993), Yanny et al.1994and references therein),and is consistent with the hypothesis that BS are more massive than main sequence stars.The luminosity-inferred lifetime of the shortest-lived,most luminous blue straggler in the core of M5is∼5×108yrs,assuming it lies on the hydrogen-burning main sequence. This corresponds to the star with V=16.0,L∼25L⊙and M∼2.15M⊙.The relaxation time in the core of M5is T rc=2×108yrs(Djorgovski1993).Hence,all BS in the core of M5are expected to be dynamically relaxed.Thus,the radial distribution of the BS is, indeed,a direct probe of their masses.In order to compare the blue straggler population from cluster to cluster,Bolte,Hesser &Stetson(1993)have deﬁned the speciﬁc frequency,F BS,as the ratio of the number of blue stragglers to the total number of stars brighter than2magnitudes below the horizontal branch at the instability strip.In the case of the central region of M5(area in common to the U,V and I HST/PC frames),where V HB=15.2,24F BS=other clusters.He suggests that gaps may provide important constraints on mixing in earlier stages of stellar evolution.We see no evidence that the gap width changes between the inner and outer parts of the core.4.Variable StarsFigure5shows the standard deviation as a function of the average U magnitude for all the stars in the F336W frames.The usual problem with outliers in Figure5(due to mismatches in star lists)was almost completely avoided because(a)the same master list for all frames(see section2.1),and(b)all images were perfectly aligned with each other.Visual inspection of the few remaining outliers immediately showed them to be mismatches and they were eliminated from our photometry.Stars with RMS magnitude of variability higher than2sigma above the mean curve were considered possible variables and were examined more closely.Most of them were faint stars located close to bright,large-amplitude variables. Twenty-eight stars stand out as bright,large-amplitude variables in Figure5,as well as one fainter,low-amplitude variable star.Seven of these variable stars had never been identiﬁed previously,and two(HST-V20and V21)were considered as a single star.All but one of the large-amplitude variables have light curves typical of RR Lyrae stars,whereas the low-amplitude variable is a blue rmation on the variables,including cross-identiﬁcation with previous papers,is presented in Table1.We note that the cataclysmic variable V101is36′′North and282′′West of the center of M5and is therefore too distant to have been included in theﬁeld of view of the Planetary Camera(70′′×70′′).4.1.A Variable Blue StragglerOf24blue stragglers identiﬁed in Figure2,only one(HST-V28)shows evidence for variability above the noise level.Although only HST-V28showed up above the2-sigma variability level in Figure5,we have examined the light curve of every blue straggler and compared them with those of nearby stars of similar magnitude in order toﬁnd possible variations undetected by our technique;no new variable showed up.But because the noise level is still relatively high between V=17and V=18(the2σvariability level varies from0.06 to0.12,corresponding to amplitudes∼0.2-0.3mag),we cannot exclude the possibility that some blue stragglers are actually small amplitude variables.The color-magnitude diagram(Figure2)shows that HST-V28is the bluest,and one of the brightest blue stragglers in M5(with M V=+2.2).Figure6shows its light curve,along with light curves of3nearby comparison stars of the same magnitude.HST-V28is obviously variable,with an amplitude∆U≥0.15mag.Unfortunately,our data do not allow us to determine the period with any precision(or even to determine if the variations are periodic).Phase dispersion minimization algorithms favor a periodicity of the order of ∼15hours(in which case this star could be an eclipsing binary),but cannot completely exclude periods shorter than∼1.9hours(typical for pulsating blue stragglers in clusters; Mateo1993).Better photometric accuracy and temporal sampling are obviously necessary to determine the period and nature of HST-V28.Guhathakurta et al.(1994)recently discovered2variables among the28blue stragglers in the core of M3.Both have photometric amplitudes∼0.4mag and periods∼6-12hours. Guhathakurta et al.suggest that both stars are dwarf cepheids.4.2.RR Lyrae StarsAmong the97genuine variables listed in Sawyer-Hogg’s(1973)catalogue,93are RR Lyrae.Recently,Kalda et al.(1987)and Kravtsov(1988,1992)searched for new variables in the central,crowded region of the cluster and found30more.So far,the light curves of only two of these new variables have been published(Kravtsov1992).A recent review of the M5RR Lyrae population has been published by Reid(1996).The U-band light curves of all RR Lyrae stars found in the HST images are shown in Figure7.Tentative periods have been determined for the9type RRc stars with a phase dispersion minimization algorithm,and the results are presented in Table1.The periods of RRab stars are too long to be determined from our observations alone.4.3.HST-V1Eclipsing binary stars are common in the periphery of M5’s core(Reid1996,Yan&Reid 1996),but star HST-V1is unique among the variables found in the core of M5.Although our observations do not cover an entire cycle(P∼0.55d−0.65d),the light curve suggests that HST-V1is a contact(or semi-detached)binary.The secondary minimum is very asymmetric, somewhat reminiscent of the near-contact binary V361Lyrae(Kaluzny1990).The strong asymmetry of the light curve of V361Lyr,more pronounced at shorter wavelengths,is thought to be caused by the presence of a hot spot on the secondary star resulting from the high mass transfer rate from the primary star.Unfortunately,HST-V1lies outside the boundaries of the F555W and F785LP frames, so its color cannot be determined.But with an average magnitude of U=15.7,HST-V1is more than two magnitudes brighter than the turnoﬀ;if it is a cluster member,at least one of its components must be a giant.5.SummaryThe main results of our paper can be summarized as follows:(1)The core of M5contains a highly centrally concentrated population of blue stragglers, similar in size to that found in47Tuc(Paresce et al.1991).(2)Of24blue stragglers detected in the HST images,only one shows signiﬁcant vari-ability above the noise level.Since our data are not sensitive enough to detect variables of amplitude≤0.2mag in the V=17-18range,we cannot exclude the possibility that some blue stragglers may be variable below that level.A more sensitive search with the refurbished HST is highly desirable.(3)We conﬁrm the existence of a0.2mag gap in the color-magnitude distribution of the horizontal branch,ﬁrst noted by Brocato et al..The nature of this gap is still unknown.(4)We have presentedﬁnding charts and light curves for27RR Lyrae variables and one probable contact binary.Among those variables,seven were previously unknown and21 had no published light curve.Support for this work was provided by NASA through grant number GO-3872from the Space Telescope Science Institute,which is operated by the Association of Universities for Research in Astronomy,Inc.,under NASA contract NAS5-26555.REFERENCESBolte,M.,Hesser,J.E.,&Stetson,P.B.1993,ApJ,408,L89Brocato,E.,Castellani,V.,&Ripepi,V.1995,AJ,109,1670Buonanno,R.,Corsi,C.E.,&Fusi Pecci,F.1981,MNRAS,196,435Djorgovski,S.G.1993,in Structure and Dynamics of Globular Clusters,ASP Conf.Ser., Vol.50,S.G.Djorgovski and G.Meylan,eds.,p.373Guhathakurta,P.,Yanny,B.,Schneider,D.P.,&Bahcall,J.N.1992,AJ,104,1790Guhathakurta,P.,Yanny,B.,Bahcall,J.N.,&Schneider,D.P.1994,AJ,108,1786 Harris,H.C.,Baum,W.A.,Hunter,D.A.,&Kreidl,T.J.1991,AJ,101,677Hesser,J.E.1988,IAU Symposium No.126,eds.J.E.Grindlay and A.G.Davis Philip,p. 65Hunter,D.A.,Faber,S.M.,Light,R.,&Shaya,E.1992,in Wide Field/Planetary camera Final Orbital/Science veriﬁcation Report,ed.S.Faber(STScI,Baltimore),chap.12 Kaluzny,J.,1990,AJ,99,1207Kaluzny,J.,&Shara,M.M.1987,ApJ,314,585Kravtsov,V.V.,1988,Astron.Tsirk.,1526,6Kravtsov,V.V.,1992a,Sov.Astron.Lett.18(4),246Kravtsov,V.V.,1992b,Sov.Astron.Lett.17(6),455Kadla,Z.I.,Gerashchenko,A.N.,Jablokova,N.V.,&Irkaev,B.N.,Astron.Tsirk.,1502, 7Mateo,M.1993,in Blue Stragglers,ed.R.A.Saﬀer(ASP Conf.Ser.53),p.74 Paresce,F.,Meylan,G.,Shara,M.M.,Baxter,D.,&Greenﬁeld,P.1991,Nature,352,297 Reid,N.1996,MNRAS,278,367Richer,H.B.,&Fahlman,G.G.1987,ApJ,316,189Sarajedini,A.1993,in Blue Stragglers,ASP Conf.Ser.,vol.53,ed.R.E.Saﬀer,p.14 Sawyer-Hogg,H.,1973,D.D.O.Pub.,Vol3.,No.6Yan,L.&Reid,I.N.1996,MNRAS,279,751Yanny,B.,Guhathakurta,P.,Schneider,D.P.,&Bahcall,J.N1994,ApJ,435,L59Fig.1.—Full HST/PCﬁeld of view(70′′×70′′)of the central region of M5.This image is the average of twenty-two F336W(U-band)exposures.Variable stars and the cluster center are identiﬁed.-2-1012342019181716151413U-I Fig.2.—Color-magnitude diagram for the stars common to the U (F336W),V(F555W)and I(F785LP)frames.RR Lyrae stars,and the variable blue straggler are shown with special symbols.050010001500050010001500Fig. 3.—Distribution of the red giants,horizontal branch stars and blue stragglers in the V frame coordinate system.The location of the U images is shown.The cluster center is identiﬁed by a cross.The circle has a radius of 20′′(∼one core radius).050010001500050010001500Fig.3.—continued050010001500050010001500Fig.3.—continuedFig.4a.—(a)Cumulative distribution of the stellar populations (BS:Blue Stragglers;HB:Horizontal Branch stars;RG:Red Giants)in the inner 50′′region of M5;(b)same as (a),but within one core radiusFig.5.—The RMS magnitude of variability as a function of the F336W magnitudes for the stars in the21frame set.The line is the2σcutoﬀ,above which the stars were considered as candidate variables and examined more closely.Genuine variables are shown with specialsymbols.Fig.6.—Light curve of HST-V28,the variable blue straggler and of three nearby(∆d≤5′′)comparison stars of similar mean magnitudeFig.7.—Light curves(ﬁlter F336W∼U-band)of the large amplitude variable stars found in the core of M5.All but one(HST-V1)are RR Lyrae stars.Fig.7.—ContinuedFig.7.—ContinuedFig.7.—Continued。

全天星图

Observers challengeJ.Cornmell - Version 1.7 - 21st September 2005 - Name Size Dec RA Mag Type Cons ID’s Month Best SeenName Size Dec RA Mag Type Cons ID’s Month Best Seen 2+16d 08m 00h 03m 10.5Gx Peg C43/NGC7814Oct 1+72d 31m 00h 13m 11Pl Cep C2/NGC40Oct 5+48d 30m 00h 33m 9.3Gx Cas C17/NGC147Oct 5+48d 19m 00h 39m 9.2Gx Cas C18/NGC185Oct Satellite galaxy of Andromeda 8+41d 40m 00h 40m 8Gx And M110/NGC205Oct Andromeda Galaxy 63+41d 16m 00h 42m 3.5Gx And M31/NGC224Oct Satellite galaxy of Andromeda 4+40d 52m 00h 42m 8.2Gx And M32/NGC221Oct 14+85d 19m 00h 43m 8.1OC Cep C1/NGC188Oct 4-11d 52m 00h 46m 8Pl Cet C56/NGC246Oct 7-20d 46m 00h 47m 8.9Gx Cet C62/NGC247Oct Sculptor Galaxy 9-25d 16m 00h 47m 7.1Gx Scl C65/NGC253Oct 8+02d 07m 01h 04m 9.3Gx Cet C51/IC1613Oct 4+35d 43m 01h 09m 10.1Gx And NGC404Oct 13+58d 19m 01h 19m 6.4OC Cas C13/NGC457Oct 4+63d 17m 01h 29m 9.5OC Cas C8/NGC559Oct 6+60d 42m 01h 33m 7.4OC Cas M103/NGC581Oct Triangulum Galaxy/Pinwheel galaxy 28+30d 38m 01h 33m 5.7Gx Tri M33/NGC598Oct 5+15d 46m 01h 36m 9.2Gx Psc M74/NGC628Oct Little Dumbell/Cork/Barbell/Butterfly 5+51d 34m 01h 42m 12Pl Per M76/NGC650Oct 16+61d 15m 01h 46m 7.1OC Cas C10/NGC663Oct 50+37d 40m 01h 57m 5.7OC And C28/NGC752Oct Double Cluster, H Persei 30+57d 08m 02h 19m 4OC Per C14/NGC869Nov 4+42d 21m 02h 22m 10Gx And C23/NGC891Nov 35+42d 46m 02h 42m 5.2OC Per M34/NGC1039Nov 3-00d 01m 02h 42m 8.8Gx Cet M77/NGC1068Nov 1+41d 31m 03h 19m 11.6Gx Per C24/NGC1275Nov 9+31d 25m 03h 29m -Nb Per NGC1333Nov 7-25d 51m 03h 33m -Pl For NGC1360Nov 18+68d 05m 03h 46m 9Gx Cam C5/IC342Nov Pleiades 110+24d 07m 03h 46m 1.6OC Tau M45Nov 8+62d 19m 04h 07m 5.7OC Cam NGC1502Dec 24+51d 13m 04h 15m 6.4OC Per NGC1528Dec Hyades 330+16d 00m 04h 27m 0.5OC Tau C41Dec 45+19d 04m 04h 46m 6.4OC Tau NGC1647Dec Flaming Star Nebula 30+34d 16m 05h 16m -Nb Aur C31/IC405Dec 9-24d 33m 05h 24m 8Gb Lep M79/NGC1904Dec 7+35d 19m 05h 28m 8.2OC Aur NGC1907Dec 21+35d 49m 05h 28m 6.4OC Aur M38/NGC1912Dec Crab Nebula 6+22d 01m 05h 34m 8.4SNR Tau M1/NGC1952Dec 14-05d 54m 05h 35m -Nb Ori NGC1980Dec Great Nebula In Orion 66-05d 27m 05h 35m 4Nb Ori M42/NGC1976Dec 20-04d 52m 05h 35m -Nb Ori NGC1977Dec de Mairan’s Nebula 20-05d 16m 05h 35m 9Nb Ori M43/NGC1982Dec 12+34d 07m 05h 36m 6OC Aur M36/NGC1960Dec Tank track nebula 30-01d 51m 05h 41m -Nb Ori NGC2024Dec 8+00d 03m 05h 46m 8Nb Ori M78/NGC2068Dec 24+32d 32m 05h 52m 5.6OC Aur M37/NGC2099Dec 5+24d 06m 06h 07m 8.6OC Gem NGC2158Jan 28+24d 19m 06h 08m 5.1OC Gem M35/NGC2168Jan Rosette Nebula -+05d 02m 06h 30m -Nb Mon C49/NGC2237Jan 24+04d 52m 06h 32m 4.8OC Mon C50/NGC2244Jan Hubble’s Variable Nebula 2+08d 43m 06h 39m -Nb Mon C46/NGC2261Jan 38-20d 43m 06h 46m 4.5OC CMa M41/NGC2287Jan 16-08d 19m 07h 03m 5.9OC Mon M50/NGC2323Jan 13-15d 37m 07h 17m 7.2OC CMa C58/NGC2360Jan 8-24d 56m 07h 18m 4.1CN CMa C64/NGC2362Jan The Peanut Nebula 1+29d 28m 07h 25m 13Pl Gem NGC2371Jan Eskimo Nebula/Clown Face Nebula 1+20d 55m 07h 29m 10Pl Gem C39/NGC2392Jan 30-14d 30m 07h 36m 4.4OC Pup M47/NGC2422Jan 9+65d 35m 07h 36m 8.4Gx Cam C7/NGC2403Jan 4+38d 52m 07h 38m 10.4Gb Lyn C25/NGC2419Jan 27-14d 49m 07h 41m 6.1OC Pup M46/NGC2437Jan 22-23d 52m 07h 44m 6.2OC Pup M93/NGC2447Jan 7-10d 46m 08h 00m 7.6OC Mon C54/NGC2506Feb 54-05d 47m 08h 13m 5.8OC Hya M48/NGC2548Feb Beehive Cluster/Praesepe 95+19d 58m 08h 40m 3.1OC Cnc M44/NGC2632Feb 30+11d 49m 08h 50m 6.9OC Cnc M67/NGC2682Feb 2+07d 01m 09h 10m 10.3Gx Cnc C48/NGC2775Feb 2+67d 55m 09h 47m 10.2Gx UMa NGC2976Feb Bode’s Galaxy or Bode’s Nebula 10+69d 04m 09h 55m 6.9Gx UMa M81/NGC3031Feb The Cigar Galaxy 4+69d 40m 09h 55m 8.4Gx UMa M82/NGC3034Feb 2+68d 43m 10h 03m 9.9Gx UMa NGC3077Mar Spindle Galaxy 2-07d 43m 10h 05m 9.2Gx Sex C53/NGC3115Mar Ghost Of Jupiter/CBS eye 21-18d 37m 10h 24m 9Pl Hya C59/NGC3242Mar 3+11d 41m 10h 43m 9.7Gx Leo M95/NGC3351Mar 3+11d 49m 10h 46m 9.2Gx Leo M96/NGC3368Mar 5+12d 34m 10h 47m 9.3Gx Leo M105/NGC3379Mar 3+55d 40m 11h 11m 10.1Gx UMa M108/NGC3556Mar Owl Nebula 3+55d 01m 11h 14m 11.2Pl UMa M97/NGC3587Mar 3+13d 04m 11h 18m 9.3Gx Leo M65/NGC3623Mar 1+18d 21m 11h 20m 10.9Gx Leo C40/NGC3626Mar 3+12d 58m 11h 20m 9Gx Leo M66/NGC3627Mar 4+13d 35m 11h 20m 9.5Gx Leo NGC3628Mar 3+53d 22m 11h 57m 9.8Gx UMa M109/NGC3992Mar Antennae or Ring-Tail galaxy 2-18d 52m 12h 01m 10.7Gx Crv C60/NGC4038Apr Antennae or Ring-Tail galaxy 1-18d 52m 12h 01m 13Gx Crv C61/NGC4039Apr 3+14d 54m 12h 13m 10.1Gx Com M98/NGC4192Apr 7+69d 28m 12h 16m 9.7Gx Dra C3/NGC4236Apr 5+37d 49m 12h 17m 10.2Gx CVn C26/NGC4244Apr Pin-Wheel Nebula 5+14d 25m 12h 18m 9.8Gx Com M99/NGC4254Apr 6+47d 17m 12h 19m 8.3Gx CVn M106/NGC4258Apr 6+04d 28m 12h 21m 9.7Gx Vir M61/NGC4303Apr Winnecke 41+58d 04m 12h 22m 9.1D*UMa M40Apr 3+15d 49m 12h 22m 9.4Gx Com M100/NGC4321Apr 3+12d 52m 12h 25m 9.3Gx Vir M84/NGC4374Apr 7+18d 10m 12h 25m 9.2Gx Com M85/NGC4382Apr 4+12d 56m 12h 26m 9.2Gx Vir M86/NGC4406Apr 3+44d 06m 12h 28m 9.4Gx CVn C21/NGC4449Apr 3C273 Brightest Quasar -+02d 06m 12h 29m 12QSO Vir 3C273Apr 5+08d 00m 12h 29m 8.4Gx Vir M49/NGC4472Apr 2+41d 37m 12h 30m 9.8Gx CVn NGC4490Apr Virgo A 7+12d 24m 12h 30m 8.6Gx Vir M87/NGC4486Apr 3+14d 25m 12h 31m 9.5Gx Com M88/NGC4501Apr 2+14d 30m 12h 35m 10.2Gx Com M91/NGC4548Apr 4+12d 33m 12h 35m 9.8Gx Vir M89/NGC4552Apr 4+27d 58m 12h 35m 9.9Gx Com C36/NGC4559Apr Needle Galaxy5+25d 58m 12h 36m 9.6Gx Com C38/NGC4565Apr 4+13d 10m 12h 36m 9.5Gx Vir M90/NGC4569Apr 3+11d 49m 12h 37m 9.8Gx Vir M58/NGC4579Apr 12-26d 45m 12h 39m 8.2Gb Hya M68/NGC4590Apr 2+61d 37m 12h 40m 11Gx UMa NGC4605Apr Sombrero Galaxy3-11d 37m 12h 40m 8.3Gx Vir M104/NGC4594Apr 2+11d 39m 12h 41m 9.8Gx Vir M59/NGC4621Apr 5+32d 31m 12h 42m 9.3Gx CVn C32/NGC4631Apr 3+11d 33m 12h 43m 8.8Gx Vir M60/NGC4649Apr 5+32d 10m 12h 43m 10.4Gx CVn NGC4656Apr 3-05d 47m 12h 48m 9.3Gx Vir C52/NGC4697Apr 5+41d 07m 12h 50m 8.2Gx CVn M94/NGC4736Apr Black-Eye Galaxy4+21d 40m 12h 56m 8.5Gx Com M64/NGC4826Apr 1+27d 58m 13h 00m 11.4Gx Com C35/NGC4889Apr 2+37d 02m 13h 10m 9.8Gx CVn C29/NGC5005Apr 13+18d 10m 13h 12m 7.7Gb Com M53/NGC5024Apr Sunflower Galaxy 5+42d 01m 13h 15m 8.6Gx CVn M63/NGC5055Apr Whirlpool Galaxy5+47d 12m 13h 29m 8.4Gx CVn M51/NGC5194Apr 11-29d 52m 13h 37m 7.6Gx Hya M83/NGC5236Apr 3+08d 52m 13h 37m 10.2Gx Boo C45/NGC5248Apr 16+28d 22m 13h 42m 6.4Gb CVn M3/NGC5272Apr The Pinwheel Galaxy 27+54d 21m 14h 03m 7.7Gx UMa M101/NGC5457May 4-26d 31m 14h 39m 10.2Gb Hya C66/NGC5694May Possibly M1021+55d 46m 15h 06m 10Gx Dra M102/NGC5866May 13-21d 01m 15h 17m 8.6Gb Lib NGC5897May 17+02d 04m 15h 18m 5.8Gb Ser M5/NGC5904May 9-22d 58m 16h 16m 7.2Gb Sco M80/NGC6093Jun 26-26d 31m 16h 23m 5.9Gb Sco M4/NGC6121Jun 10-13d 03m 16h 32m 8.1Gb Oph M107/NGC6171Jun Great Cluster In Hercules17+36d 28m 16h 41m 5.9Gb Her M13/NGC6205Jun 1+36d 49m 16h 43m 11.6Gx Her NGC6207Jun 15-01d 57m 16h 47m 6.6Gb Oph M12/NGC6218Jun 15-04d 05m 16h 57m 6.6Gb Oph M10/NGC6254Jun 14-30d 07m 17h 01m 6.6Gb Oph M62/NGC6266Jun 14-26d 16m 17h 02m 7.2Gb Oph M19/NGC6273Jun 11+43d 07m 17h 17m 6.5Gb Her M92/NGC6341Jun 9-18d 31m 17h 19m 7.9Gb Oph M9/NGC6333Jun 12-03d 15m 17h 37m 7.6Gb Oph M14/NGC6402Jun Butterfly Cluster 15-32d 13m 17h 40m 4.2OC Sco M6/NGC6405Jun Ptolemy’s Cluster80-34d 49m 17h 53m 3.3OC Sco M7/NGC6475Jun 27-19d 01m 17h 56m 5.5OC Sgr M23/NGC6494Jun Cat’s Eye Nebula 6+66d 37m 17h 58m 9Pl Dra C6/NGC6543Jun Trifid Nebula29-23d 01m 18h 02m 6.3CN Sgr M20/NGC6514Jul Lagoon Nebula/Hourglass Nebula 90-24d 22m 18h 03m 5.8Nb Sgr M8/NGC6523Jul 13-22d 30m 18h 04m 5.9OC Sgr M21/NGC6531Jul Milky Way Patch 5-18d 25m 18h 18m 11OC Sgr M24/NGC6603Jul Eagle Nebula35-13d 46m 18h 18m 6CN Ser M16/NGC6611Jul 9-17d 07m 18h 19m 6.9OC Sgr M18/NGC6613Jul The Omega, Swan, or Horseshoe Nebula46-16d 10m18h 20m 6CN Sgr M17/NGC6618Jul 11-24d 52m 18h 24m 6.9Gb Sgr M28/NGC6626Jul 7-32d 21m 18h 31m 7.7Gb Sgr M69/NGC6637Jul 32-19d 15m 18h 31m 4.6OC Sgr M25/IC4725Jul 24-23d 53m 18h 36m 5.1Gb Sgr M22/NGC6656Jul 8-32d 17m 18h 43m 8.1Gb Sgr M70/NGC6681Jul 15-09d 24m 18h 45m 8OC Sct M26/NGC6694Jul Wild Duck Cluster 14-06d 16m 18h 51m 5.8OC Sct M11/NGC6705Jul Ring Nebula3+33d 01m 18h 53m 9Pl Lyr M57/NGC6720Jul 9-30d 28m 18h 55m 7.7Gb Sgr M54/NGC6715Jul 7+30d 10m 19h 16m 8.3Gb Lyr M56/NGC6779Jul The Coathanger or Brocchi’s Cluster 60+20d 10m 19h 25m 4OC Vul Cr399Jul 19-30d 58m 19h 40m 7Gb Sgr M55/NGC6809Jul Blinking Planetary 2+50d 31m 19h 44m 10Pl Cyg C15/NGC6826Jul Barnard’s Galaxy 10-14d 48m 19h 44m 9Gx Sgr C57/NGC6822Jul 7+18d 46m 19h 53m 8.3Gb Sge M71/NGC6838Jul Dumbbell Nebula15+22d 43m 20h 00m 8.1Pl Vul M27/NGC6853Jul 20+35d 46m 20h 05m 5.2OC Cyg NGC6871Aug 6-21d 55m 20h 06m 8.6Gb Sgr M75/NGC6864Aug 7+26d 28m 20h 11m 6OC Vul C37/NGC6885Aug Crescent Nebula20+38d 21m 20h 11m -Nb Cyg C27/NGC6888Aug 7+38d 31m 20h 23m 6.6OC Cyg M29/NGC6913Aug 6+07d 24m 20h 34m 8.9Gb Del C47/NGC6934Aug 11+60d 08m 20h 34m 8.9Gx Cep C12/NGC6946Aug Veil/Lace Work/Filamentary Neb 70+30d 43m 20h 45m -SNR Cyg C34/NGC6960Aug 6-12d 31m 20h 53m 9.4Gb Aqr M72/NGC6981Aug Veil/Lace Work/Filamentary Neb 60+31d 43m 20h 56m -SNR Cyg C33/NGC6992Aug North America Nebula120+44d 19m 20h 58m -Nb Cyg C20/NGC7000Aug 3-12d 37m 20h 58m 9OC Aqr M73/NGC6994Aug 18+68d 10m 21h 00m 7CN Cep C4/NGC7023Aug 3+16d 10m 21h 01m 10.6Gb Del C42/NGC7006Aug Saturn Nebula2-11d 22m 21h 04m 8Pl Aqr C55/NGC7009Aug 12+12d 10m 21h 30m 6.4Gb Peg M15/NGC7078Aug 32+48d 25m 21h 32m 4.6OC Cyg M39/NGC7092Aug 13-00d 49m 21h 33m 6.5Gb Aqr M2/NGC7089Aug 11-23d 10m 21h 40m 7.5Gb Cap M30/NGC7099Aug Cocoon Nebula 12+47d 16m 21h 53m 7.2CN Cyg C19/IC5146Aug 21+49d 52m 22h 15m 6.4OC Lac C16/NGC7243Sep Helix Nebula13-20d 48m 22h 29m -Pl Aqr C63/NGC7293Sep 4+34d 25m 22h 37m 9.5Gx Peg C30/NGC7331Sep 30+62d 36m 22h 56m -Nb Cep C9Sep 2+12d 19m 23h 04m 11Gx Peg C44/NGC7479Sep Bubble nebula 15+61d 12m 23h 20m -Nb Cas C11/NGC7635Sep 13+61d 34m 23h 24m 6.9OC Cas M52/NGC7654Sep Blue Snowball2+42d 32m 23h 25m 9Pl And C22/NGC7662Sep 16+56d 43m 23h 56m 6.7OC Cas NGC7789Sep。

