Mass accretion rate of the galactic black hole A0620-00 in its quiescent state

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orbitrap exploris

orbitrap exploris（中英文实用版）英文文档：The Orbitrap Exploris is a powerful mass spectrometer designed for high-resolution, high-accuracy mass analysis.It utilizes a unique trap-based technology that allows for the separation and detection of ions based on their mass-to-charge ratio (m/z).This instrument is widely used in various fields such as proteomics, metabolomics, environmental analysis, and pharmaceutical research.The Orbitrap Exploris offers several advantages over other mass spectrometry techniques.Firstly, it provides excellent resolution, which enables the identification of complex peaks and the separation of closely related ions.This is particularly useful for the analysis of complex samples, where the presence of numerous interfering peaks can complicate the interpretation of the data.Secondly, the Orbitrap Exploris offers high accuracy in mass measurement, which is crucial for the accurate determination of the molecular weights and structures of unknown compounds.This feature makes it an ideal choice for protein and peptide analysis, as well as for the characterization of small molecules and metabolites.Furthermore, the Orbitrap Exploris is capable of high-throughput analysis, allowing for the rapid screening and characterization of largenumbers of samples.This is particularly beneficial for high-throughput screening applications in the pharmaceutical industry, as well as for large-scale proteomics and metabolomics studies.In summary, the Orbitrap Exploris is a state-of-the-art mass spectrometer that offers high-resolution, high-accuracy mass analysis, making it an invaluable tool for researchers in various fields.中文文档：Orbitrap Exploris 是一款强大的质谱仪，设计用于高分辨率、高准确度的质量分析。

The Mass Discrepancy-Acceleration Relation Disk Mass and the Dark Matter Distribution

a r X i v :a s t r o -p h /0403610v 4 29 S e p 2004The Mass Discrepancy-Acceleration Relation:Disk Mass and the Dark Matter DistributionStacy S.McGaughDepartment of Astronomy,University of MarylandCollege Park,MD 20742-2421ssm@ ABSTRACT The mass discrepancy in disk galaxies is shown to be well correlated with acceleration,increasing systematically with decreasing acceleration below a crit-ical scale a 0≈3700km 2s −2kpc −1=1.2×10−10m s −2.For each galaxy,there is an optimal choice of stellar mass-to-light ratio which minimizes the scatter in this mass discrepancy-acceleration relation.The same mass-to-light ratios also minimize the scatter in the baryonic Tully-Fisher relation and are in excellent agreement with the expectations of stellar population synthesis.Once the disk mass is determined in this fashion,the dark matter distribution is speciﬁed.The circular velocity attributable to the dark matter can be expressed as a simple equation which depends only on the observed distribution of baryonic mass.It is a challenge to understand how this very ﬁne-tuned coupling between mass and light comes about.Subject headings:cosmology:observations —dark matter —galaxies:kinemat-ics and dynamics —galaxies:spiral1.IntroductionThe masses of stellar disks and the distribution of mass in dark matter halos pose a coupled problem.Rotation curves provide good measures of the mass enclosed by disks.But it has been diﬃcult to disentangle how much of this mass is in the stellar disk,and how much is in the dark matter halo.Consequently,both the mass of the stellar disk and the distribution of the dark matter,ρ(r ),have been unclear.There have long been suggestions of a close connection between mass and light in spi-ral galaxies.Perhaps the most obvious is the Tully-Fisher relation (Tully &Fisher 1977).Beyond this global scaling relation,there are indications of a local coupling between mass and light(e.g.,Rubin et al.1985;Bahcall&Casertano1985;Persic&Salucci1991).One manifestation of this is in the eﬃcacy of maximum disk(e.g.,van Albada&Sancisi1986) in describing the inner parts of rotation curves.If one scales up the stellar contribution to the rotation curves of high surface brightness(HSB)spirals to the maximum allowed by the data,one oftenﬁnds a good match in the details(the“bumps and wiggles”)between the shape of the rotation curve and that predicted by the observed stellar mass(e.g.,Kalnajs 1983;Sellwood1999;Palunas&Williams2000).This only works out to some radius where dark matter must be invoked,but does suggest that the preponderance of the mass at small radii is stellar.Beyond that,it is often possible to scale up the gas component to explain the remainder of the rotation curve(Hoekstra,van Albada,&Sancisi2001).Moreover, while some dark matter may be needed to stabilize disks,detailed analyses of disk stability frequently require rather heavy disks in order to drive the observed bars and spiral fea-tures(e.g.,Athanassoula,Bosma,&Papaioannou1987;Debattista&Sellwood1998,2000; Weiner,Sellwood,&Williams2001;Fuchs2003a;Bissantz,Englmaier,&Gerhard2003; Kranz,Slyz,&Rix2003).While these lines of evidence favor nearly maximal disks in HSB spirals,there are con-tradictory indications as well.The most signiﬁcant of these is the lack of surface brightness (or scale length)residuals in the Tully-Fisher relation(Sprayberry et al.1995;Zwaan et al. 1995;Hoﬀman et al.1996;Tully&Verheijen1997).The apparent lack of inﬂuence of the distribution of disk mass on the Tully-Fisher relation suggests that disks are submaximal (McGaugh&de Blok1998a;Courteau&Rix1999).However,galaxies which occupy the same location in the Tully-Fisher plane can have very diﬀerent rotation curve shapes(de Blok&McGaugh1996;Tully&Verheijen1997).This excludes the simple hypothesis that galaxies of equal luminosity reside in identical halos with no signiﬁcant inﬂuence from the disk.Recent data for low surface brightness(LSB)disks complicate matters further.These objects show large mass discrepancies down to small radii,implying that they are dark matter dominated with very submaximal disks(de Blok&McGaugh1997).However,it is often formally possible to obtain aﬁt with something like a traditional maximum disk(where the peak velocity of the disk component is comparable to V flat),albeit at the cost of absurdly high(>10M⊙/L⊙)mass-to-light ratios(de Blok&McGaugh1997;Swaters,Madore,& Trewhella2000;McGaugh,Rubin,&de Blok2001).As anticipated by McGaugh&de Blok(1998b),density wave analyses imply nearly maximal disks for LSB galaxies(Fuchs 2002,2003b).These high mass-to-light ratios are unlikely for stellar populations,so one might consider a disk component of dark matter in addition to the usual halo.This seems contrived,and also causes problems with the baryonic Tully-Fisher relation(McGaugh etal.2000;Bell&de Jong2001).This relation between mass and rotation velocity works best,in the sense of having minimal scatter,for disk masses which are consistent with stellar population mass-to-light ratios(§3).Maximal disks in LSB galaxies increase the scatter in the baryonic Tully-Fisher relation.Among these apparently contradictory lines of evidence,there is nevertheless a clear theme.The luminous and dark components are intimately linked.This is true not only in a global sense,but also in a local one.This might be paraphrased as Renzo’s Rule:“For any feature in the luminosity proﬁle there is a corresponding feature in the rotation curve”(Sancisi2003).The distribution of baryonic mass is completely predictive of the distribution of dark matter,even in dark matter dominated LSB galaxies.Renzo’s rule is an empirical statement which is mathematically encapsulated by MOND (Milgrom1983).MOND is a modiﬁed force law hypothesized as an alternative to dark matter,and remains a viable possibility(Sanders&McGaugh2002).Even if dark matter is correct(as is widely presumed),MOND is still useful as a compact description of the mass discrepancy in spirals(Sanders&Begeman1994).In this paper,I show that the stellar mass-to-light ratios determined from MONDﬁts to rotation curves are optimal in a purely Newtonian sense.I derive a simple expression for the corresponding dark matter distribution,and generalize this to apply for any choice of stellar mass-to-light ratio.This expression provides a simple yet stringent test for dark matter theories which seek to explain rotation curves.2.The DataThe data used here are from the sample of disk galaxies collected by Sanders&McGaugh (2002)where a complete Table of galaxy properties can be found.This represents the accumulated work of a good many(and many good)people,including Begeman(1987), Begeman,Broeils,&Sanders(1991),Broeils(1992),Sanders(1996),de Blok,McGaugh, &van der Hulst(1996),de Blok(1997),Verheijen(1997),Sanders&Verheijen(1998), McGaugh&de Blok(1998a,b),de Blok&McGaugh(1998),Verheijen(2001),and Verheijen &Sancisi(2001).This is a wonderful compilation of information for investigating the details of mass distributions in spiral galaxies.The data for each galaxy includes the rotation curve and the distribution of the observed mass components.These include the stellar disk and bulge(if present),and the H i gas component.Rotation curves have been derived from velocityﬁelds of nearby galaxies.The distribution of stellar mass has been derived from a variety of passbands(see Sanders&McGaugh2002and references therein).Much of the sample has K′-band photometry(Tullyet al.1996)which provides the closest mapping between light and stellar mass.Other bands(usually R or B)go deeper,and provide consistent results,albeit with a larger scatter in theinferred mass-to-light ratio.The H i data are the most time consuming to obtain,and arethe limiting factor on the size of the sample.The H i distribution is nevertheless an essentialingredient,as the atomic gas often dominates the baryonic mass surface density at largeradii.Two examples of the data are shown in Fig.1.The rotation attributable to stars andgas is shown for both galaxies,as is the total rotation due to baryons:V2b=V2⋆+V2g.(1) These components of the velocity are derived from the observed distribution of surface bright-ness I(r)through numerical inversion of the Poisson equation:∇2Φb=4πGρb.(2) For disks,ρb=Σ(r)δ(z)whereΣ(r)is the azimuthally averaged radial surface mass dis-tribution andδ(z)is the mass distribution perpendicular to the disk.The vertical massdistribution makes little diﬀerence to the mass models unless the disk is very thick(axisratios<5:1;e.g.,de Blok et al.2003);thin disks are assumed here.A more important factoris the mass-to-light ratioΥ⋆which relates the stellar mass distribution to the observed lightdistribution[Σ(r)=Υ⋆I(r)].The mass-to-light ratio is assumed to be constant with radius1so that the observed distribution of light I(r)speciﬁes the quantity v⋆:V2⋆(r)=Υ⋆v2⋆(r).(Note that v⋆has units km s−1M−1/2⊙L1/2⊙.)The velocity due to the atomic gas component is more directly related to the observed21cmﬂux,with the correction M g=4/3M HI forhelium and metals.Molecular and ionized gas are assumed to make a negligible contributionto the baryonic mass budget.This is almost certainly fair for ionized gas,and in most casesfor molecular gas(e.g.,Olling1996).Molecular gas closely follows the distribution of starlight(Regan et al.2001),so it is subsumed2into the stellar mass-to-light ratio.The centripetal acceleration predicted by Newtonian gravity for the observed baryonicmass components isg N=V2b∂r.(3)This is related to the observed centripetal acceleration produced by all mass componentsa=V2∂r(4)by MOND throughµ(x)a=g N,(5) where x=a/a0and a0is a constant.The value of a0is taken to be the same in all cases, a0=1.2×10m s−2(Begeman et al.1991).The interpolation functionµ(x)commonly usedin rotation curveﬁtting isµ(x)=x1+x2(6)(Milgrom1983;Sanders&McGaugh2002).This is eﬀectively just a scaling of the velocity due to the baryonic component.There is a simple formula for mapping V b(r)to the total velocity V(r)(Fig.1).This procedure has only a singleﬁtting parameter,the stellar mass-to-light ratioΥ⋆.The physical origin of this scaling aside,the simple fact that it works provides a very useful constraint on the problem.The MOND procedure has been successfully applied to∼100galaxies.Two dozen of these cases have yet to be published(Swaters&Sanders2004,in preparation),leaving a useful sample of74galaxies(Sanders&McGaugh2002).This is a very large sample for data of this quality and extent.Though not a complete sample in terms of a survey,this is not important to the purpose here.What is important is coverage of the parameter space over which disk galaxies exist. The sample galaxies cover a large range in rotation velocity(V flat=50to300km s−1), luminosity(L B=5×107to2×1011L⊙),scale length(h=0.5to13kpc),central surface brightness(µB0=19.6to24.2mag.arcsec−2),and gas mass fraction(f g=M g/(M⋆+M g)= 0.07to0.95).This range covers most of the parameter space over which disk galaxies are known to reside.The eﬃcacy of MOND inﬁtting rotation curves is well established(Sanders&McGaugh 2002).The quality of theseﬁts is illustrated by Figs.2and3,which show the global rms and local velocity residuals of the MONDﬁts.The rms residuals are small,<10%in most cases (Fig.2a).Of course,some data are more accurate than others,so it is interesting to ask how MOND performs as the data improve.To this end,we restrict the sample to include only those points within each galaxy for which the formal uncertainty on the velocity is better than5%.In crude terms,this is roughly the level at which various astrophysical eﬀects limitone’s knowledge of the true circular velocity(see discussions in McGaugh et al.2001and de Blok et al.2001).This restriction removes the low accuracy points from the rotation curves of individual galaxies,and in14galaxies no data remain.The rms residuals improve after the less accurate data are rejected(Fig.2b):the best data areﬁt best by MOND.In the analysis,it is assumed that the orbits being traced are circular.This assumption must fail at some level,causing a deviation of the observed rotation curve from the circular velocity curve of the potential.This eﬀect will usually be most severe at small radii where the gradient in the rotation curve is large,and where the velocity dispersion may contribute signiﬁcantly to the total kinematic budget,especially in systems with large bulges.The assumption of circular motion will cause the MOND-predicted velocities to exceed the ob-served ones by a modest amount.This is precisely what is seen in Fig.3(a),where there is a“beard”of points at small radii with∆V=V−V MOND<0.This eﬀect is consistent with the modest amount of non-circular motion one would naturally expect for this sample.3 Two galaxies listed by Sanders&McGaugh(2002)are not included here:NGC3198 and NGC2841.These galaxies have MONDﬁts which are sensitive to the distance measure-ment,as discussed in detail by Bottema et al.(2002).It is not surprising that this should occasionally be an issue since it is acceleration which matters in MONDﬁts.Since a=V2/r, the acceleration can be uncertain(through r=θD)even if V is well measured.NGC3198 and NGC2841either fall right on target in Fig.2,and adhere to the same Tully-Fisher and mass discrepancy-acceleration relations as the other74galaxies,or they are extreme outliers from these relations,depending on their true distances(and other uncertainties,like the angle of the warp in NGC2841).If these objects can not be reconciled with MOND,then they constitute a falsiﬁcation of the theory.Such a situation would not,however,alter any of the conclusions drawn here in the context of dark matter.From this perspective,they would merely be rare cases which deviate from the norm.3.The Empirical Coupling between Mass and Light3.1.The Acceleration ScaleFrom a purely Newtonian perspective,the mass discrepancy in disk galaxies sets in at a particular acceleration scale.Whether this is also true in other systems,especially richclusters of galaxies,is less clear(Aguirre,Schaye,&Quataert2001;Sanders2003),so the discussion here is restricted to rotationally supported disk galaxies.In disks,it is very clear that acceleration is the relevant physical scale(Fig.4).The ordinate of Fig.4plots the amplitude of the mass discrepancy D,as quantiﬁed by the ratio of the gradient of the total gravitational potential to that of the baryons:D≡Φ′V2b =V2a lightweight IMF has its normalization reduced by a factor of two.This is chosen to represent the lower end of the realm of plausibility(Kroupa2002);reality is presumably bracketed between this and maximum disk.Mass-to-light ratios estimated in this fashion will not be perfect of course,but this does provide a useful estimate for what we expect for stellar populations.Colors for the galaxies are taken from the original sources where available.In other cases,they are taken from NED,4with precedence given to the RC3(de Vaucouleurs et al. 1995)where available to maximize uniformity.B−V colors were found for50of the galaxies; popsynthΥ⋆are not computed for the remainder for lack of input to equations8and9.The mass discrepancy-acceleration relation is clear in Fig.5for all choices of mass-to-light ratio.It works nearly as well for maximum disk as it does for MOND mass-to-light ratios.This is because high surface brightness galaxies are close to or in the Newtonian regime(a a0)at small radii,so the MOND and maximum disk mass-to-light ratios are similar.5The popsynth choice also works well.Individual rotation curves can be perceived in a few cases,but the number of deviant galaxies is small.Only as the mass-to-light ratio becomes implausibly small(half popsynth)does the relation begin to fall apart(as it must in the absurd limitΥ⋆→0).The scatter in the mass discrepancy-acceleration relation is minimized for MOND mass-to-light ratios.This is no accident.The trend in the data in thisﬁgure is,in eﬀect,the inverse of the MOND interpolation functionµ(x)(equation6).The MOND mass-to-light ratios have been chosen to minimize the scatter away from this function.Nevertheless,Fig.5 is a purely Newtonian diagram.We can explicitlyﬁt the data in these diagrams to describe the dependence of the mass discrepancy on acceleration with a function D(x)=µ−1(x) (Fig.4)or D(y)=µ−1[g(y)]≈µ−1/2(y)(Fig.5)where y=g N/a0.Regardless of how we choose to represent it mathematically,or whether we call it MOND or dark matter,this organization is clearly present in the data.It seems quite unlikely that this high degree of organization can be an accident.Cer-tainly it can not be a product of bad data.Systematic errors could obscure a real relation, but they can not conspire to give the appearance of one where none exists.Rather,the massdiscrepancy-acceleration relation must be a real aspect of nature.3.2.The Baryonic Tully-Fisher RelationIn addition to the local mass discrepancy-acceleration relation,there also exists the global Tully-Fisher ually expressed as a relation between luminosity and linewidth, it has long been suspected that this is a manifestation of some more fundamental relation between mass and rotation velocity(e.g.,Freeman1999).McGaugh et al.(2000)explicitly showed that there is indeed a more fundamental relation between the baryonic mass(stars plus gas)and the rotation velocity(see also Bell&de Jong2001;McGaugh2003).For galaxies with resolved rotation curves,the velocity in theﬂat part of the rotation curve, V flat,is the obvious quantity of interest,and provides an excellent correlation(Fig.6).Fig.6illustrates the baryonic Tully-Fisher relation for the same choices of mass-to-light ratio and data accuracy as in Fig.5.As in Fig.5,there is a clear correlation in all cases, though it begins to degrade for the half-popsynth case.Also as in Fig.5,the scatter is minimized for MOND mass-to-light ratios.Verheijen(1997,2001)notes that the Tully-Fisher relation for the Ursa Major cluster is remarkably tight,with only barely room for the intrinsic scatter expected from stellar population variations,let alone that expected from halo-to-halo variations.Fig.6further emphasizes that whatever physical mechanism underpins the Tully-Fisher relation,it is a remarkably strong one with much less scatter than one would nominally expect(e.g.,Eisen-stein&Loeb1996;McGaugh&de Blok1998a).This tight relation is no surprise if required by the force law.MOND requires a baryonic Tully-Fisher relation of the formM b=A V4flat.(10) Aﬁt to the data in Fig.6does indeedﬁnd a slope of4with a normalization A=50km−4s4M⊙. This is somewhat higher than the normalization of McGaugh et al.(2000),though consistent within the uncertainties.The biggest diﬀerence is that here I have only used galaxies with V flat explicitly measured from resolved rotation curves as opposed to line widths.In MOND,the normalization of the baryonic Tully-Fisher relation is A=χ/(a0G), whereχis a factor of order unity which accounts for the fact that thin disks rotate faster than the equivalent spherical mass distribution.Since the galaxies here have all beenﬁt with a0=1.2×10m s−2,we measure<χ>=0.79,as expected(McGaugh&de Blok1998b). In MOND,the baryonic Tully-Fisher relation should be perfect with no scatter.That there remains a small amount of scatter in Fig.6is simply a reﬂection of the residual uncertainties in the data.Of the choices of mass-to-light ratio considered here,there is no better choice than MOND for minimizing the scatter in the baryonic Tully-Fisher relation.Maximum disk does a good job,but does less well in this respect because low surface brightness galaxies tend to have very large maximum disk mass-to-light ratios(de Blok&McGaugh1997; Swaters et al.2000).This pushes up the scatter as a wide range of mass is inferred at a given luminosity.It also pushes up the normalization at low mass,where most galaxies are of low surface brightness(top panel of Fig.6).It is only with very high mass-to-light ratios (Υ⋆ 10M⊙/L⊙)that the stellar mass is signiﬁcant in these low mass galaxies;in the lower three panels the gas mass dominates the baryonic total and these points do not budge.Presuming mass is indeed more fundamental than luminosity,one would expect a good choice of population synthesis model mass-to-light ratios to reduce the scatter below that observed in luminosity.That is,a proper matching ofΥ⋆to each galaxy would remove the component of the scatter due to it.While this does happen with MOND,the popsynth choice does not reduce the scatter(Bell&de Jong2001),rather increasing it slightly.In retrospect,this is probably due to the fact that one expects a fair amount of scatter in the Υ⋆-color relation(equations8and9).So while the color may be a good indicator ofΥ⋆in the mean,when applied to any particular galaxy the scatter simply propagates.3.3.The Optimal Mass-to-Light RatioObtaining the mass of a spiral disk is simply a matter of choosing the right mass-to-light ratio.The MOND mass-to-light ratio appears to be optimal,even in a purely Newtonian sense,in that it minimizes the scatter in both the global baryonic Tully-Fisher relation and the local mass discrepancy-acceleration relation.This can be further tested against the expectations of stellar population synthesis models(Fig.7).The MOND mass-to-light ratios are in excellent agreement with population synthesis models.These dynamically determinedΥ⋆are completely independent of the models to which they are compared.Yet they agree well in normalization with the best-guess IMF of Bell&de Jong(2001).In addition,the expected trend ofΥ⋆with color is apparent.The K′-band mass-to-light ratio is almost independent of color,while there is a clear trend in the B-band for redder galaxies to have higher mass-to-light ratios.The slope of this relation is consistent with the models,and one can even see indications of the turndown inΥB⋆for B−V<0.5apparent in Fig.B1of Portinari,Sommer-Larsen,&Tantalo(2004).Moreover, the scatter is larger in B than in K′,again as expected.In this respect,the MOND mass-to-light ratios are more consistent with population synthesis models than popsynth itself,as the latter applies equation8or9without allowance for the expected scatter.If we accept the agreement with population models at face value,we can begin to place constraints on the IMF.Bell&de Jong(2001)argue for a“scaled”Salpeter IMF where the best mass-to-light ratio is scaled by a factor X from the familiar Salpeter IMF: .By tracing the lower envelope of the maximum disk data of Verheijen Υ⋆=XΥSalpeter⋆(1997)(lower left panel of Fig.7),Bell&de Jong(2001)argue for X=0.7.This is a good argument,but one could also argue that one expects a fair amount of scatter about the mean population line,so that a good number of disks should fall below this line even if all disks are maximal.If we take this attitude then X≈1.3provides a good description of the data. This is not particularly unreasonable from a population perspective,but there are a numberis uncomfortably high(typicallyΥB⋆≈10M⊙/L⊙for blue of individual galaxies whereΥmax⋆LSB galaxies).For the optimal mass-to-light ratios from MOND,X≈3/4.This is in quite good agreement with the detailed investigation of Kroupa&Weidner(2003),whoﬁnd0.72< X<0.83from direct integration of the observed IMF,including brown dwarfs.There is a slight tension between the mean of the B and K′bands,in that the B-band prefers slightly higher X.This may be due to residual shortcomings in the models,or may be due to the uncertainty inΥ⋆caused by that in the distance to Ursa Major(from whence come all the K′-band data).The distance determined by Sakai et al.(2000)is rather larger than that of Pierce&Tully(1988),and this cluster is by far the largest outlier from the mean6in the Sakai et al.sample.Hence the data still require reﬁnement before a deﬁnitive conclusion about the value of X can be made.Nevertheless,it is clearly in the right neighborhood,and extreme values,both high and low,can be discounted.For example,X>1.5would exceed maximum disk for the majority of K′-band cases.X<0.35(half-popsynth or less)would destroy the correlations which are clear in the data.There are now three items which point to MOND mass-to-light ratios being optimal in a purely Newtonian sense:(1)they minimize the scatter in the local mass discrepancy-acceleration relation,(2)they minimize the scatter in the global baryonic Tully-Fisher re-lation,and(3)they could hardly be in better agreement with stellar population models. The obvious conclusion is that these are in fact the correct mass-to-light ratios.This would appear to solve the long standing problem of the uncertainty in disk masses.With the disk mass speciﬁed,the dark matter distribution follows.4.The Dark Matter Distribution4.1.Constraints on Halo Parameters from the Acceleration ScaleThe presence of an acceleration scale in the data provides strong constraints on the parameters of halo models.This follows simply from the observation that there is a point (in Fig.5)at which the mass discrepancy appears.The constraints discussed here(in§4.1) do not depend on the details of MONDﬁts or the coupling of mass and light below the critical acceleration scale,but merely upon the fact that there is a critical acceleration scale.This relevance of the acceleration scale to dark matter halos has been noted by Brada& Milgrom(1999).They pointed out that one can only attribute to dark matter a maximum acceleration not already accounted for by the stars.They demonstrate that there is a formal upper limit to the halo accelerationa maxh≤ηa†,(11) where a†is the critical acceleration andηis a numerical parameter.For MOND mass-to-light ratios,a†≡a0.The value ofηdepends weakly on the adopted form of the MOND interpolation function,µ(x).This can be evaluated numerically(see Brada&Milgrom1999); for the commonly used form ofµ(x)(equation6)η=0.30which I adopt here.The range of ηspanned by plausible interpolation functions is0.25≤η≤0.37,so the particular choice of interpolation function is not very important.Phrasing the constraint in this way makes the relationship to MOND clear.However, the constraint follows simply from the observation that there is an upper limit to the force being provided by the dark halo.We can generalize the MOND result to allow for any choice of mass-to-light ratio.For each choice ofΥ⋆,the eﬀective value of a†can be determined by ﬁtting a function D(y)to each panel in Fig.5.The result is•for maximum disk:a†≈2300km2s−2kpc−1;•for popsynth:a†≈4000km2s−2kpc−1;and•for half popsynth,a†≈10,000km2s−2kpc−1.The critical acceleration for popsynth is indistinguishable from MOND:a†≈a0.For maximum disk,a†<a0,which simply says that the mass discrepancy appears at a some-what lower acceleration,as should be true by construction.A similar result can be seen in other data(e.g.,Palunas&Williams2000),though the availability of the gas component is necessary for the smooth appearance in Fig.5.The correlation appears to break down atlow accelerations if the gas component is neglected,since it is often the dominant baryonic component at large radii and low accelerations.For half popsynth,a†>a0.Theﬁt is still tolerable,but the uncertainty in a†begins to grow large.In the limitΥ⋆→0,we would of course infer mass discrepancies everywhere,so a†→∞.The scale a†represent an upper limit on the acceleration which can be caused by the dark matter halo.This can be translated to limits on halo parameters for any choice of halo model.These will be rather conservative limits,as we can only require that the maximum acceleration produced by a halo model not exceed a†.However,there is no guarantee that the maximum acceleration in any given galaxy will actually occur at the radius of maximum acceleration of a particular halo model.In addition,there is no reason to expect that real galaxies need ever exhibit accelerations as high as a†.LSB galaxies have large mass discrepancies precisely because V2/r<a0at all radii.Probably the dominant uncertainty is in the choice ofΥ⋆and hence the appropriate value of a†,though from§3the most obvious choice is a†=a0.In the following sections,I derive the limits on halo parameters which follow from the acceleration scale limit for the most common halo models.These are the constant density core pseudoisothermal halo and the cuspy NFW halo(Navarro,Frenk,&White1997).It is straightforward to derive equivalent limits for other choices of halo models,but most other models resemble one of these two in their essential features.4.1.1.Pseudoisothermal HalosTraditionally,galaxy rotation curves have beenﬁt with pseudoisothermal halos.These have constant density cores(ρ=ρc)out to a core radius R c,after which the proﬁle rolls over toρ(r)→r−2in order to produce asymptoticallyﬂat rotation curves.This functional form is very eﬀective atﬁtting rotation curves,though there is no guarantee that this is what dark matter should do.The dark matter distribution of the pseudoisothermal halo isρcρISO(r)=tan−1 rr4πGρc. While it is natural to associate V f with the observed V flat,this need not be the case in。