Entropy changes in the clustering of galaxies in a

Vol.3, No.1, 65-68 (2011)doi:10.4236/ns.2011.31009Natural ScienceEntropy changes in the clustering of galaxies in an expanding universeNaseer Iqbal1,2*, Mohammad Shafi Khan1, Tabasum Masood11Department of Physics, University of Kashmir, Srinagar, India; *Corresponding Author:2Interuniversity Centre for Astronomy and Astrophysics, Pune, India.Received 19 October 2010; revised 23 November 2010; accepted 26 November 2010.ABSTRACTIn the present work the approach-thermody- namics and statistical mechanics of gravitating systems is applied to study the entropy change in gravitational clustering of galaxies in an ex-panding universe. We derive analytically the expressions for gravitational entropy in terms of temperature T and average density n of the par-ticles (galaxies) in the given phase space cell. It is found that during the initial stage of cluster-ing of galaxies, the entropy decreases and fi-nally seems to be increasing when the system attains virial equilibrium. The entropy changes are studied for different range of measuring correlation parameter b. We attempt to provide a clearer account of this phenomena. The entropy results for a system consisting of extended mass (non-point mass) particles show a similar behaviour with that of point mass particles clustering gravitationally in an expanding uni-verse.Keywords:Gravitational Clustering; Thermodynamics; Entropy; Cosmology1. INTRODUCTIONGalaxy groups and clusters are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation [1]. They form the densest part of the large scale structure of the uni-verse. In models for the gravitational formation of struc-ture with cold dark matter, the smallest structures col-lapse first and eventually build the largest structures; clusters of galaxies are then formed relatively. The clus-ters themselves are often associated with larger groups called super-clusters. Clusters of galaxies are the most recent and most massive objects to have arisen in the hiearchical structure formation of the universe and the study of clusters tells one about the way galaxies form and evolve. The average density n and the temperature T of a gravitating system discuss some thermal history of cluster formation. For a better larger understanding of this thermal history it is important to study the entropy change resulting during the clustering phenomena be-cause the entropy is the quantity most directly changed by increasing or decreasing thermal energy of intraclus-ter gas. The purpose of the present paper is to show how entropy of the universe changes with time in a system of galaxies clustering under the influence of gravitational interaction.Entropy is a measure of how disorganised a system is. It forms an important part of second law of thermody-namics [2,3]. The concept of entropy is generally not well understood. For erupting stars, colloiding galaxies, collapsing black holes - the cosmos is a surprisingly or-derly place. Supermassive black holes, dark matter and stars are some of the contributors to the overall entropy of the universe. The microscopic explanation of entropy has been challenged both from the experimental and theoretical point of view [11,12]. Entropy is a mathe-matical formula. Standard calculations have shown that the entropy of our universe is dominated by black holes, whose entropy is of the order of their area in planck units [13]. An analysis by Chas Egan of the Australian National University in Canberra indicates that the col-lective entropy of all the supermassive black holes at the centers of galaxies is about 100 times higher than previ-ously calculated. Statistical entropy is logrithmic of the number of microstates consistent with the observed macroscopic properties of a system hence a measure of uncertainty about its precise state. Statistical mechanics explains entropy as the amount of uncertainty which remains about a system after its observable macroscopic properties have been taken into account. For a given set of macroscopic quantities like temperature and volume, the entropy is a function of the probability that the sys-tem is in various quantumn states. The more states avail-able to the system with higher probability, the greater theAll Rights Reserved.N. Iqbal et al. / Natural Science 3 (2011) 65-6866 disorder and thus greater the entropy [2]. In real experi-ments, it is quite difficult to measure the entropy of a system. The technique for doing so is based on the thermodynamic definition of entropy. We discuss the applicability of statistical mechanics and thermodynam-ics for gravitating systems and explain in what sense the entropy change S – S 0 shows a changing behaviour with respect to the measuring correlation parameter b = 0 – 1.2. THERMODYNAMIC DESCRIPTION OF GALAXY CLUSTERSA system of many point particles which interacts by Newtonian gravity is always unstable. The basic insta-bilities which may occur involve the overall contraction (or expansion) of the system, and the formation of clus-ters within the system. The rates and forms of these in-stabilities are governed by the distribution of kinetic and potential energy and the momentum among the particles. For example, a finite spherical system which approxi-mately satisfies the viral theorem, contracts slowlycompared to the crossing time ~ ()12G ρ- due to the evaporation of high energy particles [3] and the lack of equipartition among particles of different masses [4]. We consider here a thermodynamic description for the sys-tem (universe). The universe is considered to be an infi-nite gas in which each gas molecule is treated to be agalaxy. The gravitational force is a binary interaction and as a result a number of particles cluster together. We use the same approximation of binary interaction for our universe (system) consisting of large number of galaxies clustering together under the influence of gravitational force. It is important to mention here that the characteri-zation of this clustering is a problem of current interest. The physical validity of the application of thermody-namics in the clustering of galaxies and galaxy clusters has been discussed on the basis of N-body computer simulation results [5]. Equations of state for internal energy U and pressure P are of the form [6]:(3122NTU =-)b (1) (1NTP V=-)b (2) b defines the measuring correlation parameter and is dimensionless, given by [8]()202,23W nb Gm n T r K Tτξ∞=-=⎰,rdr (3)W is the potential energy and K the kinetic energy ofthe particles in a system. n N V = is the average num-ber density of the system of particles each of mass m, T is the temperature, V the volume, G is the universalgravitational constant. (),,n T r ξ is the two particle correlation function and r is the inter-particle distance. An overall study of (),n T r ξ has already been dis-cussed by [7]. For an ideal gas behaviour b = 0 and for non-ideal gas system b varies between 0 and 1. Previ-ously some workers [7,8] have derived b in the form of:331nT b nT ββ--=+ (4) Eq.4 indicates that b has a specific dependence on the combination 3nT -.3. ENTROPY CALCULATIONSThermodynamics and statistical mechanics have been found to be equal tools in describing entropy of a system. Thermodynamic entropy is a non-conserved state func-tion that is of great importance in science. Historically the concept of entropy evolved in order to explain why some processes are spontaneous and others are not; sys-tems tend to progress in the direction of increasing en-tropy [9]. Following statistical mechanics and the work carried out by [10], the grand canonical partition func-tion is given by()3213212,1!N N N N mkT Z T V V nT N πβ--⎛⎫⎡=+ ⎪⎣Λ⎝⎭⎤⎦(5)where N! is due to the distinguishability of particles. Λrepresents the volume of a phase space cell. N is the number of paricles (galaxies) with point mass approxi-mation. The Helmholtz free energy is given by:ln N A T Z =- (6)Thermodynamic description of entropy can be calcu-lated as:,N VA S T ∂⎛⎫=- ⎪∂⎝⎭ (7)The use of Eq.5 and Eq.6 in Eq.7 gives()3120ln ln 13S S n T b b -⎛⎫-=-- ⎪ ⎪⎝⎭- (8) where S 0 is an arbitary constant. From Eq.4 we write()31bn b T β-=- (9)Using Eq.9, Eq.8 becomes as3203ln S S b bT ⎡⎤-=-+⎢⎣⎦⎥ (10)Again from Eq.4All Rights Reserved.N. Iqbal et al. / Natural Science 3 (2011) 65-68 6767()13221n b T b β-⎡⎤=⎢⎣⎦⎥ (11)with the help of Eq.11, Eq.10 becomes as()011ln ln 1322S S n b b b ⎡-=-+-+⎡⎤⎣⎦⎢⎥⎣⎦⎤ (12) This is the expression for entropy of a system consist-ing of point mass particles, but actually galaxies have extended structures, therefore the point mass concept is only an approximation. For extended mass structures we make use of softening parameter ε whose value is taken between 0.01 and 0.05 (in the units of total radius). Following the same procedure, Eq.8 becomes as()320ln ln 13N S S N T N b Nb V εε⎡⎤-=---⎢⎥⎣⎦(13)For extended structures of galaxies, Eq.4 gets modi-fied to()()331nT R b nT R εβαεβαε--=+ (14)where α is a constant, R is the radius of a cell in a phase space in which number of particles (galaxies) is N and volume is V . The relation between b and b ε is given by: ()11b b b εαα=+- (15) b ε represents the correlation energy for extended mass particles clustering gravitationally in an expanding uni-verse. The above Eq.10 and Eq.12 take the form respec-tively as;()()3203ln 111bT b S S b b ααα⎡⎤⎢⎥-=-+⎢⎥+-+-⎢⎥⎣⎦1 (16) ()()()120113ln ln 2111b b b S S n b b ααα⎡⎤-⎡⎤⎢⎥⎣⎦-=-++⎢⎥+-+-⎢⎥⎣⎦1 (17)where2R R εεεα⎛⎫⎛⎫=⎪ ⎪⎝⎭⎝⎭(18)If ε = 0, α = 1 the entropy equations for extended mass galaxies are exactly same with that of a system of point mass galaxies approximation. Eq.10, Eq.12, Eq.16and Eq.17 are used here to study the entropy changes inthe cosmological many body problem. Various entropy change results S – S 0 for both the point mass approxima-tion and of extended mass approximation of particles (galaxies) are shown in (Figures 1and2). The resultshave been calculated analytically for different values ofFigure 1. (Color online) Comparison of isothermal entropy changes for non-point and point mass particles (galaxies) for an infinite gravitating system as a function of average relative temperature T and the parameter b . For non-point mass ε = 0.03 and R = 0.06 (left panel), ε = 0.04 and R = 0.04 (right panel).All Rights Reserved.N. Iqbal et al. / Natural Science 3 (2011) 65-68 68Figure 2. (Color online) Comparison of equi-density entropy changes for non-point and point mass particles (galaxies) for an infinite gravitating system as a function of average relative density n and the parameter b. For non-point mass ε= 0.03 and R = 0.04.R (cell size) corresponding to different values of soften-ing parameter ε. We study the variations of entropy changes S – S0with the changing parameter b for differ-ent values of n and T. Some graphical variations for S – S0with b for different values of n = 0, 1, 100 and aver-age temperature T = 1, 10 and 100 and by fixing value of cell size R = 0.04 and 0.06 are shown. The graphical analysis can be repeated for different values of R and by fixing values of εfor different sets like 0.04 and 0.05. From both the figures shown in 1 and 2, the dashed line represents variation for point mass particles and the solid line represents variation for extended (non-point mass) particles (galaxies) clustering together. It has been ob-served that the nature of the variation remains more or less same except with some minor difference.4. RESULTSThe formula for entropy calculated in this paper has provided a convenient way to study the entropy changes in gravitational galaxy clusters in an expanding universe. Gravity changes things that we have witnessed in this research. Clustering of galaxies in an expanding universe, which is like that of a self gravitating gas increases the gases volume which increases the entropy, but it also increases the potential energy and thus decreases the kinetic energy as particles must work against the attrac-tive gravitational field. So we expect expanding gases to cool down, and therefore there is a probability that the entropy has to decrease which gets confirmed from our theoretical calculations as shown in Figures 1 and 2. Entropy has remained an important contributor to our understanding in cosmology. Everything from gravita-tional clustering to supernova are contributors to entropy budget of the universe. A new calculation and study of entropy results given by Eqs.10, 12, 16 and 17 shows that the entropy of the universe decreases first with the clustering rate of the particles and then gradually in-creases as the system attains viral equilibrium. The gravitational entropy in this paper furthermore suggests that the universe is different than scientists had thought.5. ACKNOWLEDGEMENTSWe are thankful to Interuniversity centre for Astronomy and Astro-physics Pune India for providing a warm hospitality and facilities during the course of this work.REFERENCES[1]Voit, G.M. (2005) Tracing cosmic evolution with clus-ters of galaxies. Reviews of Modern Physics, 77, 207- 248.[2]Rief, F. (1965)Fundamentals of statistical and thermalphysics. McGraw-Hill, Tokyo.[3]Spitzer, L. and Saslaw, W.C. (1966) On the evolution ofgalactic nuclei. Astrophysical Journal, 143, 400-420.doi:10.1086/148523[4]Saslaw, W.C. and De Youngs, D.S. (1971) On the equi-partition in galactic nuclei and gravitating systems. As-trophysical Journal, 170, 423-429.doi:10.1086/151229[5]Itoh, M., Inagaki, S. and Saslaw, W.C. (1993) Gravita-tional clustering of galaxies. Astrophysical Journal, 403,476-496.doi:10.1086/172219[6]Hill, T.L. (1956) Statistical mechanics: Principles andstatistical applications. McGraw-Hill, New York.[7]Iqbal, N., Ahmad, F. and Khan, M.S. (2006) Gravita-tional clustering of galaxies in an expanding universe.Journal of Astronomy and Astrophysics, 27, 373-379.doi:10.1007/BF02709363[8]Saslaw, W.C. and Hamilton, A.J.S. (1984) Thermody-namics and galaxy clustering. Astrophysical Journal, 276, 13-25.doi:10.1086/161589[9]Mcquarrie, D.A. and Simon, J.D. (1997) Physical chem-istry: A molecular approach. University Science Books,Sausalito.[10]Ahmad, F, Saslaw, W.C. and Bhat, N.I. (2002) Statisticalmechanics of cosmological many body problem. Astro-physical Journal, 571, 576-584.doi:10.1086/340095[11]Freud, P.G. (1970) Physics: A Contemporary Perspective.Taylor and Francis Group.[12]Khinchin, A.I. (1949) Mathamatical Foundation of statis-tical mechanics. Dover Publications, New York.[13]Frampton, P., Stephen, D.H., Kephar, T.W. and Reeb, D.(2009) Classical Quantum Gravity. 26, 145005.doi:10.1088/0264-9381/26/14/145005All Rights Reserved.。

The death of massive stars - I. Observational constraints on the progenitors of type II-P s