黑洞的由来的英语作文

黑洞的由来的英语作文The Origin of Black Holes: A Journey into Cosmic Mysteries。

Introduction。

Black holes, enigmatic entities lurking in the depthsof space, have captivated the imagination of scientists and laypersons alike. Their origins, shrouded in cosmic mystery, have been the subject of intense study and speculation. In this essay, we embark on a journey to unravel the secretsof black holes, exploring their formation, properties, and significance in the universe.Formation of Black Holes。

The genesis of black holes begins with the demise of massive stars. When a massive star exhausts its nuclear fuel, it undergoes a cataclysmic event known as a supernova explosion. During this explosive phase, the outer layers ofthe star are ejected into space, while its core undergoes gravitational collapse. If the core's mass exceeds acritical threshold, it collapses into a singularity—a point of infinite density—giving birth to a black hole.The process of black hole formation can also occur through the gravitational collapse of dense stellar remnants, such as neutron stars, or through the merger of two compact objects, such as neutron stars or black holes. These pathways lead to the creation of different types of black holes, ranging from stellar-mass black holes to supermassive black holes found at the centers of galaxies.Properties of Black Holes。

黑洞介绍英语作文初一

黑洞介绍英语作文初一Title: Exploring the Mysteries of Black Holes。

Black holes are fascinating objects in the universethat have captured the imagination of scientists and the public alike. These enigmatic entities are characterized by their immense gravitational pull, which is so strong that nothing, not even light, can escape from them. In this essay, we will delve into the intriguing world of black holes and explore their properties, formation, and significance in astrophysics.To begin with, let's discuss the nature of black holes.A black hole is formed when a massive star collapses under its own gravity at the end of its life cycle. As the star's core runs out of nuclear fuel, it can no longer support its own weight, leading to a catastrophic collapse. This collapse causes the star to shrink to a point of infinite density called a singularity, surrounded by an event horizon, which marks the boundary beyond which nothing canescape.The concept of the event horizon is crucial to understanding the behavior of black holes. It represents the point of no return, beyond which the gravitational pull is so strong that even light cannot break free. This phenomenon makes black holes invisible to direct observation, as they do not emit any light themselves. Instead, scientists infer their presence through theeffects they have on surrounding matter and light.Despite their invisibility, black holes can have a profound impact on their surroundings. For example, when matter gets too close to a black hole, it is drawn into a swirling disk of gas and dust called an accretion disk. The intense friction and gravitational forces within the accretion disk cause it to heat up and emit high-energy radiation, such as X-rays, which can be detected by telescopes.Another fascinating aspect of black holes is their role in the evolution of galaxies. Supermassive black holes,which can contain the mass of millions or even billions of suns, are thought to reside at the centers of most galaxies, including our own Milky Way. These behemoths exert a powerful influence on their host galaxies, regulating the formation of stars and influencing the dynamics of galactic structures.In recent years, scientists have made significantstrides in our understanding of black holes, thanks to advances in observational techniques and theoretical modeling. For example, the Event Horizon Telescope collaboration made headlines in 2019 with the first-ever image of a black hole's silhouette, providing direct evidence of their existence.Moreover, theoretical frameworks such as Einstein's theory of general relativity have provided a mathematical description of black holes' behavior, allowing scientiststo make predictions and test them against observational data. However, many mysteries surrounding black holes remain, such as the nature of the singularity at their core and the possibility of wormholes connecting distant regionsof space-time.In conclusion, black holes are among the mostintriguing phenomena in the universe, challenging our understanding of physics and the nature of reality itself. While much progress has been made in unraveling their mysteries, there is still much we have yet to learn about these enigmatic objects. Continued research and exploration are essential if we are to unlock the secrets of black holes and expand our knowledge of the cosmos.。

银河系漫游指南英文版pdf

银河系漫游指南英文版pdfHere is the English essay with a word count of over 1000 words, as requested:The Milky Way Galactic OdysseyEmbark on a captivating journey through the vast expanse of the Milky Way Galaxy, a celestial wonder that has captivated the human imagination for millennia. As we delve into the mysteries and marvels of this galactic realm, prepare to be awestruck by the sheer scale and beauty of the cosmos that lies beyond our earthly confines.Let us begin our odyssey by venturing to the heart of the Milky Way, where the supermassive black hole known as Sagittarius A* resides. This gravitational behemoth, nearly 4 million times the mass of our Sun, anchors the center of our galaxy and exerts a powerful influence on the surrounding stars and stellar matter. As we approach this enigmatic cosmic phenomenon, we will witness the intricate dance of stars and gas clouds as they are drawn inexorably towards the event horizon, their fate forever sealed within the crushing grip of the black hole.Venturing outwards from the galactic center, we will encounter the diverse and vibrant neighborhoods that make up the Milky Way. Spiral arms, such as the Orion Arm in which our Solar System resides, are vast regions of star formation, with newborn stars and stellar nurseries dotting the landscape. We will marvel at the brilliant nebulae, glowing clouds of gas and dust that serve as the birthplaces of these young celestial bodies, their ethereal hues and intricate structures a testament to the dynamic processes that shape the galaxy.As we traverse the spiraling arms, we will come across the globular clusters – ancient, densely packed collections of stars that orbit the galactic center. These spherical assemblages, some of the oldest objects in the Milky Way, harbor valuable insights into the early history and evolution of our galaxy, their stars dating back to a time when the universe was a mere fraction of its current age.Amidst the stellar tapestry, we will discover the diverse array of stellar populations that call the Milky Way home. From the towering red giants, their brilliant crimson hues a testament to their advanced age and increased size, to the compact and enigmatic neutron stars, the collapsed remnants of once-mighty suns. Each type of star, with its unique properties and life cycle, contributes to the rich tapestry of the galactic landscape.But the Milky Way is not merely a collection of stars – it is a dynamic and ever-changing system, influenced by the complex interplay of gravity, stellar evolution, and the ever-present threat of cosmic catastrophes. We will explore the regions where massive stars meet their explosive demise, supernovae that briefly outshine entire galaxies and leave behind the dense, spinning neutron stars known as pulsars. These cataclysmic events not only shape the galactic environment but also provide the building blocks for new generations of stars and planets.As we venture deeper into the Milky Way, we will encounter the harrowing regions where the fabric of space-time is stretched and distorted by the intense gravitational fields of neutron stars and black holes. Here, we will witness the bizarre and mind-bending phenomena predicted by Einstein's theory of general relativity, from the warping of spacetime to the accretion disks that feed these cosmic monsters.Throughout our journey, we will be in awe of the sheer scale and majesty of the Milky Way. The galaxy, spanning nearly 100,000 light-years in diameter, is home to an estimated 200 to 400 billion stars, each one a unique and fascinating world unto itself. We will ponder the possibility of life elsewhere in this vast cosmic tapestry, wondering if intelligent civilizations have arisen on distant worlds and if they, too, gaze up at the night sky, marveling at the splendorof our shared galactic home.As our odyssey draws to a close, we will reflect on the profound impact that the study of the Milky Way has had on our understanding of the universe. From the groundbreaking work of pioneering astronomers to the cutting-edge research conducted with the most advanced observational tools, the Milky Way has been a constant source of fascination and discovery. And as we look to the future, we know that there are countless more secrets and mysteries waiting to be unveiled, beckoning us to continue our exploration of this awe-inspiring celestial realm.So let us embark on this Milky Way galactic odyssey, armed with a sense of wonder and a thirst for knowledge. For in unraveling the mysteries of our galactic home, we may just find the answers to some of the most profound questions that have puzzled humanity since the dawn of time.。

A Submillimeter and Radio Survey of Gamma-Ray Burst Host Galaxies A Glimpse into the Future

a rXiv:as tr o-ph/21645v21Nov22A Submillimeter and Radio Survey of Gamma-Ray Burst Host Galaxies:A Glimpse into the Future of Star Formation Studies E.Berger 1,L.L.Cowie 2,S.R.Kulkarni 1,D.A.Frail 3,H.Aussel 2,&A.J.Barger 2,4,5ABSTRACT We present the ﬁrst comprehensive search for submillimeter and radio emis-sion from the host galaxies of twenty well-localized γ-ray bursts (GRBs).With the exception of a single source,all observations were undertaken months to years after the GRB explosions to ensure negligible contamination from the afterglows.We detect the host galaxy of GRB 000418in both the sub-mm and radio,and the host galaxy of GRB 000210only in the sub-mm.These observations,in con-junction with the previous detections of the host galaxies of GRB 980703and GRB 010222,indicate that about 20%of GRB host galaxies are ultra-luminous (L >1012L ⊙)and have star formation rates of about 500M ⊙yr −1.As an en-semble,the non-detected hosts have a star formation rate of about 100M ⊙yr −1(5σ)based on their radio emission.The detected and ensemble star formation rates exceed the optically-determined values by an order of magnitude,indicat-ing signiﬁcant dust obscuration.In the same vein,the ratio of bolometric dust luminosity to UV luminosity for the hosts detected in the sub-mm and radio ranges from ∼20−800,and follows the known trend of increasing obscuration with increasing bolometric luminosity.We also show that,both as a sample and individually,the GRB host galaxies have bluer R −K colors as compared with galaxies selected in the sub-mm in the same redshift range.This possibly in-dicates that the stellar populations in the GRB hosts are on average younger,supporting the massive stellar progenitor scenario for GRBs,but it is also possible that GRB hosts are on average less dusty.Beyond the speciﬁc results presentedin this paper,the sub-mm and radio observations serve as an observational proof-of-concept in anticipation of the upcoming launch of the SWIFT GRB missionand SIRTF.These new facilities will possibly bring GRB host galaxies into theforefront of star formation studies.Subject headings:cosmology:observations—galaxies:starburst—gamma-rays:bursts—stars:formation1.IntroductionOne of the major thrusts in modern cosmology is an accurate census of star formation and star-forming galaxies in the Universe.This endeavor forms the backbone for a slew of methods(observational,analytical,and numerical)to study the process of galaxy formation and evolution over cosmic time.To date,star-forming galaxies have been selected and studied mainly in two observational windows:the rest-frame ultraviolet(UV),and rest-frame radio and far-infrared(FIR).For galaxies at high redshift these bands are shifted into the optical and radio/sub-mm,allowing observations from the ground.Still,the problem of translating the observed emission to star formation rate(SFR)involves large uncertainty.This is partly because each band traces only a minor portion of the total energy output of stars.Moreover, the optical/UV band is signiﬁcantly aﬀected by dust obscuration,thus requiring order of magnitude corrections,while the sub-mm and radio bands lack sensitivity,and therefore uncover only the most prodigiously star-forming galaxies.The main result that has emerged from star formation surveys over the past few years is exempliﬁed in the so-called Madau ly,the SFR volume density,ρSFR(z), rises steeply to z∼1,and seemingly peaks at z∼1−2.There is still some debate about the how steep the rise is,with values ranging from(1+z)1.5(Wilson et al.2002)to(1+z)4 (e.g.Madau et al.1996).The evolution beyond z∼2is even less clear since optical/UV observations indicate a decline(Madau et al.1996),while recent sub-mm observations argue for aﬂatρSFR(z)to higher redshift,z∼4(Barger,Cowie&Richards2000).Consistency with this trend can be obtained by invoking large dust corrections in the optical/UV(Steidel et al.1999).For general reviews of star formation surveys we refer the reader to Kennicut (1998),Adelberger&Steidel(2000),and Blain et al.(2002).Despite the signiﬁcant progress in thisﬁeld,our current understanding of star formation and its redshift evolution is still limited by the biases and shortcomings of current optical/UV, sub-mm,and radio selection techniques.In particular,despite the fact that the optical/UV band is sensitive to galaxies with modest star formation rates(down to a fraction of a M⊙yr−1)at high redshift,these surveys may miss the most dusty,and vigorously star-forming galaxies.Moreover,it is not clear if the simple,locally-calibrated prescriptions for correcting the observed un-obscured SFR for dust extinction(e.g.Meurer,Heckman&Calzetti1999), hold at high redshift;even if they do,these prescriptions involve an order of magnitude correction.Finally,the optical/UV surveys are magnitude limited,and therefore miss the faintest sources.Sub-mm surveys have uncovered a population of highly dust-extincted galaxies,which are usually optically faint,and have star formation rates of several hundred M⊙yr−1(e.g.Smail, Ivison&Blain1997).However,unlike optical/UV surveys,sub-mm surveys are severely sen-sitivity limited,and only detect galaxies with L bol 1012L⊙.More importantly,current sub-mm bolometer arrays(such as SCUBA)have large beams on the sky(∼15arcsec) making it diﬃcult to unambiguously identify optical counterparts(which are usually faint to begin with),and hence measure the redshifts(Smail et al.2002);in fact,of the∼200 sub-mm galaxies identiﬁed to date,only a handful have a measured redshift.Finally,trans-lating the observed sub-mm emission to a SFR requires signiﬁcant assumptions about the temperature of the dust,and the dust emission spectrum(e.g.Blain et al.2002).Surveys at decimeter radio wavelengths also suﬀer from low sensitivity,but the high as-trometric accuracy aﬀorded by synthesis arrays such as the VLA allows a sub-arcsec localiza-tion of the radio-selected galaxies.As a result,it is easier to identify the optical counterparts of these sources.Recently,this approach has been used to pre-select sources for targeted sub-mm observations resulting in an increase in the sub-mm detection rate(Barger,Cowie &Richards2000;Chapman et al.2002)and redshift determination(Chapman et al.2003). However,this method is biased towardﬁnding luminous(high SFR)sources since it requires an initial radio detection.An additional problem with radio,even more than with sub-mm, selection is contamination by active galactic nuclei(AGN).An examination of the X-ray properties of radio and sub-mm selected galaxies reveals that of the order of20%can have a signiﬁcant AGN component(Barger et al.2001).The most signiﬁcant problem with current star formation studies,however,is that the link between the optical and sub-mm/radio samples is still not well understood.The Hubble Deep Field provides a clear illustration:the brightest sub-mm source does not appear to have an optical counterpart(Hughes et al.1998),and only recently a detection has been claimed in the near-IR(K≈23.5mag;Dunlop et al.2002).Along the same line,sub-mm observations of the optically-selected Lyman break galaxies have resulted in very few detections(Chapman et al.2000;Peacock et al.2000;Chapman et al.2002),and even the brightest Lyman break galaxies appear to be faint in the sub-mm band(Baker et al. 2001).In addition,there is considerable diversity in the properties of optical counterpartsto sub-mm sources,ranging from galaxies which are faint in both the optical and near-IR (NIR)to those which are bright in both bands(Ivison et al.2000;Smail et al.2002).As a result of the unclear overlap,and the sensitivity and dust problems in the sub-mm and optical surveys,the fractions of global star formation in the optical and sub-mm/radio selected galaxies is not well constrained.It is therefore not clear if the majority of star formation takes place in ultra-luminous galaxies with very high star formation rates,or in the more abundant lower luminosity galaxies with star formation rates of a few M⊙yr−1. Given the diﬃculty with redshift identiﬁcation of sub-mm galaxies,the redshift distribution of dusty star forming galaxies remains highly uncertain.One way to alleviate some of these problems is to study a sample of galaxies that is immune to the selection biases of current optical/UV and sub-mm/radio surveys,and which may draw a more representative sample of the underlying distribution of star-forming galaxies.The host galaxies ofγ-ray bursts(GRBs)may provide one such sample.The main advantages of the sample of GRB host galaxies are:(i)The galaxies are selected with no regard to their emission properties in any wavelength regime,(ii)the dust-penetrating power of theγ-ray emission results in a sample that is completely unbiased with respect to the global dust properties of the hosts,(iii)GRBs can be observed to very high redshifts with existing missions(z 10;Lamb&Reichart2000),and as a result volume corrections for the star formation rates inferred from their hosts are trivial,(iv)the redshift of the galaxy can be determined via absorption spectroscopy of the optical afterglow,or X-ray spectroscopy allowing a redshift measurement of arbitrarily faint galaxies(the current record-holder is the host of GRB990510with R=28.5mag and z=1.619;Vreeswijk et al.2001),and(v)since there is excellent circumstantial evidence linking GRBs to massive stars(e.g.Bloom,Kulkarni&Djorgovski2002,the sample of GRB hosts is expected to trace global star formation(Blain&Natarajan2000).Of course,the sample of GRB hosts is not immune from its own problems and potential biases.The main problem is the relatively small size of the sample in comparison to both the optical and sub-mm samples6(although the number of GRB hosts with a known redshift exceeds the number of sub-mm galaxies with a measured redshift).As a result,at the present it is not possible to assess the SFR density that is implied by GRB hosts,or its redshift evolution.A bias towards sub-solar metallicity for GRB progenitors(and hence their environments)has been discussed(MacFadyen&Woosley1999;MacFadyen,Woosley &Heger2001),but it appears that very massive stars(e.g.M 35M⊙)should produceblack holes even at solar metallicity.The impact of metallicity on additional aspects of GRB formation(e.g.angular momentum,loss of hydrogen envelope)is not clear at present. Finally,given the observed dispersion in metallicity within galaxies(e.g.Alard2001;Overzier et al.2001),it is likely that even if GRBs require low metallicity progenitors,this does not imply that the galaxy as a whole has a lower than average metallicity.To date,GRB host galaxies have mainly been studied in the optical and NIR bands. With the exception of one source(GRB020124;Berger et al.2002),every GRB localized to a sub-arcsecond position has been associated with a star-forming galaxy(Bloom,Kulkarni &Djorgovski2002).These galaxies range from R≈22−29mag,have a median redshift, z ∼1,and are generally typical of star-forming galaxies at similar redshifts in terms of morphology and luminosity(Djorgovski et al.2001),with star formation rates from optical spectroscopy of∼1−10M⊙yr−1.At the same time,there are hints for higher than average ratios of[Ne III]3869to[O II]3727,possibly indicating the presence of massive stars (Djorgovski et al.2001).Only two host galaxies have been detected so far in the radio (GRB980703;Berger,Kulkarni&Frail2001)and sub-mm(GRB010222;Frail et al.2002).Here we present sub-mm and radio observations of a sample of20GRB host galaxies, ranging in redshift from about0.4to4.5(§2);one of the20sources is detected with high signiﬁcance in both the sub-mm and radio bands,and an additional source is detected in the sub-mm(§3).We compare the detected sub-mm and radio host galaxies to local and high-z ultra-luminous galaxies in§4,and derive the SFRs in§5.We then compare the inferred SFRs of the detected host galaxies,and the ensemble of undetected hosts,to optical estimates in §6.Finally,we compare the optical properties of the GRB host galaxies to those of sub-mm and radio selected star-forming galaxies(§7).2.Observations2.1.Target SelectionAt the time we conducted our survey,the sample of GRB host galaxies numbered25, twenty of which had measured redshifts.These host galaxies were localized primarily based on optical afterglows,but also using the radio and X-ray afterglow emission.Of the25host galaxies we observed eight in both the radio and sub-mm,seven in the radio,andﬁve in the sub-mm.The galaxies were drawn from the list of25hosts at random,constrained primarily by the availability of observing time.Thus,the sample presented here does not suﬀer from any obvious selection biases,with the exception of detectable afterglow emission in at least one band.Sub-mm observations of GRB afterglows,and a small number of host galaxies have been undertaken in the past.Starting in1997,Smith et al.(1999)and Smith et al.(2001)have searched for sub-mm emission from the afterglow of thirteen GRBs.While they did not detect any afterglow emission,these authors used their observations to place constraints on emission from eight host galaxies,with typical1σrms values of1.2mJy.Since these were target-of-opportunity observations,they were not always undertaken in favorable observing conditions.More recently,Barnard et al.(2002)reported targeted sub-mm observations of the host galaxies of four optically-dark GRBs(i.e.GRBs lacking an optical afterglow).They focused on these particular sources since one explanation for the lack of optical emission is obscuration by dust,which presumably points to a dusty host.None of the hosts were detected,with the possible exception of GRB000210(see§3.4),leading the authors to conclude that the hosts of dark bursts are not necessarily heavily dust obscured.Thus,the observations presented here provide the most comprehensive and bias-free search for sub-mm emission from GRB host galaxies,and theﬁrst comprehensive search for radio emission.2.2.Submillimeter ObservationsObservations in the sub-mm band were carried out using the Sub-millimeter Common User Bolometer Array(SCUBA;Holland et al.1999)on the James Clerk Maxwell Tele-scope(JCMT7).We observed the positions of thirteen well-localized GRB afterglows with the long(850µm)and short(450µm)arrays.The observations,summarized in Table1, were conducted in photometry mode with the standard nine-jiggle pattern using the central bolometer in each of the two arrays to observe the source.In the case of GRB000301C we used an oﬀ-center bolometer in each array due to high noise levels in the central bolometer.To account for variations in the sky brightness,we used a standard chopping of the secondary mirror between the on-source position and a position60arcsec away in azimuth, at a frequency of7.8125Hz.In addition,we used a two-position beam switch(nodding), in which the beam is moved oﬀ-source in each exposure to measure the sky.Measurements of the sky opacity(sky-dips)were taken approximately every two hours,and the focus andarray noise were checked at least twice during each shift.The pointing was checked approximately once per hour using several sources throughout each shift,and was generally found to vary by 3arcsec(i.e.less than one quarter of the beam size).All observations were performed in band2and3weather withτ225GHz≈0.05−0.12.The data were initially reduced with the SCUBA Data Reduction Facility(SURF)fol-lowing the standard reduction procedure.The oﬀ-position pointings were subtracted from the on-position pointings to account for chopping and nodding of the telescope.Noisy bolometers were removed to facilitate a more accurate sky subtraction(see below),and the data were thenﬂat-ﬁelded to account for the small diﬀerences in bolometer response.Ex-tinction correction was performed using a linear interpolation between skydips taken before and after each set of on-source scans.In addition to the sky subtraction oﬀered by the nodding and chopping,short-term sky contributions were subtracted by using all low-noise oﬀ-source bolometers(sky bolometers). This procedure takes advantage of the fact that the sky contribution is correlated across the array.As a result,theﬂux in the sky bolometers can be used to assess the sky contribution to theﬂux in the on-source bolometer.This procedure is especially crucial when observing weak sources,since the measuredﬂux may be dominated by the sky.We implemented the sky subtraction using SURF and our own routine using MATLAB.We found that in general the SURF sky subtraction under-estimated the sky contribution,and as a result over-estimated the sourceﬂuxes.We therefore used the results of our own analysis routine.For this purpose we calculated the median value of the two(three)outer rings of bolometers in the850µm (450µm)array,after removing noisy bolometers(deﬁned as those whose standard deviation over a whole scan deviated by more than5σfrom the median standard deviation of all sky bolometers).Following the sky subtraction,we calculated the mean and standard deviation of the mean(SDOM)for each source in a given observing shift.Noisy data were eliminated in two ways.First,the data were binned into25equal time bins,and the SDOM was calculated step-wise,i.e.at each step the data from an additional bin were added and the mean and SDOM were re-calculated.In an ideal situation where the data quality remains approximately constant,the SDOM should progressively decrease as more data are accumulated.However, if the quality of the data worsens(due to deteriorating weather conditions for example) the SDOM will increase.We therefore removed time bins in which the SDOM increased. Following this procedure,we recursively eliminated individual noisy data points using a sigma cutoﬀlevel based on the number of data points(Chauvenet’s criterion;Taylor1982)until the mean converged on a constant value.Typically,two or three iterations were required,with only a few data points rejected each time.Typically,only a few percent of the data were rejected by the two procedures.Finally,ﬂux conversion factors(FCFs)were applied to the resulting voltage measure-ments to convert the signal to ing photometry observations of Mars and Uranus,and/or secondary calibrators(OH231.8+4.2,IRC+10216,and CRL618),we found the FCFto vary between180−205Jy/V at850µm,consistent with the typical value of197±13.At450µm,the FCFs varied between250−450Jy/V.2.3.Radio ObservationsVery Large Array(VLA8):We observed12GRB afterglow positions with the VLA from April2001to February2002.All sources were observed at8.46GHz in the standard continuum mode with2×50MHz bands.In addition,GRB000418was observed at1.43and4.86GHz,and GRB0010222was observed at4.86GHz.In Table2we provide a summaryof the observations.In principle,since the median spectrum of faint radio sources between1.4and8.5GHzis Fν∝ν−0.6(Fomalont et al.2002),the ideal VLA frequency for our observations(takinginto account the sensitivity at each frequency)is1.43GHz.However,we chose to observe primarily at8.46GHz for the following reason.The majority of our observations were takenin the BnC,C,CnD,and D conﬁgurations,in which the typical synthesized beam size is∼10−40arcsec at1.43GHz,compared to∼2−8arcsec at8.46GHz.The large synthesized beam at1.43GHz,combined with the largerﬁeld of view and higher intrinsic brightnessof radio sources at this frequency,would result in a signiﬁcant decrease in sensitivity dueto source confusion.Thus,we were forced to observe at higher frequencies,in which the reduced confusion noise more than compensates for the typical steep spectrum.We chose8.46GHz rather than4.86GHz since the combination of20%higher sensitivity and60% lower confusion noise,provide a more signiﬁcant impact than the typical30%decrease in intrinsic brightness.The1.43GHz observations of GRB000418were undertaken in the Aconﬁguration,where confusion does not play a limiting role.Forﬂux calibration we used the extragalactic sources3C48(J0137+331),3C147(J0542+498), and3C286(J1331+305),while the phases were monitored using calibrator sources within∼5◦of the survey sources.We used the Astronomical Image Processing System(AIPS)for data reduction and analysis.For each source we co-added all the observations prior to producing an image,to increase theﬁnal signal-to-noise.Australia Telescope Compact Array(ATCA9):We observed the positions of four GRB afterglows during April2002,in the6A conﬁguration ing the6-km baseline resulted in a signiﬁcant decrease in confusion noise,thus allowing observations at the most advantageous frequencies.The observations are summarized in Table2.We used J1934−638forﬂux calibration,while the phase was monitored using calibrator sources within∼5◦of the survey sources.The data were reduced and analyzed using the Multichannel Image Reconstruction,Image Analysis and Display(MIRIAD)package,and AIPS.3.ResultsTheﬂux measurements at the position of each GRB are given in Tables1and2,and are plotted in Figure2.Of the20sources,only GRB000418was detected in both the radio and sub-mm with S/N>3(§3.1).One additional source,GRB000210,is detected with S/N>3 when combining our observations with those of Barnard et al.(2002).Two hosts have radio ﬂuxes with3<S/N<4(GRB000301C and GRB000926),but as we show below this is due in part to emission from the afterglow.The typical2σthresholds are about2mJy,20µJy,and70µJy in the SCUBA,VLA,and ATCA observations,respectively.In Figure2we plot all sources with S/N>3as detections, and the rest as2σupper limits.In addition,for the sources observed with the ATCA we plot both the1.4GHz upper limits,and the inferred upper limits at8.46GHz assuming a typical radio spectrum,Fν∝ν−0.6(Fomalont et al.2002).One obvious source for the observed radio and sub-mmﬂuxes(other than the putative host galaxies)is emission from the afterglows.To assess the possibility that our observa-tions are contaminated byﬂux from the afterglows we note that the observations have been undertaken at least a year after the GRB explosion10.On this timescale,the sub-mm emis-sion from the afterglow is expected to be much lower than the detection threshold of ourobservations.In fact,the brightest sub-mm afterglows to date have only reached aﬂux of a few mJy(at350GHz),and typically exhibited a fading rate of∼t−1after about one day following the burst(Smith et al.1999;Berger et al.2000;Smith et al.2001;Frail et al. 2002;Yost et al.2002).Thus,on the timescale of our observations,the expected sub-mm ﬂux from the afterglows is only∼10µJy,well below the detection threshold.The radio emission from GRB afterglows is more long-lived,and hence posses a more serious problem.However,on the typical timescale of the radio observations the8.46GHz ﬂux is expected to be at most a fewµJy(e.g.Berger et al.2000).In the following sections we discuss the individual detections in the radio and sub-mm, and also provide an estimate for the radio emission from each afterglow.3.1.GRB000418A source at the position of GRB000418is detected at four of theﬁve observing fre-quencies with S/N>3.The SCUBA source,which we designate SMM12252+2006,has a ﬂux density of Fν(350GHz)≈3.2±0.9mJy,and Fν(670GHz)≈41±19mJy.These values(Fν∝νβ),consistent with a thermal dust spectrum as imply a spectral index,β≈3.9+1.1−1.3expected if the emission is due to obscured star formation.The radio source(VLA122519.26+200611.1),is located atα(J2000)=12h25m19.255s,δ(J2000)=20◦06′11.10′′,with an uncertainty of0.1arcsec in both coordinates.This position is oﬀset from the position of the radio afterglow of GRB000418(Berger et al.2001)by ∆α=−0.40±0.14arcsec and∆δ=−0.04±0.17arcsec(Figure1).In comparison,the oﬀset measured from Keck and Hubble Space Telescope images is smaller,∆α=−0.019±0.066 arcsec and∆δ=0.012±0.058arcsec.VLA122519.26+200611.1has an observed spectral slopeβ=−0.17±0.25,ﬂatter than the typical value for faint radio galaxies,β≈−0.6(Fomalont et al.2002),and similar to the value measured for the host of GRB980703(β≈−0.32;Berger,Kulkarni&Frail2001). The source appears to be slightly extended at1.43and8.46GHz,with a size of about1 arcsec(8.8kpc at z=1.119).The expected afterglowﬂuxes at4.86and8.46GHz at the time of our observations are about5and10µJy,respectively(Berger et al.2001).At1.43GHz the afterglow contribution is expected to be about10µJy based on the4.86GHzﬂux and the afterglow spectrum Fν∝ν−0.65.Thus,despite the contribution from the afterglow,the radio detections of the host galaxy are still signiﬁcant at better than3σlevel.Correcting for the afterglowcontribution weﬁnd an actual spectral slopeβ=−0.29±0.33,consistent with the median β≈−0.6for8.46GHz radio sources with a similarﬂux(Fomalont et al.2002).As with all SCUBA detections,source confusion arising from the large beam(D FWHM≈14arcsec at350GHz and≈6arcsec at670GHz)raises the possibility that SMM12252+2006 is not associated with the host galaxy of GRB000418.Fortunately,the detection of the radio source,which is located0.4±0.1arcsec away from the position of the radio afterglow of GRB000418,indicates that SMM12252+2006and VLA122519.26+200611.1are in fact the same source—the host galaxy of GRB000418.Besides the positional coincidence of the VLA and SCUBA sources,we gain further.This conﬁdence of the association based on the spectral index between the two bands,β3501.4 spectral index is redshift dependent as a result of the diﬀerent spectral slopes in the two regimes(Carilli&Yun2000;Barger,Cowie&Richards2000).Weﬁndβ350≈0.73±0.10,1.4=0.59±0.16(for the redshift in good agreement with the Carilli&Yun(2000)value ofβ3501.4of GRB000418,z=1.119).We also detect another source,slightly extended(θ≈1arcsec),approximately1.4arcsec East and2.7arcsec South of the host of GRB000418(designated VLA122519.36+200608.4), with Fν(1.43GHz)=48±15µJy and Fν(8.46GHz)=37±12µJy(see Figure1).This source appears to be linked by a bridge of radio emission(with S/N≈1.5at both frequencies)to the host of GRB000418.The physical separation between the two sources,assuming both are at the same redshift,z=1.119,is25kpc.There is no obvious optical counterpart to this source in Hubble Space Telescope images down to about R∼27.5mag.Based purely on radio source counts at8.46GHz(Fomalont et al.2002),the expected number of sources with Fν(8.46GHz)≈37µJy in a3arcsec radius circle is only about 2.7×10−4.Thus,the coincidence of two such faint sources within3arcsec is highly suggestive of an interacting system,rather than chance superposition.Interacting radio galaxies with separations of about20kpc,and joined by a bridge of radio continuum emission have been observed locally(Condon et al.1993;Condon,Helou& Jarrett2002).In addition,optical surveys(e.g.Patton et al.2002)show that a few percent of galaxies with an absolute B-band magnitude similar to that of the host of GRB000418, have companions within about30kpc.The fraction of interacting systems is possibly much higher,∼50%,in ultra-luminous systems(such as the host of GRB000418),both locally (Sanders&Mirabel1996)and at high redshift(e.g.Ivison et al.2000).We note that with a separation of only3arcsec,the host of GRB000418and the companion galaxy fall within the SCUBA beam.Thus,it is possible that SMM12252+2006to about is in fact a superposition of both radio sources.This will change the value ofβ3501.4。