a r X i v :0809.0403v 1 [a s t r o -p h ] 2 S e p 2008Mon.Not.R.Astron.Soc.000,1–36(2006)Printed 2September 2008(MN La T E X style ﬁle v2.2)The death of massive stars -I.Observational constraintson the progenitors of type II-P supernovaeS.J.Smartt 1,J.J.Eldridge 2,R.M.Crockett 1,J.R.Maund 3,41AstrophysicsResearch Centre,School of Mathematics and Physics,Queen’s University Belfast,Belfast BT71NN,U.K.2Instituteof Astronomy,The Observatories,University of Cambridge,Madingley Road,Cambridge,CB30HA,U.K.3Department of Astronomy and McDonald Observatory,University of Texas,1University Station,C1400,Austin,TX 78712,U.S.A.4Dark Cosmology Centre,Niels Bohr Institute,University of Copenhagen,Juliane Maries Vej 30,2100Copenhagen Ø,DenmarkReleased 2006Xxxxx XXABSTRACTWe present the results of a 10.5yr,volume limited (28Mpc)search for supernova (SN)progenitor stars.In doing so we compile all SNe discovered within this volume (132,of which 27%are type Ia)and determine the relative rates of each sub-type from literature studies.The core-collapse SNe break down into 59%II-P and 29%Ib/c,with the remainder being IIb (5%),IIn(4%)and II-L (3%).There have been 20II-P SNe with high quality optical or near-IR pre-explosion images that allow a meaningful search for the progenitor stars.In four cases they are clearly red supergiants,one case is unconstrained,two fall on compact coeval star clusters and the other 13have no progenitor detected.We review and update all the available data for the host galaxies and SN environments (distance,metallicity and extinction)and determine masses and upper mass estimates for these 20progenitor stars using the STARS stellar evolutionary code and a single consistent homogeneous method.A maximum likelihood calculation suggests that the minimum stellar mass for a type II-P to form is m min =8.5+1−1.5M ⊙and the maximum mass for II-P progenitors is m max =16.5±1.5M ⊙,assuming a Salpeter initial mass function holds for the progenitor population (in therange Γ=−1.35+0.3−0.7).The minimum mass is consistent with current estimates for white dwarf progenitor masses,but the maximum mass does not appear consistent with massive star populations in Local Group galaxies.Red supergiants in the Local Group have masses up to 25M ⊙and the minimum mass to produce a Wolf-Rayet star in single star evolution (between solar and LMC metallicity)is similarly 25-30M ⊙.The reason we have not detected any high mass red supergiant progenitors above 17M ⊙is unclear,but we estimate that it is statistically signiﬁcant at 2.4σconﬁdence.Two simple reasons for this could be that we have systematically underestimated the progenitor masses due to dust extinction or that stars between 17-25M ⊙produce other kinds of SNe which are not II-P.We discuss these possibilities and ﬁnd that neither provides a satisfactory solution.We term this discrepancy the “red supergiant problem”and speculate that these stars could have core masses high enough to form black holes and SNe which are too faint to have been detected.We compare the 56Ni masses ejected in the SNe to the progenitor mass estimates and ﬁnd that low luminosity SNe with low 56Ni production are most likely to arise from explosions of low mass progenitors near the mass threshold that can produce a core-collapse.Key words:stars:evolution -stars:supergiants -supernovae:general -supernovae:individual -galaxies :stellar content1INTRODUCTIONStars which are born with masses above a critical thresh-old mass of around 8M ⊙have long been thought to produce supernovae when their cores collapse at a point when nu-clear burning no longer provides support against gravity.Supernovae were ﬁrst suggested to be a new class of astro-physical phenomena by Baade &Zwicky (1934)and since then detailed study has allowed them to be split into phys-2S.J.Smartt et al.ical types:the thermonuclear explosions and core-collapse supernovae(CCSNe).The CCSNe form when their cores evolve to iron white dwarfs and detailed stellar evolution-ary models predict a minimum mass for this to occur of between7-12M⊙(Heger et al.2003;Eldridge&Tout2004b; Siess2007;Poelarends et al.2008).The CCSNe form a diverse group in terms of their spectral and photometric properties and the classiﬁcation scheme has arisen primar-ily based on the appearance of their optical spectra,but also supplemented with their photometric behaviour(Filippenko 1997).There are the H-rich type II SNe,which are sub-classiﬁed into II-P(plateau lightcurves),II-L(linear decline lightcurves),IIn(narrow emission lines),and some peculiar events,generically labelled II-pec.The H-deﬁcient SNe are split into Ib and Ic depending on whether He is visible and a hybrid class of IIb(type II events which metamorphose into Ib SNe)has also been uncovered.The evolutionary stage of the progenitor star(i.e.its position in the HR diagram and chemical composition of its atmosphere)very likely dictates what type of CCSN is produced.Determining what types of stars produce which types of SNe and what mass range can support a CCSN is a ma-jor goal in modern studies of these explosions.Theﬁrst at-tempts relied primarily on linking the results of stellar evo-lutionary models to the spectral(and photometric)evolu-tion of the SNe.(e.g.Arnett1980;Chevalier1976)More re-cently Hamuy(2003)and Nadyozhin(2003)have studied the lightcurves and ejecta velocities of II-P SNe to estimate the mass of the material ejected.These studies tend to favour quite large masses for progenitor stars,with Hamuy sug-gesting ranges of10-50M⊙and Nadyozhin10-30M⊙.How-ever when SN1987A exploded a new opportunity arose. The SN was in a galaxy close enough that its progenitor star could be easily identiﬁed.A blue supergiant star of around15-20M⊙was identiﬁed and it is clear that this ob-ject no longer exists(Gilmozzi et al.1987;Walborn et al. 1989;Podsiadlowski1992)The fact that it was a compact blue supergiant was a key factor in enabling the community to understand the event as a whole.A progenitor was also detected for the next closest explosion(SN1993J in M81) and the binary nature of the progenitor helped understand the physical reason behind the II-b type given to the event (Aldering et al.1994;Podsiaklowski et al.1993).Studies of the environments of CCSNe after discov-ery have been ongoing for many years with authors look-ing for correlations between the ages of starformation re-gions and the type of SNe that occur.For example van Dyk (1992)and van Dyk et al.(1996)suggested that there was no clear diﬀerence in the spatial distributions of type Ib/c and type II SNe compared to giant H ii regions in their host galaxies.They concluded that they hence arose from parent populations of similar mass.However recently both James&Anderson(2006)and Kelly et al.(2007)suggest that the stripped type Ic SNe are more likely to follow re-gions of either high surface brightness or high Hαemis-sion than type II SNe.A larger sample of nearby core-collapse events and Hαcorrelations has been compiled by Anderson&James(2008)indicating that there is a progres-sive trend for Ib/c SNe to be associated with Hαemission regions,in the sense that Ic show the closest association with galactic Hαemission,then comes the Ib and then type II. While these eﬀorts are very valuable to discern diﬀerences in progenitor channel,it is diﬃcult to assign deﬁnitive mass ranges to the progenitor systems from spatial correlations alone.A much more direct way to determine the type of star that exploded is to search directly for progenitors in im-ages of the host galaxies taken before explosion.The ease of access to large telescope data archives makes this search fea-sible for nearby events.There are now a number of groups around the world that are competitively searching for pro-genitor stars in such archive images.Particularly with the Hubble Space Telescope(HST)it has become possible to re-solve massive stellar populations out to at least20Mpc.In this case the information on each progenitor is much more detailed and quantitative than can be achieved with the unresolved environment studies,but there are fewer events which allow such a study.Early work with HST concentrated on looking at the en-vironments of SNe(Barth et al.1996;Van Dyk et al.1999). But it has now become possible to search directly for progen-itor stars and carry out concerted campaigns on the near-est events.Three of theﬁrst type II SNe to have excel-lent HST and ground-based pre-explosion were the II-P SNe 1999gi,1999em and2001du(Smartt et al.2001,2002,2003; Van Dyk et al.2003b).In all there was no detection of a pro-genitor,but meaningful limits were derived.Leonard et al. (2003)and Leonard et al.(2002)subsequently showed the importance of having reliable distances to the host galaxies of the SN progenitors in order to constrain the upper mass limits.Eﬀorts toﬁnd progenitors continued(Smartt et al. 2003;Van Dyk et al.2003a)until theﬁrst conﬁrmation of a red supergiant progenitor of a type II-P explosion in prediscovery HST and Gemini-North images(Smartt et al. 2004).Unambiguous detections in HST images require the SN to be located on the pre-explosion images with accura-cies of around10milliarcseconds,which requires follow-up images of the SN to be taken at HST or corrected adap-tive optics ground-based images(Maund&Smartt2005; Gal-Yam et al.2005;Crockett et al.2008).The next clear and unambiguous detection of a progenitor star was also a red supergiant in M51(SN2005cs;Maund et al.2005; Li et al.2006).And the recent discovery of SN2008bk in NGC7793(3.9Mpc)has produced detections in IJHK of a red progenitor star(Mattila et al.2008).The near-IR spec-tral energy(SED)distribution of the SN2008bk progenitor is the best sampled SED yet of any red supergiant progen-itor and matches a late M4I spectral type with moderate extinction of A V≃1and an initial mass around8-9M⊙. There have been claims of the detections of others such as 2004A(Hendry et al.2006),2004et(Li et al.2005),2006my and2006ov(Li et al.2007)and we review these in this pa-per.An additional method that has much to oﬀer thisﬁeld is locating SNe directly coincident with compact,coeval star clusters.If the age of the cluster can be determined then a main-sequence turn-oﬀage,and turn-oﬀmass can lead di-rectly to an estimate of the progenitor star mass(e.g.2004dj in NCG2403as studied by Ma´ız-Apell´a niz et al.2004).The detection and characterisation of progenitor stars has the potential to directly link the type of star to the SN explo-sion characteristics,(e.g.the amount of56Ni synthesised in explosive O and Si burning and the total energy of the ex-plosion)and also to set quantitative limits on progenitor mass ranges.The latter is of great interest to compare toThe death of massive stars3the highest mass white dwarf progenitors and to the stars that form neutron stars and black holes after core-collapse.Work in thisﬁeld has progressed substantially in the last8years and compilations of progenitor properties have been made by Smartt et al.(2003);Gal-Yam et al.(2007); Li et al.(2007);Kochanek et al.(2008).However these com-pilations are somewhat ad-hoc,incomplete and potentially biased as they do not deﬁne the selection criterion for inclu-sion rigorously.In addition the results are based on diﬀer-ent methods for estimating the progenitor masses and upper limits(in terms of measurement and the theoretical models employed).The goal of this series of two papers is to deﬁne the selection criteria for inclusion(a volume and time lim-ited survey)and to determine the physical parameters of the progenitor stars(luminosities and masses,or limits thereon) in a homogeneous and consistent way.Only then is it pos-sible to reliably estimate the population parameters.This paper speciﬁcally deals with the type II SNe and all but two of theﬁnal sample of twenty have been conﬁrmed as type II-P.A companion paper will discuss the stripped SNe of types IIb,Ib and Ic which are drawn from the same volume and time limited survey(Crockett et al.2008,in prep).In addition to the supernova with pre-explosion images we discuss in the paper there are three SNe with progen-itor detections that fall outside either our time or volume deﬁnition.Those are SN1987A,SN1993J and SN2005gl. Discussions of theﬁrst two are well documented in the literature(e.g.Walborn et al.1989;Aldering et al.1994; Van Dyk et al.2002;Maund et al.2004);1987A will be dis-cussed later in this paper and the implications of1993J will be discussed in the2nd paper in this series.SN2005gl is a type IIn in NGC266at approximately66Mpc,hence al-though a progenitor is detected by Gal-Yam et al.(2007)it does not fall within our distance limit.Gal-Yam et al.(2007) suggest that this was a very massive star with M V≃−10.3 and very likely a luminous blue variable(although with only a detection in a singleﬁlter,the blue colour is not con-ﬁrmed).This is evidence that very massive stars do explode as bright SNe and is a point we will return to in the discus-sion.This paper starts with deﬁning the sample from which the targets with high quality pre-explosion images are drawn.A consistent and homogeneous analysis method is then deﬁned and justiﬁed.We then review previous detec-tions(and add some new data)to build the data required for analysis and then statistically analyse the results.We follow this with an extensive discussion.2THE SAMPLE OF LOCAL UNIVERSE SUPERNOV AEThe observational data for this paper are compiled from many sources in the recent literature but the sample selec-tion requires some justiﬁcation and explanation if the later comparisons and discussions of physical parameters are to be meaningful.We have selected SNe for inclusion based on the following selection criteria,and we justify the choice of criteria where appropriate.2.1Deﬁnition and selectionWe consider all core collapse SNe discovered in the ten year period between1998January1and2008June30.The ear-lier date was chosen as the sensible start point for the con-certed eﬀorts toﬁnd SNe in archive pre-discovery images due to the fact that the local SN discovery rate had reached a sig-niﬁcant level(van den Bergh et al.2005),and we estimate the amount of imaging of nearby galaxies in the Hubble Space Telescope(HST)archive had become rich enough that coin-cidences were likely to occur.This was also the eﬀective date of the start of concerted eﬀorts to search for SN progenitors. Since the late1990’s our group(Smartt et al.2001,2002), and others(e.g.Van Dyk et al.2003a;Gal-Yam et al.2005) have been systematically searching for pre-explosion images of core-collapse SNe in nearby galaxies.We have further re-stricted our sample to galaxies with recessional velocities less than2000km s−1,eﬀectively restricting us to a volume limited sample.The recessional velocities,corrected for the infall of the Local Group towards Virgo cluster,of all nearby galaxies hosting SNe were taken from the HyperLEDA1 (Paturel et al.2003)database.We emphasise that we have used the corrected velocities to apply the selection criterion of2000km s−1and assuming H0=72km s−1Mpc−1,this lo-cal volume has a limit of28Mpc.During this period,and in this volume,there have been 138SNe candidates discovered and all are listed in the Asi-ago2,CfA3and Sternberg Astronomical Institute4cata-logues.Of course these are simply compilations of discover-ies reported in the International Astronomical Union(IAU) Circulars and these catalogues normally list the discovery magnitudes and types reported in theﬁrst IAU announce-ment.It often happens that the SN classiﬁcation is revised or reﬁned with subsequent higher quality spectra,or longer monitoring.Both can reveal peculiarities and transforma-tions,or simply give a more secure classiﬁcation.In partic-ular the sub-classiﬁcation of II-P can be added when signiﬁ-cant light curve information is gathered.Hence we have care-fully checked the classiﬁcation of each event,and have gone further and classiﬁed those supernovae listed as“II”into the subtypes II-P and II-L or IIn where possible.This was done using the following criteria in order.Firstly the refereed literature was searched and a classiﬁcation taken from pub-lished photometric and spectroscopic results.Secondly un-published,professional spectra and lightcurves where taken from reliable sources such as those of the Carnegie Su-pernova Project(Hamuy et al.2006)and the Asiago data archive(Turatto2000).Thirdly amateur lightcurves avail-able on the web were checked and,if possible,a II-P classiﬁ-cation was made if a clear and unambiguous plateau lasting longer than30days was recorded.The vast majority of II-P SNe have plateau phases lasting signiﬁcantly longer than30 days,in fact most are around90-110days(Pastorello2003; Hamuy2003;Pastorello et al.2004)and there is no clear evidence that plateaus of shorter duration are particularly common.However to observe such a long plateau necessarily means the SN must have been discovered close to explosion. 1http://leda.univ-lyon1.fr2http://web.pd.astro.it/supern/snean.txt3/cfa/ps/lists/Supernovae.html4http://www.sai.msu.su/sn/sncat/4S.J.Smartt et al.This is often not the case,and we have chosen to take30 days simply as an indicator that an extended plateau phase is evident.In all cases of our subclassiﬁcations of type II SNe,we believe the designations not to be controversial or ambiguous and for only9events classed as type II were we unable to assign a subtype.In these cases the supernovae were generally discovered late in the nebular phase.It is of-ten diﬃcult to distinguish Ib and Ic SNe from single spectra taken at an unknown epoch,and indeed there are6events for which authors have listed Ib/c classiﬁcations and we cannot improve on these classiﬁcations.All of the individual SNe are listed in Table A1.There are only two SNe which have not had a classiﬁcation spectrum reported in the literature, 1998cf and1999gs and these are ignored in the following frequency comparison.We realise that the classiﬁcations into the standard bins is somewhat simplistic.In particular there are some SNe that show evidence of interaction with the circumstel-lar medium,which result in narrow lines(usually of H or He)superimposed on the spectrum.When narrow lines of H dominate the spectrum then the IIn designation is of-ten used by the community,but some II-P and Ibc SNe do show evidence of this behaviour at a weaker level.The most striking example recently is that of the SN2006jc-like objects and the two examples in our sample are2006jc and2002ao(see Pastorello et al.2007;Foley et al.2007; Pastorello et al.2008).These show broad lined spectra re-sembling type Ic SNe(in that they do not exhibit H or He in the high velocity ejecta),but have strong and nar-row He emission lines and weak Hαemission.This has led Pastorello et al.(2008)to term this class of objects Ibn. However rather than introducing this small and very spe-ciﬁc class of events,we will class them as Ic SNe as this is a fair description of the underlying spectrum of the SN ejecta. Giving them a simple Ib label could be argued as being mis-leading in that they do not exhibit the broad,He absorption typical of this class of H-deﬁcient events.The label Ibn is certainly a valid type for them but in this paper it is too speciﬁc to be a useful addition to the compiled subtypes. We will discuss these objects further in the second paper in this series which concerns the stripped events(Crockett et al.in prep.).2.2The relative frequencies of core-collapse SNe In Table1we list the relative frequency of each subtype oc-curring in our sample.This is a volume limited relative fre-quency rate of SN types.There may well have been undiscov-ered local SNe in this period e.g.dust extinguished events, or events which exploded in solar conjunction which were missed at late times.However given the distance limit im-posed(µ=32.3)and the range in the absolute magnitudes of each subtype(Richardson et al.2002)it is unlikely that there is a serious bias in the relative number of the diﬀerent subtypes.One caveat to this is if there is a substantial num-ber of intrinsically faint SNe that may have gone undetected if they have typical magnitudes below about−13.The na-ture of the faint optical transient in M85(Kulkarni et al.2007;Ofek et al.2008)is currently debated,and could con-ceivably be a core-collapse SN(Pastorello et al.2007,seeSect.2.4).If a large number of intrinsically very faint SNeare evading discovery by current pointed surveys it couldTable1.The relative frequency of SNe types discovered between1998-2008(10.5yrs)in galaxies with recessional velocities lessthan2000kms−1,and type taken from Table A1.The relativefrequency of all types and the relative frequency of only core-collapse SNe are listed separately.Relative Core-Collapse onlyII-P5439.158.7II-L 2.5 1.8 2.7IIn 3.5 2.5 3.8IIb5 3.6 5.4Ib9 6.59.8Ic1813.019.6Ia3726.8...LBVs7 5.1...Unclassiﬁed2 1.4...The death of massive stars5where a Ib or Ic classiﬁcation seems secure).We did not in-clude the2unclassiﬁed SNe in any of the rate estimates. Seven of the events originally announced as SNe in Table A1have been shown to actually be outbursts of luminous blue variables(LBVs)similar to those seen historically in Local Group LBVs such asη-Carinae and P-Cygni.These are1999bw(Filippenko et al.1999),2000ch(Wagner et al. 2004),2001ac(Matheson&Calkins2001),2002kg or NGC2403-V37(Weis&Bomans2005;Maund et al.2006; Van Dyk et al.2006),2003gm(Maund et al.2006),2006fp (Blondin et al.2006),2007sv(Harutyunyan et al.2007). Hence we remove these from the rates of CCSNe since they are not true SN explosions.Table1lists the relative frequen-cies of core-collapse SNe.It is clear that the types II-L and IIn are intrinsically quite rare and the vast majority of core-collapse events are SNe II-P.Such a breakdown of subtypes has been suggested before(Li et al.2007;Cappellaro et al. 1999)although this is theﬁrst time quantitative volume lim-ited statistics have been compiled and presented.The pre-liminary analysis by Li et al.(2007)of68LOSS only discov-ered events(within30Mpc)in9years suggests68:26:2:4per cent breakdown between II:Ib/c:IIb:IIn.Perhaps the ratio of most interest is the Ibc/II ratio which has been used by previous studies to try to place constraints on progenitor populations(Prieto et al.2008;Prantzos&Boissier2003; Eldridge2007).These three studies have estimated the ratio as a function of metallicityﬁnding that,at approximately solar metallicity(Z⊙),the ratio is N Ibc/N II≃0.4±0.1(Pois-sonian uncertainty)and this goes down to around0.1at 0.3Z⊙(although with fairly small numbers in each metallic-ity bin).The ratios at approximately Z⊙are fairly similar to what weﬁnd(N Ib/c/N II=0.45±0.13)and as discussed below in Sect.4and Sect.5our SN population is likely drawn from metallicities in the range0.5-1.0Z⊙due to the fact that nearby,high starformation rate galaxies are those that are most frequently monitored for SNe.A full analysis of the chemical composition of the sites of the SNe in this volume limited sample would be desirable.We will discuss the SN rates more in Sect.8.2.The absolute rates of the diﬀerent types in the stan-dard supernova units(1SNu=1SN(100yr)−1(1010L B⊙)−1) is much more diﬃcult to assess given that detailed knowl-edge of the sampling frequency for each galaxy and search strategy is required(see Cappellaro et al.1999).The LOSS team will address this(Leaman et al.2004)and will provide the best estimate of the local rates so far.While we cannot derive the SN rate in standard units,the numbers in Ta-ble1serve as a good guide to the relative numbers of SNe expected in future surveys,when used in conjunction with absolute magnitude distributions(assuming the local galaxy population is cosmically representative).If bias factors af-fecting the relative rate of discovery of the diﬀerent types are minor,then these rates are a direct consequence of the initial mass function combined with stellar evolution which is dependent on mass,metallicity,duplicity and initial ro-tation rate.The numbers of SNe we have tabulated give a lower limit on the number of types per Gpc−3yr−1,which is at least a useful comparison to higher redshift estimates and also when considering the rates of Gamma-Ray Bursts (GRBs)and X-ray Flashes(XRFs).The volume enclosed by the28Mpc limit is9.2×10−5Gpc3;hence the local rate of CCSN explosions is likely to be 9.6×104Gpc−3yr−1and the local Ibc SN rate is 2.7×104Gpc−3yr−1.The latter is in reasonable agreement with the∼2×104Gpc−3yr−1 put forward by Guetta&Della Valle(2007),based on the Cappellaro et al.(1999)rates and local galaxy luminosity functions.Of the100core-collapse SNe and LBV classiﬁed out-bursts,the host galaxies of46of them were imaged by HST with either the Wide-Field-Planetary-Camera2(WFPC2) or Advanced Camera for Surveys(ACS)before explosion. However given the smallﬁeld of view of both of these cam-eras(2.6′and3′respectively)the site of the SNe did not al-ways fall on theﬁeld-of-view(FOV)of the cameras.Of these 46,only26had images of the SN site in the camera FOV, an overall hit rate of26per cent.A column is included in Table A1which speciﬁes whether or not the galaxy was ob-served by HST before explosion and if the SN falls on one of the camera FOVs.A further6have had high quality ground-based images of the SN site taken before explosion and they are also included in this compilation.The observational sam-ple for this paper,and its companion studying the stripped events(Crockett et al.2008,in prep.)is thus all of the core-collapse SNe which fulﬁll the above criteria and have good quality pre-explosion imagery.We have conﬁrmed that there are no other SNe in Table A1with HST pre-discovery im-ages.We cannot make the same deﬁnitive statement about ground-based images given the amount of inhomogeneous imaging data around.But our manual searching of all well maintained large telescope archives suggests it is highly un-likely that further high quality images of any of these events will surface i.e.images with sub-arcsec resolution with the depth to detect a large fraction of the galaxy’s massive stel-lar population.As such we have a well deﬁned sample in terms of distance and time.The rest of this paper focuses on the progenitor properties of the20type II SNe listed in Table2,of which18are conﬁrmed II-P and two are of un-certain subtype(1999an and2003ie).The other twelve su-pernovae which are likely to have had stripped progenitors: 2000ds(Ib),2000ew(Ic),2001B(Ib),2001ci(Ic),2002ap (Ic),2003jg(Ib/c),2004gt(Ib/c),2005ae(IIb),2005V(Ibc), 2005cz(Ib),2007gr(Ic),2008ax(IIb),will be discussed in a companion analysis paper(Crockett et al.in prep.).2.3The relative frequencies of SN1987A-likeeventsIn this volume limited sample,there is only one SN which has been conclusively shown to be similar to SN1987A,that is SN1998A(Pastorello et al.2005).SN1987A had a pecu-liar lightcurve and distinctly strong Ba ii lines(probably a temperature eﬀect)and an asymmetric Hαproﬁle during itsﬁrst∼40days of evolution and the community would have been very unlikely to miss such events as they would have created great interest.There is one other relatively nearby event that has a SN1987A-like appearance,which is2000cb(Hamuy2001)in IC1158.This one however has a V vir=2017km s−1,which puts it just beyond our selec-tion criteria.We shall see in Sect.5.9that Harutyunyan et al. (2008)suggest that a single spectrum of SN2003ie shows similarities to1987A but it is not well studied enough to be deﬁnitive.Hence even if we would include2000cb and 2003ie in our sample we can certainly say that1987A events。

Deep HST Observations of Star Clusters in NGC 1275

a rXiv:as tr o-ph/98219v12Fe b1998Deep HST Observations of Star Clusters in NGC 12751Matthew N.Carlson 2,Jon A.Holtzman 2,Alan M.Watson 3,Carl J.Grillmair 4,Jeremy R.Mould 5,Gilda E.Ballester 6,Christopher J.Burrows 7,John T.Clarke 6,David Crisp 4,Robin W.Evans 4,John S.Gallagher III 8,Richard E.Griﬃths 9,J.JeﬀHester 10,John G.Hoessel 8,Paul A.Scowen 10,Karl R.Stapelfeldt 4,John T.Trauger 4,and James A.Westphal 11ABSTRACT We present an analysis of compact star clusters in deep HST/WFPC2images of NGC 1275.B and R band photometry of roughly 3000clusters shows a bimodality in the B-R colors,suggesting that distinct old and young clusterpopulations are present.The small spread in the colors of the blue clusters isconsistent with the hypothesis that they are a single age population,with aninferred age of0.1to1Gyr.The luminosity function shows increasing numbersof blue clusters to the limit of our photometry,which reaches several magnitudespast the turnover predicted if the cluster population were identical to currentGalactic globulars seen at a younger age.The blue clusters have a spatialdistribution which is more centrally peaked than that of the red clusters.Theindividual clusters are slightly resolved,with core radii<∼0.75pc if they havemodiﬁed Hubble proﬁles.We estimate the speciﬁc frequencies of the old andyoung populations and discuss the uncertainties in these estimates.Weﬁnd thatthe speciﬁc frequency of the young population in NGC1275is currently largerthan that of the old population and will remain so as the young populationevolves,even if the majority of the low mass clusters are eventually destroyed.If the young population formed during a previous merger,this suggests thatmergers can increase the speciﬁc frequency of globulars in a galaxy.However,the presently observed young population likely contains too few clusters to havea signiﬁcant impact on the overall speciﬁc frequency as it will be observed inthe future.1.IntroductionEarly HST observations of NGC1275,the central galaxy in the Perseus cluster, revealed a population of about60blue(V-R∼0.3)star clusters surrounding the nucleus (Holtzman et al.1992).The color of these clusters suggests an age of roughly300million years based on the models of Charlot and Bruzual(1991).Spectra of the brightest object (Zepf et al.1995)also suggest an age of0.1to0.9Gyr,based on a comparison of the observed line widths to those predicted by the models of Bruzual and Charlot(1993).None of the clusters seem to have Hαemission,with the exception of one object found by Shields &Filippenko(1990),which appears to be a much younger object.The blue clusters in the original WFPC1images appear unresolved,suggesting sizes of less than15parsecs.The brightest object has V=18.9,which corresponds to M V=-15.8for H0=75km/s/Mpc and cz=5264km/s(Strauss et al.1992).The brightnesses of the blue clusters suggest masses of between2×104and1×108M⊙,depending on the assumed age and distance, if one assumes that the objects are star clusters with a Salpeter IMF.The observed sizes, luminosities,and the estimated masses suggest that these objects may be young analogues of globular clusters.In the past several years,massive young clusters have been observed in a variety of other galaxies.Lutz(1991)detected young globular cluster candidates in a ground-based study of the merger remnant NGC3597,and these have been conﬁrmed to be compact by HST observations(Holtzman et al.1996).Candidate young globular clusters have also been found in other interacting systems,including NGC7252(Whitmore et al.1993), NGC4038/9(Whitmore&Schweizer1995),NGC3921(Schweizer et al.1996),among others.A few massive clusters are seen in the starburst galaxy NGC253(Watson et al.1996),while others have been detected in the ring galaxies NGC1097and NGC6951 (Barth et al.1995)and the dwarf galaxies NGC1569,NGC1705(O’Connell et al.1994), and He2-10(Conti&Vacca1994).While no generally accepted picture has emerged as to what conditions lead to the formation of young clusters,galaxy interactions appear to be an important component.It is particularly diﬃcult to determine the precise mechanism responsible for the presence of these objects in NGC1275because of the myriad peculiarities of this galaxy, including the presence of a signiﬁcant amount of dust,streamers of Hαemission,an active nucleus,and the location of the galaxy at the center of a coolingﬂow in the Perseus cluster. Two hypotheses have been oﬀered for the origin of these clusters,namely,that they were formed from the substantial mass deposition of the Perseus cluster coolingﬂow(200M⊙/yr) or that the cluster formation was triggered by a galaxy-galaxy interaction.Holtzman et al.(1992)preferred the latter hypothesis based on the observed lack of spread in the WFPC1colors,which implies a common age for the objects,and the appearance of a ripple in the galaxy light which suggests that a previous interaction may have occurred.Richer et al.(1993)found larger color spreads in high resolution CFHT images and preferred the coolingﬂow hypothesis.However,Holtzman et al.(1996)did not detect young clusters in three of a sample of four other coolingﬂow galaxies;the central cluster galaxy in Abell1795 may have a few clusters,but it also has a peculiar morphology which suggests a previous interaction.The merger hypothesis is particularly interesting in light of the theory that elliptical galaxies form through mergers and the observation that ellipticals have higher speciﬁc frequencies of globular clusters than spirals,where the speciﬁc frequency is a measure of the number of globular clusters per unit luminosity of the host galaxy.Ashman&Zepf (1992)investigate the proposition that clusters might form during mergers and suggest that,in such an event,cluster formation would occur in a brief burst,resulting in a set of newly formed clusters with a common age and color.This would lead to a cluster system with a bimodal distribution of cluster colors reﬂecting the diﬀerence in metallicity or age (or both)between the original and the newly formed clusters.They predict that the spatial distribution of the younger clusters would be more sharply peaked toward the center of thegalaxy than that of the old cluster system,because the old globular cluster populations of the two progenitor galaxies would remain spatially extended and probably be dynamically heated during the merger,while the new clusters would be formed out of gas which becomes more centrally concentrated during a merger.However,as Harris et al.(1995)note,an increase in speciﬁc frequency as a result of a merger requires not only that globular clusters form during such an event,but that they form preferentially over non-cluster stars as compared to the ratio of clusters to background stars in the progenitor galaxies.Few estimates of the speciﬁc frequency of these young cluster systems exist.Watson et al.(1996)suggest that the4young clusters in NGC253most likely have formed with a large speciﬁc frequency.In the merger remnant NGC3921Schweizer et al.(1996)ﬁnd that the blue clusters will increase the overall number of clusters enough that the galaxy will come to have the speciﬁc frequency of an elliptical ler et al.(1997)ﬁnd that the speciﬁc frequency of globular clusters in the merger remnant NGC7252will rise over the next15Gyr as the background population fades to resemble that of an elliptical. These results all suggest that interactions can increase the speciﬁc frequency in a galaxy.Luminosity functions of old globular cluster systems have been well studied and used as a part of the extragalactic distance scale because of their uniformity from galaxy to galaxy;they are roughly Gaussian in shape with a peak near M V=-7.3(Harris1996).The luminosity functions of most of the recently discovered young cluster systems are poorly determined because of either small number statistics(few young clusters in the galaxy)or incompleteness.A notable exception is the young cluster system in NGC4038/9,which shows no turnover to two magnitudes fainter than the turnover predicted for a typical old cluster system,even after allowing for the expected fading of the clusters based on stellar population models.Based on this,van den Bergh(1995)argues that this cluster system may be intrinsically diﬀerent from old globular cluster systems.However,Mateo (1993)notes that,at least in the LMC,the observed increasing cluster luminosity function is well modelled by a combination of globular and open clusters.Also,several authors have recently suggested that substantial numbers of clusters may be destroyed over a Hubble time(Gnedin&Ostriker1997;Elmegreen&Efremov1997);mechanisms include evaporation and tidal disruption by galactic bulges and disks.We have obtained WFPC2images of NGC1275which go about4magnitudes deeper (in the red)than the WFPC1observations of Holtzman et al.(1992).These observations provide more accurate colors than previous observations and probe the cluster population to approximately2.5magnitudes fainter than the turnover expected if this population is identical to the Galactic globular cluster system seen at an younger age.Section2brieﬂy summarizes the observations and the reductions.Section3discussesour analysis and potential sources of error.In section4we present our results including the photometry,luminosity function of the clusters,surface density distribution,an estimate of the speciﬁc frequency,and analysis of the sizes of the objects.2.Observations&Data ReductionObservations of NGC1275were made with the WFPC2on1995November16in the F450W and F702Wﬁlters.Exposure times in F450W were200,1000,and3×1300 seconds.In F702W the exposures were200,900,1000,and2×1300seconds.The F450W and F702Wﬁlters are roughly similar to broad band B and Rﬁlters.The data were reduced using the procedures discussed by Holtzman et al.(1995a). The individual exposures were all taken with a common pointing,and the frames in each color were combined.Cosmic rays were rejected in the averaging based on the expected variance from photon statistics and readout noise;an extra term was included in the expected variance which was proportional to the signal in the pixel to allow for small pointing diﬀerences between frames.3.AnalysisCombined color images of NGC1275in the PC and in the WFPC2ﬁelds are shown in Figures1a and1b,respectively.The nucleus is in the center of the PC,and the other bright point source in the PC is a foreground F star(Hughes&Robson1991).Almost all of the remaining point sources are candidate star clusters in NGC1275.To detect the compact clusters,we summed the two colors and subtracted a5×5 boxcar-smoothed version of this image.We divided this by the square root of the smoothed image to provide an image whose units were proportional to the local noise(assuming the noise is dominated by the background,as is the case here).We then used IRAF’s DAOFIND to detect objects on the resulting image,in order to provide a uniform detection threshold in signal-to-noise ratio across the image.The choice of detection threshold was determined by minimizing the number of spurious detections and maximizing the number of faint objects detected,judging from a visual inspection.Objects wereﬁltered by shape based on roundness and sharpness criteria computed by DAOFIND;we required-1< roundness<1and0.2<sharpness<1.Several areas of the frame were masked out, including the galaxy nucleus,the bright saturated star in the PC,and a few bright stars and galaxies in the WFs.Aperture photometry was performed using a1-pixel radius aperture in both the PC and the WFs.The small aperture was used to reduce background related errors,which are large in the central region of the galaxy.Sky values were determined by taking an estimate of the mode in a background annulus;in the PC,the annulus was2pixels wide with an inner radius of12pixels,while in each WF the corresponding annulus was3pixels wide with an inner radius of6pixels.We chose to use small sky annuli because the galaxy background is variable on small scales.Corrections from1-pixel apertureﬂux toﬂux within0.5′′were determined from the nine brightest sources.The average aperture corrections were1.03and1.15magnitudes in the PC frame for F450W and F702W,respectively,and0.63and0.71magnitudes in the WFs.These are slightly larger than the corrections for bright point sources measured by Holtzman et al.(1995a),but this is expected if these objects are slightly resolved.In the PC,measured aperture corrections varied on the order of0.05mag between diﬀerent objects.Measured variations in the aperture corrections for the individual WFs were∼0.02 mag,so an average aperture correction was assumed for all three.If there is an intrinsic spread in cluster sizes,using a single aperture correction for all objects would lead to systematic errors in the derived magnitudes.Toﬁrst order,however,colors are unaﬀected by such a spread.The transformations from HST magnitudes(F450W,F702W)to Cousins magnitudes(B,R)were made using the transformations given by Holtzman et al.(1995b).Foreground Galactic extinction in the direction of NGC1275was taken to be A B= 0.70(Burstein&Heiles1984).We determined the extinction in the WFPC2passbands by numerically integrating the product of an A star spectrum,theﬁlter transmission,the system response,and an extinction curve from Cardelli et al.(1989)derived assumingR V=3.1.An A star was used because of its similarity to the observed spectrum of the bright clusters.This gave A F450W=0.69and A F702W=0.40.These estimates do not include internal extinction,however,which may be important in NGC1275since patchy dust is evident;this is discussed further below.Potential photometry errors include intrinsic Poisson error in the signal,error in the aperture correction,and error in the background level determination.Typical errors were estimated from the simulated clusters from our completeness tests and are shown in Figure 2.The dashed lines in color and magnitude indicate input magnitudes for the artiﬁcial clusters.Completeness was estimated by generating simulated objects at each of9diﬀerent input magnitudes(23.75to27.75in B).The simulated objects were given the same noise characteristics as real objects.In the PC,1000objects were placed randomly in each of3 separate annuli to better model the variation of completeness with distance from the centerof the galaxy.Each set of artiﬁcial clusters was given a spatial distribution which mimicked the distribution of the brightest(B<25)blue and red clusters.In the WFs,the1000 artiﬁcial objects were placed randomly in a uniform distribution.On each chip,a PSF of one of the isolated bright clusters was used to create the simulated objects(the use of other objects gave comparable results).Two sets of artiﬁcial objects were placed to estimate the diﬀerence in detection eﬃciency for objects of two diﬀerent colors;the two sets of simulated clusters were given B-R=0.7and B-R=1.6,comparable to the colors of the observed cluster populations(next section).The derived average completeness(weighted by the spatial distribution of the observed clusters)as a function of B magnitude is shown in Figure3for the whole image as well as for the section which fell in the PC.We estimated the number of foreground stars based on the models of Bahcall and Soneira(1980)and expect<4objects with B<27in the PC.Since we expect such small numbers of foreground stars,we have neglected them.4.Results4.1.PhotometryWe present the photometry of all detected objects in NGC1275by plotting color against apparent magnitude in Figure4a.Extinction-corrected absolute magnitudes and colors are shown as well,using a distance of70.2Mpc determined by assuming pure Hubble ﬂow with H0=75km/s/Mpc.Weﬁnd1181blue objects(B-R<1.1)and1855red objects. Distinct red and blue populations are seen,although there is signiﬁcant color scatter. Roughly50%of the blue objects are seen in the PC,as compared to about15%of the red objects.These objects cannot be single stars because they are marginally resolved and because they are too bright.With the exception of the Shields-Filippenko object,the objects lack Hαemission(Holtzman et al.1992),which precludes their being emission line objects. Consequently,they are probably star clusters,as supported by spectroscopy of the brightest object(Zepf et al.1995).They are brighter and more compact than open clusters in the Galaxy;the brightest object is250times brighter than the brightest Galactic open cluster. Their closest analog seems to be globular clusters,although the inferred ages are much smaller(see below).To test whether the observed color scatter is likely to be related to internal extinction within NGC1275and photometric errors from errors in background subtraction,we show in Figure4b only clusters in the southwestern half of the PC frame which have estimatedphotometric errors of less than0.15mag in both B and R.This region was chosen because it contains fewer obvious signatures of dust than the northeastern region.In fact,weﬁnd that the spread in color among the blue objects in Figure4b is consistent with that associated with photometric errors(cf.Figure2),supporting the conclusion that the observed color spread within the two populations is likely to be caused by the variation of internal extinction in the environment of the galaxy,rather than diﬀerences in age.We conclude that the blue clusters are a single color,single age population,with the spread in colors coming from Poisson errors and background subtraction errors.Figure4b shows a distinct bimodality in the cluster population,consistent with the presence of two discrete populations.The blue clusters have a typical dereddened(B-R)0∼0.4.This is much bluer than typical old globular clusters,which have(B-R)0∼1.2(Harris1996).The uniformity of the colors suggests that the clusters were formed in a relatively short duration single burst rather than an ongoing or continuous process.Figure5shows the magnitude and color evolution of a single burst population for a variety of metallicities,assuming a Salpeter initial mass function from0.1to125M⊙and a total mass of1M⊙(Bruzual&Charlot 1993).If we compare the measured colors of the blue clusters in the PC to the models,we infer ages of107to109years,allowing for small possible systematic errors in the models and the data as well as the unknown metallicity of the objects.We note that the clusters are far too blue to be explained by a metallicity eﬀect alone.Ages younger than107years are ruled out by the absence of Hαemission from the clusters.Spectra of the clusters(Zepf et al.1995)argue for a several hundred Myr old population dominated in the blue by A type stars.It is also simply less probable that we that we should happen to observe these clusters at a younger age.The LMC has a number of compact clusters with comparable colors(van den Bergh 1981).These objects are substantially fainter than the brightest objects in NGC1275, implying that they are less massive.Still,observations of blue clusters in the LMC,where we can directly measure ages using the main sequence turnoﬀin color-magnitude diagrams, give us a less model dependent idea of the spread in colors that could be expected from a spread in ages.Figure6shows the distribution of B-V versus age for LMC clusters;ages are from Elson&Fall(1988)and Hodge(1981,1983),and colors from van den Bergh(1981). Between108and109years,we see that the integrated colors of the clusters cover a range of 0.3in B-V.This argues against a large spread in the ages for the NGC1275clusters,which show no such spread in colors.While our observations were in B and R,not B and V,the color spread in B-R for the same age range would be0.8magnitudes,assuming a V-R vs B-R relation from the population synthesis models.Given ages,we can estimate masses for the clusters based on their luminosities.Age estimates of108and109years give mass estimates for the brightest object of2×107and 108M⊙,respectively.Blue clusters at our completeness limit of B=27have masses of2×104to105M⊙.These masses are very comparable with those of Milky Way globulars, which typically have masses between104and3×106M⊙,with a handful of clusters with M<104M⊙(Mandushev,Spassova,&Staneva1991,Pryor and Meylan1993).Our mass estimates depend on the assumption of a Salpeter IMF.Two of the three brightest objects in the southwest half of the PC(Figure4b)have much redder colors than the rest of the blue clusters(B-R of0.95and1.23).While these objects are close to the nucleus,they are bright enough that errors in determining the galaxy background are not a large source of error.Possible explanations are reddening by dust,a younger age(slightly less than107years old)when the integrated light is dominated by red supergiants(Leitherer&Heckman,1995),or the identiﬁcation of these objects with late type foreground stars.For the redder object,the last interpretation is supported by our measurement of sizes(§4.5),since it appears to be unresolved while almost all other objects appear marginally resolved.We suggest that the objects with B-R∼1.6(∼1.3dereddened)are the old population of globular clusters around NGC1275.These are slightly redder than Galactic globular clusters which have an average(B-R)0∼1.2.The brightest(M B=-10.7)has a magnitude similar to the brightest globulars seen in other central cluster galaxies.4.2.Luminosity FunctionFigure7a shows the B luminosity function for the blue clusters(B-R<1.1),and Figure7b shows the B luminosity function for the red clusters(B-R>1.1).The dotted lines in each plot show the results after correction for incompleteness.The luminosity function of the blue clusters looks distinctly diﬀerent from that expected for a typical old globular cluster population at a younger age.While the Galactic globular cluster luminosity function is Gaussian in shape with peak at M B∼-6.6andσ=1.0mag(Harris1996),the luminosity function for the clusters in NGC1275is more closelyﬁt by a exponential.If we were to observe the current Galactic globular cluster system at an age of500million years and at the distance of NGC1275(and the same Galactic extinction),we would observe a turnover in the luminosity function at B∼24(H0=75km/s/Mpc).This prediction assumes4magnitudes(13Gyr)of fading as suggested by the models of Bruzual&Charlot (1993).Our photometry is complete at the50%level to3magnitudes fainter than this,yet there is no evidence of a turnover in the luminosity function of the clusters in NGC1275.The luminosity function of the blue clusters has the same trend as that of Galactic open clusters,namely,an increasing number of clusters at fainter magnitudes with no turnover (van den Bergh and LaFontaine1984).However,the most luminous clusters in NGC1275 are brighter than any observed Galactic open clusters,despite being older than the brightest of them.The compactness as inferred from the HST images is also diﬀerent from that of open clusters(§4.5).Mateo(1993)ﬁnds that an increasing luminosity function for clusters in the LMC can be produced by a mixed population of true globulars and open clusters.In NGC1275,a similar explanation would require a large number of open clusters which are far more massive than any Galactic open clusters.Consequently,as a system,these clusters are diﬀerent from any cluster system seen in Local Group galaxies.As individual objects, however,the physical properties appear most similar to globular clusters.In Figure8,we compare the luminosity function of clusters in NGC1275with the luminosity functions in several of the other galaxies where reasonable numbers of blue clusters are found,as well as with the luminosity functions of Milky Way clusters.Dashed lines show rough completeness limits for the diﬀerent observations,and dotted lines give the location of the expected turnover given the various age estimates of the clusters.There is no strong evidence in any of the young cluster systems for an intrinsic turnover in the luminosity function.If these objects will evolve to look like the Galactic globular cluster system,some mechanism must preferentially destroy low luminosity,low mass clusters on timescalesof13Gyr.Two possibilities are tidal disruption and evaporation(Gnedin&Ostriker 1997;Elmegreen&Efremov1997).For tidal disruption to preferentially destroy low mass clusters,such clusters must have a lower mean density than more massive clusters. Evaporation through two-body relaxation can preferentially destroy lower mass clusters as their stars escape the cluster potential well and are captured by the gravitational potential well of the galaxy.Gnedin and Ostriker(1997)predict that from half to three quarters of the initial globular cluster population in a galaxy may be destroyed by a combination of these processes in a Hubble time.4.3.Surface Density ProﬁleFigure9shows the surface density distribution of red and blue clusters(open triangles andﬁlled triangles,respectively).Corrections have been made for incomplete annuli at large radii,for masked areas,and for diﬀering completeness levels with distance from the bright galaxy center.Error bars are simple Poisson errors in counts of clusters.The central area,within18pixels(0.8arcsec)from the core of the galaxy,has been omitted from thesurface density proﬁle due to the bright nucleus.It is clear that the blue clusters are more centrally concentrated than the red ones.Weﬁt the surface density distribution of the blue and red cluster systems from4′′to120′′with power laws.For the blue clusters,weﬁnd that a power law slope of-1.3 provides a reasonableﬁt over the entire range.For the red clusters,we note aﬂattening in the inner portion of the distribution andﬁt the surface density with two power laws. Inside0′.5,we measure a slope of-0.6,while outside0′.5weﬁnd a slope of-1.0.Flattening in the central part of the surface density distribution of a globular cluster system is also seen in other similar galaxies,such as M87(McLaughlin1995)and NGC5128(Harris et al.1984).Our measurements for the distribution of old clusters are in good agreement with those of Kaisler et al.(1996).However,they adopt a power law slope of-1.3,based on the observational relation between galaxy magnitude and power law slope of the surface density distribution of the globular cluster system(Harris et al.1986,1993).We note that our measured outer slope is sensitive to the choice of break point between the inner and outer regions;the data show a sign of steepening even more in the outermost parts. The spatial distribution of the clusters agrees with the galaxy merger model of Ashman and Zepf(1992),which predicts that the younger clusters will be peaked towards the center of the galaxy,while the older clusters will be moreﬂattened in their distribution.4.4.Speciﬁc FrequencyThe speciﬁc frequency of globular clusters in a galaxy is given byS N=N T100.4(15+M V)(Harris and van den Bergh1981)where N T is the total number of clusters and M V is the absolute V magnitude of the galaxy.This is of interest in light of the hypothesis that elliptical galaxies form via mergers of spirals and the observation that ellipticals havea higher speciﬁc frequency of globular clusters than spirals.Consequently,the merger hypothesis requires that globular clusters form during mergers with a higher speciﬁc frequency than that of the progenitor population.Also,it requires that clusters form in numbers comparable to those of the old cluster population(Zepf&Ashman1993).To address these questions,we calculate the speciﬁc frequency of the old population,the current speciﬁc frequency of the merger related population,and the predicted speciﬁc frequency of the merger related population in13Gyr.To calculate speciﬁc frequencies,we need to estimate the total number of clusters。

2024年09版小学5年级上册第5次英语第2单元真题(含答案)