很全面的资料-中子星与黑洞 Neutron Stars and Black Holes

If you could compress Earth to a smaller radius => higher escape velocity from the surface.
vesc
vesc
The Schwarzschild Radius
=> There is a limiting radius where the escape velocity reaches the speed of light, c:
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars:
Neutron stars can not exist with masses > 3 Msun
We know of no mechanism to halt the collapse of a compact object with > 3 Msun. It will collapse into a single point – a singularity:
=> A Black Hole!
Escape Velocity
Pulsars / Neutron Stars
Neutron star surface has a temperature of ~ 1 million K.
Cas A in X-rays
Wien’s displacement law,
lmax = 3,000,000 nm / T[K] gives a maximum wavelength of lmax = 3 nm, which corresponds to X-rays.

有关银河的文章英语

有关银河的英文文章The Milky Way, often referred to as the Galaxy, is a vast and magnificent spiral of stars, dust, gas, and other celestial bodies that we call home. It is named for its appearance in the night sky as a hazy, milky band of light that stretches across the heavens. This ethereal glow is actually the combined light of billions of stars that are too far away to be seen individually. The Milky Way is not just a beautiful sight to behold; it is also a complex and fascinating system that has captivated the minds of astronomers and scientists for centuries.The Milky Way is a barred spiral galaxy, meaning it has a central bar-shaped region with spiral arms extending outward from it. It is enormous, containing an estimated 200 billion stars and spanning a diameter of approximately 100,000 light-years. Our own Sun is just one of these stars, located on the inner edge of one of the spiral arms, about 26,000 light-years from the Galactic Center.One of the most intriguing aspects of the Milky Way is its structure. The galaxy is composed of three main components: the disk, which contains the stars, gas, and dust; the halo, a spherical region that extends beyond the disk and is populated by older stars and globular clusters; and the central bulge, a dense region at the heart of the galaxy that contains mostly older stars.The disk of the Milky Way is where most of the action takes place. It is made up of stars, gas, and dust that are organized into spiral arms. These arms are not solid structures, but rather regions of higher density that are separated by gaps. The arms are home to star-forming regions, where clouds of gas and dust collapse under their own gravity to form new stars. The M ilky Way’s spiral structure is thought to be caused by gravitational interactions between the stars and gas in the disk, as wellas the influence of the central black hole.The halo of the Milky Way is a spherical region that surrounds the disk and extends outward for hundreds of thousands of light-years. It is populated by older stars that are metal-poor and have orbits that take them far away from the plane of the disk. The halo also contains globular clusters, which are tightly packed groups of thousands to millions of stars that orbit the center of the galaxy.At the heart of the Milky Way lies the central bulge, a dense region that is packed with stars. This region is thought to be the site of intense star formation in the early history of the galaxy. It is also home to a supermassive black hole known as Sagittarius A*, which has a mass equivalent to millions of Suns. This black hole exerts a powerful gravitational influence on the surrounding stars and gas, shaping the structure of the galaxy.Studying the Milky Way has been a challenging task for astronomers due to our position within it. We cannot see the galaxy as a whole, as we are embedded within its disk. However, advances in technology and observation techniques have allowed us to piece together a comprehensive picture of our galactic home. We have mapped its structure using radio waves, X-rays, and visible light, revealing the locations of stars, gas, dust, and other components.The Milky Way is not static; it is constantly evolving. New stars are being born in star-forming regions, while older stars are dying and expelling their outer layers into space. The galaxy is also growing through the accretion of smaller galaxies and star clusters. In fact, our own Milky Way is destined to merge with our nearest neighbor, the Andromeda Galaxy, in several billion years.Despite our advances in understanding the Milky Way, there are still many mysteries surrounding it. We do not fully understand how spiral galaxies like our own form and evolve. We also know little about the nature of dark matter, which is thought to make up a significant portion of the mass of the galaxy but has never been directly detected.In conclusion, the Milky Way is more than just a pretty sight in the night sky; it is our home, a vast and complex system that contains billions of stars and countless other celestial bodies. It has captivated the imaginations of people throughout history and continues to inspire awe and wonder in those who gaze upon it. As we continue to explore and study our galactic home, we will undoubtedly uncover more secrets and mysteries that lie hidden within its depths.。

Core Formation in Giant Gaseous Protoplanets

Core Formation in Giant Gaseous ProtoplanetsRavit Helled ∗and Gerald SchubertDepartment of Earth and Space Sciences and Institute of Geophysics and Planetary Physics,University of California,Los Angeles,CA 900951567,USA E-mail addresses:rhelled@ (R.Helled);schubert@ (G.Schubert)∗corresponding author Abstract Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1M Saturn to 10M Jupiter .Giant protoplanets with masses of 5M Jupiter or larger are found to be too hot for grain sedimentation to form a silicate core.Smaller protoplanets are cold enough to allow grain settling and core formation.Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature.It is predicted that massive giant planets will not have cores,while smaller planets will have small rocky cores whose masses depend on the planetary mass,the amount of solids within the body,and the disk environment.The protoplanets are found to be too hot to allow the existence of icy grains,and therefore the cores are predicted not to contain any ices.It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets.These predictions provide a test of the disk instability model of gas giant planet formation.The core masses of Jupiter and Saturn were found to be ∼0.25M ⊕and ∼0.5M ⊕,respectively.The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included.The ﬁnal core mass will depend on planetesimal size,the time at which planetesimals are formed,and the size distribution of the material added to the protoplanet.Jupiter’s core mass can vary from 2to 12M ⊕.Saturn’s core mass is found to be ∼8M ⊕.1a r X i v :0808.2787v 1 [a s t r o -p h ] 20 A u g 20081IntroductionThe discovery over the last decade of extra-solar giant planets has increased interest in understanding the mechanism of giant planet formation(Lissauer&Stevenson,2007,Guillot,2007).Currently,there are two models for the formation of gas giant planets:’core accretion’,the conventional model,and’disk instability’. The core accretion model suggests that the formation of a giant planet starts with planetesimal coagulation followed by accretion of a gaseous envelope.Once the core and envelope masses become equal,the rate of gas accretion increases signiﬁcantly,leading to a hydrodynamic collapse of the atmosphere on top of the solid core(e.g.,Pollack et al.,1996;Liassuer&Stevenson,2007).The disk instability model suggests that gas giant planets form as a result of gravitational fragmentation in the protoplanetary disk(e.g.,Boss,1997, 2007;Mayer,2000,2007).As self-gravitating clumps are created,dust grains can coagulate and sediment to form a core(Boss,1997).While in the core accretion model all giant planets are predicted to have rather similar core masses(∼10M⊕),giant planets formed by disk instability can,in principle,have no core. In the disk instability model,formation of a core is not a requirement,and the core mass would depend on the internal temperature of the protoplanet,the amount of available refractory material,the grain size distribution,and the strength of convection(see Helled et al.,2008for further details).In this paper we simulate the evolution of gas giant protoplanets created by disk instability and investigate how the core mass varies with the mass of the protoplanet.2ModelEvolutionIt is still unknown whether objects formed by a gravitational instability can cool fast enough to remain bound objects that evolve to giant protoplanets(Raﬁkov,2007).More detailed numerical simulations and further investigations are required before this question can be answered.For the purpose of this paper we assume that clumps formed by disk instability are gravitationally bound and contract further to form gaseous protoplanets.To model the evolution of the protoplanets we assume gravitationally bound,spherical,homogenous and static bodies with a solar composition.The clumps are taken to be isolated,so no interaction with the surrounding disk is allowed.Under such conditions the bodies radiate away gravitational energy while their radii decrease.We concentrate on the initial stage in which the bodies are cold enough to allow the survival of silicate grains.This stage is known as the’pre-collapse’stage in which the protoplanets contract quasi-statically(DeCampli&Cameron,1979;Bodenheimer et al.,1980).The duration of this stage is inversely proportional to the initial mass of the body,so more massive protoplanets evolve faster.The pre-collapse2stage ends when molecular hydrogen starts to dissociate at the center of the body and a hydrodynamic collapse ensues(DeCampli&Cameron,1979;Bodenheimer et al.,1980).To model the evolution of protoplanets during the pre-collapse stage,we use a planetary evolution code that solves the standard equations of stellar evolution(hydrostatic balance,mass conservation,energy conservation,and heat transport).The code uses the interpolated equation of state of Saumon et al.(1995) for hydrogen and helium.The opacity is based on the work of Alexander&Ferguson(1994)and the low-temperature grain opacity is based on the work of Pollack et al.(1985).The opacity includes both gas and grain,the latter based on the size distribution relevant for interstellar grains.Weﬁnd the initial quasi-static states based on a preliminary model of a simulated clump kindly provided by P.Bodenheimer.Further details regarding the evolutionary model can be found in Helled et al.(2006,2008).We follow the evolution of clumps with masses of1M S,1,3,5,7and10M J(M S and M J being the mass of Saturn and Jupiter,respectively).Internal temperatures decrease and the time-scale of the pre-collapse stage increases with decreasing protoplanetary mass.The evolution of Jupiter and Saturn mass protoplanets is shown in Figure1.The central pressure,central temperature,radius,and eﬀective temperature as a function of time are presented.The evolution in theﬁgures is shown up to the point when the central temperature reaches∼1300K,the evaporation temperature of silicates,and core formation stops.The contraction rate of a Saturn mass protoplanet is slower,and its central pressure and temperature are lower compared with the Jupiter mass protoplanet.The pre-collapse time-scale of the low mass body is longer,and as a result grains inside it have a longer time to grow and sediment to the center.[Fig.1]The initial states are chosen so that the protoplanets are extended and have low densities and tempera-tures and yet are gravitationally bound to insure further contraction(Boss,1997;Mayer et al.,2002).Table1 presents the surface density,central pressure,central and eﬀective temperatures,radius and luminosity of the initial states of the protoplanets.More massive bodies can be more extended but they have higher internal temperatures.The surface density decreases for larger bodies but the central pressure,central temperature and central density increase with increasing mass.Massive bodies are hotter and larger and therefore are more luminous.Figure2presents the initial temperature-pressure proﬁles for protoplanets with1,5and10 Jupiter masses.As can be seen from theﬁgure,the central temperature and pressure increase with increasing mass.[Table.1][Fig.2]3The densities and temperatures of protoplanets formed by a gravitational instability are unknown,and diﬀerent numerical models predict diﬀerent characteristics.Simulations by Boss(1997,2007)predict lower-density and colder protoplanets than the simulations of Mayer et al.(2002,2004).The latterﬁnd denser and hotter conﬁgurations,with central temperatures reaching∼1000K shortly after formation.Indeed,for clumps with masses larger than∼1M J weﬁnd central temperatures of that order.The low surface densities of the protoplanets are a few times the mean density of the disk’s midplane,as expected for bodies created by a gravitational instability(DeCampli&Cameron,1979).Though our choice of initial states is not well constrained,the evolution of the protoplanets depends mostly on their mass and is rather insensitive to the details of the initial states(DeCampli&Cameron,1979).Figure3presents the evolution of a Jupiter-mass protoplanet for three diﬀerent initial states.The dotted curve represents a Jupiter mass object with an initial radius of∼0.5AU and a central temperature of360K.The solid and dashed-dotted curves show the evolution of Jupiter mass objects with initial radii of∼0.3and0.2AU and central temperatures of560 and800K,respectively.Although the evolution of the objects is not identical,it is similar and physical parameters do not diﬀer from each other by more than a factor of two.Diﬀerences are largest at the beginning of the evolution and decrease with time.Diﬀerences are found to be unimportant with regard to their eﬀects on core formation.When the central temperature of the protoplanets reaches∼1300K,dust grains evaporate and formation of the core stops.Protoplanets with masses of5M J or larger have central temperatures high enough to evaporate the grains even in their initial states and therefore they cannot form a core.[Fig.3]SedimentationIn order to examine whether core formation is possible,the sedimentation rate of the grains has to be computed.The number of grains within the body can change due to the combined processes of coagulation and sedimentation,and is given by the Smoluchowski equation(Wetherill1990),∂n(m,r,t)∂t =12mκ(m ,m−m )n(m ,r,t)n(m−m ,r,t)dm−n(m,r,t)∞κ(m,m )n(m ,r,t)dm −∇·F.(1) At each radius in the protoplanet r at some time t the number density of grains of mass between m and m+dm is given by n(m,r,t)dm.κ(m,m ),the collision kernel,is the probability that a grain of mass m will collide with and stick to a grain of mass m .Collisions occur due to the Brownian motion of the grains4and the fact that larger grains with higher sedimentation speeds can overtake smaller grains.In convective regions,where diﬀerent size grains respond diﬀerently to ﬂuctuations in the gas,we use the approximation of Weidenschilling (1986),based on the work of Volk and collaborators (Volk et al.1980;Markiewicz et al.1991),which takes into account the relative velocities between diﬀerent size grains in a turbulent gas.We assume that whenever two grains meet and collide,they stick to form a bigger grain.The ﬁrst integral gives the rate of formation of grains of mass m while the second integral is equal to the rate at which grains of mass m are removed as a result of collisions with grains of any other mass.The third term on the right side ∇·F is the ’transport term’.Transport of grains is possible due to sedimentation of grains (gravita-tional settling)or via turbulent transport in the convective regions.In the absence of convection the ﬂux of grains of mass m due to sedimentation is given by F sed (m,r,t )=n (m,r,t )v sed (m,r,t )where v sed (m,r,t )is the sedimentation velocity of a grain of mass m at planetary radius r and time t .The sedimentation velocity is found from the force balance between the local gravitational force and the gas drag on the grain (Podolak,2003).In the case of convective transport,we use an eddy diﬀusion approximation where the ﬂux is given by F conv (m,r,t )=−K (r,t ) ∂n (m,r,t )∂r+n (m,r,t )H (r,t ) where H (r,t )is the pressure scale height and K (r,t )is the eddy diﬀusion coeﬃcient,which is given by K =vH where v is the convective speed of the gas.The convective speeds are estimated from the mixing length recipe (MLR).Another eﬀect that can change the grain distribution is grain sublimation,which occurs when the ambi-ent temperature is high enough to evaporate the grains.Following Podolak (2003),we take the rate of vaporization to be dm dt =a 2P vap (T ) 8πµN A kT,(2)where a is the grain’s radius,T is the grain’s surface temperature,µis the mean molecular weight of the grain material taken to be 50(g/mole),P vap =10−24605T +13.176(dynes cm −2)is the vapor pressure of rocks(Podolak et al.,1988),k is Boltzmann’s constant,and N A is Avogadro’s number.The surface temperature of the grain is taken to be the same as the temperature of the surrounding gas.As can be seen from equation 2,the evaporation rate is a function of the grain size.One can estimate the evaporation time as a function of temperature by computing m/(dmdt )where m is the grain’s mass.Since the mass of a grain is proportionalto a 3,the evaporation time is proportional to a ,so larger grains require more time to evaporate.We take the evaporation temperature to be the temperature at which the evaporation time is shorter than ∼1year.We ﬁnd that for the grain sizes considered here (1,0.1and 0.01cm),the evaporation temperature can diﬀer by up to ∼100K.We take the lower bound of this range and set the evaporation temperature to be 1300K.The grains are assumed to be solid silicate spheres with a density of 3.4g cm −3and initial size a 0and are initially homogeneously mixed within the protoplanet.The size distribution is divided among bins with radii a i that are logarithmically spaced in mass.The size of a grain in bin i ,a i ,is taken to be a 02i/3.5The total number of bins is chosen to allow the grains to grow to sizes of at least10cm.Initially,only the smallest mass bin is populated,and as the grains collide and grow the larger size bins areﬁlled.An object of solar composition is expected to have2%of heavy elements,but this mass also includes the volatile material(ices and organics).The mass of the refractory material is expected to be∼1/3of the heavy element mass,and is taken to be0.0067%of the total mass.Re-condensation and breakup of grains are not included in the calculation.More details of the model can be found in Podolak(2003)and Helled et al.(2008).3ResultsMassive clumps can be extended and still be gravitationally bound but their internal temperatures are found to be too high to allow the grains to sediment and form a core.Weﬁnd that silicate grains evaporate immediately in objects of5M J or larger,and instead of contributing to core formation,the grains evaporate in the planetary envelope enriching it with refractory material.Protoplanets with smaller masses are cold enough to let the grains survive.We follow the silicate grains as they grow and sediment towards the center of the protoplanet.In convective regions,the grains are carried by the convective eddies until they grow large enough to decouple from the gas and settle to the center.Weﬁnd that once grains grow to sizes of 10cm or larger(the exact value depends on the convection velocity which changes with depth,time and planetary mass),they are massive enough to decouple from the gas,sediment to the center and form a core. The region of the core is represented by the innermost shell in the models,and its size varies with planetary mass.However,for all the cases considered here the size of this region is large(∼1011cm)and it contains gas in addition to the settled grains.Although this region might not represent a core in the traditional sense, the grains in this region remain there and they could eventually form a small silicate core in the center.The large number density of grains in the central region leads to frequent collisions that result in further growth. In addition,grains in the central region are typically larger than10cm,and therefore they are too large to be carried upward by convection into the planetary envelope.Once the central temperature is high enough to evaporate silicates(∼1300K)core growth stops.The refractory material inside the core region could segregate from hydrogen and helium and form an inner dense region.Table2lists the derived core masses for diﬀerent initial grain sizes(1,0.1and0.001cm)in protoplanets with masses between1M S to10M J.Table2also gives the time available for core formation,i.e.,the time it takes the body to reach internal temperatures of∼1300K.[Table.2]Weﬁnd that the core mass is not simply proportional to the mass of the protoplanet.More massive protoplanets contain a larger amount of silicate grains but at the same time,the protoplanets are hotter6and evolve faster.As a result,the available time to form a core decreases as protoplanet mass increases. Another eﬀect that delays core formation in more massive bodies is the higher convective velocities.The convectiveﬂux is found to be more vigorous in massive bodies,so grains have to grow to larger sizes in order to decouple from gas and sediment to the center.Low-mass clumps have the lowest convective velocities and longest evolution-a conﬁguration that supports core formation.However,due to their low mass theﬁnal core mass is relatively small.The resulting core masses for grains with initial radii between0.01cm and1cm are found to be very similar. This is due to the fact that small grains are coupled to the gas and have to grow to larger sizes(greater than∼10cm in radius)in order to to overcome the convectiveﬂux and settle to the center.Grains with smaller sizes than the ones considered here(<0.001cm)are expected to result in similar core masses.The growth of small grains is very fast due to the large number density that results in frequent collisions and further growth(Helled et al.2008).Grains with initial sizes larger then the sizes considered here would be large enough to quickly decouple from the gas and settle to the center.For these grain sizes,the core mass will be proportional to the planetary mass in protoplanets smaller than5M J.However,such initial sizes seem unrealistically large for the early formation time of gaseous protoplanets by a gravitational instability (Boss,1997).The last column in Table2gives the percentage of the core mass compared to the available grain mass.A Saturn mass body can sediment more than80%of the grain mass to its center,while more massive protoplanets sediment only∼10%of the available mass.Jupiter and SaturnA Saturn mass object is found to have the slowest contraction rate which leads to sedimentation of a larger amount of solids in comparison to a Jupiter mass object.In this study only grains originally present in the body were considered,and theﬁnal core masses were found to be∼0.25and0.5M⊕for Jupiter and Saturn, respectively.In reality,protoplanets are embedded in the protoplanetary disk surrounding the young sun, and planetesimal accretion is likely to take place.Planetesimal accretion can add a signiﬁcant amount of refractory material to the protoplanet that can settle to the center and increase theﬁnal core mass(Helled et al.,2006;2008).Although conditions in the solar nebula are unknown,its characteristics can be estimated and therefore the planetesimal accretion rate of proto-Jupiter and proto-Saturn can be approximated.We assume that Jupiter and Saturn have not migrated signiﬁcantly and deﬁne the total mass of solids in their feeding zones as(Pollack et al.1996),M solids=π(a2out−a2in)σsolids,(3) where a in and a out are the inner and outer radii of the planetary feeding zone,respectively.The solid surface density of the disk is taken to beσ=10g cm−2for Jupiter(5.2AU)andσ=3g cm−2for Saturn(9.5AU),7values that are a factor of∼3times higher than the”minimum-mass solar nebula”(MMSN)values(Pollack et al.,1996).The planetary feeding zone represents the zone in which solid planetesimals are uniformly spread on either side of the orbit to a distance a f,and its size changes with the eccentricity and inclination of the planetesimals’orbits and the planetary Hill sphere radius(Pollack et al.1996).a out=a+a f and a in=a−a f,where a is the planet’s semimajor axis.Following Pollack et al.(1996),we take a f∼2×1013 cm and a f∼2.6×1013cm for Jupiter and Saturn,respectively.The size of the feeding zone is taken to be constant with time,so planetesimals cannot get into or out of the feeding zone.Under these assumptions, the mass of solids in Jupiter’s and Saturn’s feeding zone are found to be∼35M⊕,and∼23M⊕,respectively.For simplicity,we assume that a similar percentage of the grains sediments to the core as in the case when only the grains originally present in the body were considered(previous section).In principle,when plan-etesimals are accreted they lose material due to gas drag as they pass through the planetary envelope until they break or get fully evaporated.As a planetesimal penetrates deeper into the interior,the surrounding density increases,the drag force is stronger,and more material can evaporate.In that case the additional silicates will tend to be more concentrated in central regions.Our assumption,that the additional material is distributed in proportion to the gas density,results in a concentration of silicates toward the center(Helled et al.,2008).The planetesimals are assumed to be composed of a mixture of ice,silicates and CHON(an average density of∼2g cm−3).Again,since the solid material contains ices and organics as well as silicates,the available rocky material is smaller(∼1/3of the total mass)and is taken to be∼12M⊕and8M⊕for Jupiter and Saturn,respectively.Theﬁnal core masses of Jupiter and Saturn can change with planetesimal size,the time in which planetesimals are formed,and the size distribution in which the additional material is added to the protoplanets.Three possible scenarios are considered:1.Planetesimals are present during the pre-collapse stage and the additional material is added as smallgrains:For planetesimal sizes of10km(or smaller),weﬁnd that the long contraction times of the protoplanets insure the accretion of all the solid material in their feeding zone before the internal temperatures become high enough to evaporate the rocky material.Taking the accreted material added to the protoplanet as small grains with similar sizes as the ones originally present in the body, Saturn’s core is found to be as big as8M⊕,while Jupiter’s core mass does not exceed2M⊕.2.Planetesimals are present during the pre-collapse stage and the additional material is added as plan-etesimal fragments:There is a good chance that the size distribution of the additional material is quite diﬀerent from that of the initial grain distribution in the envelope.As a planetesimal passes through the planetary envelope pressure gradients across the planetesimal can exceed the material strength of8the body,resulting in planetesimal fragmentation(Podolak et al.,1988).Although some fraction of the planetesimal mass will be evaporated in the envelope as the planetesimal passes through the gas, most of the mass will be in fragments of a few meters in size.Fragments with these sizes have high sedimentation speeds and will settle to the center almost immediately.Most of the accreted mass will then be in the core region.Theﬁnal core masses of Jupiter and Saturn can then be as large as∼12 M⊕and8M⊕,respectively.3.Planetesimals are not present during the pre-collapse stage:Gravitational instabilities occur relativelyearly in the history of the protoplanetary disk(∼103years)and it is not clear whether planetesimals have been formed(Boss,1997;Dominik et al.,2007).If planetesimals are not yet formed,there will be no additional material contributing to core formation and the core masses of Jupiter and Saturn will be as small as0.25M⊕and0.5M⊕,respectively(Table2).The planetesimals could be accreted at a later stage of the planetary evolution when the protoplanets are signiﬁcantly hotter.In this case,the accreted material will contribute to the planetary envelope enrichment in silicates,ices and organics.In this scenario Jupiter and Saturn core masses are too low compared to theoretical models that estimate Jupiter and Saturn core masses(Saumon&Guillot,2004).4Discussion and ConclusionsWe followed the evolution of gaseous protoplanets formed by disk instability.We considered protoplanets with masses between1Saturn mass and10Jupiter masses,a mass range that covers most of the observed mass range of extra-solar giant planets.The protoplanets were taken to be extended and yet gravitationally bound to insure further contraction.We examined the possibility of core formation as a result of sedimenta-tion of silicate grains.Grain settling can occur in protoplanets which are cold enough and have a contraction time-scale long enough for the grains to grow(decouple from the convectiveﬂux in convective regions)and sediment to the center.The grain sedimentation process is found to be favorable for low mass bodies,due to lower internal temperatures,lower convective velocities and longer contraction time in the pre-collapse stage.Weﬁnd that protoplanets with masses of≥5M J are too hot to allow core formation and therefore will have no solid cores.The core masses presented in Table2are given under the assumption that the protoplanets are isolated and the grain mass is taken to be a small fraction(∼0.007%)of the planetary mass.As discussed earlier, planetesimal accretion can add a signiﬁcant amount of refractory material to the protoplanets(Helled et al.,2006,2008).However,the accreted material contributes to core formation only if accretion occurs before the internal temperatures are high enough to evaporate the grains.Only protoplanets with masses lower than5M J will have larger cores than presented in Table2.In the case of more massive protoplanets,the9additional solids would only enrich the planetary envelope with silicates,ices and organics regardless of the accretion timing.If a signiﬁcant amount of material is accreted during the pre-collapse stage,the core mass in low mass protoplanets is expected to be inversely proportional to the planetary mass.Theﬁnal core mass will not only depend on the time at which the solids are captured but also on the solid surface density of the protoplanetary disk,the distance at which the planet is formed,etc.We estimated theﬁnal core masses of Jupiter and Saturn when planetesimal accretion was included.However,due to uncertainties in the size distribution of the accreted material as it enters the protoplanet,a range of core masses is found.Jupiter and Saturn core mass can change from2to12M⊕,and∼8M⊕,respectively(see previous section).The results presented here are most robust for protoplanets with masses≥5M J.The temperature gradient inside these bodies is least eﬀected by stellar heating,and in addition,the core size is unaﬀected by planetes-imal accretion,since these planets have no core due to their high internal temperatures.If heavy elements are added due to planetesimal accretion they will be spread throughout the planet’s interior.Our conclusion that massive giant planets have no solid cores diﬀers from the core accretion model which predicts that massive giant planets have a solid core of the order of∼10M⊕(Pollack et al.,1996;Hubickyj et al.,2005). Future determination of the core mass of massive extra-solar giant planets could help to distinguish between the two possible mechanisms for giant planet formation.Gravitational settling of dust is also known to occur in brown dwarf atmospheres.Grain sedimentation ex-plains the element depletion,spectra and weather-like features in cool brown dwarf atmospheres(Woitke& Helling,2002).In a similar process as considered here,drops of dust with sizes large enough to overcome the convectiveﬂux settle below the visible atmospheres,forming cloud layers(Ackerman&Marley,2001;Helling &Woitke,2006).Grain sedimentation(and cloud formation)can therefore,also occur in a later stage of the evolution of the bodies considered here.However,in this case the dust depletion in the atmosphere will not be a result of core formation,but grain settling below the observed atmosphere.This process imparts further complexity to observational tests of the theory.Our results rely on several assumptions.The protoplanets were taken to be isolated so radiation from the young star was not included.Clumps forming in planetary disks are exposed to stellar radiation,especially in the inner part of the disk.Stellar radiation can heat the bodies,increasing the internal temperatures and inhibiting core formation.To keep the calculation as general as possible we chose to make no assump-tions regarding the location of the clump.In addition,since in the disk instability model protoplanets are usually formed in the cold outer regions where the disk is cold enough to become gravitationally unstable (Boss,1997;Mayer et al.,2002)stellar radiation is expected to be relatively weak.Nevertheless,the eﬀect of stellar radiation should be included in future work,especially due to the possibility of inward migration that can place the bodies in regions where stellar radiation is stronger(Papaloizou et al.,2007).The core formation process itself was not included in the evolutionary simulation.Grain settling can gener-10。