2024年09版小学5年级上册英语第2单元真题(含答案)考试时间：100分钟（总分:140）A卷一、综合题(共计100题共100分)1. 填空题：I can ______ (说) three languages.2. 听力题：I love to _____ stories before bedtime. (hear)3. 选择题：What is the primary ingredient in guacamole?A. TomatoB. AvocadoC. OnionD. Pepper答案:B4. 选择题：What is the freezing point of water?A. 0°CB. 50°CC. 100°CD. 25°C答案:A5. 选择题：What is the name of the vast region containing thousands of galaxies?A. SuperclusterB. Galaxy ClusterC. NebulaD. Cosmic Web6. 填空题：A stork delivers ________________ (婴儿) in stories.7. 选择题：What do we call a person who repairs cars?A. MechanicB. ElectricianC. PlumberD. Carpenter答案：A8. 选择题：What is the name of the famous scientist who developed the theory of relativity?A. NewtonB. EinsteinC. GalileoD. Curie答案:B9. 填空题：I wish I could take my __________ (玩具名) everywhere I go.10. 填空题：My uncle tells me about his .11. 选择题：What do we call the time when the sun goes down?A. MorningB. NoonC. EveningD. Night答案: C12. 听力题：The outer core is responsible for the Earth’s ______ field.13. 听力题：The chemical formula for phosphoric acid is _____.14. 填空题：A ________ (湾) is a recess in the shoreline.15. 选择题：What is the name of the famous American holiday celebrated on the third Monday of February?A. Presidents' DayB. Labor DayC. Memorial DayD. Independence Day答案:A16. 听力题：Hydrochloric acid is found in our ________.17. 听力题：A _______ is a substance that can conduct electricity when dissolved in water.18. 听力题：My brother is a ______. He enjoys coding games.19. 填空题：My favorite pet is a ______ (狗) who loves to cuddle.20. 听力题：We go to _____ (bed/school) at night.21. 填空题：The ______ (蟋蟀) chirps at night in the grass.22. 选择题：What is the main ingredient in chocolate?A. SugarB. CocoaC. MilkD. Flour答案:B23. 选择题：What is the primary color of the sky on a clear day?A. BlueB. GreenC. YellowD. Red答案: A. Blue24. 填空题：Her _____ (音乐盒) plays a lovely tune.25. 听力题：I enjoy _______ (listening) to music.26. 选择题：What do you call a story that is made up?A. FictionB. Non-fictionC. BiographyD. History答案: A. Fiction27. 填空题：Planting native species can support local ______. (种植本地物种可以支持当地生态系统。

Ongoing massive star formation in the bulge of M51

a rXiv:as tr o-ph/11234v13Dec21Ongoing massive star formation in the bulge of mers 1,2N.Panagia 3,4S.Scuderi 5M.Romaniello 6M.Spaans 7W.J.de Wit 1,2R.Kirshner 8February 1,2008ABSTRACT We present a study of HST −W F P C 2observations of the inner kpc of the interacting galaxy M51in six bands from 2550˚A to 8140˚A .The images show an oval shaped area (which we call “bulge”)of about 11×16arcsec or 450×650pc around the nucleus that is dominated by a smooth “yellow/reddish”background population with overimposed dust lanes.These dust lanes are the inner extensions of the spiral arms.The extinction properties,derived in four ﬁelds in and outside dust lanes,is similar to the Galactic extinction law.The reddish stellar population has an intrinsic color of (B −V )0≃1.0suggesting an age in excess of 5Gyrs.We found 30bright point-like sources in the bulge of of M51i.e.within 110to 350pc from the nucleus.The point sources have 21.4<V <24.3,many of which are blue with B −V <0and are bright in the UV with 19.8<m 2550<22.0.These objects appear to be located in elongated “strings”which follow the general pattern of the dust lanes around the nucleus.The spectral energy distributions of the point-like sources are compared with those predicted for models of clusters or single stars.There are three reasons to conclude that most of these point sources are isolated massive stars (or very small groups of a few isolated massive stars)rather than clusters:(a)The energy distributions of most objects are best ﬁtted with models of single stars of M V between -6.1and -9.1,temperatures between 4000and 50000K,and with 4.2<log L/L ⊙<7.2,and 12<M ∗<200M ⊙.(b)In the HR diagram the sources follow the Humphreys-Davidson luminosity upper limit for massive stars.(c)The distribution of the sources in the HR diagram shows a gap in the range of20000<T eﬀ<10000K,which agrees with the rapid crossing of the HRD by stars,but not ofclusters.We have derived upper limits to the total mass of lower mass stars(M∗<10M⊙),that couldbe“hiding”within the point sources.For the“bluest”sources the upper limit is only a fewhundred M⊙.We conclude that the formation of massive stars outside clusters(or in very low mass clusters)is occurring in the bulge of M51.The estimated star formation rate in the bulge of M51is1to2×10−3M⊙yr−1,depending on the adopted IMF.With the observed total amount of gas in the bulge,∼4×105M⊙,andthe observed normal gas to dust ratio of∼150,this star formation rate could be sustained forabout2to4×108years.This suggests that the ongoing massive star formation in the bulge ofM51is fed/triggered by the interaction with its companion about4×108years ago.The starformation in the bulge of M51ia compared with tat in bulges of other spirals.Theoretical predictions of star formation suggest that isolated massive stars might be formed in clouds in which H2,[OI]63µm and[CII]158µm are the dominant coolants.This is expectedto occur in regions of rather low optical depth,A V≤1,with a hot source that can dissociatethe CO molecules.These conditions are met in the bulge of M51,where the extinction is lowand where CO can be destroyed by the radiation from the bright nuclear starburst cluster inthe center.The mode of formation of massive stars in the bulge of M51may resemble thestar formation in the early Universe,when the CO and dust contents were low due to the lowmetallicity.Subject headings:galaxies:bulge–galaxies:spiral–galaxies:interaction–stars:formation–stars:evolution–1.IntroductionThe spiral galaxy M51(NGC5194,the Whirlpool nebula)and its peculiar companion galaxy NGC 5195form a typical example of galaxy interactions.After the pioneering hydrodynamical simulations by Toomre and Toomre(1972),several authors have tried to explain the grand design spiral shape and the tidal arms of this interacting system.Hernquist(1990)and Barnes(1998)have critically discussed the successes and the problems of explaining the morphology of the NGC5194/5195system,in particular the radial velocities of the two galaxies,the two-armed spiral structure of M51,the connecting tidal arm and the large H i arm.The best model is found for a relative orbit that is almost in the plane of M51,for a mass ratio of NGC5194/5195≃2,a pericenter distance of17to20kpc and a time since pericenter of 2.5×108<t<4×108yrs(Barnes1998).The NGC5194/5195system is ideally suited for the study of triggered star formation due to galaxy-galaxy interactions.For this reason we have started a series of studies on the diﬀerent aspects of star formation in M51,based on HST−W F P C2observations in six broadbandﬁlters.The nucleus was studied by Scuderi et al.(2001;hereafter called Paper I),who found that it contains a total stellar mass of about2×107M⊙within the central17pc and a bright point source of2×106M⊙within the inner2pc. In this paper we study the properties of the elongated“yellow/reddish”region around the nucleus,hereafter called“the bulge”,and of30bright point-like sources that we discovered in it.These point sources indicate ongoing star formation in the bulge region,which is otherwise dominated by old(>5Gyrs)stars(Paper I).The full HST−W F P C2image of M51is published is Paper I.The image shows that the nucleus issurrounded by an elongated bulge of about460×860pc that is dominated by an old stellar population. The spiral arms containing H II regions start outside the bulge.We adopt a distance of d=8.4±0.6 kpc,corresponding to a distance modulus of29.62±0.16,which is based on the brightness distribution of planetary nebulae(Feldmeier,Ciardullo&Jacoby1997).At this distance,1arcsec corresponds to a linear distance of40.7pc,one HST−P C pixel of0.046”corresponds to1.87pc and an HST−W F C pixel of 0.1”corresponds to4.1pc.In§2we describe the observations and the data reduction.In§3we discuss the interstellar extinction in the bulge.In§4we describe the properties of30bright point-like sources in this region.In§5their energy distributions are compared with those predicted for clusters with diﬀerent ages and mass,and for single stars of diﬀerent eﬀective temperatures and radii.We will show that most of them are very luminous young stars(single or multiple),rather than clusters.The star formation rate in the bulge of M51is derived in§6.In§7we compare the formation of massive stars in the bulge of M51with clusters near the Galactic center,in the interaction region of the Antennae galaxies,and in the bulges of other spiral galaxies.We also discuss the predicted mode of star formation under the conditions that prevail near the nucleus of M51. The conclusions are given in§8.2.Observations and Data ReductionM51was observed with HST−W F P C2on May12,1994and on January15,1995as part of the HST Supernova Intensive Study(SINS)program to study SN1994I(e.g.,Millard et al.1999).The galaxy was observed through the wide bandﬁlters F255W and F336W in1994and through the wide bandﬁlters F439W,F555W,F675W and F814W in1995.We will refer to theseﬁlters as the UV,U,B,V,R,and I ﬁlters.The observations in the UV,U and Bﬁlters were split into four,three and two exposures of500, 400,700s respectively,while a single exposure of600s was taken with the remainingﬁlters.The data were processed through the PODPS(Post Observation Data Processing System)pipeline for bias removal andﬂatﬁelding.The removal of the cosmic rays in the UV,U and B images was accomplished by combining the available exposures.For the images taken in the other threeﬁlters we used a simple procedure,which consists in combining images obtained in adjacent bands,that allowed us to remove most of the contribution from the cosmic rays(see Paper1).Unfortunately the corrected images still showed some residual contamination from cosmic rays which could have aﬀected the photometry.To obtain a list of the point-like sources in eachﬁlter we used an unsharp masking method.This was done because of the complexity of the background emission.In fact,it seems that most of the point-like sources lie on or close to dust lanes that are the inner extensions of the spiral arms structures.The method consisted in smoothing each image using a Gaussian with4pixels FWHM and then subtracting the smoothed image from the original image.From each image the list of sources was obtained by picking up all the objects above a threshold,variable from about3to13times the local value of the background depending on the ﬁlter.These lists contained also residual cosmic rays so we“cross–correlated”them,selecting only those objects that were present in at least two diﬀerentﬁlters.This procedure was applied only to the opticalﬁlters.The UV and U images were taken8months earlier than the optical images,which means that the orientation of the spacecraft was not the same in the two epochs.In the1995observations the nucleus of M51was near the center of the PC-images,but in1994 the images were centered on SN1994I and the nucleus was at the edge of the PC-image.This means that the UV and U observations of about half of the point sources were made with the PC-camera and the restwere made with the WF-camera.To obtain the photometry of the point-like sources in the UV and Uﬁlters weﬁrst took the list containing the positions(pixel coordinates)of the point-like sources in the optical images and rotated the image,taking the position of SN1994I as origin,to match the diﬀerent orientation.In this way we identiﬁed the same point-like sources in the UV images as in the optical images.We performed aperture photometry using an aperture radius of2pixels and calculating the sky background in an annulus with internal and external radius of5and8pixels respectively.The correction for the aperture was obtained from a theoretical PSF obtained with Tiny Tim(Krist&Burrows1994).The ﬂux calibration was obtained using the internal calibration of the W F P C2,using the spectrum of Vega as photometric zero-point(Whitmore1995).The uncertainty in the photometry was computed by taking into account photon noise,background noise and CCD read-out noise only.Charge transfer and distortion eﬀects were not taken into account.Tests showed that these eﬀects have little inﬂuence on the colours(less than about0.03magn)and on the magnitudes(less than0.04magn).Figure1shows the B-image taken with the Planetary Camera.The bulge region is indicated.Figure2 shows the region of the bulge enlarged.The symbols and the marked areas are described below.3.The interstellar extinctionThe region around the nucleus of M51,in an area of about11×16arcsec=460×680pc,appears “yellow/reddish”in the HST images.The light from this region,the bulge,is dominated by an old stellar population.The brightness distribution in the bulge is smooth and homogeneous in color apart from the many darker“lanes”which are obviously due to dust extinction,see Fig. 2.Assuming a homogeneous stellar distribution in color and magnitudes,the extinction can be studied by comparing the magnitudes and colors of the dusty regions with those in adjacent regions were the extinction appears to be small.To this purpose we have selected in the bulge four areas with diﬀerent extinctions(Fields A to D). The locations of theseﬁelds are indicated in Fig.2.For each of theﬁelds we constructed mλversus V and color-color plots of all the pixels.Figure3shows the mλversus V plots forﬁelds A and C.Assuming that the background population of bulge stars has a uniform colour(see Paper I),the slopes of the relations give the extinction ratios.The range of the magnitudes in eachﬁeld provide an estimate of the maximum extinction values.Weﬁnd that the extinction in the bulge is small and has a maximim value of about0.25 in E(B−V),in agreement with Paper I.The resulting values of the extinction ratios are listed in Table1where the values are also compared with the Galactic values for the same HSTﬁlters based on the extinction curve of Savage and Mathis (1979).The Galactic values were derived by applying the extinction curve to the stellar energy distribution of an unreddened A0-star and then convolving the resulting spectrum with the HSTﬁlter characteristics (for details,see Romaniello1998,and Romaniello et al.2001).The table shows that the extinction ratios are quite similar to those of our Galaxy,which suggests that the extinction curve of the two galaxies are about the same.Scuderi et al.(2001)have reached the same conclusion for the M51nuclear region,but using a somewhat diﬀerent method.Hill et al.(1997)have shown on the basis of a study of H II regions observed with the Ultraviolet Imaging Telescope that the far-UV extinction of M51is smaller than in the Galaxy,A152/E(B−V)=6.80 for M51compared to8.33for the Galaxy.This is not in contradiction with our results,because the far-UVFig.1.—The negative F439W image of M51taken with the HST Planetary Camera.Theﬁeld is36.8×36.7 arcsec or1.48×1.48kpc.The nucleus and the spiral arms are clearly visible.The rectangle indicates the “bulge region”that is enlarged in Figure2.The dust lanes in the bulge follow a spiral structure as if they are the inner extensions of the spiral arms seen at larger distance.Fig. 2.—The negative F439W image of the region of11×16arcsec or450×650pc around the nucleus of M51observed with the HST−P C-camera.Apart from the nucleus and the dust lanes,the region has a smooth structure with colors indicating an old,>5×109yrs,population.The fourﬁelds,used for studying the extinction curve and the location of the“bulge point sources”are indicated.extinction atλ<2100˚A is known to vary drastically both in the Galaxy and in the LMC between diﬀerent regions.In the above described analysis we have treated the extinction as a foreground eﬀect.This is justiﬁed by the small values of E(B−V)<0.25,for which the eﬀect of the extinction on theﬂux is independent of the depth distribution of the dust.The fact that weﬁnd an extinction curve closely resembling the Galactic one provides additional support to the justiﬁcation of the adopted method.4.Bright point sources in the bulgeThe HST−P C image of the central region of M51(see Fig.2)shows the presence of bright pixel-size spots,with21.4<V<24.4.We have estimated the sizes of the sources,using radial proﬁleﬁtting using radial proﬁleﬁtting of the F555W images.The vast majority,21out of30,are deﬁnitely point sources.Six sources have a too high background to allow a reliable size determination.All of them are rather blue with B−V<0.32(see below).Two sources(nrs11and13)are possibly extended,but they have a low peak countrate and are rather faint.One of these,nr11,is a very red source with B−V=1.8whereas nr13 is a blue source with B−V=−0.09(see below).Only one source,nr4with B−V=0.90is deﬁnitely resolved.If its intrinsic intensity distribution is Gaussian,it has an intrinsic FWHM of0.06arcsec,which corresponds to2.4pc at the distance of M51.Assuming that the sample of sources that have no reliable FWHM determination contains the same fraction of extended sources as the rest,we conclude that our sample may contain no more than4extended sources.From here-on the sources will be called“bulge point sources”.Could the bulge point sources be back-ground galaxies?Using the number and magnitude distribution of galaxies in the Hubble Deep Field(Williams et al.1996),Gonzalez et al.(1998)derived the expected number and brightness distribution of background galaxies in the HST−W F chips of an observation similar to the ones of M51.Our detection limit is about23.5magn in V and I,due to the bright background by the old stellar background population in the bulge.From the study of Gonzalez et al.(1998)weﬁnd that about13background galaxies in V and25in I above the detection limit are expected in the three W F-chips together.The bulge of M51covers an area wchich is only17%of the P C-chip and1.5%of the three W F-chips together.So we expect that the bulge image contains about0.2background galaxies in V Table1:Reddening in the Galaxy and in the bulge of M51E(B−I)/E(B−V) 2.222.14±0.25E(V−I)/E(B−V) 1.521.15±0.25E(R−I)/E(B−V)0.660.37±0.15A UV/E(B−V) 6.71A U/E(B−V) 5.04A B/E(B−V) 4.17A V/E(B−V) 3.26A R/E(B−V) 2.46A I/E(B−V) 1.90Fig.3.—The m λversus V plots (in the Vega-magnitude sytem)for the B ,R and I bands of the ﬁelds A (left)and C (right)of the bulge used for the study of the extinction law in the bulge.The slope of these relations deﬁne the extinction ratios A λ/A V .and0.3in I.Moreover background galaxies would not be point sources.Even the extended source nr4, with its FWHM of0.6arsec,is too small to be a background galaxy(unless it is a QSO).It is most likely a small cluster.4.1.The location of the bulge point sourcesThe location of the bulge point sources is indicated in Fig.2.The points are not randomly distributed, but seem to be located preferentially in an ellipse(with major axis running from upper left to lower right) or in strings around the nucleus.This agrees with the general appearance of the region around the nucleus as observed in the Bﬁlter:the darker lanes also indicate spiral arms which can be traced down to the nucleus.The main spiral arms originate at a larger distance∼13′′∼500pc from the nucleus,i.e.just outside the range of Fig2(see Figure1).Figure4shows the locations and the numberings of the point sources.From the originally selected33 sources,3have been removed because we could not derive reliable photometry.These are indicated by the number zero.The numbers of the remaining30other sources are indicated.The coordinates of the sources are listed in Table2..4.2.Photometry of the bulge point sourcesThe integratedﬂuxes of the point sources were measured in the UV,U,B,V,R and I bands,as described in Sect.2,and converted into Vega-magnitudes,where UV=U=B=V=R=I=0for Vega (Whitmore1995).Fourteen out of the30point sources could not be measured in the UV and U band because they are too faint.For these point sources we adopted safe brightness upper limits of UV=21.4 and U=22.3,which correspond to the magnitudes(minus its uncertainty)of the faintest point sources that were detected in the UV and U band images.Sources nr26and27,which are located close together, could not be measured separately in the UV and U images of the WF-chips.We measured the combined magnitudes of the two sources:UV=19.79±0.11and U=20.51±0.06.These two sources are resolved in the other bands,where they are in the PC-chip.Since the energy distributions of the two sources in the B,V,R,I bands are very similar with a mean magnitude diﬀerence of0.30,we adopt the same diﬀerence for the UV and U magnitudes,and derived the magnitudes of the two individual sources.The magnitudes of all bulge point sources are listed in Table2.Most sources have B−V colors between−0.5and+1.0with two red exceptions near B−V≃+2.0 (nrs3and11)and one very uncertain blue exception,namely nr16with B−V=−2.5.Most sources with B−V<+0.5are detected in the UV and U band.The three bluest UV sources are nrs12,26and 27which have−2.1<U−V<−1.7and−3.1<UV−V<−2.6.These must be hot objects with little or no extinction.The colors of the majority of the point sources,in the range of−0.3≤B−V≤+1.0, correspond to spectral types between O and G5,if there were no extinction.The reddest point sources,nrs 3and11,have B−V=+2.2and+1.8respectively,which correspond to unreddened M stars.Fig.4.—The location and the numbers of the30point sources in the Bulge of M51,that are studied in this paper.Sources with number zero were in the original selection(see Figure2)but were not studied because of the lack of reliable photometry.The cross indicates the location of the nucleus of M51(Paper I).Theorientation is the same as in Fig.2–12–Table2:Bulge point sources as clusters or starsSTARSNr nr obs E(B−V)log T eﬀlog L∗χ2Rmagn K L⊙3.27 3.450.20 5.35+0.80−0.052.720.300.18 5.35+1.30−0.000.709.70+0.005.63F0.90−0.805.28F0.390.488.70+0.08−0.220.008.90+0.004.85F14.47−0.062.46 2.180.00 6.20+0.00−0.000.008.74+0.004.43F0.03−0.092.720.400.12 6.60+0.00−0.000.009.18+0.004.48F0.08−0.182.790.700.18 6.45+0.00−0.100.469.65+0.005.08F 1.40−1.480.00 5.60+0.252.6412.49−0.000.027.25+0.052.823.23−0.002.88 1.580.28 6.20+0.20−0.850.02 6.65+0.002.76 5.00−0.202.71F 6.150.007.00+0.00−0.000.22 5.30+0.302.890.32−0.303.65F18.730.207.48+1.34−0.000.008.85+0.003.88F 5.63−0.375.22F 2.860.189.18+0.37−0.360.20 6.45+0.002.79 1.89−0.002.950.170.20 6.50+0.00−0.000.02 6.20+0.002.43 1.47−0.050.007.54+0.003.25F11.83−0.000.00 6.35+0.052.58 2.48−0.002.42 1.980.00 6.40+0.00−0.000.029.40+0.004.69F0.09−0.222.42 2.710.00 5.50+0.00−0.000.22 6.20+0.202.550.05−0.55a:M i is the initial mass of the clusters.F:Frascati cluster model was adopted.–13–5.Modelling the energy distribution of the bulge point sourcesThe bulge point sources have visual magnitudes between21.4and24.4corresponding to−8.2<M V<−5.2if there were no extinction.For a mean reddening of E(B−V)≃0.3(see below)the absolute magnitudes are about−9.1≤M V≤−6.1.This means that the bulge point sources could be either small clusters or very bright stars.We will consider both possibilities.5.1.Bulge point sources as clustersIf the blue point sources are clusters,they cannot be very massive.For instance a cluster with an initial mass of106M⊙and an age of2×106years will have a visual absolute magnitude of M V=−15.3 (Leitherer&Heckman,1995).At the distance of M51and with an extinction of E(B−V)=0.3the cluster will have V≃15.3.The observed point sources are7to9magnitudes fainter,so their initial mass must have been a few102to a few103M⊙.For clusters of such a small mass,the colors and magnitudes cannot be accurately predicted because they will depend on the evolutionary stage of one or few of the most luminous and most massive stars.Therefore,the results ofﬁtting the observed energy distributions to models should only be considered as a rough estimate of the cluster parameters.We haveﬁtted the observed energy distributions of the bulge point sources with those predicted for instantaneously formed clusters,from Leitherer&Heckman(1995),henceforth called“LH-models”and from the Frascati-group(see below),henceforth called the“Frascati-models”.We adopted the LH-models of clusters with solar metallicity,with an IMF ofα=2.35(Salpeter’s value)and with an upper mass cut-oﬀof100M⊙and a lower mass cut-oﬀof1M⊙.These models cover an age range from0.2to300Myrs.The predicted magnitude in the F255W band was derived from their magnitude at2100˚A and the slope of the spectral energy distribution between2100and3000˚A. The”Frascati-models”were calculated by Romaniello(1997)from the evolutionary tracks of Brocato&Castellani(1993)and Cassisi et al.(1994)using the WFPC2magnitudes derived from the stellar atmosphere models by Kurucz(1993).These models are for instantaneous formation of a cluster of solar metallicity stars in the mass range of0.6to25M⊙,distributed according to Salpeter’s IMF.These models cover an age range of10to5000Myr.The LH-models are expected to more accurate for the younger clusters,because they are based on the evolutionary tracks of the Geneva-group which include massive stars. The Frascati models are expected to be more accurate for the old clusters,because they include stars with masses down to0.6M⊙.For both sets of cluster-models the magnitudes were calculated directly from the predicted energy distributions,using the W F P C2ﬁlter calibration(Whitmore1995).These magnitudes will be compared directly with the observed magnitudes,so we do not have to apply the“Holtzman et al.”(1995)colour correction,which is needed when the magnitudes of the models are given in the standard ﬁlters.Forﬁtting the predicted to the observed energy distributions we used a three dimensional maximum likelyhood method.The free parameters are E(B−V),the initial mass,M i,and age,t.We corrected the observed magnitudes for extinction in the range of0.00<E(B−V)<2.0in steps of0.02.The extinction values listed in Table1were adopted.The weighting factors are chosen as w i=1/(∆m i)2where∆m i is the uncertainty in the magnitude.For sources that were not detected in the UV and U images we adopted brightness upper limits of UV>21.4and U>22.3,as discussed above.The uncertainty in theﬁtting of the UV and U magnitudes to the models depends more strongly on the accuracy of the adopted extinction curve than on the accuracy of the observed magnitudes.This uncertainty of the short wavelengthﬁtting–14–will be larger for objects with large values of E(B−V).To take this into account we have added an extra term in the uncertainty of∆UV=1.5E(B−V)and∆U=1.0E(B−V)in the modelﬁtting of the UV and U magnitudes,with a minimum uncertainty of(∆UV)min=0.15and(∆U)min=0.10.This implies that theﬁtting had be done in two steps:ﬁrst with the normal values of∆m i toﬁnd the bestﬁt of the cluster parameters and E(B−V)and then with the extra uncertainty in the UV and U magnitudes.The values of E(B−V)of the second iteration turn out to be very similar to those of theﬁrst iteration.The resultingﬁts of the LH-models and the Frascati-models were compared and one of the two was adopted,based on the following criteria:(a)signiﬁcantly smaller reducedχ2R;(b)signiﬁcantly smaller value of E(B−V).This last criterium is used because all reliableﬁts(smallχ2R)have a small extinction and because the study of the extinction(see§3)showed that E(B−V)is very small in the bulge.Soif the energy distribution can beﬁtted with a young cluster of high extinction or an older cluster of low extinction,we adopted the second solution.The uncertainties in the ages and initial masses are derived from the requirement that onlyﬁts withχ2R<χ2R(min)+1are acceptable.This corresponds to the68% conﬁdence range.The results are listed in the left half of Table2and theﬁts are shown in Figure5a.For most sources a ﬁt with a reasonably small value ofχ2R∼<3is found,however7sources have a high value ofχ2R>5.The cluster parameters of these models are not reliable.The results in Table2conﬁrm our previous estimate that the young clusters have a low mass.More than half of the clusters have an initial mass smaller than about1000M⊙.Only old clusters with t>500Myrs have M i>104M⊙.This is due to the detection limit.A cluster with an initial mass is below5×103M⊙fades below the detection limit at an age of about 300Myrs(Leitherer&Heckmann,1995).5.2.Bulge point sources as individual starsWe have alsoﬁtted the energy distributions of the bulge point sources to those predicted by model atmospheres of Kurucz(1993).For this purpose we selected15models with temperatures ranging from 3750K to50000K and the lowest gravities in the grid of model atmospheres.We realize that the Kurucz blanketed LTE-model atmospheres may not be very accurate for the hottest stars where Non-LTE eﬀects and atmospheric extension eﬀects may play a role.So these models are not expected to give accurate values of the stellar parameters based on W F P C2-photometry.However,they serve the present purpose of obtaining an indication of the eﬀective temperature and luminosity of the bulge point sources.The models wereﬁtted to the observations using a three dimensional maximum likelyhood method.The free parameters are E(B−V),T eﬀand radius R∗.Toﬁt the observed energy distributions to those of model atmospheres,we corrected the observed magnitudes for extinction in the range of0.00<E(B−V)<2.0in steps of0.02(similar to theﬁt of the cluster models).The resulting dereddened energy distributions were compared to those of the model atmospheres and the best-ﬁt model was determined.The twoﬁt parameters for the shape of the energy distributions are E(B−V),T eﬀ.Theﬁt parameter for the absolute magnitude is the angular diameter or radius of the star.The weights of theﬁtting are the same as described in the previous section.To take into account the uncertainty in the extinction at the wavelengths of the UV and Uﬁlter,we have added an extra uncertainty∆UV and∆U,as described in the previous section.The results are listed in the right hand side of Table2.We list the values of E(B−V),T eﬀand log L/L⊙and the value of the reducedχ2R of theﬁt.The range of acceptable parameters was determined in the same way as for clusters,i.e.the acceptable models haveχ2R<χ2R(min)+1.Notice that for almost all。