Bimodal Galaxies and Bimodality in Globular Cluster Systems

a r X i v :a s t r o -p h /0511291v 1 10 N o v 2005Bimodal Galaxies and Bimodality in Globular Cluster SystemsDuncan A.ForbesCentre for Astrophysics &Supercomputing,Swinburne University,Hawthorn,VIC 3122,Australiadforbes@.au ABSTRACT Various galaxy properties are not continuous over a large range in mass,but rather reveal a remarkable transition or ‘bimodality’at a stellar mass of 3×1010M ⊙.These properties include colors,stellar populations,Xray emission and mass-to-light ratios.This behavior has been interpreted as the transition from hot to cold ﬂows by Dekel &Birnboim (2005).Here we explore whether globular cluster (GC)systems also reveal a bimodal nature with regard to this critical mass scale.Globular clusters probe star for-mation at early epochs in the Universe and survive subsequent galaxy mergers and accretions.We use new data from the ACS Virgo Cluster Survey (Peng et al.2005),which provides a homogeneous sample of the GC systems around one hundred Virgo early-type galaxies covering a range of ﬁve hundred in galaxy mass.Their classiﬁcation of the GC color distributions is taken to examine a key quantity –the number of GCs per unit galaxy luminosity.Below the critical mass,this quantity (called the GC speciﬁc frequency)increases dramatically in its mean value and spread.This increase may be due to regulated star formation in low mass galaxies,which in turn is due to mass loss via winds and the tran-sition from hot to cold gas accretion ﬂows.We also note that above the criticalmass,galaxies possess two GC subpopulations (with blue and red mean colors)but below this mass,galaxies reveal an increasing proportion of single (blue)GC systems.Subject headings:globular clusters;clusters:individual:Virgo;galaxies:ellipti-cal;galaxies:formation1.IntroductionThe general galaxy population reveals a bimodal color-magnitude distribution (Lilly et al.1995),which is seen in both the local Universe by SDSS (Blanton et al.2005)and outto modest redshifts in COMBO17(Bell et al.2004).This blue/red bimodality shows a well-deﬁned transition at a stellar mass of about3×1010M⊙or halo mass of6×1011M⊙(e.g. in SDSS by Kauﬀmann et al.2003).Other galaxy properties,such as stellar populations (in2dFGRS by Madgwick et al.2003),Xray properties(O‘Sullivan et al.2001)and galaxy mass-to-light ratios(Marinoni&Hudson2002)also reveal a bimodality about this critical stellar mass(see Dekel&Birnboim2005for a more complete list).This bimodality has been interpreted in terms of whether the accreted material under-goes a virial shock when it enters the galaxy halo(a hotﬂow)or not(a coldﬂow).Recent simulations show that the transition from hot to cold mode accretion occurs at the same critical stellar mass as the observed galaxy bimodality(Keres et al.2005;Dekel&Birnboim 2005).It is of interest to know whether globular cluster(GC)systems show a dichotomy along with the general galaxy population or if their properties are continous over a large range in galaxy mass.The spectra of GCs in massive galaxies indicate that the bulk of the GCs are old,i.e.≥10Gyrs with formation at epochs z f≥2(e.g.Strader et al.2005a).The situation for low mass galaxies is less well constrained.However,recent Keck spectra of GCs in the Virgo dwarf VCC1087indicate that they are also old and hence formed in the very early stages of the dwarf galaxy formation(Beasley et al.2005).Thus GCs are formed during the earliest star and galaxy formation processes in the Universe.Being of single age and chemical composition,they do not suﬀer from the complication of multiple star formation events as their host galaxies do.They are also fairly robust,with many surviving the process of galaxy mergers and accretions.Globular clusters therefore provide a useful probe of the early stages of galaxy formation and their subsequent evolution.The number of globular clusters per unit galaxy luminosity(called speciﬁc frequency)is a key measure of GC systems,which varies with Hubble type and environment(see review by Elmegreen1999).In this Letter we examine how the GC speciﬁc frequency varies in relation to the critical mass and hence how it relates to the widely observed bimodality in galaxy properties.From the Advanced Camera for Surveys(ACS)Virgo Cluster Survey, Peng et al.(2005)noted that the only property of GC systems that varied with the critical stellar mass was the fraction of red GCs,i.e.it is nearly constant for high masses and declines rapidly for low masses.Strader et al.(2005b)studied the total speciﬁc frequency for a subset of37Virgo dwarf galaxies(all with masses below the critical mass).They found no strong diﬀerence between dE and dE,N dwarfs,contrary to the earlier claims of Miller et al.(1998) using WFPC2data.Here,using the ACS data of Peng et al.,we extend these earlier works to investigate the GC speciﬁc frequency for a homogeneous sample of one hundred early-type galaxies in the Virgo cluster.We also brieﬂy discuss the implications for GC and galaxyformation.2.Observational DataThe ACS Virgo Cluster Survey(Cote et al.2004)consists of deep g and z band imagingof the100brightest early-type galaxies in the Virgo cluster,using the ACS on-board theHubble Space Telescope.This survey has the advantages of increased depth,spatial coverageand metallicity sensitivity(to detect any GC subpopulations)compared to previous WFPC2 studies(e.g.Forbes et al.1996;Larsen et al.2001;Kundu&Whitmore2001).Blankﬁelds were used to assist in determining the background contamination rate,which is very low. The integration times are such as to include∼90%of the GC luminosity function;the spatial coverage is complete for small galaxies but severely incomplete for the GC systems of the largest galaxies(see below for further details).Recently Peng et al.(2005)examined the g−z GC color distributions for each galaxy in the survey(only VCC1627had no detectable GCs).A number of galaxies revealed bi-modal GC color distributions in the largest homogeneous sample of GC systems to date. Such bimodality has been detected in the GC systems of numerous large galaxies(e.g.Zepf &Ashman1993;Forbes et al.1996;Larsen et al.2001;Kundu&Whitmore2001).This color bimodality indicates two distinct GC subpopulations are present–one blue and one red.These subpopulations are thought,from spectroscopy,to be metal-poor and metal-rich respectively,both being≥10Gyrs old with hints that the red GCs may be slightly younger than the blue GCs(e.g.Strader et al.2005a).Other GC properties,such as their orbits and spatial distributions,are also distinct when separated into blue/red subpopulations.Peng et al.determined mean colors for the blue and red subpopulations if the distribution wasstatistically bimodal;for unimodal color distributions,the GCs are all blue.They also list the number of GCs observed and the blue/red fraction in bimodal systems.From this data we have determined the speciﬁc frequencies of the blue and red GCs separately,i.e.S Nblue=f blue×N GC×100.4(M V+15)(1) S Nred=f red×N GC×100.4(M V+15)(2) where f is the fraction of blue or red GCs,N GC is the total number of GCs and M V is the galaxy absolute V-band magnitude calculated from the B-band values listed in Cote etal.(2004)assuming B–V=0.9with no reddening and m–M=31.09.Ideally one would liketo explore the relation between GC subpopulations and the appropriateﬁeld stars withinthe galaxy,but resolving individual stellar populations is currently only possible for the very nearest elliptical galaxies(e.g.Harris,Harris&Poole1999).3.ResultsIn Fig.1we plot the S Nblue and S Nred separately against the host galaxy stellar mass. To calculate stellar masses we have assumed a constant M/L V=5from the dynamical study of Virgo dwarf galaxies by Geha et al.(2002).We note that a similar value is obtained by Fukugita et al.(1998).This gives a range in mass of a factor of∼500.The data points with an S Nred value of zero indicate the GC systems that appear unimodal in color,i.e.the GCs are all attributed to the blue subpopulation by Peng et al.(2005).For such systems we show typical errors.The plot also shows the critical stellar mass of3×1010M⊙(equivalent to M V=–19.6),about which the general galaxy population reveals a bimodality in properties (see summary by Dekel&Birnboim2005).The compact elliptical NGC4486B(VCC1297) has been excluded from this plot as it has an abnormally high speciﬁc frequency of S Nblue= 9.5and S Nred=4.1(this is probably due to a combination of tidal stripping reducing the galaxy’s luminosity and contamination from M87’s extensive GC system;Peng et al.2005).Figure1shows that below the critical mass galaxies reveal a wide range in GC speciﬁc frequencies,whereas above the critical mass the speciﬁc frequencies are conﬁned to a rela-tively narrow range.For masses below the critical mass we include a curve showing a galaxy mass-to-light ratio M/L V∝M−2/3(Dekel&Birnboim2005),which corresponds to L V∝M5/3.The vertical normalization is arbitrary.Below a mass of109M⊙the trend for higher S N values continues(Durrell et al.1996) but appears to halt at galaxy masses of∼107M⊙which have no GC systems(Forbes et al.2000;Strader et al.2005a).This lower mass limit for the occurrence of GC systems may be set by atomic cooling,which is ineﬃcient for virial temperatures less than104K corresponding to halo masses less than108M⊙(Moore et al.2005).Above the critical mass,both the red and blue speciﬁc frequencies are fairly constant. For galaxies with masses3×1010<M/M⊙<3×1011the mean S Nred=0.51±0.05 and the mean S Nblue=0.75±0.06.Figure1also shows the location of the bulge speciﬁc frequency for M31and the Milky Way from Forbes et al.(2001),i.e.the total number of red GCs per unit bulge stellar mass.Within the errors,the S Nred of the bulges of these two spiral galaxies are consistent with the trend seen in the Virgo early-type galaxies.For the more massive galaxies,the ACS Virgo Cluster Survey is missing a signiﬁcant fraction of the GC system beyond its3.4×3.4arcminﬁeld-of-view which would render theS N value a signiﬁcant underestimate,however this only signiﬁcantly aﬀects a small fraction of the overall survey.For example,the GC system of Virgo’s brightest galaxy M49(VCC 1226)extends out to23arcmin and has a total GC population of5,900(Rhode&Zepf2001). For Virgo dwarf galaxies,Durrell et al.(1996)ﬁnd that the entire GC system is contained within0.5arcmin.The transition from partial to full areal coverage by the ACS is not well deﬁned but occurs at intermediate galaxy luminosities.For example,a wide area study of the GC system in the low luminosity(M B=–19.35)Fornax elliptical NGC1374suggests about83%of the GC system would lie within the ACSﬁeld-of-view if placed at the Virgo distance.This galaxy would be the16th brightest in the ACS Virgo sample.An additional, but smaller eﬀect,for the brightest galaxies is that the blue-to-red GC ratio will also be underestimated as blue GCs are preferentially located in galaxy outer regions.4.DiscussionFigure1shows that GC speciﬁc frequencies reveal a large range in values below the critical stellar mass,and that speciﬁc frequencies are generally higher in lower mass galaxies. If GCs form at early epochs and with a similar eﬃciency for all galaxies(McLaughin1999; Moore et al.2005),then some mechanism must be reducing the stellar mass in low mass galaxies to raise the GC speciﬁc frequencies.Physical mechanisms for regulating the stellar mass include:tidal stripping from the interaction of a dwarf galaxy with a massive galaxy (e.g.Mayer et al.2001;Forbes et al.2003),ram pressure stripping of dwarf galaxies(van Zee, Skillman&Haynes2004),photoionization at early epochs that suppresses further globular cluster and star formation(Beasley et al.2002;Santos2003;Bekki2005;Moore et al.2005), supernova feedback and mass loss via winds(Durrell et al.1996;Dekel&Silk1986)and cold accretionﬂows(Keres et al.2005;Dekel&Birnboim2005).The latter has the advantage of explaining the remarkable transition in GC speciﬁc frequency at the critical stellar mass seen in Fig.1,as well as the bimodality in galaxian properties.We note that a halo mass-to-light ratio of the form M/L V∝M−2/3given by Dekel &Birnboim(2005),equivalent to L V∝M5/3,provides a reasonable representation of the increasing GC speciﬁc frequency with decreasing mass.However there is still substantial spread in the S N values.In other words,below the critical mass the number of GCs per unit galaxy mass appears to vary from galaxy to galaxy assuming the mass-to-light ratio varies in a systematic way with halo mass.This may indicate a variation of baryonic to halo dark mass.Above the critical mass there is evidence for a fairly constant S Nred,i.e.a constant number of red GCs per unit galaxy luminosity,which may extend to the bulge component ofspirals asﬁrst suggested by Forbes et al.(2001).This would support the idea that spheroid growth is intimately linked to the formation of red GCs.Interestingly,the correlation between the mean color of the GC subpopulations and galaxy luminosity(or mass)does not show a strong break or change in slope at the critical stellar mass.For example,both Strader et al.(2005b)and Peng et al.(2005)found a continuous GC color–galaxy luminosity trend in the ACS Virgo Cluster Survey data used here.Thus the number of GCs per unit galaxy luminosity and the blue-to-red fractions change at the critical mass,whereas the individual properties responsible for GC colors (e.g.age and metallicity)do not change abruptly.This is consistent with the idea that GC individual properties areﬁxed at early epochs,whereas galaxy properties(such as total luminosity)can be modiﬁed by subsequent evolution.In terms of the evolutionary scenario outlined by Dekel&Birnboim(2005),low mass galaxies at high redshift are largely blue starforming disks which grow by accretion and cold ﬂows.Supernova feedback and mass loss regulate their star formation.Shock-heating at a lower redshift in dense environments shutoﬀs the coldﬂows,which in turn suppresses any further star formation.These galaxies move quickly onto the red sequence.Subsequent gas-poor(‘dry’)merging allows the red sequence to extend from low mass galaxies to the most massive ellipticals seen today.Star formation via cold accretionﬂows is thought to be very eﬃcient,thus to explain the higher speciﬁc frequency of low mass galaxies as seen in Fig.1GC formation must be even more eﬃcient or the stellar luminosity is subsequently reduced.In nearby galaxies for which we can assign the blue GCs(assumed to be theﬁrst formed)to the appropriate fraction of the galaxy starlight(e.g.NGC5128;Harris,Harris&Poole1999)high S Nblue values,and hence high GC formation eﬃciencies,are inferred.So it may be possible that early GC formation in low mass galaxies is similarly enhanced relative to the star formation but this is very hard to verify observationally.Reduction of the stellar luminosity(e.g.due to supernova winds,stripping etc)is also a possibility.An additional feature of the critical mass is that it represents the onset of unimodal GC color distributions(with the exception of the star-forming SB0galaxy NGC4340(VCC 654)which may have its luminosity enhanced by ongoing star formation).Thus essentially all galaxies above the critical mass possess bimodal GC color distributions,i.e.evidence for blue and red GC subpopulations.Below the critical mass,the frequency of unimodal (i.e.blue only)GC color distributions increases,and conversely the incidence of bimodality decreases,for decreasing host galaxy mass(see Table1).We speculate that this tendency towards blue-only GC systems may be related to diﬀer-ent evolutionary paths for dwarf galaxies in cluster environments.For example if a bulgeless dIrr is transformed into a dSph/dE via tidal stripping(Mayer et al.2001),then we might expect the resulting dSph/dE to have few if any red GCs.The diversity of kinematic proper-ties for dwarfs(both non-rotating and rotating systems have been found)suggests multiple evolutionary paths are possible(e.g.van Zee,Skillman&Haynes2004).We note that the kinematic anisotropy parameter reveals increased scatter for dwarf galaxies below the critical mass,reminiscent of Fig.1.5.ConclusionsLarge surveys such as the2dF,SDSS and COMBO17have focused attention on the fact that the general galaxy population reveals a bimodality in properties at a critical stellar mass of∼3×1010M⊙.These properties are largely bimodal in nature,and include blue vs red colors,discrete vs diﬀuse sources for the Xray emission and disk vs bulge domination.To this list,we add another two properties that reveal a bimodality around this critical mass,namely:•Above the critical mass galaxies reveal a relatively narrow range in globular cluster speciﬁc frequencies,whereas below they show an increasing mean value and spread.•Above the critical mass galaxies possess two globular cluster subpopulations,below they increasingly reveal single blue globular cluster populations.Several physical mechanisms,which regulate star formation,may explain the increased speciﬁc frequencies of low mass galaxies,however the observed transition corresponds to the critical stellar mass which would therefore favor an origin in supernova feedback and accretionﬂows as suggested by Dekel and co-workers.We thank the ARC forﬁnancial support.We thank K.Bekki,rsen,R.Proctor,L. Spitler for useful discussions.The referee is also thanked for several useful suggestions.REFERENCESBeasley,M.,Baugh,C.,Forbes,D.,Sharples,R.,Frenk,C.,2002,MNRAS,333,383 Beasley,M.,et al.2005,MNRAS,submittedBekki,K.,2005,ApJL,626,93Bell,E.,et al.2004,ApJ,608,752Blanton,M.,Eisenstein,D.,Hogg,D.,Schlegel,D.,Brinkmann,J.,2005,ApJ,629,143 Cote,P.,et al.2004,ApJS,153,223Dekel,A.,Silk,J.,1986,ApJ,303,39Dekel,A.,Birnboim,Y.,2005,astro-ph/0412300Durrell,P.,Harris,W.,Geisler,D.,Pudritz,R.,1996,AJ,112,972Elmegreen,B.,1999,in Toward a New Millennium in Galaxy Morphology,ed.D.Block,I.Puerari,A.Stockton and D.Ferreira,Kluwer DordrechtForbes,D.,Franx,M.,Illingworth,G.,Carollo,C.,1996,ApJ,467,126Forbes,D.,Masters,K.,Minniti,D.,Barmby,P.,2000,A&A,358,471Forbes,D.,Brodie,J.,Larsen,S.,2001,ApJ,556,83Forbes,D.,Beasley,M.,Bekki,K.,Brodie,J.,Strader,J.,2003,Science,301,1217 Fugukita,M.,Hogan,C.,Peebles,P.,1998,ApJ,503,518Geha,M.,Guhathakurta,P.,van der Marel,R.,2002,AJ,124,3073Harris,G.,Harris,W.,Poole,G.,1999,AJ,117,855Kauﬀmann,G.,et al.2003,MNRAS,341,54Keres,Katz,N.,Weinberg,D.,Dave,R.,2005,MNRAS,363,2Kundu,A.,Whitmore,B.,2001,AJ,121,2950Larsen,S.,Brodie,J.,Huchra,J.,Forbes,D.,Grillmair,C.,2001,AJ,121,2974Lilly,S.,Tresse,L.,Hammer,F.,Crampton,D.,Le Fevre,O.,1995,ApJ,455,108 Madgwick,D.,Somerville,R.,Lahav,O.,Ellis,R.,2003,MNRAS,343,871Marinoni,C.,Hudson,M.,2002,ApJ,569,101Mayer,L.,et al.2001,ApJ,559,754McLaughlin,D.,1999,AJ,117,2398Miller,B.,Lotz,J.,Ferguson,H.,Stiavelli,M.,Whitmore,B.,1998,ApJL,508,133 Moore,B.,Diemand,J.,Madau,P.,Zemp,M.,Stadel,J.,2005,MNRAS,in prep.O’Sullivan,E.,Forbes,D.,Ponman,T.,2001,MNRAS,328,461Peng,E.,et al.2005,astro-ph/0509654Rhode,K.,Zepf,S.,2001,AJ,121,210Santos,M.,2003,in Extragalactic Globular Cluster Systems,ed.M.Kissler-Patig,Springer Heidelberg,p348Strader,J.,Brodie,J.,Forbes,D.,2004,AJ,127,3431Strader,J.,Brodie,J.,Cenarro,A.,Beasley,M.,Forbes,D.,2005a,AJ,130,1315 Strader,J.,Brodie,J.,Spitler,L.,Beasley,M.,2005b,astro-ph/0508001van Zee,L.,Skillman,E.,Haynes,M.,2004,AJ,128,121Zepf,S.,Ashman,K.,1993,MNRAS,264,611Fig.1.—Globular cluster speciﬁc frequency S N versus host galaxy stellar mass.The blue ﬁlled circles indicate the blue S N and the red open circles the red S N values for Virgo cluster early-type galaxies.Galaxies with no red GCs are indicated by red open circles of value zero. The S N values of high mass galaxies are underestimated due to the limited ACSﬁeld-of-view.A vertical dashed line is located at the critical stellar mass of3×1010M⊙(or M V=–19.6, a constant M/L V=5is assumed).Galaxies below the critical stellar mass reveal a wide range of globular cluster speciﬁc frequencies and an increasing proportion of galaxies have unimodal blue GC systems.The redﬁlled squares with error bars represent the bulge S N values for M31and the Milky Way.The solid curve represents a galaxy luminosity L V∝Mass5/3dependence(see text for details).–11–Table1.Fraction of Unimodal GC Color Distributions Log Mass(M⊙)No.of Galaxies%Unimodal。