Sensitivity of Galaxy Cluster Morphologies to Omega_0 and P(k)

a rXiv:as tr o-ph/96951v16Se p1996To Appear in MNRAS Sensitivity of Galaxy Cluster Morphologies to Ω0and P (k )David A.Buote 1Department of Physics and Center for Space Research 37-241Massachusetts Institute of Technology 77Massachusetts Avenue,Cambridge,MA 02139,USA buote@ Guohong Xu Board of Studies in Astronomy and Astrophysics,University of California at Santa Cruz,Santa Cruz,CA 95064,USA xu@ ABSTRACT We examine the sensitivity of the spatial morphologies of galaxy clusters to Ω0and P (k )using high-resolution N-body simulations with large dynamic range.Variants of the standard CDM model are considered having diﬀerent spatial curvatures,SCDM (Ω0=1),OCDM (Ω0=0.35),LCDM (Ω0=0.35,λ0=0.65),and diﬀerent normalizations,σ8.We also explore critical density models with diﬀerent spectral indices,n ,of the scale-free power spectrum,P (k )∝k n .Cluster X-ray morphologies are quantiﬁed with power ratios (PRs),where we take for the X-ray emissivity j gas ∝ρ2DM ,which we argue is a suitable approximation for analysis of PRs.We ﬁnd that Ω0primarily inﬂuences the means of the PR distributions whereas the power spectrum (n and σ8)primarily aﬀects their variances:log 10(P 3/P 0)is the cleanest probe of Ω0since its mean is very sensitive to Ω0but very insensitive to P (k ).The PR means easily distinguish the SCDM and OCDM models,while the SCDM and LCDM means show a more modest,but signiﬁcant,diﬀerence (∼3σ).The OCDM and LCDM models are largely indistinguishable in terms of the PRs.Finally,we compared these models to a sample of ROSAT clusters and ﬁnd that the PR means of the SCDM clusters exceed the ROSAT means with a high formal level of signiﬁcance (∼4σ).Though the formal signiﬁcance level of this ρ2DM /X-ray comparison should be considered only approximate,we argue that taking into account the hydrodynamics and cooling will not reconcile a discrepancy this large.The PR means of the OCDM clusters areconsistent,and the means of the LCDM clusters are marginally consistent,with thoseof the ROSAT clusters.Thus,we conclude that cluster morphologies strongly disfavorΩ0=1,CDM while favoring low density,CDM models with or without a cosmologicalconstant.Subject headings:galaxies:clusters:general–galaxies:evolution–galaxies:structure–X-rays:galaxies–cosmology:theory1.IntroductionThe quest forΩ0,the current ratio of the mean mass density of the universe to the critical density required for closure,has been a focus of the research eﬀorts of many astrophysicists involving a variety of diﬀerent techniques.At present,most observational evidence suggests a universe with sub-critical matter density,perhaps with a cosmological constant making up the diﬀerence required for a critical universe(e.g.,Coles&Ellis1994;Ostriker&Steinhardt1995). The possibility of measuringΩ0using the amount of“substructure”in galaxy clusters has thus generated some interest,“This is a critical area for further research,as it directly tests forΩin dense lumps,so both observational and theoretical studies on a careful quantitative level would be well rewarded.”(Ostriker1993).Early analytical work(e.g.,Richstone,Loeb,&Turner1992)and simulations(Evrard et al. 1993;Mohr et al.1995)found that the morphologies of X-ray clusters strongly favoredΩ0∼1 over low-density universes.Along with P OT ENT analysis of cosmic velocityﬁelds(e.g.,Dekel 1994),these substructure analyses were the only indicators in support of a critical value ofΩ0. However,the analytical results(e.g.,Kauﬀmann&White1993;Nakamura,Hattori,&Mineshige 1995),simulations(e.g.,Jing et al.1994),and morphological statistics(e.g.,Buote&Tsai1995b) have been criticized rendering the previous conclusions aboutΩ0uncertain.Buote&Tsai(1995b,hereafter BTa)introduced the power ratios(PRs)for quantifying the spatial morphologies of clusters in terms of their dynamical states.The PRs essentially measure the square of the ratio of a higher order moment of the two-dimensional gravitational potential to the monopole term computed within a circular aperture,where the radius is speciﬁed by a metric scale(e.g.,1Mpc).Buote&Tsai(1996,hereafter BTb)computed PRs of ROSAT X-ray images for a sample of59clusters and discovered that the clusters are strongly correlated in PR space,obeying an“evolutionary track”which describes the dynamical evolution of the clusters (in projection).Tsai&Buote(1996,hereafter TB)studied the PRs of a small sample of clusters formed in the hydrodynamical simulation of Navarro,Frenk,&White(1995)and veriﬁed the interpretation of the“evolutionary track”.In contrast to the previous studies(e.g.,Richstone et al.1992;Mohr et al.1995),TB concluded that their small cluster sample,formed in a standard Ω0=1,CDM simulation,possessed too much substructure(as quantiﬁed by the PRs)with respect to the ROSAT clusters,and thus favored a lower value ofΩ0.However,a statistically large sample of clusters is important for studies of cluster morphologies. The PRs are most eﬀective at categorizing clusters into diﬀerent broad morphological types;i.e.the distinction between equal-sized bimodals and single-component clusters is more easily quantiﬁed than are small deviations in ellipticities and core radii between single-component clusters (see BTa).The eﬃciency of the PRs at classifying clusters into a broad range of morphological types is illustrated by their success at quantitatively discriminating the ROSAT clusters along the lines of the morphological classes of Jones&Forman(1992)(see BTb).There is a lower frequency of nearly equal-sized bimodals in the ROSAT sample than clusters with more regular morphologies.Hence,to make most eﬀective use of the PRs the models need to be adequately sampled(i.e.simulations have enough clusters)to ensure that relatively rare regions of PR-space are suﬃciently populated.In this paper we build on the previous studies and investigate the ability of the PRs to distinguish between models having diﬀerent values ofΩ0.Unlike the previous theoretical studies of cluster morphologies mentioned above,we also consider models having diﬀerent power spectra, P(k),since P(k)should aﬀect the structures of clusters as well.At the time we began this project it was too computationally costly to use hydrodynamical simulations to generate for several cosmological models a large,statistically robust,number of clusters with suﬃcient resolution.To satisfy the above criteria and computational feasibility we instead used pure N-body simulations.The organization of the paper is as follows.We discuss the selection of cosmological models in§2.1;the speciﬁcations of the N-body simulations in§2.2;the validity of using dark-matter-only simulations to generate X-ray images and the construction of the images in§2.3;and computation of the PRs in§2.4.We analyze the models having diﬀerent values ofΩ0and a cosmological constant in§3,and models with diﬀerent spectral slopes andσ8in§4.The implications of the results for all of the models and comparison of the simulations to the ROSAT sample of BTb is discussed in§5.Finally,in§6we present our conclusions.2.Simulations2.1.Cosmological ModelsTo test the sensitivity of cluster morphologies to the cosmological density parameter due to matter,Ω0,and the power spectrum of densityﬂuctuations,P(k),we examined several variants of the standard Cold Dark Matter(CDM)model(e.g.,Ostriker1993).In Table1we list the models and their relevant parameters:Ω0;λ0=Λ/3H20,whereΛis a cosmological constant and H0is the present value of the Hubble parameter;the spectral index,n,of the scale-free power spectrum of densityﬂuctuations,P(k)∝k n;andσ8,the present rms densityﬂuctuations in spheres of radius 8h−1Mpc,where h is deﬁned by H0=100h km s−1Mpc−1.The parameters of the open CDM model(OCDM)and low-density,ﬂat model(LCDM)were chosen to be consistent with current observations(e.g.,Ostriker&Steinhardt1995).Their normalizations were set according to theσ8−Ω0relationship of Eke,Cole,&Frenk(1996)to agree with the observed abundance of X-ray clusters.The biased CDM model(BCDM)was also normalized in this way.However,the BCDM simulation,because it hasΩ0=1,necessarily has poorer resolution(i.e.fewer particles per cluster)than the OCDM and LCDM models due to theﬁxed box size of our simulations(see§2.3).For the purposes of our investigation of cluster morphologies it is paramount to compare simulations having similar resolution.Hence we use the SCDM model(withσ8=1)as our primaryΩ0=1simulation for analysis,which has resolution equivalent to the OCDM and LCDM simulations.(We show in§4.4that the means of the PR distributions for BCDM and SCDM are very similar which turns out to be most important for examining the eﬀects ofΩ0.)Hence,the SCDM,OCDM,and LCDM models allow us to explore the eﬀects ofΩ0andλ0on the cluster morphologies;comparing SCDM and BCDM provides information on the inﬂuence ofσ8.We explore the eﬀects of diﬀerent P(k)on the PRs using the scale-free models,which have diﬀerent n from SCDM.For the scale-free models we normalized each to the same characteristic mass,M⋆,deﬁned to be(Cole&Lacey1996)the mass scale when the linear rms densityﬂuctuation is equal toδc,the critical density for a uniform spherically symmetric perturbation to collapse to a singularity.ForΩ0=1,the linear theory predictsδc≈1.686(e.g.,Padmanabhan 1993).We take the SCDM model withσ8=1as a reference for these scale-free models which gives a characteristic mass of1014M⊙.This procedure allows a consistent means to normalize the scale-free models relative to each other on the mass scales of clusters.Unfortunately,as a result of this normalization procedure,at earlier times the models have diﬀerent large-scale power and thus the cluster mass functions are diﬀerent for each of the models.The scale-free model with n=−1.5is similar to the SCDM model and will be used to“calibrate”the scale-free models with respect to the other models(see Table1).2.2.N-body Cluster SampleWe use the Tree-Particle-Mesh(TPM)N-body code(Xu1995b)to simulate the dissipationless formation of structure in a universeﬁlled with cold dark matter.The simulations consist of1283 particles in a square box of width200h−1Mpc.The gravitational softening length is25h−1kpc which translates to a nominal resolution of∼50h−1kpc.This resolution is suﬃcient for exploring the structure of clusters with PRs in apertures of radii R ap∼>0.5Mpc;for a discussion of the related eﬀects of resolution on the performance of PRs on ROSAT X-ray images see Buote&Tsai (1995b,§4).All of the realizations have the same initial random phase.For each simulation we located the39most massive clusters using a version of the DENMAX algorithm(Bertschinger&Gelb1991)modiﬁed by Xu(1995a).This convenient selection criterion yields well deﬁned samples for each simulation and allows consistent statistical comparison between diﬀerent simulations which is the principal goal of our present investigation.For thevarious cosmological models we explore(see Table1)these clusters generally have masses ranging from(0.3−3)×h−11015M⊙,which correspond to typical cluster masses observed in X-ray(e.g., Edge et al.1990;David et.al.1993)and optically(e.g.,Carlberg et.al.1995)selected samples.2.3.X-ray Images2.3.1.Motivation for j g∝ρ2DMBy letting the gas density trace the dark matter density(ρgas∝ρDM)and by assuming that the plasma emissivity of the gas is constant,we computed the X-ray emissivity of the clusters, j g∝ρ2DM.Given its importance on the results presented in this paper,here we discuss at some length the suitability of this approximation.(Cooling of the gas is discussed in§5.1.)For clusters in the process of formation or merging,the gas can have hot spots appearing where gas is being shock heated(e.g.,Frenk,Evrard,Summers,&White1996).One eﬀect of such temperatureﬂuctuations on the intrinsic X-ray emissivity is that the intrinsic plasma emissivity will vary substantially over the cluster thus rendering j g∝ρ2DM a poor approximation.However, the intrinsic X-ray emissivity is not observed,but rather that which is convolved with the spectral response of the detector.For ROSAT observations of clusters with the PSPC,the plasma emissivity is nearly constant over the relevant ranges of temperatures(NRA91-OSSA-3,Appendix F,ROSAT Mission Description),and thus temperatureﬂuctuations contribute negligibly to variations in the emissivity;for previous discussions of this issue for the PRs see BTa and TB.A more serious issue is whether the shocking gas invalidates theρgas∝ρDM approximation, in which case the dynamical state inferred from the gas would not reﬂect that of the underlying mass.TB,who analyzed the hydrodynamical simulation of Navarro et al.(1995a),showed that the PRs computed for both the gas and the dark matter gave similar indications of the dynamical states of the simulated clusters(see§4of TB).In particular,this applied at early times when the clusters underwent mergers with massive subclusters.2Hence,our approximation for the X-ray emissivity should be reasonable even during the early,formative stages of clusters.Another possible concern with settingρgas∝ρDM is that a gas in hydrostatic equilibrium, which should be a more appropriate description for clusters in the later stages of their evolution, traces the shape of the potential of the gravitating matter which is necessarily rounder than the underlying mass;if the gas is rounder,then the PRs will be smaller.However,the core radius(or scale length)of the radial proﬁle of the gas also inﬂuences the PRs.In fact,clusters with larger core radii have larger PRs;see BTa who computed PRs for toy X-ray cluster models having a variety of ellipticities and core radii.When isothermal gas,which is a good approximation for a nearly relaxed cluster,is added to the potential generated by an average cluster formed in aΩ0=1,CDM simulation,the gas necessarily has a larger core radius than that of the dark matter(see Figure14of Navarro,Frenk, &White1995b).Hence,a gas in hydrostatic equilibrium will have a larger core radius than that of the dark matter,at least in the context of the CDM models we are studying.Considering the competing eﬀects of smaller ellipticity and larger core radii(factors of2-3in each),and from consulting Table6of BTa,we conclude that no clear bias in the PRs is to be expected by assuming that the gas follows the dark matter.In further support of this conclusion are the similarities of the morphologies of clusters in the N-body study of Jing et al.(1995).Using centroid-shifts and axial ratios theyﬁnd similar results whenρgas∝ρDM and when the gas is in hydrostatic equilibrium(see their Figures5,6,and8).2.3.2.Construction of the ImagesHaving chosen our representation for the X-ray emissivity,we then generated two-dimensional “images”for each cluster.A rectangular box of dimensions4×4×10h−3Mpc3with random orientation was constructed about each cluster.We converted the particle distribution for each cluster to a mass densityﬁeld using the interpolation technique employed in Smoothed Particle Hydrodynamics(SPH)(e.g.,Hernquist&Katz1989),from which the X-ray emissivity was generated,j g∝ρ2DM.The SPH interpolation calculates the density at a grid point by searching for the nearest neighbors and is thus more robust and physical than other linear interpolation schemes like Cloud-in-Cell.For our SPH interpolation we use20neighbors and the spline kernel described in Hernquist&Katz.The interpolation result is independent of the cell we choose for the X-ray emissivity calculations.Typically,the boxes contained∼2500particles for a cluster;e.g.,SCDM(1799-3965),OCDM (1359-3656),LCDM(1439-3877),and BCDM(603-1740).We projected the emissivity along the long edge of the box into a square4×4h−2Mpc2“image”consisting of“pixels”of width20h−1 kpc.This pixel width was chosen suﬃciently small so as not to inhibit reliable computation the PRs.We do not add statistical noise or other eﬀects associated with real observations to the X-ray images since our principal objective is to examine the intrinsic response of cluster morphologies to diﬀerent cosmological parameters.However,the investigation of observational eﬀects on the PRs by BTa,and the derived error bars on the PRs from ROSAT clusters by BTb,do not show any large systematic biases;comparison of the simulations to the ROSAT cluster sample is discussed in§5.2.4.Power RatiosThe PRs are derived from the multipole expansion of the two-dimensional gravitational potential,Ψ(R,φ),generated by the mass density,Σ(R,φ),interior to R,Ψ(R,φ)=−2Ga0ln 1mR m(a m cos mφ+b m sin mφ),(1) whereφis the azimuthal angle,G is the gravitational constant and,a m(R)= R′≤RΣ( x′) R′ m cos mφ′d2x′,(2)b m(R)= R′≤RΣ( x′) R′ m sin mφ′d2x′.(3) Because of various advantageous properties of X-ray images of clusters,we associate the surface mass density,Σ,with X-ray surface brightness,ΣX(which is derived from the projection ofρ2DM –see previous section);for more complete discussions of this association see BTa and TB.The square of each term on the right hand side of eq.(1)integrated over the boundary of a circular aperture of radius R ap is given by(ignoring factors of2G),P m=1P0,(6) which we shall henceforward analyze in this paper.Since the P m depend on the origin of the chosen coordinate system,we consider two choices for the origin.First,we take the aperture to lie at the centroid ofΣX;i.e.where P1vanishes. Of these centroided P R m,P R2,P R3,and P R4prove to be the most useful for studying cluster morphologies(see BTa).In order to extract information from the dipole term,we also consider theorigin located at the peak ofΣX.We denote this dipole ratio by P(pk)1/P(pk),and its logarithmP R(pk)1,to distinguish it from the centroided power ratios.To obtain the centroid ofΣX in a consistent manner for all clusters we adopted the following procedure.First,when projecting the cluster(see§2.3),the cluster was roughly centered on the X-ray image by eye.For each image we computed the centroid in a circular aperture withR ap=1.5h−1Mpc located about theﬁeld center.This centroid was then used as our initial center for each cluster;see BTa for a description of how the peak ofΣX is located.In addition to considering the P R m individually,we also analyze the cluster distributions along the“evolutionary tracks”in the(P R2,P R4)and(P R2,P R3)planes obeyed by the ROSAT clusters of BTb.We refer the reader to TB for a detailed discussion of the cluster properties along the evolutionary tracks.Using the augmented Edge et al.(1990)sample of BTb we recomputed the lines deﬁning the evolutionary tracks of the ROSAT data for the1h−180Mpc apertures.This was done since TB selected a subset of the clusters based on P R m measurement uncertainty rather thanﬂux. Following TB weﬁt P R4=a+bP R2considering the uncertainties in both axes;a similarﬁt was done for the(P R2,P R3)plane.We obtained a=−0.92,b=1.18for the(P R2,P R4)track which we denote by P R2−4.Similarly,for the(P R2,P R3)track,which we denote by P R2−3,we obtained a=−0.49,b=1.16.These results are nearly the same found by TB for the slightlydiﬀerent sample.To facilitate comparison to a previous study of the P R m of ROSAT clusters(BTb),we compute P R m of the simulated clusters in apertures ranging in radius from0.5h−180Mpc to1.5h−180 Mpc(H0=80h80km s−1Mpc−1)in steps of0.25h−180Mpc;i.e.(0.4−1.2)h−1Mpc in steps of 0.2h−1Mpc.We refer the reader to§2of BTa and§2of TB for discussions of the advantages of using a series ofﬁxed metric aperture sizes to study cluster morphologies.3.P R m for Models with DiﬀerentΩ0andλ0First we consider clusters formed in the SCDM,OCDM,and LCDM models.Contour plots for16of the clusters formed in each of the models are displayed in Figures1,2,and3.In Figure4we show the(P R2,P R4)plane for the0.5h−180Mpc and1.0h−180Mpc apertures;the SCDM model appears in each plot for comparison.The clusters in each of the models exhibit tight correlations very similar to the evolutionary tracks of the ROSAT clusters(BTb)and the simulated hydrodynamic clusters(Ω0=1)of Navarro et al.(1995a)studied by TB.Along the evolutionary tracks a shift in the means of the P R m is easily noticeable in the0.5h−180Mpc aperture,being most apparent for the SCDM-OCDM models.The spread of the P R m along the track in the1.0h−180Mpc aperture for SCDM-OCDM also appears to be diﬀerent.The distributions perpendicular to P R2−4do not show discrepancies obvious to the eye.At this time we shift our focus away from the evolutionary tracks and instead analyzethe individual P R m distributions,which prove to be more powerful for distinguishing between cosmological models as we show below.We give the individual P R m distributions of clusters in the three models for the0.5h−180Mpc and1.0h−180Mpc apertures in Figures5and6.We found it most useful to compare these distributions in terms of their means,variances,and Kolmogorov-Smirnov (KS)statistics.For the number of clusters in each of our simulations(39)higher order statisticslike the skewness and kurtosis are unreliable“high variance”distribution shape estimates(e.g., Bird&Beers1993).We did consider more robust statistics like the“Asymmetry Index”(AI), which measures a quantity similar to the skewness,and the“Tail Index”(TI),which is similar to the Kurtosis(Bird&Beers1993).However,we found that they did not clearly provide useful information in addition to the lower order statistics and KS test,and thus we do not discuss them further.3The means and standard deviations for the(0.5,0.75,1.0)h−180Mpc apertures are listed in Table2.As a possible aid to understanding the relationships between the values in Table7, we plot in Figure7the standard deviation vs the mean for the0.75h−180Mpc aperture.We do not present the results for the larger apertures because they did not signiﬁcantly improve thedo not ability to distinguish between the models.Moreover,we found that P R4and P R(pk)1provide much useful information in addition to P R2and P R3.Generally P R4tracks the behavior of P R2,though showing less power to discriminate between models;the similarity to P R2isis similar to,but understandable given the strong correlation shown in Figure4.Likewise,P R(pk)1not quite so eﬀective as,P R3.For compactness,thus,we shall henceforward mostly restrict our discussion to results for P R2and P R3in the(0.5,0.75,1.0)h−180Mpc apertures.We compare the means,standard deviations,and total distributions of the models in Table 3using standard non-parametric tests as described in Press et al.(1994).The Student’s t-test, which compares the means of two distributions,computes a value,p t,indicating the probability that the distributions have signiﬁcantly diﬀerent means.Similarly,the F-test,which compares the variances of two distributions,computes a value,p F,indicating the probability that the distributions have signiﬁcantly diﬀerent variances.Finally,the KS test,which compares the overall shape of two distributions,computes a value,p KS,indicating the probability that the distributions originate from the same parent population;the probabilities listed in Table3are given as percents;i.e.decimal probability times100.Note that for the cases where the F-test gives a probability less than5%we use the variant of the t-test appropriate for distributions with signiﬁcantly diﬀerent variances(i.e.program tutest in Press et.al.).3.1.SCDM vs.OCDMAs is clear from inspection of Figures4-7,and Tables2-3,the means of the P R m of the SCDM model exceed those of OCDM.In terms of the t-test the signiﬁcance of the diﬀerences is very high.Of all the P R m,generally the means of P R2and P R3exhibit the largest signiﬁcant diﬀerences;the most signiﬁcant diﬀerences are seen for P R3in the0.5h−180Mpc aperture,p t=0.02%,and for P R2in the0.75h−180Mpc aperture,p t=0.06%.Hence,though diﬀerent inall the apertures,the discrepancy in the means is most signiﬁcant for the smallest apertures, (0.5,0.75)h−180Mpc.The variances of P R3in the SCDM model are essentially consistent at all radii with their corresponding values in OCDM.However,for P R2the variances are consistent at0.75h−180Mpc, but marginally inconsistent at(0.5,1.0)h−180Mpc(and inconsistent at(1.25,1.5)h−180Mpc).The KS test generally indicates a signiﬁcant diﬀerence in SCDM and OCDM when also indicated by the t-test,or the t-test and F-test together.The level of discrepancy is usually not as signiﬁcant as given by the t-test,except when p F is small as well.Since the KS test does not indicate discrepancy when both the t-test and F-test indicate similarity,we conclude that higher order properties of the PR distributions are probably not very important for the SCDM and OCDM models(at least for the samples of39clusters in our simulations).Since this qualitative behavior holds for the other model comparisons,we shall not emphasize the KS tests henceforward.Finally,in terms of the various signiﬁcance tests weﬁnd that the P R2−4distribution essentially gives a weighted probability of the individual P R2and P R4distributions;i.e.it does not enhance the discrepancy in the individual distributions.Perpendicular to P R2−4the distributions are consistent.The same behavior is seen for P R2−3as well.This behavior is seen for the remaining model comparisons in this section so we will not discuss the joint distributions further.3.2.SCDM vs.LCDMThe P R m means for the SCDM clusters also systematically exceed those in the LCDM model, however the signiﬁcance of the diﬀerence is not as large as with the OCDM clusters.The largest discrepancy is observed for P R2in the(0.75,1.0)h−180Mpc apertures for which p t=(0.7%,0.8%). The other P R m show only a marginal discrepancy in the means.For apertures(0.5,0.75)h−180Mpc, P R3has p t=(4%,3%),but is quite consistent at larger radii.The variances for the SCDM and LCDM models are consistent for essentially all radii and all P R m.3.3.OCDM vs.LCDMThe P R m means for the LCDM clusters appear to systematically exceed those in the OCDM model,however the formal signiﬁcances of the diﬀerences are quite low.The means are entirely consistent at all radii for P R2.However,P R3shows a marginal diﬀerence in the0.5h−180Mpc aperture(p t=9%).The variances of the P R m of the OCDM and LCDM models behave similarly as with the SCDM and OCDM comparison above,as expected since the SCDM-LCDM variances are essentially identical.However,the degree of discrepancy is not as pronounced.3.4.Performance Evaluation I.The means of the individual P R m distributions generally exhibit the most signiﬁcantdiﬀerences between the SCDM,OCDM,and LCDM models;the variances are much less sensitive to the models,with P R3showing no signiﬁcant variance diﬀerences.The larger means for the P R m in the SCDM models are expected from the arguments of,e.g.,Richstone et al.(1992).That is,in a sub-critical universe the growth of densityﬂuctuations ceased at an early epoch and so present-day clusters should show less“substructure”than in anΩ0=1universe where formation continues to the present.Clusters with more structure will have systematically larger values of the P R m.The P R m whose means show the most signiﬁcant diﬀerences between the models are P R2 and P R3,where P R2typically performs best for apertures(0.75,1.0)h−180Mpc and P R3is mostis often the least eﬀective P R m foreﬀective for(0.5,0.75)h−180Mpc.Although useful,P R(pk)1diﬀerentiating models in terms of its mean;this relatively weak performance of the dipole ratio with respect to other moments is echoed in the results of Jing et al.(1995)who found that their measure of an axial ratio performed better than a centroid shift for discriminating between models (see their tables3-6).4.P R m for Models with Diﬀerent n andσ8In this section we investigate the eﬀects of diﬀerent power spectra for models otherwise conforming to the speciﬁcations of the SCDM model.First,we examine models with diﬀerent spectral indices of the scale-free power spectrum(P(k)∝k n),n=0,−1,−1.5,−2.Then we examine the BCDM model which has a lower power-spectrum normalization as expressed byσ8. As in the previous section,weﬁnd the(0.5,0.75,1.0)h−180Mpc apertures to be more useful than thedo not provide much useful information in addition to larger apertures,and that P R4and P R(pk)1that provided by P R2and P R3.Hence,for compactness we again mostly restrict the discussion to P R2and P R3in the smaller apertures.4.1.n=−1.5vs.SCDMBefore analyzing the P R m of models with diﬀerent n we calibrate the scale-free models by comparing the n=−1.5scale-free model to the SCDM model since they should have similar properties(see§2.1).Weﬁnd that the means,variances,and KS statistics of the centroided P R m for the SCDM and n=−1.5models are entirely consistent for all aperture radii with only one possible exception.The variances of P R3exhibit a marginal(p F=5%)discrepancy in the0.5h−180 Mpc aperture.The signiﬁcance of this variance discrepancy should be treated with caution given the complete consistency of the means(p t=31%)and KS(32%)test at this radius as well as the。