有关天文学的单词

absolute stability 绝对稳定性absorbing dust mass 致吸尘物质absorption trough 吸收槽abundance standard 丰度标准星accreting binary 吸积双星accretion column 吸积柱accretion flow 吸积流accretion mound 吸积堆accretion ring 吸积环accretion stream 吸积流acoustic mode 声模active binary 活动双星active chromosphere binary 活动色球双星active chromosphere star 活动色球星active optics 主动光学actuator 促动器Adams ring 亚当斯环adaptive optics 自适应光学additional perturbation 附加摄动AGB, asymptotic giant branch 渐近巨星支Alexis, Array of Low-Energy X-ray 〈阿列克希斯〉低能X 射线Imaging Sensors 成象飞行器AM Herculis star 武仙AM 型星amplitude spectrum 变幅谱angular elongation 距角anonymous galaxy 未名星系anonymous object 未名天体anti-jovian point 对木点annular-total eclipse 全环食aperture photometry 孔径测光APM, Automated Photographic Measuring 〈APM〉底片自动测量仪systemapoapse 远质心点apoapse distance 远质心距apogalacticon 远银心点apomartian 远火点apparent association 表观成协apparent luminosity function 视光度函数apparent superluminal motion 视超光速运动apsidal advance 拱线进动apsidal precession 拱线进动Arcturus group 大角星群area image sensor 面成象敏感器area photometry 面源测光area spectroscopy 面源分光argument of pericentre 近心点幅角ASCA, Advanced Satellite for Cosmology〈ASCA〉宇宙学和天体物理学and Astrophysics 高新卫星asteroidal dynamics 小行星动力学asteroidal resonance 小行星共振asteroid family 小行星族asteroid-like object 类小行星天体asteroseismology 星震学astration 物质改造astroparticle physics 天文粒子物理学astrostatistics 天文统计学asymptotic branch 渐近支asymptotic branch giant 渐近支巨星atmospheric parameter 大气参数ATNT, Australia Telescope National 澳大利亚国立望远镜FacilityATT, Advanced Technology Telescope 〈ATT〉高新技术望远镜automated measuring machine 天文底片自动测量仪automatic photooelectric telescope 自动光电测光望远镜( APT )AXAF, Advanced X-ray Astrophysical 高新X射线天体物理台FacilityBaade's window 巴德窗Baade—Wesselink analysis 巴德—韦塞林克分析Baade—Wesselink mass 巴德—韦塞林克质量Baade—Wesselink method 巴德—韦塞林克方法Baade—Wesselink radius 巴德—韦塞林克半径background galaxy 背景星系Barnard's galaxy ( NGC 6822 ) 巴纳德星系barycentric dynamical time ( TDB ) 质心力学时Belinda 天卫十四Bianca 天卫八bidimensional spectrography 二维摄谱bidimensional spectroscopy 二维分光Big-Bang nucleosynthesis 大爆炸核合成binarity 成双性binary asteroid 双小行星binary flare star 耀变双星binary millisecond pulsar 毫秒脉冲双星binary protostar 原双星bioastronomy 生物天文学bipolar jet 双极喷流bipolar outflow 偶极外向流bipolar planetary nebula 双极行星状星云blazar 耀变体blazarlike activity 类耀活动blazarlike object 耀变体Black-eye galaxy ( M 64 ) 黑眼星系BL Lacertae object 蝎虎天体BL Lacertid 蝎虎天体blue compact galaxy ( BCG ) 蓝致密星系blue straggler 蓝离散星bolometric albedo 热反照率bolometric light curve 全波光变曲线bolometric temperature 热温度Bootes void 牧夫巨洞bow-shock nebula 弓形激波星云box photometry 方格测光broad-band imaging 宽波段成象broad-line radio galaxy ( BLRG ) 宽线射电星系buried channel CCD 埋沟型CCDButterfly nebula 蝴蝶星云BY Draconis star 天龙BY 型星BY Draconis variable 天龙BY 型变星CAMC, Carlsberg Automatic Meridian 卡尔斯伯格自动子午环Circlecannibalism 吞食cannibalized galaxy 被吞星系cannibalizing galaxy 吞食星系cannibalizing of galaxies 星系吞食carbon dwarf 碳矮星Cassegrain spectrograph 卡焦摄谱仪Cassini 〈卡西尼〉土星探测器Cat's Eye nebula ( NGC 6543 ) 猫眼星云CCD astronomy CCD 天文学CCD camera CCD 照相机CCD photometry CCD 测光CCD spectrograph CCD 摄谱仪CCD spectrum CCD 光谱celestial clock 天体钟celestial mechanician 天体力学家celestial thermal background 天空热背景辐射celestial thermal background radiation 天空热背景辐射central overlap technique 中心重迭法Centaurus arm 半人马臂Cepheid distance 造父距离CFHT, Canada-Franch-Hawaii Telecope 〈CFHT〉望远镜CGRO, Compton Gamma-Ray Observatory 〈康普顿〉γ射线天文台chaos 混沌chaotic dynamics 混沌动力学chaotic layer 混沌层chaotic region 混沌区chemically peculiar star 化学特殊星Christmas Tree cluster ( NGC 2264 ) 圣诞树星团chromosphere-corona transition zone 色球-日冕过渡层chromospheric activity 色球活动chromospherically active banary 色球活动双星chromospherically active star 色球活动星chromospheric line 色球谱线chromospheric matirial 色球物质chromospheric spectrum 色球光谱CID, charge injected device CID、电荷注入器件circular solution 圆轨解circumnuclear star-formation 核周产星circumscribed halo 外接日晕circumstellar dust disk 星周尘盘circumstellar material 星周物质circumsystem material 双星周物质classical Algol system 经典大陵双星classical quasar 经典类星体classical R Coronae Borealis star 经典北冕R 型星classical T Tauri star 经典金牛T 型星Clementine 〈克莱芒蒂娜〉环月测绘飞行器closure phase imaging 锁相成象cluster centre 团中心cluster galaxy 团星系COBE, Cosmic Background Explorer 宇宙背景探测器coded mask imaging 编码掩模成象coded mask telescope 编码掩模望远镜collapsing cloud 坍缩云cometary burst 彗暴cometary dynamics 彗星动力学cometary flare 彗耀cometary H Ⅱregion 彗状电离氢区cometary outburst 彗爆发cometary proplyd 彗状原行星盘comet shower 彗星雨common proper-motion binary 共自行双星common proper-motion pair 共自行星对compact binary galaxy 致密双重星系compact cluster 致密星团; 致密星系团compact flare 致密耀斑composite diagram method 复合图法composite spectrum binary 复谱双星computational astrophysics 计算天体物理computational celestial mechanics 计算天体力学contact copying 接触复制contraction age 收缩年龄convective envelope 对流包层cooling flow 冷却流co-orbital satellite 共轨卫星coplanar orbits 共面轨道Copernicus 〈哥白尼〉卫星coprocessor 协处理器Cordelia 天卫六core-dominated quasar ( CDQ ) 核占优类星体coronal abundance 冕区丰度coronal activity 星冕活动、日冕活动coronal dividing line 冕区分界线coronal gas 星冕气体、日冕气体coronal green line 星冕绿线、日冕绿线coronal helmet 冕盔coronal magnetic energy 冕区磁能coronal red line 星冕红线、日冕红线cosmic abundance 宇宙丰度cosmic string 宇宙弦cosmic void 宇宙巨洞COSMOS 〈COSMOS〉底片自动测量仪C-O white dwarf 碳氧白矮星Cowling approximation 柯林近似Cowling mechnism 柯林机制Crescent nebula ( NGC 6888 ) 蛾眉月星云Cressida 天卫九critical equipotential lobe 临界等位瓣cross-correlation method 交叉相关法cross-correlation technique 交叉相关法cross disperser prism 横向色散棱镜crustal dynamics 星壳动力学cryogenic camera 致冷照相机cushion distortion 枕形畸变cut-off error 截断误差Cyclops project 〈独眼神〉计划D abundance 氘丰度Dactyl 艾卫dark halo 暗晕data acquisition 数据采集decline phase 下降阶段deep-field observation 深天区观测density arm 密度臂density profile 密度轮廓dereddening 红化改正Desdemona 天卫十destabiliizing effect 去稳效应dew shield 露罩diagonal mirror 对角镜diagnostic diagram 诊断图differential reddening 较差红化diffuse density 漫射密度diffuse dwarf 弥漫矮星系diffuse X-ray 弥漫X 射线diffusion approximation 扩散近似digital optical sky survey 数字光学巡天digital sky survey 数字巡天disappearance 掩始cisconnection event 断尾事件dish 碟形天线disk globular cluster 盘族球状星团dispersion measure 频散量度dissector 析象管distance estimator 估距关系distribution parameter 分布参数disturbed galaxy 受扰星系disturbing galaxy 扰动星系Dobsonian mounting 多布森装置Dobsonian reflector 多布森反射望远镜Dobsonian telescope 多布森望远镜dominant galaxy 主星系double-mode cepheid 双模造父变星double-mode pulsator 双模脉动星double-mode RR Lyrae star 双模天琴RR 型星double-ring galaxy 双环星系DQ Herculis star 武仙DQ 型星dredge-up 上翻drift scanning 漂移扫描driving system 驱动系统dumbbell radio galaxy 哑铃状射电星系Du Pont Telescope 杜邦望远镜dust ring 尘环dwarf carbon star 碳矮星dwarf spheroidal 矮球状星系dwarf spheroidal galaxy 矮球状星系dwarf spiral 矮旋涡星系dwarf spiral galaxy 矮旋涡星系dynamical age 动力学年龄dynamical astronomy 动力天文dynamical evolution 动力学演化Alcor 辅(位于大熊座)Algol 大陵武(位于英仙座)Alioth 玉衡(北斗五)(位于大熊座)Alkaid, Benetnasch 摇光（北斗七)(位于大熊座)Alphard 星宿一(位于大熊座)Altair 牵牛星(河鼓二，牛郎星)(位于天鹰座) Andromeda 仙女座Antares 大火(心宿二)(位于天蝎座)Antlia 唧筒座Apus 天燕座Aquarius 宝瓶座Aquila 天鹰座Ara 天坛座Arcturus 大角(位于牧夫座)Aries 白羊座Auriga 御夫座autumnal equinoctial point 秋分点Bellatrix 参宿五(位于猎户座)Betelgeuse 参宿四(位于猎户座)Big Dipper 北斗七星(位于大熊座)Bootes 牧夫座Caelum 雕具座Camelopardalis 鹿豹座Cancer 巨蟹座Canes Venatici 猎犬座Canis Mayor, Greater Dog 大犬座Canis Minor, Lesser Dog 小犬座Canopus 老人星(位于船底座)Capella 五车二(位于御夫座)Capricorn 摩羯座Capricornus 摩羯座Carina 船底座Cassiopeia 仙后座Castor 北河二(位于双子座)celestial equator 天赤道Centaurus 半人马座Cepheus 仙王座Cetus 天鲸座Chamaeleon 变色龙座Circinus 圆规座Columba 天鸽座Coma Berenices 后发座Corona Australis 南冕座Corona Borealis 北冕座Corvus 乌鸦座Crater 巨爵座Crux 南十字座Cygnus 天鹅座declination circle 赤纬Delphinus 海豚座Deneb 天津四(位于天鹅座)Denebola 五帝座一(位于大熊座)Dorado 剑鱼座Draco 天龙座Dubhe 天枢(北斗一)(位于大熊座)ecliptic 黄道Equuleus 小马座Eridanus 波江座Fomalhaut 北落师门(位于南鱼座)Fornax 天炉座Gemini 双子座Great Bear, Ursa Major 大熊座Grus 天鹤座Hamal 娄宿一(位于白羊座)Hercules 武仙座Horologium 时钟座Hydra 长蛇座Hydrus 水蛇座Indus 印第安座Lacerta 蝎虎座Leo Minor 小狮座Leo 狮子座Lepus 天兔座Libra 天秤座Little Bear, Ursa Minor 小熊座Lupus 豺狼座Lynx 天猫座Lyra 天琴座Markab 室宿一(位于飞马座)Megrez 天权(北斗四)(位于大熊座)Merak 天璇(北斗二)(位于大熊座)Mirach 奎宿九(位于仙女座)Mirfac 天船三(位于英仙座)Mizar 开阳(北斗六)(位于大熊座)Monoceros 麒麟座Mosca 苍蝇座Nicroscopium 显微镜座Norma 矩尺座Octans 南极座Ophiuchus 蛇夫座Orion 猎户座Pavo 孔雀座Pegasus 飞马座Perseus 英仙座Phecda 天玑(北斗三)(位于大熊座)Phoenix 凤凰座Pictor 绘架座Pisces 双鱼座Piscis Austrinus 南鱼座Pleiades 昴星团Polaris, polestar 北极星（勾陈一)(位于小熊座)Pollux 北河三(位于双子座)Procyon 南河三(位于小犬座)Puppis 船尾座Pyxis 罗盘座Rasalhague 侯(位于蛇夫座)Regulus 轩辕十四(位于大熊座)Reticulum 网罟座Rigel 参宿七(位于猎户座)Sagitta 天箭座Sagittarius 人马座Scheat 室宿二(位于飞马座)Schedar 王良四(位于仙后座)Scorpio, Scorpius 天蝎座Sculptor 玉夫座Scutum 盾牌座Serpens 巨蛇座Sextans 六分仪座Sirius, Dog Star 天狼星(位于大犬座)Spica 角宿一(位于室女座)summer solstice 夏至点Taurus 金牛座Telescopium 望远镜座Thuban 右枢(紫微右垣一）(位于天龙座)Triangulum Australe 南三角座Triangulum 三角座tropic of Cancer 北回归线Tucana 杜鹃座Vega 织女星(织女一)(位于天琴座)Vela 船帆座vernal equinoctial point 春分点Virgo 室女座Volans 飞鱼座Vulpecula 狐狸座Wagoner, Waggoner 御夫座。

天文词汇中英文对照(推荐文档)

天文词汇中英文对照（源自网络，仅供参考）天文词汇检索（按英文字母序）(A)absolute bolometric magnitude绝对热星等：量测恒星的绝对星等时，如果我们能同时侦测到所有的波长，所量测到就是绝对热星等。

absolute visual magnitude (Mv)绝对视星等：恒星的真正亮度。

定义为恒星在距离我们 10 秒差距 (32.6光年) 时的视星等。

absolute zero绝对零度，绝对零点：温度的最低点。

在绝对零度时，不可能再抽取物质、原子或分子里的粒子的动能。

absorption line吸收谱线：光谱里的暗线。

来自天体的光，被原子或分子选择性的吸收，导致那部分的光从星光中被消去，留下一条条的暗线。

absorption spectrum (dark line spectrum)吸收光谱：含有吸收谱线的光谱。

acceleration 加速度：速度对时间的变率。

速度在方向或速率的改变，就代表有加速度的存在。

参考速度(velocity) 。

acceleration of gravity重力加速度：量测天体附近重力强度的物理量。

accretion吸积：粘合较小的固体粒子，形成更大粒子的过程。

accretion disk吸积盘：指白矮星、中子星或黑洞等致密天体周围，由气体所形成的盘状天体。

Achernar水委一：波江座α星。

achondrites无球粒陨石：不含球粒(chondrules) 或挥发性物质的石陨石。

achromatic lens消色差透镜：由两种不同材质的透镜组合而成，消色差透镜的用途是把两种不同颜色的光聚焦到同一点，或称为修正色像差(chromatic aberration)。

active galactic nucleus (AGN)活跃星系核：活跃星系中央的能量源。

active galaxy活跃星系：一种会发生极大量无线电波、X射线、珈玛射线辐射的星系。

active optics活动光学：由计算机控制，来改变光学组件的位置和形状，以补偿大气扰动所产生的散焦效应之光学系统。

Calculation_of_Mass_Stopping_Power_and_Range_of_Pr

https:///journal/ijmpceroISSN Online: 2168-5444ISSN Print: 2168-5436Calculation of Mass Stopping Power and Range of Protons as Well as Important Radiation Quantities in Some Biological Human Bodyparts (Water, Muscle, Skeletaland Bone, Cortical)Ahlam S. Almutairi1, Khalda T. Osman21Department of Physics, College of Science, Qassim University, AL-Rass, Saudi Arabia2Department of Physics, College of Science, Qassim University, Buraydah, Saudi Arabia/licenses/by/4.0/In many fields, such as radiation dosimetry, radiation biology, and many others,A. S. Almutairi, K. T. Osmanradiation chemistry, radiotherapy, and nuclear physics, the stopping power, ener-gy loss, rangestraggling, and equivalent dose rate of ions in the air, tissue, and polymers are very important. The use of protons or heavier ions as an alternative to external photon beams in radiotherapy is increasing, with the reason being that they preserve the target dose, ensure a higher dose delivered to the tumor, and can transfer energy in the form of a point shot through diseased tissue due to the Bragg curve [1]. The stopping power of charged particles has been meas-ured using a variety of ways, including direct energyloss measurements through films, backscattering from thick substrates with deposited absorbing layers, gamma resonance shift measurements, self-supporting methods, and indirect verification of the stopping power based on alpha energy losses in the air have all been reported as methods for measuring the stopping power of charged par-ticles. [2] [3] [4].In the present work, the electronic mass stopping power and range of proton in some biological human body parts (Water, Muscle, Skeletaland Bone, Cortical) are calculated using the Bethe-Bloch formula as reported in the references. As it is known in any therapeutic unit with protons, it needs to calculate the absorbed dose, the equivalent dose to the tissue, and the effective dose according to the energy of the protons. Therefore, in this work, a variety of radiation quan-tities such as thickness, absorbed dose, equivalent dose, and effective dose of the protons in Water, Muscle, Skeletal and Bone, Cortical were also computed in pro-ton energy range 0.04 - 200 MeV.2. Methods2.1. Calculations of Electronic Mass Stopping PowerBethe was the first person to use quantum mechanical studies on stopping pow-er. The Bethe theory of stopping power is valid when the projectile’s velocity surpasses the Bohr velocity. In Bethe’s theory, the goal is assumed to be charged particle. In Bethe’s approach to energy loss, the Born approximation is employed to represent inelastic collisions between heavy particles and atomic electrons. In this theory, the projectile heavy particle is as assumed to be structureless, whe-reas the target nucleus is assumed to be infinitely massive [4]. F or the energy range 0.04 - 200 MeV, the Bethe mass stopping power equation [4] [5] [6] [7] was used:()3122d 5.0810ln d E z nF I x βρβρ−×−=− (1) where β is v /c where v is the proton velocity and c is light velocity, I is the mean excitation energy and F (β) is given by()62221.0210ln 1F ββββ×=−− (2) n is calculated using the following relation:A. S. Almutairi, K. T. Osmanav Zn N Aρ= (3) where N a Avogadro number, ρ is the density of substances and Ζ/A is the ratio of atomic number to the mass number of substances. The basic data for human body tissues are given in Table 1. The calculated mass stopping power of protons for Water, Muscle, Skeletal and Bone, Cortical are based on Bethe equation after substituting the constants from Table 1. In Table 2 the compositions of the hu-man tissues are given [8].2.2. Calculations of RangeThe range of a heavy particle is the straight distance it travels within the target. Light particles like electrons and positrons scatter widely throughout the path of targets due to their low mass, making it difficult to determine their journey du-ration. The path length of light particles has been calculated with remarkable success using Monte Carlo methods, which are based on a broad class of computa-tional algorithms. On the other hand, heavy particles like protons have a practi-cally straight line path length. The range of protons can be calculated using nu-merical integration methods. The Continuous Slowing Down Approximation (CSDA), on the other hand, is a straightforward and extensively used method for finding a variable’s range. This study used a simple and standard method for calculating the range of heavy particles such as protons in the targets. The CSDA approach uses incident particles to constantly lose energy in the route of the tar-gets. neglects energy loss fluctuations. The range, R for an incident proton in the CSDA method is given as [1] [4] [7]:()d fE E ER MS E =∫(4)Table 1. Basic data for calculating mass stopping powers.I (eV)n (electrons/m 3)Z ADensity ρ (g/m 3) Substances 75 3.341 × 1029 0.555 1,000,000 Water 74.6 3.476 ×1029 0.550 1,050,000 Muscle, Skeletal 1125.894 ×10290.511,920,000Bone, CorticalTable 2. Elemental composition of Water, Muscle, Skeletal and Bone, Cortical tissues.Composition Substances H(0.111898), O(0.888102)Water C(0.143000), N(0.034000), H(0.102000), O(0.710000), Na(0.001000),P(0.002000), k(0.004000), Cl(0.001000), S(0.003000) Muscle, Skeletal C(0.155000), N(0.042000), H(0.034000), O(0.435000), Na(0.001000),P(0.103000), S(0.003000), Ca(0.225000), Mg(0.002000)Bone, CorticalA. S. Almutairi, K. T. Osmanwhere, 0E is the initial energy of incident charged particle in material, f E is the final energy of incident charged particle in material and ()MS E is the mass stopping power.2.3. Calculations of Thickness, Absorbed Dose,Equivalent Dose and Effective DoseThickness of proton in the tissue or substance is given byRT ρ=(5)where R (in g/cm 2) is the range and is ρ the density of the tissue or substance [9] Absorbed dose in (in rad): It is the transfer of an amount of energy of 100 erg per gram of the absorbent material when protons pass over it and is given by the following relation: [9]1371.610J 10erg 1rad 100erg1grm 1MeV 1J gramE D −×= (6)where E is the proton energy. Equivalent dose: is given byTR RH W D =×∑ (7)where D is the absorbed dose and R W is the weighting factor of radiation (pro-ton) [9]Effective dose: is given byT T TE W H =∑ (8)where T W is the weighting factor of tissue or substance [9];where 0.12T W = for Water, Muscle, Skeletal and Bone, Cortical and 5R W = for protons [10].2.4. The Percentage Error of DifferenceThe percentage error of difference for the mass stopping power and range of protons in given biological human body parts is calculated byPSTAR result Present result% error100PSTAR result−=× (9)3. Results and DiscussionThe results of mass stopping power and range of protons in some biological human body parts (Water, Muscle, Skeletal and Bone, Cortical) are given in Ta-ble 3. In Figures 1-3 the mass stopping power of biological human body parts and their compositions are plotted using MathLab program and it is noted that the mass stopping power of all substances and tissues is approximately equal to t the average values of its compositions. The comparison between the present calculated electronic mass stopping powers and that of PSTAR program [8] areA. S. Almutairi, K. T. OsmanTable 3. Values of electronicmass stopping power (in MeV cm 2/g) of Water, Muscle, Skeletal and Bone, Cortical tissues.Mass stopping power (in MeV cm 2/g)Proton energy (MeV)Bone, CorticalMuscle, Skeletal WaterError% PSTAR This Work Error% PSTAR This Work Error% PSTAR Thiswork 172.21 648.4 −468.188 63.31 763.9 280.2840 60.29 732.4 290.8147 0.04 74.09 708.7 183.5666 13.65 835.5 721.4194 8.91 805 733.2987 0.06 44.71 726 401.4380 3.39 854.5 825.5114 −1.33 826 837.0064 0.08 32.51 718.4 484.8158 0.70 842.8 836.9089 −3.87 816.1 847.7091 0.1 14.46 580.5 496.5740 −3.46 669.4 692.5518 −5.912 661.3 700.4432 0.2 4.74 394 375.3311 −3.64 466.3 483.2825 −3.51 471.9 488.4735 0.4 2.36 307 299.7432 −3.41 363.2 375.5942 −3.14 368 379.5403 0.6 1.47 254.9 251.1486 −3.37 300 310.1025 −3.10 303.9 313.3203 0.8 1.07 219.6 217.2573 −10.25 241 265.7017 −2.93 260.8 268.4361 1.0 1.13 135.5 133.9751 −2.16 156.8 160.1849 −2.02 158.6 161.8006 2.0 2.21 81.42 79.6218 −0.76 93.01 93.7174 −0.65 94.04 94.6491 4.0 2.97 59.76 57.9867 0.09 67.83 67.7684 0.21 68.58 68.4376 6.0 3.52 47.77 46.0890 0.69 54 53.6292 0.81 54.60 54.1565 8.0 3.99 40.08 38.4770 1.18 45.17 44.6350 1.31 45.67 45.0727 10.0 5.93 23.07 21.7030 3.12 25.78 24.9752 3.27 26.07 25.2182 20.0 7.57 16.67 15.4082 4.83 18.56 17.6633 4.93 18.76 17.8345 30.0 9.17 13.26 12.0447 6.42 14.72 13.7744 6.54 14.88 13.9076 40.0 10.60 11.11 9.9320 7.89 12.31 11.3390 8.05 12.45 11.4484 50.0 12.01 9.63 8.4736 9.37 10.66 9.6615 9.51 10.78 9.7547 60.0 13.42 8.55 7.4023 10.78 9.45 8.4315 10.86 9.55 8.5127 70.0 14.77 7.72 6.5800 12.21 8.53 7.4886 12.29 8.62 7.5606 80.0 16.04 7.06 5.9276 13.57 7.8 6.7414 13.63 7.88 6.8062 90.0 17.36 6.53 5.3965 14.93 7.21 6.1338 14.94 7.28 6.1927 100.0 - 4.9553 - 5.6294 - 5.6835 110.0 - 4.5826 - 5.2036 - 5.2536 120.0 - 4.2632 - 4.8391 - 4.8856 130.0 - 3.9864 - 4.5234 - 4.5667 140.0 23.44 4.89 3.7440 21.06 5.38 4.2470 21.18 5.44 4.2877 150.0 - 3.5298 - 4.0029 - 4.0413 160.0 - 3.3392 - 3.7858 - 3.8221 170.0 - 3.1683 - 3.5912 - 3.6257 180.0 - 3.0142 - 3.4159 - 3.4486 190.0 28.854.042.874526.644.443.257026.774.493.2882200.0A. S. Almutairi, K. T. OsmanFigure 1. Mass stopping power of Water and its composition.Figure 2. Mass stopping power of Muscle, Skeletal and its composition.Figure 3. Mass stopping power of Bone, Cortical and its composition.shown in Figures 4-6 angood agreements between two results are observed in energy range 1 - 200 MeV.In Table 4 the ranges of protons in some Biological human body parts (Water, Muscle, Skeletal and Bone, Cortical) are given. In Figures 7-9 a comparison be-tween present results of ranges and that of PSTAR data are shown in energyA. S. Almutairi, K. T. OsmanFigure 4. Mass stopping power of Water versus0.05Z E A.Figure 5. Mass stopping power of Muscle, Skeletal versus0.05Z E A.range 0.1 - 200 MeV and good agreements are observed. In Table 5 and Table 6 the thickness, LET, absorbed dose, effective and equivalent dose are given. In Table 7 and Table 8, the empirical formulae for calculating mass stopping pow-ers and ranges for protons in some biological human body parts (Water, Muscle Skeletal and Bone, Cortical) are given with the percentage difference error.4. ConclusionIn this work, calculations of mass stopping power and range of protons incidentA. S. Almutairi, K. T. OsmanFigure 6. Mass stopping power of Bone, Cortical versus0.05Z E A.Figure 7. Range of Water versus0.05Z E A.on the three different biological human parts (Water, Muscle, Skeletal and Bone, Cortical) have been done and the following conclusions are drawn:1) The mass stopping power of the Water, Muscle, Skeletal and Bone, and Cortical is equal to the average value of mass stopping power of their composi-tions in energy range 0.04 - 200 MeV.2) Values for mass stopping power and ranges of protons in Water, Muscle, Skeletal and Bone, Cortical are in good agreement with the data of PSTAR pro-gram. The percentage value of error difference was between 0.09% - 28.88% forA. S. Almutairi, K. T. OsmanFigure 8. Range of Muscle, Skeletal versus0.05Z E A.Figure 9. Range of Bone, Cortical versus0.05Z E Amass stopping power and was between 3.99% - 79.47% for range at proton ener-gy ranging 0.04 - 200 MeV.3) It was also observed that the maximum value of mass stopping power was at 0.1 MeV and after that, the mass stopping power start to decrease with in-creasing proton energy as expected.A. S. Almutairi, K. T. OsmanTable 4. Values of range (in g/cm 2) of Water, Muscle, Skeletal and Bone, Cortical tissues.Range (g/cm 2)Protonenergy (MeV) Bone, CorticalMuscle, SkeletalWaterError% PSTAR This Work Error% PSTARThis WorkError% PSTARThis Work74.27 7.86 × 10−5 2.022 × 1−5 78.25 6.96 × 10−5 1.514 × 10−5 79.47 7.25 × 10−5 1.488 × 10−5 0.04 75.06 1.06 × 10−4 3.991 × 1−5 67.93 9.39 × 10−5 3.011 × 10−5 72.48 9.78 × 10−5 2.691 × 10−5 0.06 51.75 1.34×10−4 6.465 × 1−5 58.08 1.17 × 10−4 4.905 × 10−5 60.12 1.21 × 10−4 4.825 × 10−5 0.08 41.61 1.61 × 10−4 9.400 × 1−5 48.84 1.40 × 10−4 7.162 × 10−5 51.41 1.45 × 10−4 7.046 × 10−5 0.1 3.99 3.13 × 10−4 3.005 × 1−4 14.392.71 × 10−42.320 × 10−4 18.432.80 × 10−4 2.284 × 10−4 0.2 30.41 7.37 × 10−4 9.611 × 1−4 −18.39 6.35 × 10−4 7.518 × 10−4 −10.33 6.42 × 10−4 7.407 × 10−4 0.4 −46.15 0.0013 0.0019 −25.0 0.0012 0.0015 −36.36 0.0011 0.0015 0.6 −55.0 0.0020 0.0031 −41.18 0.0017 0.0024 −41.18 0.0017 0.0024 0.8 −60.71 0.0028 0.0045 −50.0 0.0024 0.0036 −45.83 0.0024 0.0035 1.0 −75 0.008 0.014 −53.33 0.0075 0.0115 −46.67 0.0075 0.011 2.0 −60.72 0.028 0.045 −55.42 0.024 0.0373 −50.00 0.024 0.0364.0 −57.91 0.057 0.090 −48.60 0.050 0.0743 −48.98 0.049 0.073 6.0 −53.69 0.095 0.146 −45.78 0.083 0.1210 −45.12 0.082 0.119 8.0 −51.71 0.14 0.2124 −47.17 0.12 0.1766 −58.18 0.11 0.174 10.0 −41.46 0.48 0.679 −36.19 0.42 0.572 −34.76 0.42 0.566 20.0 −35.35 0.99 1.340 −32.92 0.89 1.183 −27.95 0.88 1.126 30.0 −30 1.67 2.171 −23.60 1.50 1.854 −23.99 1.48 1.835 40.0 −26.28 2.50 3.157 −20.85 2.24 2.707 −20.72 2.22 2.680 50.0 −23.51 3.47 4.286 −18.21 3.12 3.688 −18.54 3.08 3.651 60.0 −21.47 4.57 5.551 −16.52 4.11 4.789 −16.54 4.07 4.743 70.0 −19.73 5.80 6.944 −14.86 5.23 6.007 −15.09 5.17 5.950 80.0 −18.32 7.15 8.460 −13.72 6.45 7.335 −13.89 6.38 7.266 90.0 −17.12 8.62 10.096 −12.58 7.79 8.770 −12.84 7.70 8.689 100.0 - 11.845 - 10.309 - 10.214 110.0 - 13.706 - 11.949 - 11.840 120.0 - 15.675 - 13.686 - 13.562 130.0 - 17.750 - 15.519 - 15.380 140.0 −13.35 17.58 19.927 −9.51 15.93 17.445 −9.71 15.76 17.290 150.0 - 22.205 - 19.463 - 19.291 160.0 - 24.581 - 21.571 - 21.382 170.0 - 27.054 - 23.767 - 23.560 180.0 - 29.622 - 26.050 - 25.824 190.0 −11.7828.8832.283−8.4226.2128.417−8.6525.9328.172200.0(MeV)Water Macles, SkeletalThickness(cm)LET(MeV/cm)AbsorbedDose × 10−8(rad)EquivalentDose × 10−8(rem)EffectiveDose × 10−8(rem)Thickness(cm)LET(MeV/cm)AbsorbedDose× 10−8(rad)EquivalentDose× 10−8(rem)EffectiveDose ×10−8(rem)0.04 1.488 × 10−5290.81470.0640.3200.034 1.441 × 10−5294.2980.0640.3200.034 0.06 2.691 × 10−5733.29870.0960.4800.057 2.868 × 10−5757.4900.0960.4800.057 0.08 4.825 × 10−5837.00640.1280.6400.076 4.671 × 10−5866.7870.1280.6400.076 0.17.046 × 10−5847.70910.1600.8000.096 6.821 × 10−5878.7540.1600.8000.096 0.2 2.284 × 10−4700.44320.320 1.6000.192 2.210 × 10−4727.1790.320 1.6000.192 0.47.407 × 10−4488.47350.640 3.2000.3847.160 × 10−4507.4460.640 3.2000.384 0.60.0015379.54030.960 4.8000.5760.0014394.3730.960 4.8000.5760.80.0024313.3203 1.280 6.4000.7680.0023325.607 1.280 6.4000.7681.00.0035268.4361 1.60080.9600.0034278.986 1.60080.9602.00.011161.80063.20016 1.9200.0110168.194 3.20016 1.9204.00.03694.6491 6.40032 3.8400.035698.403 6.40032 3.840 6.00.07368.43769.600485.7600.070771.1569.60048 5.760 8.00.11954.156512.800647.6800.115256.31012.800647.680 10.00.17445.072716809.6000.168246.86616809.600 20.00.56625.21823216019.2000.54526.2243216019.200 30.0 1.12617.83454824028.800 1.08418.5464824028.800 40.0 1.83513.90766432038.400 1.76514.4636432038.400 50.0 2.68011.44848040048 2.57811.9058040048 60.0 3.6519.75479648057.600 3.51210.1449648057.600 70.0 4.7438.512711256067.200 4.5618.853********.200 80.0 5.9507.560612864076.800 5.7217.86312864076.800 90.07.266 6.806214472086.400 6.9867.07814472086.400 100.08.689 6.1927160800968.353 6.44016080096 110.010.214 5.6835176880105.609.818 5.910176880105.60 120.011.840 5.2536192960115.2011.380 5.463192960115.20 130.013.562 4.88562081040124.8013.034 5.0812081040124.80 140.015.380 4.56672241120134.4014.780 4.7492241120134.40 150.017.290 4.2877240120014416.615 4.4592401200144 160.019.291 4.04132561280153.6018.537 4.2032561280153.60 170.021.382 3.82212721360163.2020.544 3.9752721360163.20 180.023.560 3.62572881440172.8022.635 3.7702881440172.80 190.025.824 3.44863041520182.4024.809 3.5863041520182.40 200.028.172 3.2882320160019227.064 3.4193201600192E (MeV)Bone, CorticalThickness (cm) LET (MeV/cm)AbsorbedDose × 10−8 (rad)EquivalentDose × 10−8 (rem)EffectiveDose × 10−8 (rem)0.04 1.053 × 10−5−898.921 0.064 0.320 0.034 0.06 2.078 × 10−5352.447 0.096 0.480 0.057 0.08 3.367 × 10−5770.761 0.128 0.640 0.076 0.1 4.896 × 10−5930.846 0.160 0.800 0.096 0.2 1.565 × 10−4953.422 0.320 1.600 0.192 0.4 5.006 × 10−4720.635 0.640 3.200 0.384 0.6 9.881 × 10−4575.506 0.960 4.800 0.5760.8 0.0016 482.205 1.280 6.400 0.7681.0 0.0023 417.134 1.600 8 0.9602.0 0.0074 257.2323.200 16 1.9204.0 0.023 152.873 6.400 32 3.840 6.0 0.047 111.334 9.600 485.760 8.0 0.076 88.490 12.800 64 7.680 10.0 0.110 73.875 16 80 9.600 20.0 0.353 41.669 32 160 19.200 30.0 0.698 29.583 48 240 28.800 40.0 1.131 23.125 64 320 38.400 50.0 1.644 19.069 80 400 48 60.0 2.232 16.269 96 480 57.600 70.0 2.891 14.212 112 560 67.200 80.0 3.616 12.633 128 640 76.800 90.0 4.406 11.380 144 720 86.400 100.0 5.258 10.361 160 800 96 110.0 6.169 9.514 176 880 105.60 120.0 7.1388.798 192 960 115.20 130.0 8.164 8.185 208 1040 124.80 140.09.244 7.653 224 1120 134.40 150.0 10.378 7.188 240 1200 144 160.0 11.565 6.777 256 1280 153.60 170.0 12.802 6.411 272 1360 163.20 180.0 14.090 6.083 288 1440 172.80 190.0 15.428 5.787 304 1520 182.40 200.0 16.814 5.519 320 1600 192the empirical formulae for calculating mass stopping powersSubstances11e x y A y =+PSTARThis workA 1 = 5.60379 × 108t 1 = −0.03805, y ₒ = 1.2486R 2 = 0.99998 A 1 = 7.13118 × 108t 1 = −0.03752, y ₒ = 0.31402R 2 = 0.99998 WaterA 1 = 5.2736 × 108, t 1 = −0.03784, y ₒ = 1.08913R 2 = 0.99998 A 1 = 6.760 × 108t 1 = −0.03729, y ₒ = 0.17554R 2 = 0.99999 Muscle, SkeletalA 1 = 2.99461 × 108, t 1 = −0.03638, y ₒ = 0.71424R 2 = 1A 1 = 3.12078 × 108 t 1 = −0.03626, y ₒ = −0.34842R 2 = 1Bone, CorticalTable 8. The empirical formulae for calculating range.Substances1PSTARThis workA 1 = 6.50318 × 10−15 t 1 = 0.02013, y ₒ = −0.05453R 2 = 0.99988 A 1 = 2.33355 × 10−14t 1 = 0.02082, y ₒ = −0.03587R 2 = 0.9999 WaterA 1 = 5.65636 × 10−15 t 1 = 0.01985, y ₒ = −0.06137R 2 = 0.99992 A 1 = 2.04888 × 10−14 t 1 = 0.02053, y ₒ = −0.03963R 2 = 0.99996 Muscle, SkeletalA 1 = 5.09688 × 10−15 t 1 = 0.01844, y ₒ = −0.04659R 2 = 0.99988A 1 = 2.054547 × 10−14 t 1 = 0.01924, y ₒ = −0.03062R 2 = 99986Bone, Cortical4) The empirical formulae suggested for mass stopping power are simple and accurate at proton energy (1 - 200 MeV) while the empirical formulae suggested for proton range give a good result compared to calculated values at proton energy (4 - 200 MeV).5) Also in this study, some radiation quantities were calculated, such as linear energy transfer, adsorbed dose, and effective and equivalent dose that give good information to those interested in proton therapy.AcknowledgementsThe authors thank the Department of Physics, Qassim University, for their sup-port and encouragement of this research.Conflicts of InterestThe authors declare no conflicts of interest regarding the publication of this paper.References[1]Tufan, M.C. and Gümüs, H. ( 2008) Stopping Power Calculations of Compounds byUsing Thomas-Fermi-Dirac-Weizsäcker Density Functional. Acta Physica Polonica A, 114, 703-711.https:///10.12693/APhysPolA.114.703[2]Ahmed, I., Nowrin, H. and Dhar, H. (2020) Stopping Power and Range Calculationsof Protons in Human Tissues. Baghdad Science Journal, 17, Article No. 1223.https:///10.21123/bsj.2020.17.4.1223[3]Usta, M., Tufan, M.Ç., Aydın, G. and Bozkurt, A. (2018) Stopping Power and DoseCalculations with Analytical and Monte Carlo Methods for Protons and Prompt Gamma Range Verification. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 897, 106-113. https:///10.1016/j.nima.2018.04.045[4]Almutairi, A.S. and Osman, K.T. (2021) Mass Stopping Power and Range of Protonsin Biological Human Body Tissues (Ovary, Lung and Breast). 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(2019) Density-Dependent Energy Loss ofProtons in Pb and Be Targets and Percent Mass-Stopping Power from Bethe-Bloch Formula and Bichsel-Sternheimer Data within 1-12 MeV Energy Range: A Comparative Study Based on Bland-Altman Analysis. Journal of Medical Imaging and Radiation Sciences, 50, 149-156.https:///science/article/abs/pii/S1939865418301413https:///10.1016/j.jmir.2018.10.003[8]Berger, M.J. (1995) ESTAR, PSTAR and ASTAR: Computer Programs for Calculat-ing Stopping Powers and Ranges for Electrons, Protons and Helium Ions. Report No. IAEA-TECDOC-799.https:///search/search.aspx?orig_q=RN:26064969[9]Al-Rubaii, T.A.J.Y. (2018). Calculation of the Stopping Power and Range for alphaparticles in Some Materials and Tissues. Doctoral Dissertation, University of Bagh-dad, Baghdad.https:///profile/Taghreed-Younis-2/publication/332061210_Calcul ation_of_the_Stopping_Power_and_Range_for_alpha_particles_in_Some_Materials_an d_Tissues/links/5cc0970092851c8d2202e331/Calculation-of-the-Stopping-Power-and-R ange-for-alpha-particles-in-Some-Materials-and-Tissues.pdf[10]Akber, S.F. (2014) Tissue Weighting F actor and Its Clinical Relevance. Journal ofRadiotherapy in Practice, 13, 119-122.https:///core/journals/journal-of-radiotherapy-in-practice/articl e/abs/tissue-weighting-factor-and-its-clinical-relevance/5B736C9DC434244B5B1CB 14E8DE35B74https:///10.1017/S1460396913000423。

窄线赛弗特I型星系中可能具有吸积盘热辐射起源的软X射线超

窄线赛弗特I型星系中可能具有吸积盘热辐射起源的软X射线超李晔【摘要】理论上,低质量高吸积率活动星系核的标准吸积盘黑体热辐射有可能形成软X射线波段的超出.然而,活动星系核的软X射线超温度为0.1 keV左右,显著高于标准吸积盘理论预言的最高有效温度.只有Yuan等人在2010年报道的RXJ1633+4718是一个例外,其软超温度为32.5±-8.06.0eV,显著小于0.1 keV,并与吸积盘理论预言的温度相符；此外,其光度也符合吸积盘的理论预期.因此该软X射线超很可能起源于吸积盘的热辐射.这一类源对于吸积盘理论和软X射线超的研究都有重要意义.文中使用ROSAT PSPC数据,在所有已知的窄线赛弗特I型星系(Narrow Line Seyfert I galaxies,NLSIs)中寻找类似于RXJ1633+4718的源,即软X射线超可能起源于吸积盘热辐射的源.分析了150个源的245条光谱,其中58个源的90条光谱具有显著的软X射线超.样本中软X射线超温度分布的平均值-Tsoft为0.10 keV,标准偏差为0.03 keV.除了RX J1633+4718外,只有3个源的软X射线超温度小于60 eV,而且温度接近吸积盘最高温度.这个结果表明,类似于RX J1633+4718的具有低温软X射线超的源很稀少.最后,在具有黑洞质量估计的26个源中,软超温度与黑洞质量MBH、爱丁顿比L/LEdd及预期吸积盘最高温度Tmax都没有明显的关联性,与前人的结果一致.%It is theoretically expected that the thermal radiation from accretion disks of Active Galactic Nuclei (AGNs) with low black hole mass would contribute to the soft X-ray band and result in an excess emission. However, the temperatures of the observed soft X-ray excess of AGNs are typically around 0.1 keV, significantly higher than those predicted by the standard disk model. There is only oneexception found so far, R.X J1633+4718, which has a significantly low soft excess temperature of 32.5l+8.0-6.0 eV, consistent with the maximum temperature as well as the luminosity of the predicted disk emission(Yuan et al. 2010).rnIn this paper, we search for RX J1633 like AGNs, whose soft X-ray excess temperature is close to the maximum temperature of accretion disk, in all known Narrow Line Seyfert I galaxies (NLSIs) observed with ROSAT PSPC in the archive. We analyzed the PSPC spectra of 150 NLSIs (245 observations) in total, 58 (90 observations) of which show significantly soft X-ray excess emission. In addition to RX J1633+4718, only 3 objects (4 observations) show soft X-ray excess temperatures less than 60 eV and close to the theoretical prediction of the disk emission. They form a sample of candidates for future follow-up studies. Our result indicates that RX J1633+4718 like objects are very rare. The correlations between the temperature of the soft X-ray excess and black hole mass as well as the Eddington ratio are also investigated, and no correlation is found. This confirms the previous results, and implies that the soft X-ray excess of most AGNs should originate from other mechanisms rather than the thermal emission of the accretion disk.【期刊名称】《天文学进展》【年(卷),期】2013(031)001【总页数】14页(P110-123)【关键词】活动星系核;吸积盘X射线热辐射;软X射线超【作者】李晔【作者单位】中国科学院国家天文台/云南天文台,昆明650011;中国科学院大学,北京100049;中国科学院国家天文台,北京100012【正文语种】中文【中图分类】P157.6活动星系核中心存在超大质量黑洞，物质落入中心黑洞的过程中形成吸积流，并产生辐射[1-3]。

Probing the nature of compact dark object at the Galactic Center by gravitational lensing

Keywords: supermassive neutrino star, dark matter, gravitational lensing.
∗ †
E-mail:capozziello@vaxsa.csied.unisa.it E-mail:geriov@vaxsa.csied.unisa.it
Abstract The long–standing issues of determination of the mass distribution and nature of the center of our Galaxy could be probed by a lensing experiment capable of testing the spatial and velocity distributions of stars nearby and beyond it. We propose a lensing toy–model which could be a further evidence that a massive consensation (e.g. a neutrino condensation) is a good candidate to explain the data ruling out the presence of a supermassive black hole.
Probing the nature of compact dark object at the Galactic Center by gravitational lensing
arXiv:astro-ph/9907201v1 15 Jul 1999
S. Capozziello1∗and G. Iovane1† 1 Dipartimento

The nature of hypervelocity stars as inferred from their galactic trajectories

Bromley et al. (2006) have performed numerical simulations of the ejection mechanism. They derive the following relation between ejection velocity, vej, binary separation, abin, masses of the binary components, M1 and M2, and the mass of the black hole Mbh:
⋆ E-mail: K.M.Svensson@
the galactic restframe via
vrf = vr + (10 cos l cos b + 5.2 sin l cos b + 7.2 sin b)km s−1
+ 220 km s−1 sin l cos b. (1)
We further show that the one high-velocity system observed to be moving towards the Galactic Centre, SDSS J172226.55+594155.9, could not have originated in the Galactic Centre; rather, we identify it as a halo object.
Karl M. Svensson⋆, Ross P. Chory, Box 43, SE-221 00, Lund, Sweden.
Accepted 2007 September 24. Received 2007 September 21; in original form 2007 August 02