The evolution of clustering and bias in the galaxy distribution

a rXiv:as tr o-ph/98528v115May1998The evolution of clustering and bias in the galaxy distribution B y J.A.Peacock Institute for Astronomy,Royal Observatory,Edinburgh EH93HJ,UK This paper reviews the measurements of galaxy correlations at high redshifts,and discusses how these may be understood in models of hierarchical gravita-tional collapse.The clustering of galaxies at redshift one is much weaker than at present,and this is consistent with the rate of growth of structure expected in an open universe.If Ω=1,this observation would imply that bias increases at high redshift,in conﬂict with observed M/L values for known high-z clusters.At redshift 3,the population of Lyman-limit galaxies displays clustering which is of similar amplitude to that seen today.This is most naturally understood if the Lyman-limit population is a set of rare recently-formed objects.Knowing both the clustering and the abundance of these objects,it is possible to deduce em-pirically the ﬂuctuation spectrum required on scales which cannot be measured today owing to gravitational nonlinearities.Of existing physical models for the ﬂuctuation spectrum,the results are most closely matched by a low-density spa-tially ﬂat universe.This conclusion is reinforced by an empirical analysis of CMB anisotropies,in which the present-day ﬂuctuation spectrum is forced to have the observed form.Open models are strongly disfavoured,leaving ΛCDM as the most successful simple model for structure formation.2J.A.Peacockcommon parameterization for the correlation function in comoving coordinates:ξ(r,z)=[r/r0]−γ(1+z)−(3−γ+ǫ),(1.2) whereǫ=0is stable clustering;ǫ=γ−3is constant comoving clustering;ǫ=γ−1isΩ=1linear-theory evolution.Although this equation is frequently encountered,it is probably not appli-cable to the real world,because most data inhabit the intermediate regime of 1<∼ξ<∼100.Peacock(1997)showed that the expected evolution in this quasilin-ear regime is signiﬁcantly more rapid:up toǫ≃3.(b)General aspects of biasOf course,there are good reasons to expect that the galaxy distribution will not follow that of the dark matter.The main empirical argument in this direction comes from the masses of rich clusters of galaxies.It has long been known that attempts to‘weigh’the universe by multiplying the overall luminosity density by cluster M/L ratios give apparent density parameters in the rangeΩ≃0.2to0.3 (e.g.Carlberg et al.1996).An alternative argument is to use the abundance of rich clusters of galaxies in order to infer the rms fractional density contrast in spheres of radius8h−1Mpc. This calculation has been carried out several diﬀerent ways,with general agree-ment on aﬁgure close to(1.3)σ8≃0.57Ω−0.56m(White,Efstathiou&Frenk1993;Eke,Cole&Frenk1996;Viana&Liddle1996). The observed apparent value ofσ8in,for example,APM galaxies(Maddox,Efs-tathiou&Sutherland1996)is about0.95(ignoring nonlinear corrections,which are small in practice,although this is not obvious in advance).This says that Ω=1needs substantial positive bias,but thatΩ<∼0.4needs anti bias.Although this cluster normalization argument depends on the assumption that the density ﬁeld obeys Gaussian statistics,the result is in reasonable agreement with what is inferred from cluster M/L ratios.What eﬀect does bias have on common statistical measures of clustering such as correlation functions?We could be perverse and assume that the mass and lightﬁelds are completely unrelated.If however we are prepared to make the more sensible assumption that the light density is a nonlinear but local function of the mass density,then there is a very nice result due to Coles(1993):the bias is a monotonic function of scale.Explicitly,if scale-dependent bias is deﬁned asb(r)≡[ξgalaxy(r)/ξmass(r)]1/2,(1.4) then b(r)varies monotonically with scale under rather general assumptions about the densityﬁeld.Furthermore,at large r,the bias will tend to a constant value which is the linear response of the galaxy-formation process.There is certainly empirical evidence that bias in the real universe does work this way.Consider Fig.1,taken from Peacock(1997).This compares dimen-sionless power spectra(∆2(k)=dσ2/d ln k)for IRAS and APM galaxies.The comparison is made in real space,so as to avoid distortions due to peculiar veloc-ities.For IRAS galaxies,the real-space power was obtained from the the projectedThe evolution of galaxy clustering and bias3Figure1.The real-space power spectra of optically-selected APM galaxies(solid circles)and IRAS galaxies(open circles),taken from Peacock(1997).IRAS galaxies show weaker clustering, consistent with their suppression in high-density regions relative to optical galaxies.The relative bias is a monotonic but slowly-varying function of scale.correlation function:Ξ(r)= ∞−∞ξ[(r2+x2)1/2]dx.(1.5)Saunders,Rowan-Robinson&Lawrence(1992)describe how this statistic can be converted to other measures of real-space correlation.For the APM galaxies, Baugh&Efstathiou(1993;1994)deprojected Limber’s equation for the angular correlation function w(θ)(discussed below).These diﬀerent methods yield rather similar power spectra,with a relative bias that is perhaps only about1.2on large scale,increasing to about1.5on small scales.The power-law portion for k>∼0.2h Mpc−1is the clear signature of nonlinear gravitational evolution,and the slow scale-dependence of bias gives encouragement that the galaxy correlations give a good measure of the shape of the underlying massﬂuctuation spectrum.2.Observations of high-redshift clustering(a)Clustering at redshift1At z=0,there is a degeneracy betweenΩand the true normalization of the spectrum.Since the evolution of clustering with redshift depends onΩ,studies at higher redshifts should be capable of breaking this degeneracy.This can be done without using a complete faint redshift survey,by using the angular clustering of aﬂux-limited survey.If the form of the redshift distribution is known,the projection eﬀects can be disentangled in order to estimate the3D clustering at the average redshift of the sample.For small angles,and where the redshift shell being studied is thicker than the scale of any clustering,the spatial and angular4J.A.Peacockcorrelation functions are related by Limber’s equation(e.g.Peebles1980): w(θ)= ∞0y4φ2(y)C(y)dy ∞−∞ξ([x2+y2θ2]1/2,z)dx,(2.1)where y is dimensionless comoving distance(transverse part of the FRW metric is[R(t)y dθ]2),and C(y)=[1−ky2]−1/2;the selection function for radius y is normalized so that y2φ(y)C(y)dy=1.Less well known,but simpler,is the Fourier analogue of this relation:π∆2θ(K)=The evolution of galaxy clustering and bias5 ever,the M/L argument is more powerful since only a single cluster is required, and a complete survey is not necessary.Two particularly good candidates at z≃0.8are described by Clowe et al.(1998);these are clusters where signiﬁcant weak gravitational-lensing distortions are seen,allowing a robust determination of the total cluster mass.The mean V-band M/L in these clusters is230Solar units,which is close to typical values in z=0clusters.However,the comoving V-band luminosity density of the universe is higher at early times than at present by about a factor(1+z)2.5(Lilly et al.1996),so this is equivalent to M/L≃1000, implying an apparent‘Ω’of close to unity.In summary,the known degree of bias today coupled with the moderate evolution in correlation function back to z=1 implies that,forΩ=1,the galaxy distribution at this time would have to consist very nearly of a‘painted-on’pattern that is not accompanied by signiﬁcant mass ﬂuctuations.Such a picture cannot be reconciled with the healthy M/L ratios that are observed in real clusters at these redshifts,and this seems to be a strong argument that we do not live in an Einstein-de Sitter universe.(b)Clustering of Lyman-limit galaxies at redshift3The most exciting recent development in observational studies of galaxy clus-tering is the detection by Steidel et al.(1997)of strong clustering in the popula-tion of Lyman-limit galaxies at z≃3.The evidence takes the form of a redshift histogram binned at∆z=0.04resolution over aﬁeld8.7′×17.6′in extent.For Ω=1and z=3,this probes the densityﬁeld using a cell with dimensionscell=15.4×7.6×15.0[h−1Mpc]3.(2.3) Conveniently,this has a volume equivalent to a sphere of radius7.5h−1Mpc,so it is easy to measure the bias directly by reference to the known value ofσ8.Since the degree of bias is large,redshift-space distortions from coherent infall are small; the cell is also large enough that the distortions of small-scale random velocities at the few hundred km s−1level are also ing the model of equation (11)of Peacock(1997)for the anisotropic redshift-space power spectrum and integrating over the exact anisotropic window function,the above simple volume argument is found to be accurate to a few per cent for reasonable power spectra:σcell≃b(z=3)σ7.5(z=3),(2.4) deﬁning the bias factor at this scale.The results of section1(see also Mo& White1996)suggest that the scale-dependence of bias should be weak.In order to estimateσcell,simulations of synthetic redshift histograms were made,using the method of Poisson-sampled lognormal realizations described by Broadhurst,Taylor&Peacock(1995):using aχ2statistic to quantify the nonuni-formity of the redshift histogram,it appears thatσcell≃0.9is required in order for theﬁeld of Steidel et al.(1997)to be typical.It is then straightforward to ob-tain the bias parameter since,for a present-day correlation functionξ(r)∝r−1.8,σ7.5(z=3)=σ8×[8/7.5]1.8/2×1/4≃0.146,(2.5) implyingb(z=3|Ω=1)≃0.9/0.146≃6.2.(2.6) Steidel et al.(1997)use a rather diﬀerent analysis which concentrates on the highest peak alone,and obtain a minimum bias of6,with a preferred value of8.6J.A.PeacockThey use the Eke et al.(1996)value ofσ8=0.52,which is on the low side of the published range of ingσ8=0.55would lower their preferred b to 7.6.Note that,with both these methods,it is much easier to rule out a low value of b than a high one;given a singleﬁeld,it is possible that a relatively‘quiet’region of space has been sampled,and that much larger spikes remain to be found elsewhere.A more detailed analysis of several furtherﬁelds by Adelberger et al. (1998)in fact yields a biasﬁgure very close to that given above,so theﬁrstﬁeld was apparently not unrepresentative.Having arrived at aﬁgure for bias ifΩ=1,it is easy to translate to other models,sinceσcell is observed,independent of cosmology.For lowΩmodels, the cell volume will increase by a factor[S2k(r)dr]/[S2k(r1)dr1];comparing with present-dayﬂuctuations on this larger scale will tend to increase the bias.How-ever,for lowΩ,two other eﬀects increase the predicted densityﬂuctuation at z=3:the cluster constraint increases the present-dayﬂuctuation by a factor Ω−0.56,and the growth between redshift3and the present will be less than a factor of4.Applying these corrections givesb(z=3|Ω=0.3)The evolution of galaxy clustering and bias7 87GB survey(Loan,Lahav&Wall1997),but these were of only bare signiﬁcance (although,in retrospect,the level of clustering in87GB is consistent with the FIRST measurement).Discussion of the87GB and FIRST results in terms of Limber’s equation has tended to focus on values ofǫin the region of0.Cress et al.(1996)concluded that the w(θ)results were consistent with the PN91 value of r0≃10h−1Mpc(although they were not very speciﬁc aboutǫ).Loan et al.(1997)measured w(1◦)≃0.005for a5-GHz limit of50mJy,and inferred r0≃12h−1Mpc forǫ=0,falling to r0≃9h−1Mpc forǫ=−1.The reason for this strong degeneracy between r0andǫis that r0parame-terizes the z=0clustering,whereas the observations refer to a typical redshift of around unity.This means that r0(z=1)can be inferred quite robustly to be about7.5h−1Mpc,without much dependence on the rate of evolution.Since the strength of clustering for optical galaxies at z=1is known to correspond to the much smaller number of r0≃2h−1Mpc(e.g.Le F`e vre et al.1996),we see that radio galaxies at this redshift have a relative bias parameter of close to 3.The explanation for this high degree of bias is probably similar to that which applies in the case of QSOs:in both cases we are dealing with AGN hosted by rare massive galaxies.3.Formation and bias of high-redshift galaxiesThe challenge now is to ask how these results can be understood in cur-rent models for cosmological structure formation.It is widely believed that the sequence of cosmological structure formation was hierarchical,originating in a density power spectrum with increasingﬂuctuations on small scales.The large-wavelength portion of this spectrum is accessible to observation today through studies of galaxy clustering in the linear and quasilinear regimes.However,non-linear evolution has eﬀectively erased any information on the initial spectrum for wavelengths below about1Mpc.The most sensitive way of measuring the spectrum on smaller scales is via the abundances of high-redshift objects;the amplitude ofﬂuctuations on scales of individual galaxies governs the redshift at which these objectsﬁrst undergo gravitational collapse.The small-scale am-plitude also inﬂuences clustering,since rare early-forming objects are strongly correlated,asﬁrst realized by Kaiser(1984).It is therefore possible to use obser-vations of the abundances and clustering of high-redshift galaxies to estimate the power spectrum on small scales,and the following section summarizes the results of this exercise,as given by Peacock et al.(1998).(a)Press-Schechter apparatusThe standard framework for interpreting the abundances of high-redshift objects in terms of structure-formation models,was outlined by Efstathiou& Rees(1988).The formalism of Press&Schechter(1974)gives a way of calculating the fraction F c of the mass in the universe which has collapsed into objects more massive than some limit M:F c(>M,z)=1−erf δc2σ(M) .(3.1)8J.A.PeacockHere,σ(M)is the rms fractional density contrast obtained byﬁltering the linear-theory densityﬁeld on the required scale.In practice,thisﬁltering is usually performed with a spherical‘top hat’ﬁlter of radius R,with a corresponding mass of4πρb R3/3,whereρb is the background density.The numberδc is the linear-theory critical overdensity,which for a‘top-hat’overdensity undergoing spherical collapse is1.686–virtually independent ofΩ.This form describes numerical simulations very well(see e.g.Ma&Bertschinger1994).The main assumption is that the densityﬁeld obeys Gaussian statistics,which is true in most inﬂationary models.Given some estimate of F c,the numberσ(R)can then be inferred.Note that for rare objects this is a pleasingly robust process:a large error in F c will give only a small error inσ(R),because the abundance is exponentially sensitive toσ.Total masses are of course ill-deﬁned,and a better quantity to use is the velocity dispersion.Virial equilibrium for a halo of mass M and proper radius r demands a circular orbital velocity ofV2c=GMΩ1/2m(1+z c)1/2f 1/6c.(3.3)Here,z c is the redshift of virialization;Ωm is the present value of the matter density parameter;f c is the density contrast at virialization of the newly-collapsed object relative to the background,which is adequately approximated byf c=178/Ω0.6m(z c),(3.4) with only a slight sensitivity to whetherΛis non-zero(Eke,Cole&Frenk1996).For isothermal-sphere haloes,the velocity dispersion isσv=V c/√The evolution of galaxy clustering and bias9 and the more recent estimate of0.025from Tytler et al.(1996),thenΩHIF c=2for the dark halo.A more recent measurement of the velocity width of the Hαemission line in one of these objects gives a dispersion of closer to100km s−1(Pettini,private communication),consistent with the median velocity width for Lyαof140km s−1 measured in similar galaxies in the HDF(Lowenthal et al.1997).Of course,these ﬁgures could underestimate the total velocity dispersion,since they are dominated by emission from the central regions only.For the present,the range of values σv=100to320km s−1will be adopted,and the sensitivity to the assumed velocity will be indicated.In practice,this uncertainty in the velocity does not produce an important uncertainty in the conclusions.(3)Red radio galaxies An especially interesting set of objects are the reddest optical identiﬁcations of1-mJy radio galaxies,for which deep absorption-line spectroscopy has proved that the red colours result from a well-evolved stellar population,with a minimum stellar age of3.5Gyr for53W091at z=1.55(Dun-10J.A.Peacocklop et al.1996;Spinrad et al.1997),and4.0Gyr for53W069at z=1.43(Dunlop 1998;Dey et al.1998).Such ages push the formation era for these galaxies back to extremely high redshifts,and it is of interest to ask what level of small-scale power is needed in order to allow this early formation.Two extremely red galaxies were found at z=1.43and1.55,over an area 1.68×10−3sr,so a minimal comoving density is from one galaxy in this redshift range:N(Ω=1)>∼10−5.87(h−1Mpc)−3.(3.9) Thisﬁgure is comparable to the density of the richest Abell clusters,and is thus in reasonable agreement with the discovery that rich high-redshift clusters appear to contain radio-quiet examples of similarly red galaxies(Dickinson1995).Since the velocity dispersions of these galaxies are not observed,they must be inferred indirectly.This is possible because of the known present-day Faber-Jackson relation for ellipticals.For53W091,the large-aperture absolute magni-tude isM V(z=1.55|Ω=1)≃−21.62−5log10h(3.10) (measured direct in the rest frame).According to Solar-metallicity spectral syn-thesis models,this would be expected to fade by about0.9mag.between z=1.55 and the present,for anΩ=1model of present age14Gyr(note that Bender et al.1996have observed a shift in the zero-point of the M−σv relation out to z=0.37of a consistent size).If we compare these numbers with theσv–M V relation for Coma(m−M=34.3for h=1)taken from Dressler(1984),this predicts velocity dispersions in the rangeσv=222to292km s−1.(3.11) This is a very reasonable range for a giant elliptical,and it adopted in the following analysis.Having established an abundance and an equivalent circular velocity for these galaxies,the treatment of them will diﬀer in one critical way from the Lyman-αand Lyman-limit galaxies.For these,the normal Press-Schechter approach as-sumes the systems under study to be newly born.For the Lyman-αand Lyman-limit galaxies,this may not be a bad approximation,since they are evolving rapidly and/or display high levels of star-formation activity.For the radio galax-ies,conversely,their inactivity suggests that they may have existed as discrete systems at redshifts much higher than z≃1.5.The strategy will therefore be to apply the Press-Schechter machinery at some unknown formation redshift,and see what range of redshift gives a consistent degree of inhomogeneity.4.The small-scaleﬂuctuation spectrum(a)The empirical spectrumFig.2shows theσ(R)data which result from the Press-Schechter analysis, for three cosmologies.Theσ(R)numbers measured at various high redshifts have been translated to z=0using the appropriate linear growth law for density perturbations.The open symbols give the results for the Lyman-limit(largest R)and Lyman-α(smallest R)systems.The approximately horizontal error bars showThe evolution of galaxy clustering and bias11Figure2.Theradius R.Thecircles)Theredshifts2,4,...The horizontal errors correspond to diﬀerent choices for the circular velocities of the dark-matter haloes that host the galaxies.The shaded region at large R gives the results inferred from galaxy clustering.The lines show CDM and MDM predictions,with a large-scale normalization ofσ8=0.55forΩ=1orσ8=1for the low-density models.the eﬀect of the quoted range of velocity dispersions for aﬁxed abundance;the vertical errors show the eﬀect of changing the abundance by a factor2atﬁxed velocity dispersion.The locus implied by the red radio galaxies sits in between. The diﬀerent points show the eﬀects of varying collapse redshift:z c=2,4,...,12 [lowest redshift gives lowestσ(R)].Clearly,collapse redshifts of6–8are favoured12J.A.Peacockfor consistency with the other data on high-redshift galaxies,independent of the-oretical preconceptions and independent of the age of these galaxies.This level of power(σ[R]≃2for R≃1h−1Mpc)is also in very close agreement with the level of power required to produce the observed structure in the Lyman alpha forest(Croft et al.1998),so there is a good case to be made that theﬂuctu-ation spectrum has now been measured in a consistent fashion down to below R≃1h−1Mpc.The shaded region at larger R shows the results deduced from clustering data (Peacock1997).It is clear anΩ=1universe requires the power spectrum at small scales to be higher than would be expected on the basis of an extrapolation from the large-scale spectrum.Depending on assumptions about the scale-dependence of bias,such a‘feature’in the linear spectrum may also be required in order to satisfy the small-scale present-day nonlinear galaxy clustering(Peacock1997). Conversely,for low-density models,the empirical small-scale spectrum appears to match reasonably smoothly onto the large-scale data.Fig.2also compares the empirical data with various physical power spectra.A CDM model(using the transfer function of Bardeen et al.1986)with shape parameterΓ=Ωh=0.25is shown as a reference for all models.This appears to have approximately the correct shape,although it overpredicts the level of small-scale power somewhat in the low-density cases.A better empirical shape is given by MDM withΩh≃0.4andΩν≃0.3.However,this model only makes physical sense in a universe with highΩ,and so it is only shown as the lowest curve in Fig.2c,reproduced from theﬁtting formula of Pogosyan&Starobinsky(1995; see also Ma1996).This curve fails to supply the required small-scale power,by about a factor3inσ;loweringΩνto0.2still leaves a very large discrepancy. This conclusion is in agreement with e.g.Mo&Miralda-Escud´e(1994),Ma& Bertschinger(1994),Ma et al.(1997)and Gardner et al.(1997).All the models in Fig.2assume n=1;in fact,consistency with the COBE results for this choice ofσ8andΩh requires a signiﬁcant tilt forﬂat low-density CDM models,n≃0.9(whereas open CDM models require n substantially above unity).Over the range of scales probed by LSS,changes in n are largely degenerate with changes inΩh,but the small-scale power is more sensitive to tilt than to Ωh.Tilting theΩ=1models is not attractive,since it increases the tendency for model predictions to lie below the data.However,a tilted low-Ωﬂat CDM model would agree moderately well with the data on all scales,with the exception of the ‘bump’around R≃30h−1Mpc.Testing the reality of this feature will therefore be an important task for future generations of redshift survey.(b)Collapse redshifts and ages for red radio galaxiesAre the collapse redshifts inferred above consistent with the age data on the red radio galaxies?First bear in mind that in a hierarchy some of the stars in a galaxy will inevitably form in sub-units before the epoch of collapse.At the time ofﬁnal collapse,the typical stellar age will be some fractionαof the age of the universe at that time:age=t(z obs)−t(z c)+αt(z c).(4.1) We can rule outα=1(i.e.all stars forming in small subunits just after the big bang).For present-day ellipticals,the tight colour-magnitude relation only allows an approximate doubling of the mass through mergers since the termination ofThe evolution of galaxy clustering and bias13Figure3.The age of a galaxy at z=1.5,as a function of its collapse redshift(assuming an instantaneous burst of star formation).The various lines showΩ=1[solid];openΩ=0.3 [dotted];ﬂatΩ=0.3[dashed].In all cases,the present age of the universe is forced to be14 Gyr.star formation(Bower at al.1992).This corresponds toα≃0.3(Peacock1991).A non-zeroαjust corresponds to scaling the collapse redshift asapparent(1+z c)∝(1−α)−2/3,(4.2) since t∝(1+z)−3/2at high redshifts for all cosmologies.For example,a galaxy which collapsed at z=6would have an apparent age corresponding to a collapse redshift of7.9forα=0.3.Converting the ages for the galaxies to an apparent collapse redshift depends on the cosmological model,but particularly on H0.Some of this uncertainty may be circumvented byﬁxing the age of the universe.After all,it is of no interest to ask about formation redshifts in a model with e.g.Ω=1,h=0.7when the whole universe then has an age of only9.5Gyr.IfΩ=1is to be tenable then either h<0.5against all the evidence or there must be an error in the stellar evolution timescale.If the stellar timescales are wrong by aﬁxed factor,then these two possibilities are degenerate.It therefore makes sense to measure galaxy ages only in units of the age of the universe–or,equivalently,to choose freely an apparent Hubble constant which gives the universe an age comparable to that inferred for globular clusters.In this spirit,Fig.3gives apparent ages as a function of eﬀective collapse redshift for models in which the age of the universe is forced to be14 Gyr(e.g.Jimenez et al.1996).This plot shows that the ages of the red radio galaxies are not permitted very much freedom.Formation redshifts in the range6to8predict an age of close to 3.0Gyr forΩ=1,or3.7Gyr for low-density models,irrespective of whetherΛis nonzero.The age-z c relation is ratherﬂat,and this gives a robust estimate of age once we have some idea of z c through the abundance arguments.It is therefore14J.A.Peacockrather satisfying that the ages inferred from matching the rest-frame UV spectra of these galaxies are close to the aboveﬁgures.(c)The global picture of galaxy formationIt is interesting to note that it has been possible to construct a consistent picture which incorporates both the large numbers of star-forming galaxies at z<∼3and the existence of old systems which must have formed at very much larger redshifts.A recent conclusion from the numbers of Lyman-limit galaxies and the star-formation rates seen at z≃1has been that the global history of star formation peaked at z≃2(Madau et al.1996).This leaves open two possibilities for the very old systems:either they are the rare precursors of this process,and form unusually early,or they are a relic of a second peak in activity at higher redshift,such as is commonly invoked for the origin of all spheroidal components. While such a bimodal history of star formation cannot be rejected,the rareness of the red radio galaxies indicates that there is no diﬃculty with the former picture. This can be demonstrated quantitatively by integrating the total amount of star formation at high redshift.According to Madau et al.,The star-formation rate at z=4is˙ρ∗≃107.3h M⊙Gyr−1Mpc−3,(4.3) declining roughly as(1+z)−4.This is probably a underestimate by a factor of at least3,as indicated by suggestions of dust in the Lyman-limit galaxies(Pettini et al.1997),and by the prediction of Pei&Fall(1995),based on high-z element abundances.If we scale by a factor3,and integrate toﬁnd the total density in stars produced at z>6,this yieldsρ∗(z f>6)≃106.2M⊙Mpc−3.(4.4) Since the red mJy galaxies have a density of10−5.87h3Mpc−3and stellar masses of order1011M⊙,there is clearly no conﬂict with the idea that these galaxies are theﬁrst stellar systems of L∗size which form en route to the general era of star and galaxy formation.(d)Predictions for biased clustering at high redshiftsAn interesting aspect of these results is that the level of power on1-Mpc scales is only moderate:σ(1h−1Mpc)≃2.At z≃3,the correspondingﬁgure would have been much lower,making systems like the Lyman-limit galaxies rather rare.For Gaussianﬂuctuations,as assumed in the Press-Schechter analysis,such systems will be expected to display spatial correlations which are strongly biased with respect to the underlying mass.The linear bias parameter depends on the rareness of theﬂuctuation and the rms of the underlyingﬁeld asb=1+ν2−1δc(4.5)(Kaiser1984;Cole&Kaiser1989;Mo&White1996),whereν=δc/σ,andσ2is the fractional mass variance at the redshift of interest.In this analysis,δc=1.686is assumed.Variations in this number of order10 per cent have been suggested by authors who have studied theﬁt of the Press-Schechter model to numerical data.These changes would merely scale b−1by a small amount;the key parameter isν,which is set entirely by the collapsed。

ClussCluster包用户说明说明书

Package‘ClussCluster’October12,2022Type PackageTitle Simultaneous Detection of Clusters and Cluster-Speciﬁc Genes inHigh-Throughput Transcriptome DataVersion0.1.0Description Implements a new method'ClussCluster'descried in Ge Jiang and Jun Li,``Simultane-ous Detection of Clusters and Cluster-Speciﬁc Genes in High-throughput Transcrip-tome Data''(Unpublished).Simultaneously perform clustering analysis and signature gene selection on high-dimensional transcriptome data sets.To do so,'ClussCluster'incorporates a Lasso-type regularization penalty term to the objective function of K-means so that cell-type-speciﬁc signature genes can be identiﬁed while clustering the cells.Depends R(>=2.10.0)Suggests knitr,rmarkdown(>=1.13)VignetteBuilder knitrImports stats(>=3.5.0),utils(>=3.5.0),VennDiagram,scales(>=1.0.0),reshape2(>=1.4.3),ggplot2(>=3.1.0),rlang(>=0.3.4)License GPL-3Encoding UTF-8LazyData trueRoxygenNote6.1.1NeedsCompilation noAuthor Li Jun[cre],Jiang Ge[aut],Wang Chuanqi[ctb]Maintainer Li Jun<*************>Repository CRANDate/Publication2019-07-0216:30:16UTC12ClussCluster R topics documented:ClussCluster (2)ﬁlter_gene (3)Hou_sim (4)plot_ClussCluster (5)plot_ClussCluster_Gap (6)print_ClussCluster (7)print_ClussCluster_Gap (7)sim_dat (8)Index9 ClussCluster Performs simultaneous detection of cell types and cell-type-speciﬁcsignature genesDescriptionClussCluster takes the single-cell transcriptome data and returns an object containing cell types and type-speciﬁc signature gene setsSelects the tuning parameter in a permutation approach.The tuning parameter controls the L1 bound on w,the feature weights.UsageClussCluster(x,nclust=NULL,centers=NULL,ws=NULL,nepoch.max=10,theta=NULL,seed=1,nstart=20,iter.max=50,verbose=FALSE)ClussCluster_Gap(x,nclust=NULL,B=20,centers=NULL,ws=NULL,nepoch.max=10,theta=NULL,seed=1,nstart=20,iter.max=50,verbose=FALSE)Argumentsx An nxp data matrix.There are n cells and p genes.nclust Number of clusters desired if the cluster centers are not provided.If both are provided,nclust must equal the number of cluster centers.centers A set of initial(distinct)cluster centres if the number of clusters(nclust)is null.If both are provided,the number of cluster centres must equal nclust.ws One or multiple candidate tuning parameters to be evaluated and compared.De-termines the sparsity of the selected genes.Should be greater than1.nepoch.max The maximum number of epochs.In one epoch,each cell will be evaluated to determine if its label needs to be updated.ﬁlter_gene3 theta Optional argument.If provided,theta are used as the initial cluster labels of the ClussCluster algorithm;if not,K-means is performed to produce starting clusterlabels.seed This seed is used wherever K-means is used.nstart Argument passed to kmeans.It is the number of random sets used in kmeans.iter.max Argument passed to kmeans.The maximum number of iterations allowed.verbose Print the updates inside every epoch?If TRUE,the updates of cluster label and the value of objective function will be printed out.B Number of permutation samples.DetailsTakes the normalized and log transformed number of reads mapped to genes(e.g.,log(RPKM+1) or log(TPM+1)where RPKM stands for Reads Per Kilobase of transcript per Million mapped reads and TPM stands for transcripts per million)but NOT centered.Valuea list containing the optimal tuning parameter,s,group labels of clustering,theta,and type-speciﬁcweights of genes,w.a list containig a vector of candidate tuning parameters,ws,the corresponding values of objectivefunction,O,a matrix of values of objective function for each permuted data and tuning param-eter,O_b,gap statistics and their one standard deviations,Gap and sd.Gap,the result given by ClussCluster,run,the tuning parameters with the largest Gap statistic and within one standard deviation of the largest Gap statistic,bestw and onesd.bestwExamplesdata(Hou_sim)hou.dat<-Hou_sim$xrun.ft<-filter_gene(hou.dat)hou.test<-ClussCluster(run.ft$dat.ft,nclust=3,ws=4,verbose=FALSE)filter_gene Gene FilterDescriptionFilters out genes that are not suitable for differential expression analysis.Usagefilter_gene(dfname,minmean=2,n0prop=0.2,minsd=1)4Hou_simArgumentsdfname name of the expression data frameminmean minimum mean expression for each genen0prop minimum proportion of zero expression(count)for each geneminsd minimum standard deviation of expression for each geneDetailsTakes an expression data frame that has been properly normalized but NOT centered.It returns a list with the slot dat.ft being the data set that satisﬁes the pre-set thresholds on minumum mean, standard deviation(sd),and proportion of zeros(n0prop)for each gene.If the data has already been centered,one can still apply theﬁlters of mean and sd but not n0prop. Valuea list containing the data set with genes satisfying the thresholds,dat.ft,the name of dat.ft,andthe indices of those kept genes,index.Examplesdat<-matrix(rnbinom(300*60,mu=2,size=1),300,60)dat_filtered<-filter_gene(dat,minmean=2,n0prop=0.2,minsd=1)Hou_sim A truncated subset of the scRNA-seq expression data set from Hou et.al(2016)DescriptionThis data contains expression levels(normalized and log-transformed)for33cells and100genes. Usagedata(Hou_sim)FormatAn object containing the following variables:x An expression data frame of33HCC cells on100genes.y Numerical group indicator of all cells.gnames Gene names of all genes.snames Cell names of all cells.groups Cell group names.note A simple note of the data set.DetailsThis data contains raw expression levels(log-transformed but not centered)for33HCC cells and 100genes.The33cells belongs to three different subpopulations and exhibited different biological characteristics.For descriptions of how we generated this data,please refer to the paper.Sourcehttps:///geo/query/acc.cgi?acc=GSE65364ReferencesHou,Yu,et al."Single-cell triple omics sequencing reveals genetic,epigenetic,and transcriptomic heterogeneity in hepatocellular carcinomas."Cell research26.3(2016):304-319.Examplesdata(Hou_sim)data<-Hou_sim$xplot_ClussCluster Plots the results of ClussClusterDescriptionPlots the number of signature genes against the tuning parameters if multiple tuning parameters are evaluated in the object.If only one is included,then plot_ClussCluster returns a venn diagram and a heatmap at this particular tuning parameter.Usageplot_ClussCluster(object,m=10,snames=NULL,gnames=NULL,...)top.m.hm(object,m,snames=NULL,gnames=NULL,...)Argumentsobject An object that is obtained by applying the ClussCluster function to the data set.m The number of top signature genes selected to produce the heatmap.snames The names of the cells.gnames The names of the genes...Addtional parameters,sent to the methodDetailsTakes the normalized and log transformed number of reads mapped to genes(e.g.,log(RPKM+1) or log(TPM+1)where RPKM stands for Reads Per Kilobase of transcript per Million mapped reads and TPM stands for transcripts per million)but NOT centered.If multiple tuning parameters are evaluated in the object,the number of signature genes is computed for each cluster and is plotted against the tuning parameters.Each color and line type corresponds to a cell type.If only one tuning parameter is evaluated,two plots will be produced.One is the venn diagram of the cell-type-speciﬁc genes,the other is the heatmap of the data with the cells and top m signature genes.See more details in the paper.Valuea ggplot2object of the heatmap with top signature genes selected by ClussClusterExamplesdata(Hou_sim)<-ClussCluster(Hou_sim$x,nclust=3,ws=c(2.4,5,8.8))plot_ClussCluster(,m=5,snames=Hou$snames,gnames=Hou$gnames)plot_ClussCluster_Gap Plots the results of ClussCluster_GapDescriptionPlots the gap statistics and number of genes selected as the tuning parameter varies.Usageplot_ClussCluster_Gap(object)Argumentsobject object obtained from ClussCluster_Gap()print_ClussCluster7 print_ClussCluster Prints out the results of ClussClusterDescriptionPrints out the results of ClussClusterUsageprint_ClussCluster(object)Argumentsobject An object that is obtained by applying the ClussCluster function to the data set.print_ClussCluster_GapPrints out the results of ClussCluster_Gap Prints the gap statisticsand number of genes selected for each candidate tuning parameter.DescriptionPrints out the results of ClussCluster_Gap Prints the gap statistics and number of genes selected for each candidate tuning parameter.Usageprint_ClussCluster_Gap(object)Argumentsobject An object that is obtained by applying the ClussCluster_Gap function to the data set.8sim_dat sim_dat A simulated expression data set.DescriptionAn example data set containing expressing levels for60cells and200genes.The60cells belong to4cell types with15cells each.Each cell type is uniquely associated with30signature genes,i.e.,theﬁrst cell type is associated with theﬁrst30genes,the second cell type is associated withthe next30genes,so on and so forth.The remaining80genes show indistinct expression patterns among the four cell types and are considered as noise genes.Usagedata(sim_dat)FormatA data frame with60cells on200genes.ValueA simulated dataset used to demonstrate the application of ClussCluster.Examplesdata(sim_dat)head(sim_dat)Index∗datasetsHou_sim,4sim_dat,8ClussCluster,2ClussCluster_Gap(ClussCluster),2filter_gene,3Hou_sim,4plot_ClussCluster,5plot_ClussCluster_Gap,6print_ClussCluster,7print_ClussCluster_Gap,7sim_dat,8top.m.hm(plot_ClussCluster),59。