Massive Coronae of Galaxies

a r X i v :a s t r o -p h /0508040v 1 1 A u g 2005Massive Coronae of GalaxiesMasataka FukugitaInstitute for Cosmic Ray Research,University of Tokyo,Kashiwa 277-8582,JapanandInstitute for Advanced Study,Princeton,NJ 08540USAP.J.E.PeeblesJoseph Henry Laboratories,Princeton University,Princeton,NJ 08544USAABSTRACTThere is reason to suspect that about half of the baryons are in pressure-supported plasma in the halos of normal galaxies,drawn in by gravity along with about half of the dark matter.To be consistent with the observations this baryonic component,the corona,would have to be hotter than the kinetic temperature of the dark matter in the halo so as to produce acceptable central electron densities.We ascribe this hotter plasma temperature to the addition of entropy prior to and during assembly of the system,in an analogy to cluster formation.The plasma cooling time would be longer than the gravitational collapse time but,in the inner parts,shorter than the Hubble time,making the corona thermally unstable to the formation of a cloudy structure that may be in line with what is indicated by quasar absorption line systems.The corona of an isolated spiral galaxy would be a source of soft X-ray and recombination radiation,adding to the more commonly discussed eﬀects of stars and supernovae.In this picture the mass in the corona is much larger than the mass in condensed baryons in a spiral galaxy.The corona thus would be a substantial reservoir of diﬀuse baryons that are settling and adding to the mass in interstellar matter and stars,so that star formation in isolated spirals will continue well beyond the present epoch.Subject headings:cosmology;galaxies:halos1.IntroductionDynamics and weak lensing suggest that a sig-niﬁcant fraction of the dark matter is in the viri-alized halos of L ∼L ∗galaxies.Gravity would have tended to draw a like fraction of the barons into the galaxies.Since the observed mass in condensed baryons —stars and the interstellar medium —is only about 8%of the total we have been led to consider the idea that roughly half of the baryons are in pressure-supported plasma in the outer parts of the galaxies (Fukugita,Hogan &Peebles 1998;Fukugita &Peebles 2004,FP).This is a modern variant of Spitzer’s (1956)galacticcorona,and the extent of the coronae we are con-sidering,about 300kpc radius,is in line with the proposal by Bahcall &Spitzer (1969)that galac-tic coronae may be responsible for quasar absorp-tion lines.The massive corona picture is related to the evidence that X-ray detected groups con-tain cosmologically appreciable mass in plasma (Mulchaey 2000),and the search for a possibly signiﬁcant plasma mass in the Local Group (Ras-mussen &Pedersen 2001and references therein).Since groups are not much larger than the virial-ized parts of an individual galaxy the constraints on the plasma properties are similar.Here we are considering the possibility that there is a cosmo-logically signiﬁcant mass in the coronae of indi-vidual L∼L∗spiral galaxies,and our goal is to present an observationally acceptable model for the present-day structure of such a massive corona.The starting idea for the model is that the bulk of the baryonic mass of a galaxy is in plasma gravi-tationally bound to the galaxy at near hydrostatic pressure equilibrium and at density low enough that the cooling time is longer than the Hubble time.At smaller radii the shorter cooling time would cause some of the plasma to settle toward the center of the galaxy,tending to relax to a near steadyﬂow,in analogy to a coolingﬂow of intra-cluster plasma(e.g.Fabian1988;Sarazin1988). Theﬁrst point to consider is that the plasma cool-ing time for most of the baryons in a virialized halo can be longer than the Hubble time,meaning the massive coronae can still be present if initial con-ditions allow the needed minimal clumping of the plasma.This is discussed in§2.Our model for the halo mass distribution to which the corona is gravitationally bound diﬀers from FP in two ways.First,we adjust the velocity dispersion to the value appropriate for an L∼L∗spiral galaxy.Second,we allow for the possibility of a less sharp truncation of the edge of the halo mass distribution,which we show can produce a more reasonable-looking galaxy-mass cross corre-lation function.We allow the possibility that heat-ing of the corona as it collapsed made it warmer than the temperature characteristic of the dark matter,in analogy to what is observed in clusters of galaxies(Allen et al.2004).We assume that in the inner parts of the corona,where the cool-ing time is less than the Hubble time,the plasma typically has relaxed to a near steady state,not se-riously disturbed by recent merging events or by energy sources such as supernovae,massive stars, or an active galactic nucleus.Since quasar absorp-tion lines show quite modest mass in atomic hy-drogen at radii 30kpc around galaxies(Chen et al.2001),our model requires that the rate of con-version of plasma to condensed forms of baryons is signiﬁcant only near the optically luminous parts of the galaxy.The model should also meet the re-quirement that the massive halo is consistent with soft X-ray observations of nearby galaxies and the integrated background.We construct two exam-ples of corona models under these conditions on the simple plan of spherically symmetric quasi-isothermal structures.Section3explains the mod-els and compares them to the observations.Wediscuss possible directions for further work in§4.There are alternative pictures for the presentstate of the baryons originally associated with thedark matter now in halos of galaxies.Shocks may have made most of this baryonic matter too hotto fall into massive halos.This is in line with the idea currently under discussion that there is asubstantial baryon mass in warm-hot intergalacticmatter at temperatures in the range∼105−107K (e.g.Dav´e et al.2001),but it is diﬃcult to seewhat could have produced a local shock power-ful enough to have prevented ongoing accretion of baryons by the Milky Way and Andromeda galaxy: the Virgo Cluster seems to be too far away,the galaxy velocity dispersion near the local sheet of galaxies seems to be too small,and if gravity pro-duced the local void it would not have been ac-companied by production of a shock.Other ideas assume that the baryons did fall into halos along with the dark matter.Possible,though we suspect unlikely,is the idea that most of these baryons col-lapsed to a condensed form that is not readily ob-servable,such as brown dwarfs.These condensed baryons would have to be distributed through the dark halo,because there is not room for them in the luminous parts of normal galaxies.This could be indicated by the extended diﬀuse glow of light around M87(Arp and Bertola1969),but it requires a considerable departure from observed initial stellar mass functions;it may be related to the local MACHO population(Alcock et al. 2000),though the indicated mass range,between 0.15and0.9M⊙if a halo component,is a prob-lem.Silk(2003)develops the idea that supernova-driven winds may have blown most of the baryons out of the massive halos of protogalaxies.The en-ergy required is modest but,as Silk discusses,the eﬃciency of entrainment might be questioned.A low density wind would tend to drive convection through the coronae,leaving behind most of the baryons,while locally deposited energy likely is radiated away rather than being adding to the en-tropy of the ambient material.Our conclusion is that the alternative,the massive corona picture, is worth exploring.2.The Cooling Rate in the Outer CoronaThis discussion of the characteristic plasma cooling time for baryons in a virialized halo takes all parameters from FP.It is not signiﬁcantly af-fected by the adjustments to the halo mass model discussed in the next section.We start with a measure of the plasma density at the nominal virial radius r200of a newly relaxed halo.The density of mass contained by r200is200 times the critical Einstein-de Sitter value,and the mass densityρ200at r200is one third of that if the density run within r200isρ∼r−2.To sim-plify this discussion we take it that the baryons and dark matter have the same spatial distribu-tion,so the mass fraction in baryons at r200is the ratio of the mass density parametersΩb=0.045 andΩm=0.28in baryons and in all matter.(The baryon segregation discussed in§3.3slightly re-duces the cooling time at r200.)With primeval helium abundance Y p=0.248the mean mass per particle isµ=0.59times the proton mass m p, and this measure of the plasma particle number density at r200isΩbρ200n200=Λn e,200(n200−n e,200)=50Gyr.(2) If the velocity dispersionσis independent of time the plasma density at r200in this expression scales as the square of Hubble’s constant and the ratio ofpreserves the total mass but distributes it in a way that gives a betterﬁt to the galaxy-mass cross cor-relation function(Model2).Parameters appropri-ate for the massive halo of a spiral galaxy are pre-sented in§3.2,the corona models are developed in §3.3,and the observational tests are discussed in §§3.3and3.4.3.1.The Mass DistributionIn the halo model in FP,which is the basis for our corona Model1,the total mass densityρas a function of radius r isρ(r)=σ2√2σatr<r v,the mass within the radius r v isM v=2σ2r v/G,(5) and the mean density of mass within r v is200 times the Einstein-de Sitter value,that is,r v= r200.In the model to be discussed next we keep r v at the value in equation(4)but adjust the mass distribution in a way that decreases r200.The FP estimate of the one-dimensional mass-weighted velocity dispersion averaged over galaxy types isσ=160km s−1.(6) The eﬀective number density of galaxies isn g=0.017h3Mpc−3,(7) where the Hubble parameter is H0=70km s−1 Mpc−1,that is,h=0.7.With these numbers the mass fraction within distance r v from the center of a galaxy isf g=M v n g2πGr2(1+ηr/r v),r≤r x=r veη−1The model for the halo structure is tested by the galaxy-mass cross correlation functionξgρ, which we approximate as(Seldner&Peebles1977; Cooray&Sheth2002)ξgρ(r)=f gθ(r)2r vθ(d)d2−γd d dµd2+r2−2r dµis the distance from the center of the neighbor to the point of observation of the mass density.This ex-pression assumes the mass fraction1−f g(eq.[8]) not in halos is homogeneously distributed,which seems reasonable at r∼100kpc but at r 1Mpc may underestimateξgρ.The dashed line in Figure1is the galaxy-mass cross correlation functionξgρfor theρ∝r−2 halo model in equation(4),the solid line isξgρfor the halo model in equation(9),and the dot-ted line is the Sheldon et al.(2004)power law ﬁt to their weak lensing measurement,ξgρ= (5.4Mpc/hr)1.79.FP chose theρ∝r−2model to agree with theξgρmeasurement as well as the cir-cular velocities observed at smaller radii.Theﬁt to the former is indeed close,butξgρis somewhat high at r∼200kpc because halos overlap,and the abrupt cutoﬀinρ(r)produces a pronounced shoulder inξgρat r=r v.The steeper halo den-sity run at r∼r v in theη=1model removes the excess and reduces the shoulder.A still larger value forηwould make the shoulder even smaller but it would produce an undesirable dip inξgρat r∼100kpc.At r>r x both models fall below the measuredξgρ.We attribute this to the mass frac-tion1−f g that we suspect is clustered on scales ∼1Mpc.We conclude that the models withη→0and η=1both give useful approximations to the mas-sive halos of L∼L∗galaxies,within the con-siderable uncertainties,but that theη=1case produces the betterﬁt to the galaxy-mass cross correlation function.3.2.The Massive Halo of a Spiral GalaxyWe are considering the idea thatﬁeld galaxies have massive coronae with baryon mass fractions close to the cosmic mean.For late galaxy types it is appropriate to use a lower velocity dispersion than the average over types in equation(6).We adopt the FP value for spirals,σlate=140km s−1.(11) This deﬁnes the eﬀective temperature,T v=µm pσ2late/k=1.4×106K,(12) and the late-type halo parameters(eqs.[4]and [5]),r v=280kpc,M v=2.6×1012M⊙.(13) An estimate of the mean mass of the Milky Way and the Andromeda galaxy from the dynamics of relative motions of the nearby galaxies is2.3×1012M⊙(Peebles1995),reasonably close to M v with our choice ofσlate.The conventional deﬁnition of the virialized part of a galaxy is that within the radius r200at which the enclosed density of mass is200times the Einstein-de Sitter value.In our late-type halo Model1,withη→0in equation(9),r200=r v= 280kpc.In Model2,withη=1,the density of mass within r x is40times the Einstein-de Sit-ter value,or140times the present mean matter density.The lower density in the outer parts of this model reduces the conventional virial radius to r200=240kpc and it reduces the density pa-rameter of the mass within r200in spiral galax-ies fromΩv=0.08in Model1toΩv=0.05in Model2.One should bear in mind,however,that the region of near dynamical equilibrium may ex-tend beyond r200.3.3.The Corona of a Spiral GalaxyIn the FP inventory the condensed mass is13% of the total baryon mass in a galaxy(from eq.[27] and entries3.1a,3.9and3.10in Table1in FP), leaving the massM corona=0.87M vΩb/Ωm=3.6×1011M⊙(14)for the massive corona of our characteristic spiral galaxy.Since the cooling time in the denser inner part of this corona is shorter than the Hubble time,and the Milky Way seems not to have been substan-tially disturbed by mergers since redshift z 1 (Gilmore,Wyse&Norris2001),we are assuming that the inner corona of a spiral typically has had time since the last major merger to have relaxed to a near steady rate of settling.This steady state means the particle number density n(r)and the inward streamingﬂow v(r)are such that the par-ticleﬂux entering the shell of radius r,˙N=4πr2nv,(15) is nearly independent of r outside the region where the condensed baryons are accumulating.Theﬂux of entropy into the shell r is s˙N,where the entropy per particle is s=k ln T3/2/n,so the condition for a stationary energy distribution at radius r iskT˙N dn=4πr2Λ(T)n e(n−n e).(16)Expressed in terms of the cooling time(as in eq.[2])the particle numberﬂux is˙N=6πnr3d ln T3/2/n.(17)Equations(15)and(16)are the steady-state ver-sions of the mass and energy equations used in analyses of cluster coolingﬂows(Fabian1988; Sarazin1988).Where the cooling time is greater than the free-fall time∼r/σthe plasma may be pressure-supported,and one might use the condition that˙N is constant with the equation of hydrostatic equi-librium,dr2µn e m p,(18) to compute the plasma temperature and density as functions of radius.We adopt a simpler approach, by noting that if the plasma temperature is inde-pendent of radius and the particle number density varies as n∝r−3/2then equation(16)indicates that˙N is constant,as wanted under the condition that signiﬁcant amounts of mass are dropping out of the corona only near the optical radius of thegalaxy.Fig. 2.—Electron number densities for Model1 (the dashed line)and Model2(the solid line). Both take the plasma temperature to be T= 4T v/3.In corona Model1we take the mass distribu-tion to beρ∝r−2(eq.[4])and we take the plasma temperature to be T e=4T v/3so the plasma den-sity varies as r−3/2,making˙N constant.This is a special case of Cavaliere’s(1973)beta model with β≡T v/T e=3/4.The dashed line in Figure2 shows the electron number density in this model with the parameters in equations(11)to(14).At heavy element abundance10−1.5times Solar and plasma temperature T e=4T v/3=1.8×106K the Sutherland-Dopita cooling function isΛ= 10−23.02erg cm3s−1.At primeval element abun-dance the cooling function is half this value.The massﬂux dM cond/dt=µm p˙N in this model for the corona,computed from equation(16),isdM cond/dt=14M⊙yr−1(10−1.5Solar),dM cond/dt=7M⊙yr−1(primeval).(19)This is the rate at which mass is entering the con-densed baryon components.It may be compared to the FP estimate of the present mean star for-mation rate per spiral galaxy(from the ratio of FP eqs.[30]and[52]with the spiral fraction0.7),dM star/dt=1.7M⊙y−1.(20)Fig. 3.—Theﬂux of mass out of the corona in Model2with heavy element abundance10−1.5 times Solar.The upper curve is the ratio of the plasma cooling time to the Hubble time.The lower curve is the measure of the massﬂux in equa-tion(16).Where the curve is dotted the cooling time is longer than the Hubble time and the ex-pression for the massﬂux need not apply.This is less than theﬂux of mass out of the corona in Model1even at primeval element abundances. Since we know of no place where the condensed baryons might be accumulating at the rates in equation(19)the indication is that˙N in Model1 is too large by a modest but signiﬁcant factor.We can remedy the problem by reducing n e. In Model2this is done by adopting the density proﬁle in the modiﬁed halo model in equation(9) withη=1while keeping the plasma temperature at T=4T v/3.Since the mass distribution is not isothermal this is not aβmodel,but at r r v the mass density run is close enough toρ∼r−2 for our purpose.This is illustrated in Figure3:at r 60kpc the cooling time is less than the Hubble time,so we want˙N to be independent of radius, and we see that this is reasonably well satisﬁed at massﬂuxdM cond/dt≃1M⊙yr−1(Model2)(21) for heavy element abundance10−1.5times Solar, and half this value at primeval element abun-dances.At larger radii˙N shows a substantial vari-ation with radius but this need not matter because here the plasma cooling time is long and the steady ﬂow condition need not apply.The massﬂux out of the corona in Model2 (eq[21])is satisfactorily close to the present star formation rate(eq.[20]).We continue the discus-sion of observational tests of the massive corona models in§3.4and§4,after commenting on the nature of the plasma distribution in our models.In both corona models the plasma is warmer than the eﬀective temperature of the dark matter. This moves the baryons toward the outer parts of the corona,making the baryon mass fraction in the central parts smaller than the cosmic value. This eﬀect is more conspicuous in Model2,where the halo is more extended,further lowering the electron density in the inner part of the halo by moving more baryons to the outskirts.The sup-pression of the baryon mass fraction in the inner parts of a massive halo is observed in clusters of galaxies,as shown by Allen et al.(2004)and ref-erences therein,and we assume the cause of the suppression may be the same for clusters and mas-sive galaxies:entropy is added to the plasma prior to and during assembly of the system.Figure4illustrates the situation in Model2. The upper solid curve is the total mass contained within radius r(eq.[9]withη=1)as a function of r.The lower solid curve is the sum of the corona and condensed baryon mass contained within r, and the dotted curves show the two separate com-ponents.We represent the condensed mass by the formM cond(<r)=2σ2late r gFig. 4.—The mass contained within a centered sphere in Model 2.The upper solid curve is the total included mass in baryons plus dark matter.The lower solid curve is the total baryon mass.The dotted curves show the two dominant baryon components,the plasma mass in the corona and the more concentrated baryon mass in condensed forms (eq.[22]).one half of the total,in agreement with what is known about the dark mass distribution in the Milky Way.Since the total condensed baryon mass agrees with the FP estimate from what is observed we conclude that this is a reasonable rep-resentation of the condensed mass distribution.At r =20kpc the included baryon mass is close to the total condensed mass,6×1010M ⊙,and the subdominant mass in the corona is causing the slow increase in included mass with increasing ra-dius.The included masses in condensed baryons and the corona plasma are equal at r =180kpc in Model 2.At this radius the total baryon mass frac-tion is 0.09,or 56percent of the cosmic value.This suppression of the baryon fraction is comparable to what is observed in relaxed clusters of galax-ies at one quarter of the virial radius (Allen et al.2004).The signiﬁcant diﬀerence is that in spirals only half of the baryons within r ∼200kpc areinFig. 5.—Dispersion measures along the lines of sight to pulsars in globular clusters.In order of increasing distance d sin |b |from the plane they are 47Tuc,M15,M13,M5,M30,NGC1851,M3,and M53.The lines assume a close to homogeneous corona with electron density n e =0.001cm −3in the lower line and n e =0.002cm −3in the upper line.the coronal plasma,while the other half is in con-densed forms.This diﬀerence might be expected from the shorter cooling times in galactic coronae.The included baryon mass fraction reaches the cos-mic mean at radius r x (eq.[9]),at the right-hand edge of the ﬁgure.This would be replaced by a smooth transition to the cosmic value in a more realistic model for the corona.3.4.Observational TestsParameters characteristic of our two models are summarized in Table 1.We have already discussed the entry for the rate of settling of the corona;the results for Model 1(eq.[19])motivate Model 2(eq.[21]).Here we consider other observational tests.If the Milky Way has a close to standard mas-sive corona then the dispersion measures of pul-sars outside the disk oﬀer a useful probe of the plasma density in the inner corona.Manchester et al.(2005)list 2dispersion measures of pulsarsTable1Massive Corona ParametersModel1Model2 in the Magellanic clouds and in eight globular clus-ters that are more than2kpc from the plane ofthe galaxy.Dispersion measures for the globularcluster pulsars are plotted inﬁgure5.The twolines assume a plane parallel plasma disk com-ponent with scale height≪2kpc and surfacedensity15pc cm−3together with a near homo-geneous corona.This value for the plasma surfacedensity in the disk is not inconsistent with whatis observed for pulsars closer to the central plane(Cordes&Lazio2005,ﬁg.1).There is not com-pelling evidence for detection of a corona outsidethe disk component,but one sees from theﬁg-ure that the data would allow a corona with localnumber density in the range0.001cm−3 n e 0.002cm−3.(23)The electron density in Model2at r=10kpc,n e=0.0026cm−3,is reasonably consistent withthis.In Model1n e is high,but we note in§4that this could be because clumping of the plasmasubstantially enhances the cooling rate and lowersn e at r∼10kpc.Pulsars in the Magellanic Clouds have disper-sion measures∼100cm−3pc,which we can takeas a bound on the contribution from the corona.This corresponds to mean density¯n e(MC)≃0.002cm−3,(24)along the line of sight to the Magellanic Clouds.Table1lists the mean electron density averagedin the radial direction from r=10kpc to r=50kpc.The models are not inconsistent withequation(24).ity,the integral of the surface brightness overthe observed part of the galaxy is a recieved en-ergyﬂux density f and the eﬀective luminosity isL0=4πD2f if the distance to the galaxy is D.We compute this luminosity derived from a mea-surement of the energyﬂux density received froma cylinder of radiusρcentered on the galaxy asL0=4π r x0r2drF(r)j(r),(25)where F(r)is the fraction of a sphere of radius rcentered on the galaxy that falls within the cylin-der of radiusρ.Thus F=1at r<ρandF(r)=1− 8πǫ(29)The characteristic galaxy number density is n g(eq.[7]),the spiral fraction is f s=0.7,we approx-imate the time integral as L dt/(1+z)≃0.5Lt,with t=10Gyr and L constant at the values inTable1forρ>10kpc,and the factorǫ=0.3keVin the denominator approximates the width of thespectral energy distribution.This estimate,listedin the second line from the bottom of Table1,ignores the shift of the photon energies out ofthe band of detection,so if L were close to con-stant it would be a considerable overestimate.Wu,Fabian,&Nulsen(2001)point out that the coronaX-ray luminosity could have been substantiallylarger in the past,meaning equation(29)couldbe an underestimate,but that depends on howthe galaxies and their coronae formed and evolved.We conclude that our picture for the present-daystate of massive coronae in spiral galaxies does notconﬂict with the soft X-ray background measure-ment,within the considerable uncertainties.The X-ray emission from coronae contributes tothe local ionizing radiation,as Maloney&Bland-Hawthorn(1999)note in their discussion of plasmadistributed through the Local Group.An observersituated near the center of a corona wouldﬁndthat the radiation energy density produced by thecorona is roughly isotropic at1u=be dominated by the disk.With photoionization cross sectionσ∝ν−3,andσ(νo)=10−17.1cm2at the hydrogen photoionization threshold,the pho-toionization rate near the center of the corona isΓ≃σo cu/(3kT),(31) The numerical results are listed in Table1.The Penton et al.(2000)estimate of the rate of ion-ization by the intergalactic background radiation,Γ=10−13.6s−1,is comparable to what might be expected from the corona in Model1.In Model2 it appears that massive coronae would not be sig-niﬁcant local sources of ionizing radiation.4.DiscussionWe have argued for the viability of the idea that about half of the baryons are in gravitation-ally bound coronae in the dark matter halos of galaxies.In our models the mass distribution is designed toﬁt the galaxy-mass cross correlation function(Fig.1),under the assumption of near monolithic massive halos,and the coronae are as-sumed to have relaxed to a steady coolingﬂow. Under these conditions the corona electron den-sity run is not likely to be much outside the two curves in Figure2:a lower density than in Model2 would bring the density in the outer parts of the corona closer to the global mean than seems rea-sonable for matter that has relaxed to dynamical equilibrium,and a density greater than or compa-rable to Model1would cause substantial problems with the observations.A better massive halo model would replace the sharp truncation of the mass and baryon densi-ties at r=r x with a physically realistic tran-sition to the intergalactic medium,but what is relevant for the inner structure of a corona in a near steady state is the situation where the plasma cooling time is comparable to the Hubble time,at r∼60kpc:the plasma with longer cooling times serves as a reservoir supplying theﬂow to smaller radii.Conditions at this transition to near steady ﬂow likely depend on departures from spherical symmetry,as may be caused by tidal interactions with neighboring massive halos or ongoing accre-tion.One might also have to consider rotational support in the inner parts of the corona,and possi-bly magneticﬁeld pressure.But such reﬁnements might await clearer evidence that massive coronae really exist.Model2appears to be observationally accept-able.It should be noted,however,that this model depends on the assumption of a smoothly dis-tributed plasma,which may not be accurate,be-cause the plasma is thermally unstable to the growth of densityﬂuctuations that decrease the cooling times and so reduce the electron density run from what is shown in Figure1.3That may make the X-ray luminosity of the corona signiﬁ-cantly smaller than our estimate.The thermal in-stability may be expected to have a lesser eﬀect on theﬂux of mass from the corona into condensed forms of baryons,because this is determined by conditions where the cooling time and the ther-mal instability growth time both are comparable to the Hubble time.Model1appears to be marginally unaccept-able:the most serious problem is the large rate of production of condensed baryons(eq.[19]).It is worth noting,however,that if galactic winds removed about half of the baryons in the corona, leaving the rest with the radial distribution in Model1,it would reduce the massﬂux by a factor of four,leaving a still substantial baryon mass in coronae and an acceptable and interesting present rate of production of condensed forms of baryons.The near coincidence between theﬂux of mass out of the corona(eq.[21])and the present star formation rate(eq.[20])in Model2—or in Model1with half the plasma mass we have been assuming—agrees with Larson’s(1972)con-jecture that gas isﬂowing into the interstellar medium at the rate the interstellar medium is be-ing converted to stars.Inﬂow to the disk at about this rateﬁgures in current discussions of the his-tory of the thin disk of the Milky Way(as reviewed by Pagel1997;Matteucci2001).The high veloc-ity clouds often are mentioned as a source for the inﬂow,but the absence of analogs around other galaxies makes this unlikely(Pisano et al.2004). Mass settling out of the corona seems to be a vi-able alternative.In this picture star formation in an isolated spiral galaxy will continue for a con-siderable time to come.We have not analyzed compatibility of the mas-。

Mass Accretion onto T Tauri Stars

a r X i v :a s t r o -p h /0606682v 1 28 J u n 2006Mon.Not.R.Astron.Soc.000,1–17(2006)Printed 5February 2008(MN L A T E X style ﬁle v2.2)Mass Accretion onto T Tauri StarsS.G.Gregory 1⋆,M.Jardine 1,I.Simpson 1and J.-F.Donati 21School of Physics and Astronomy,University of St Andrews,North Haugh,St Andrews,Fife,KY169SS,U.K.2Laboratoired’Astrophysique,Observatoire Midi-Pyr´e n´e es,14Av.E.Belin,F-31400Toulouse,FranceABSTRACTIt is now accepted that accretion onto classical T Tauri stars is controlled by thestellar magnetosphere,yet to date most accretion models have assumed that their magnetic ﬁelds are dipolar.By considering a simple steady state accretion model with both dipolar and complex magnetic ﬁelds we ﬁnd a correlation between massaccretion rate and stellar mass of the form ˙M ∝M α∗,with our results consistentwithin observed scatter.For any particular stellar mass there can be several orders of magnitude diﬀerence in the mass accretion rate,with accretion ﬁlling factors of a few percent.We demonstrate that the ﬁeld geometry has a signiﬁcant eﬀect in controlling the location and distribution of hot spots,formed on the stellar surface from the high velocity impact of accreting material.We ﬁnd that hot spots are often at mid to low latitudes,in contrast to what is expected for accretion to dipolar ﬁelds,and that particularly for higher mass stars,the accretion ﬂow is predominantly carried by open ﬁeld lines.Key words:Stars:pre-main sequence –Stars:magnetic ﬁelds –Stars:spots –Stars:formation –Stars:coronae –Stars:low mass,brown dwarfs1INTRODUCTIONClassical T Tauri stars (CTTSs)are young,low mass,pre-main sequence stars that are actively accreting from a sur-rounding disc which is the eventual birth-place of planets.Uchida &Shibata (1984)suggested that the magnetic ﬁeld of a CTTS disrupts the inner disc.In the early 1990s several magnetospheric accretion models were developed (K¨o nigl 1991;Collier Cameron &Campbell 1993;Shu et al.1994)where material is lifted from the disc plane and is channelled along dipolar magnetic ﬁeld lines onto the star,terminating in a shock at the photosphere.In an idealised model of a CTTS’s magnetic ﬁeld there are closed ﬁeld lines close to the star that contain the X-ray emitting corona,whilst at larger radii,there are closed ﬁeld lines which thread the cir-cumstellar disc.It is along this latter set of ﬁeld lines that accretion may proceed.There are also regions of open ﬁeld which carry outﬂows in the form of a wind,and in some cases,as large collimated bipolar jets.Magnetospheric accretion models assume that CTTSs possess magnetic ﬁelds that are strong enough to dis-rupt the disc at a distance of a few stellar radii.Such strong ﬁelds have been detected in a number of systems using a variety of techniques.Average surface ﬁelds of 1-3kG have been detected most successfully by exploit-ing the Zeeman eﬀect,both through Zeeman broaden-ing (e.g.Johns-Krull,Valenti &Koresko 1999b)and from⋆E-mail:sg64@the circular polarisation of lines which are sensitive to the presence of a magnetic ﬁeld (e.g.Johns-Krull et al.1999a;Symington et al.2005;Daou,Johns-Krull &Valenti 2006).Field detections have also been made from the increase in line equivalent width (Basri,Marcy &Valenti 1992;Guenther et al.1999)and also from electron cyclotron maser emission,a coherent emission process from mildly rel-ativistic electrons trapped inside ﬂux tubes close to the star (Smith et al.2003).The mean magnetic ﬁeld strengths de-tected so far appear to be roughly constant across all stars (Valenti &Johns-Krull 2004).Traditionally magnetospheric accretion models have as-sumed the CTTSs have dipolar magnetic ﬁelds.Dipole ﬁelds (or inclined dipole ﬁelds)have been successively used to ex-plain some of the observations of CTTSs (e.g.the photopo-larimetric variability of AA Tau,O’Sullivan et al.2005),but fail to account for others.Valenti &Johns-Krull (2004)present magnetic ﬁeld measurements for a number of stars,and despite detecting strong average surface ﬁelds from Zee-man broadening,often measurements of the longitudinal (line-of-sight)ﬁeld component (obtained from photospheric lines)are consistent with no net circular polarisation.This can be interpreted as there being many regions of opposite polarity on the stellar surface,giving rise to oppositely po-larised signals which cancel each other out giving a net polar-isation signal of zero.This suggests that CTTSs have mag-netic ﬁelds which are highly complex,particularly close to the stellar surface;however,as Valenti &Johns-Krull (2004)point out,as the higher order multi-pole ﬁeld components2S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donatiwill drop oﬀquickly with distance from the star,the dipole component may still remain dominant at the inner edge of the disc.Also their measurements of the circular polarisa-tion of the HeI5876˚A emission line(believed to form in the base of accretion columns)are wellﬁtted by a simple model of a single magnetic spot on the surface of the star,suggest-ing that the accretingﬁeld may be well ordered,despite the surfaceﬁeld being complex.The fractional surface area of a CTTS which is covered in hot spots,the accretionﬁlling factor f acc, is inferred from observations to be small;typically of order one percent(Muzerolle et al.2003;Calvet et al. 2004;Valenti&Johns-Krull2004;Symington et al.2005; Muzerolle et al.2005).Dipolar magneticﬁeld mod-els predict accretionﬁlling factors which are too large.This,combined with the polarisation results,led Johns-Krull&Gaﬀord(2002)to generalise the Shu X-wind model(Shu et al.1994)to include multipolar,rather than dipolar,magneticﬁelds.With the assumption that the av-erage surfaceﬁeld strength does not vary much from star to star the generalised Shu X-wind model predicts a corre-lation between the stellar and accretion parameters of the form R2∗f acc∝(M∗˙MP rot)1/2,a prediction that matches observations reasonably well.In this paper we present a model of the accretion pro-cess using both dipolar and complex magneticﬁelds.We apply our model to a large sample of pre-main sequence stars obtained from the Chandra Orion Ultradeep Project (COUP;Getman et al.2005),in order to test if our model can reproduce the observed correlation between mass accre-tion rate and stellar mass.An increase in˙M with M∗was originally noted by Rebull et al.(2000)and subsequently by White&Ghez(2001)and Rebull et al.(2002).The cor-relation was then found to extend to very low mass ob-jects and accreting brown dwarfs by White&Basri(2003) and Muzerolle et al.(2003),and to the higher mass,inter-mediate mass T Tauri stars,by Calvet et al.(2004).Fur-ther low mass data has recently been added by Natta et al. (2004),Mohanty,Jayawardhana&Basri(2005)and by Muzerolle et al.(2005)who obtain a correlation of the form ˙M∝M2.1∗,with as much as three orders of magnitude scatter in the measured mass accretion rate at any par-ticular stellar mass.However,Calvet et al.(2004)point out that due to a bias against the detection of higher mass stars with lower mass accretion rates,the power may be less than2.1.Further data for accreting stars in the ρ−Ophiuchus star forming region has recently been added by Natta,Testi&Randich(2006).The physical origin of the correlation between M∗and ˙M,and the large scatter in measured˙M values,is not clear;however several ideas have been put forward.First, increased X-ray emission in higher mass T Tauri stars (Preibisch et al.2005;Jardine et al.2006)may cause an in-crease in disc ionisation,leading to a more eﬃcient magne-torotational instability and therefore a higher mass accretion rate(Calvet et al.2004).Second,Padoan et al.(2005)ar-gue that the correlation˙M∝M2∗arises from Bondi-Hoyle accretion,with the star-disc system gathering mass as it moves through the parent cloud.In their model the observed scatter in˙M arises from variations in stellar velocities,gas densities and sound speeds.Mohanty et al.(2005)provide a detailed discussion of both of these suggestions.Third,Alexander&Armitage(2006)suggest that the correlation may arise from variations in the disc initial conditions com-bined with the resulting viscous evolution of the disc.Intheir model they assume that the initial disc mass scales linearly with the stellar mass,M d∝M∗,which,upon mak-ing this assumption,eventually leads them to the conclusionthat brown dwarfs(the lowest mass accretors)should have discs which are larger than higher mass accretors.However, if it is the case that the initial disc mass increases more steeply with stellar mass,M d∝M2∗,then the stellar mass -accretion rate correlation can be reproduced with smaller brown dwarf discs of low mass(of order one Jupiter mass). Thus the Alexander&Armitage(2006)suggestion,if cor-rect,will soon be directly veriﬁable by observations.Fourth, Natta et al.(2006)suggest that the large scatter in the cor-relation between˙M and M∗may arise from the inﬂuence of close companion stars,or by time variable accretion.It should however be noted that Clarke&Pringle(2006)take a more conservative view by demonstrating that a steep cor-relation between˙M and M∗may arise as a consequence of detection/selection limitations,and as such˙M∝M2∗is per-haps not a true representation of the correlation between˙M and M∗.In§2we describe how magneticﬁelds are extrapolated from observed surface magnetograms.In§3we consider ac-cretion onto an aligned,and then a tilted dipoleﬁeld,to develop a simple steady state accretion model and to inves-tigate how tilting theﬁeld aﬀects the mass accretion rate.In §4these ideas are extended by considering magneticﬁelds with a realistic degree of complexity and we apply our accre-tion model to study the correlation between mass accretion rate and stellar mass,whilst§5contains our conclusions.2REALISTIC MAGNETIC FIELDSFrom Zeeman-Doppler images it is possible to extrapolate stellar magneticﬁelds by assuming that theﬁeld is po-tential.At the moment we do not have the necessary ob-servations of CTTSs,but we do have for the solar like stars LQ Hya and AB Dor(Donati&Collier Cameron 1997;Donati et al.1997;Donati1999;Donati et al.1999; Donati et al.2003),which have diﬀerentﬁeld topologies (Jardine,Collier Cameron&Donati2002a;Hussain et al. 2002;McIvor et al.2003;McIvor et al.2004).Using their ﬁeld structures as an example we can adjust the stellar pa-rameters(mass,radius and rotation period)to construct a simple model of a CTTS,surrounded by a thin accretion disc.The method for extrapolating magneticﬁelds follows that employed by Jardine et al.(2002a).Assuming the mag-neticﬁeld B is potential,or current-free,then∇×B=0. This condition is satisﬁed by writing theﬁeld in terms of a scalarﬂux functionΨ,such that B=−∇Ψ.Thus in order to ensure that theﬁeld is divergence-free(∇·B=0),Ψmust satisfy Laplace’s equation,∇2Ψ=0;the solution of which is a linear combination of spherical harmonics,Ψ=Nl=1l m=−l a lm r l+b lm r−(l+1) P lm(θ)e imφ,(1) where P lm denote the associated Legendre functions.It thenMass Accretion onto T Tauri Stars3 follows that the magneticﬁeld components at any point(r,θ,φ)are,B r=−Nl=1l m=−l[la lm r l−1−(l+1)b lm r−(l+2)]P lm(θ)e imφ(2)Bθ=−Nl=1l m=−l[a lm r l−1+b lm r−(l+2)]dsinθime imφ.(4)The coeﬃcients a lm and b lm are determined from the radial ﬁeld at the stellar surface obtained from Zeeman-Doppler maps and also by assuming that at some height R s above the surface(known as the source surface)theﬁeld be-comes radial and hence Bθ(R s)=0,emulating the eﬀect of the corona blowing openﬁeld lines to form a stellar wind (Altschuler&Newkirk1969).In order to extrapolate the ﬁeld we used a modiﬁed version of a code originally devel-oped by van Ballegooijen,Cartledge&Priest(1998).2.1Coronal extentWe determine the maximum possible extent of the corona (which is the extent of the source surface)by determining the maximum radius at which a magneticﬁeld could contain the coronal gas.Since a dipoleﬁeld falls oﬀwith radius most slowly,we use this to set the source surface.For a given sur-face magnetogram we calculate the dipoleﬁeld that has the same averageﬁeld strength.We then need to calculate the hydrostatic pressure along eachﬁeld line.For an isothermal corona and assuming that the plasma along theﬁeld is in hydrostatic equilibrium then,p s=p0exp 1r2+ω2r sin2θ,ω2r sinθcosθ,0 .(6) We can then calculate how the plasmaβ,the ratio of gas to magnetic pressure,changes along eachﬁeld line.If at any point along aﬁeld lineβ>1then we assume that the ﬁeld line is blown open.This eﬀect is incorporated into our model by setting the coronal(gas)pressure to zero whenever it exceeds the magnetic pressure(β>1).We also set the coronal pressure to zero for openﬁeld lines,which have one foot point on the star and one at inﬁnity.The gas pressure, and therefore the plasmaβ,is dependent upon the choice of p0which is a free parameter of our model.Jardine et al. (2006)provide a detailed explanation of how p0,the coronal base(gas)pressure,can be scaled to the magnetic pressure at aﬁeld line foot point,so we provide only an outline here. We assume that the base pressure is proportional to the magnetic pressure then p0=KB20,a technique which has Table1.Data for CTTSs from Valenti&Johns-Krull(2004) DF Tau0.17 3.98.5 2.47CY Tau0.58 1.47.59.554S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donati(a)(b)Figure1.Field lines which could support accretionﬂows for a model of a CTTS with aﬁeld topology that resembles(a)LQ Hya, obtained using the DF Tau parameters from Table1,and(b)AB Dor using the CY Tau parameters.The stellar surface is coloured to show the strength of the radial component of theﬁeld,with red representing1kG and black-1kG.Field lines have been drawn from the corotation radius.For the lower mass star,DF Tau,the natural extent of its corona would be beyond corotation and therefore there is a mixture of open and closedﬁeld lines threading the disc at R co.The higher mass star,CY Tau,has a more compact corona and material ﬂows along openﬁeld lines from corotation.measure in the same way as Jardine et al.(2006).To de-termine if aﬁeld line can accrete weﬁnd where it threads the disc and calculate if the eﬀective gravity along the path of theﬁeld line points inwards,towards the star.From this subset ofﬁeld lines we select those which haveβ<1along their length.In other words,for any given solid angle we assume that accretion can occur along theﬁrstﬁeld line within the corotation radius which is able to contain the coronal plasma.We assume that the loading of disc mate-rial onto theﬁeld lines is inﬁnitely eﬃcient,such that the ﬁrstﬁeld line at any azimuth which satisﬁes the accretion conditions will accrete,and thatﬁeld lines interior to this are shielded from the accretionﬂow.We also assume that the accretingﬁeld is static and is therefore not distorted by the disc or by the process of accretion.In§3.3we consider in more detail how to determine whichﬁeld lines are able to support accretionﬂows,in order to calculate mass accretion rates and accretionﬁlling factors.Fig.1shows theﬁrst set ofﬁeld lines which may be accreting,obtained by surrounding theﬁeld extrapolations of LQ Hya and AB Dor with a thin wedge-shaped accretion disc,with an opening angle of approximately10◦.In§3we develop a model for isothermal accretionﬂows where mate-rial leaves the disc at a low subsonic speed,but arrives at the star with a large supersonic speed.Not all of theﬁeld lines in Fig.1are capable of supporting such accretionﬂows, and instead represent the maximum possible set ofﬁeld lines which may be accreting.We assume a coronal temperature of10MK and obtain the gas pressure at the base of eachﬁeld line as discussed in§2.1and by Jardine et al.(2006).The natural extent of the corona of DF Tau would be beyond the corotation radius and therefore accretion occurs along a mixture of closed and openﬁeld lines from corotation.One suggestion for how accretion may proceed along openﬁeld lines is that an openﬁeld line which stretches out into the disc,may reconnect with another openﬁeld line for long enough for accretion to occur,only to be sheared open once again.This is of particular importance for the higher mass stars,such as CY Tau,where in some cases weﬁnd that the inner edge of the disc is sitting in a reservoir of radial openﬁeld lines.This may have important implications for the transfer of torques between the disc and star.However more work is needed here in order to develop models for accretion along openﬁeld lines.Theseﬁeld extrapolations suggest that accretion may occur alongﬁeld lines that have very diﬀerent geometries. Indeed,a substantial fraction of the total mass accretion rate may be carried on openﬁeld lines.Before developing a detailed model of the mass accretion process,however,we ﬁrst consider the simple case of a tilted dipole.While this is an idealisation of the true stellarﬁeld it allows us to clarify the role that the geometry of theﬁeld may have in governing the mass accretion process.3ACCRETION TO A DIPOLEWe have constructed two simple analytic models as sketched in Fig.2.Theﬁrst case is for a star with a dipolarﬁeld with the dipole momentµaligned with the stellar rotation axisΩ.In standard spherical coordinates thisﬁeld may be described as,B= 2µr3sinθ,0 ,(7)Mass Accretion onto T Tauri Stars5Figure 2.An aligned and tilted dipole ﬁeld geometry.The aligned dipole (left)with a ﬁeld line in the star’s meridional plane,with the dipole moment µaligned with the stellar rotation axis Ω,and the perpendicular dipole (right)with a ﬁeld line in the star’s equatorial plane,with µperpendicular to Ω.The averagesurfaceﬁeldstrength matches that considered by Jardine et al.(2006)with yellow (blue)representing the positive (negative)magnetic pole.a scenario that allows us to model accretion ﬂows along ﬁeldlines in the star’s meridional plane.If we then take this ﬁeld structure and tilt it by π/2radians such that µnow lies in the star’s equatorial plane,perpendicular to Ω,then those ﬁeld lines which ran north-south in the meridional plane,now lie east-west in the equatorial plane,with,B =2µr 3sin φ.(8)Throughout we shall refer to these cases as the perpendic-ular dipole for the tilted dipole ﬁeld and the aligned dipole for the aligned dipole ﬁeld.To do this we consider steady isothermal accretion ﬂows from a thin accretion disc ori-ented such that the disc normal is parallel to the stellar rotation axis.An initial sonic Mach number,M ,is ascribed to the accreting material.We then calculate the pressure and velocity proﬁles,relative to arbitrary initial conditions deﬁned at the disc plane.We calculate the ratio of pressure p at each point along a ﬁeld line,relative to that at the disc,p d ;and then from this we calculate how the Mach number of the ﬂow changes along the ﬁeld.The path of a ﬁeld line may be described by B rrdθ=B φB d=R d4−3r2µ+1dsv 2ds+ρg ef f ·ˆs ,(14)since the Coriolis term (−2ρω×v )does not contribute for ﬂows along the ﬁeld,and where ˆs (r )is a unit vector along the path of the ﬁeld line.Throughout terms with a sub-script d will denote quantities deﬁned at the disc;for exam-ple ρd ,p d ,v d and B d are respectively the density,pressure,velocity along the ﬁeld and the magnetic ﬁeld strength as deﬁned at the plane of the disc,a radial distance R d from the centre of the star.Integrating equation (14)from the disc plane to some position along the ﬁeld line at a distance r from the stellar centre,and using the isothermal equation of state for an ideal gas,p =ρc 2s ,gives,lnpc 2s−1ds (ρvA )=0(16)dB=p d v dp d+1pB2M 2−1c s=Mp dB d,(20)where in both cases M =v d /c s denotes the initial sonic Mach number at which the accretion ﬂow leaves the plane6S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donati of the disc.It is then possible toﬁnd the pressure at eachpoint along aﬁeld line,relative to the pressure at the disc(p/p d),byﬁnding the roots of(19).Once these roots havebeen found the velocity proﬁle can be obtained from(20)by calculating how the Mach number of theﬂow varies asmaterial moves from the disc to the star.3.2Pressure and velocity proﬁlesFor the perpendicular dipole,in the star’s equatorial plane,the eﬀective gravity has only a radial component,g ef f= −GM∗p d +1r 6 4−3r p 2−1 R d−1R∗c2s(23)Φc=1c s 2.(24)The roots of(22)give the pressure at some point along a ﬁeld line loop which is a radial distance r from the stellar centre.For the aligned dipole,in the star’s meridional plane, the eﬀective gravity has both an r andθcomponent,g ef f= −GM∗p d +1r 6 4−3r p 2−1R d−1R d =0.(26)The only diﬀerence from the perpendicular dipole is in the ﬁnal term.For a CTTS with a mass of0.5M⊙,radius2R⊙and a rotation period of7days we have calculated the pressure and velocity structure along accreting dipoleﬁeld lines,for a range of accretionﬂow temperatures,starting radii and ini-tial sonic Mach numbers.Figs.3(a)and3(b)show a typical pressure and velocity proﬁle for the perpendicular dipole, whilst those for the aligned dipole are qualitatively similar. The pressure proﬁle shows how the ratio p/p d,where p is the pressure along theﬁeld line and p d the pressure at the disc, varies as theﬂow moves from the disc to the star(plotted logarithmically for clarity).The velocity proﬁle shows how the Mach number of theﬂow changes along theﬁeld line.For diﬀerent accretionﬂow temperatures and starting radii the resulting proﬁles are similar,except in a few select cases, as discussed in the next section.Fig.3is for an accretion ﬂow leaving the disc at R d=6.0R∗,which is approximately the equatorial corotation radius R co where,R co= GM∗Mass Accretion onto T Tauri Stars7(a)(b)Figure3.The resulting pressure and velocity proﬁles for accretion along equatorial dipoleﬁeld lines.The inner edge of the disc is at R d=6.0R∗which is approximately the corotation radius.Diﬀerent lines represent diﬀerent initial velocities.accretionﬂows.We further check to ensure that the plasma beta resulting from accretion remains<1along their length. Therefore,at any particular azimuth,accretion occurs along theﬁrstﬁeld line at,or slightly within,the corotation radius; theﬁeld line must be able to contain the coronal plasma and have a sonic point along its length.In order to determine if aﬁeld line can support a transonic accretionﬂow,theﬁrst step is toﬁnd the pressure and velocity structure its length, which will be similar to those described in§3.2.To do this we need to determine the initial Mach number that would produce an accretionﬂow.We can achieve this by determin-ing if aﬁeld line has a sonic point as discussed in Appendix A.To calculate a mass accretion rate we require the veloc-ity and density of each accretionﬂow at the stellar surface, and also the surface area of the star covered in hot spots. For an assumed accretionﬂow temperature we determine the initial Mach number required to generate a transonic velocity proﬁle,along eachﬁeld line,and determine the in-fall velocity from(20).At every point along aﬁeld line we know the ratio of pressure at that point,to that at the disc, p/p d.For an isothermal equation of state p∝ρ,so we also know the ratio of densitiesρ/ρd at every point along the accretingﬁeld line.Thus for a given disc midplane density ρd,we can estimate the density at the stellar surfaceρ∗. Throughout we assume a constant disc midplane density of ρd=5.0×10−9gcm−3,a resonable value at the corotation radius for T Tauri stars(e.g.Boss1996).The mass accre-tion rate may be expressed in terms of quantities deﬁned at the disc plane,with˙M∝ρd.Therefore raising or lowering ρd directly increases or decreases˙M.We estimate the to-tal surface area of the star covered in accretion hot spots by summing the area of individual grid cells which contain accretingﬁeld line foot points.For each grid cell i(of area A i)on the stellar surface we obtain the average in-fall ve-locity¯v∗and average density¯ρ∗of material accreting into that cell.Most grid cells do not contain any accretingﬁeld line foot points and therefore do not contribute to the mass accretion rate.The mass accretion rate is then the sum over all cells i containing accretingﬁeld line foot points,˙M= i˙M i= i[A¯v∗¯ρ∗]i.(28) The mass accretion rate can be expressed equivalently as ˙M=ρdv d A d,where A d is the surface area of the disc that contributes to accretion(which depends on the radial extent of accretingﬁeld lines within the disc).Using the surface area of grid cells within the disc which contain accreting ﬁeld lines to estimate A d,we obtain˙M values that are com-parable to those calculated from(28).Therefore it makes little diﬀerence which formulation for˙M is used.The accre-tionﬁlling factor f acc,the fractional surface area of the star covered in hot spots,is then calculated from,f acc= i A i8S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donati(a)(b)(c)(d)Figure4.(a)The change in mass accretion rate and(b)the accretionﬁlling factor as a function ofβ,for accretion to dipoleﬁelds whereβis the obliquity-the angle between the rotation and magnetic poles,for accretionﬂow temperatures of1000K(solid),2500K (dotted),5000K(short dash),7500K(long dash)and10000K(dash-dot).(c)and(d)show how the contribution to the accretionﬁlling factor from accreting closed and openﬁeld changes withβ.The DF Tau parameters from Table1have been used.There are no open accretingﬁeld lines for the T acc=1000K case.ofβ.This,in part,can be attributed to the increase in theamount of openﬁeld lines which thread the disc,and are ableto support accretion asβis increased(see Fig.4(d)).As thedipole is tilted fromβ=0◦to10◦the mass accretion rateis reduced(see Fig.4(a)).This can be understood by thechanging shape of the closedﬁeld lines asβis increased.Foraccretion along aligned dipoleﬁeld lines,accreting materialmayﬂow along two identical paths from the disc to the star;that is it may accrete either onto the northern,or the south-ern hemisphere.Once the dipole has been tilted through asmall angle,the path along theﬁeld onto each hemispherechanges,with one segment of the closedﬁeld line loop beingshallower than before and curved towards the star,and theother being longer.This longer segment bulges out slightly,so that materialﬂowing along suchﬁeld lines follows a pathwhich initially curves away from the star,before loopingback around to the stellar surface.This creates a diﬀerencein initial Mach numbers necessary to create transonic accre-tionﬂows along the diﬀerentﬁeld line segments,with thenet result that some closedﬁeld line segments are no longerMass Accretion onto T Tauri Stars9(a)(b)(c)(d)Figure 5.The stellar surface with white (black)points indicating the closed (open)accreting ﬁeld line foot points for accretion to a dipole with obliquity (a)β=0◦,the aligned dipole,where accretion proceeds onto two rings in opposite hemispheres;(b)β=15◦where the accretion rings have been distorted and open ﬁeld lines produce the small bands centred on 180◦and 360◦longitude;(c)β=45◦where accretion occurs predominantly along the open ﬁeld lines and (d)β=90◦,the perpendicular dipole,where accretion occurs in bars around the star’s equator.All are for an accretion ﬂow temperature of 104K.The average surface ﬁeld strength matches that considered by Jardine et al.(2006)with yellow (blue)representing the positive (negative)magnetic pole.able to accrete transonically when β=10◦(see Fig.4(c)).As the dipole is tilted further from β=10◦to ≈30◦−40◦the mass accretion rate increases in all but the lowest T acc cases.This is because once the dipole has been tilted far enough the open ﬁeld lines (those that have foot points at latitudes closer to the magnetic axis)begin to intersect the disc (see Fig.4(d)).There are therefore more possible paths that material can take from the disc to the star,causing anincrease in ˙M(again in all but the lower T acc cases).As βis further increased the amount of accreting closed ﬁeld lines continues to reduce,whilst the amount of open ﬁeld lines threading the disc reaches a maximum,and we therefore see a trend of falling mass accretion rates towards the largest values of β.The accretion ﬂow temperature is important in deter-mining whether open ﬁeld lines are able to support transonic accretion ﬂows.From Figs.4(c)and 4(d)it is clear that the contribution to accretion from the closed ﬁeld is constant for all values of T acc ,whereas the contribution from the open ﬁeld depends strongly on T acc ,with more open ﬁeld lines accreting at higher accretion ﬂow temperatures.At the low-est accretion ﬂow temperature which we consider (1000K),there are no open ﬁeld lines able to support transonic ac-cretion,even for the large values of βwhere there are many such ﬁeld lines passing through the disc.This can be under-stood as follows.For transonic accretion a sonic point mustexist on a ﬁeld line.At a sonic point v =c s ;applying this to (20),substituting into (19)and rearranging gives,1dsv 2−c 2s=g ef f ·ˆs −c 2sds,(30)from which it can be seen that there exists some critical radius r c where either v =c s or dv/ds =0.Clearly at this critical radius the two terms on the RHS of (30)must be equal,c 2s ds=g ef f ·ˆs ,(31)where all the terms are evaluated at r c .It should be noted that (31)may also be obtained by ﬁnding the maximum turning point of (A5),consistent with our argument in Ap-pendix A.The condition for a sonic point to exist on any ﬁeld line,open or closed,may be expressed as equation (31).ˆs is a unit vector along the path of the ﬁeld which may be written as ˆs =B /B ,which we can use to rewrite (31)as,c 2sdB。