Biased galaxy formation in the fields of high-redshift AGN

合集下载

Galaxy clustering in the Herschel deep field

a r X i v :a s t r o -p h /0007224v 1 17 J u l 2000Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 1February 2008(MN L A T E X style ﬁle v1.4)Galaxy clustering in the Herschel deep ﬁeldH.J.McCracken 1,3,T.Shanks 1,N.Metcalfe 1,R.Fong 1A.Campos 1,21Departmentof Physics,University of Durham Science Laboratories,South Rd,Durham DH13LE.2Instituto de Matematicas y Fisica Fundamental (CSIC)Serrano 113bis,E-28006Madrid,Spain 3Present address:Laboratoire d’Astrophysique de Marseille,13376Marseille Cedex 12,France1February 2008ABSTRACTWe present a study of the angular correlation function as measured in the William Herschel Deep Field,a high galactic latitude ﬁeld which has been the subject of an ex-tensive observing campaign from optical to infrared wavelengths.It covers 50arcmin 2and with it we are able to investigate the scaling of the angular correlation function to B ∼28,R,I ∼26,K ∼20and H ∼22.5.We compare our measurements to re-sults obtained from the smaller Hubble Deep Field.To interpret our results,we use a model which correctly predicts colours,number counts and redshift distributions for the faint galaxy population.We ﬁnd that at ﬁxed separation the amplitude of ω(θ)measured in BRI bandpasses is lower than the predictions of a model containing with no luminosity evolution and stable clustering growth in proper co-ordinates.However,in the near-infrared bandpasses,our measurements are consistent with the predictions of an essentially non-evolving K −selected galaxy redshift distribution.In the range B ∼27−28we ﬁnd that our correlation amplitudes are independent of magnitude,which is consistent with the observed ﬂattening of the number count slope and cor-respondingly slower increase of the cosmological volume element expected at these magnitudes.If our luminosity evolution models provide a correct description of the underlying redshift distributions (and comparisons to available observations at brighter magni-tudes suggest they do),then our measurements in all bandpasses are consistent with a rapid growth of galaxy clustering (0<ǫ<2in the normal parametrisation)on the sub-Mpc scales which our survey probes.We demonstrate that this rapid growth of clustering is consistent with the predictions of biased models of galaxy formation,which indicate that a rapid rate of clustering growth is expected for the intrinsically faint galaxies which dominate our survey.1INTRODUCTIONThe projected two-point galaxy correlation function ω(θ)has proved to be one of the most enduring statistics in ob-servational cosmology.This is a consequence of the relative ease with which it may be measured;for each galaxy,all one requires is positions and magnitudes.Starting with the early studies of clustering in the local universe using Schmidt plates (Groth &Peebles 1977)to more recent works using CCD-based detectors (Efstathiou et al.1991;Pritchet &In-fante 1992)these studies have probed galaxy clustering to very faint magnitudes.Normally,these surveys measure how the amplitude of the projected angular correlation function at a ﬁxed angular separation,A ω,varies as a function of sam-ple limiting magnitude –the “scaling relation”.Usually,this relation has been parametrised in terms of “epsilon mod-els”in which the three-dimensional correlation length r 0(z )scales monotonically with redshift (Groth &Peebles 1977;Phillipps et al.1978).These models also require a choice ofcosmology and knowledge of the underlying redshift distri-butions for each magnitude-limited sample.In this paper we will investigate the projected angu-lar clustering of the faint ﬁeld galaxy population.We char-acterise galaxy clustering as a function of sample limiting magnitude in BRIKH bandpasses.Our primary dataset is a deep,ground based survey of an area called ’the William Herschel deep ﬁeld’(WHDF).This has been described in several recent papers (Metcalfe et al.1996;McCracken et al.2000).Covering ∼50arcmin 2this survey comprises an area ∼10times larger area than the separate HDF-N and HDF-S ﬁelds.For comparison,we also present a complementary analysis of clustering amplitudes measured in these smaller ﬁelds,utilising the catalogues produced in Metcalfe et al (2000).Although similar studies of ω(θ)exist in the lit-erature (Efstathiou et al.1991;Roche et al.1993;Brain-erd,Smail,&Mould 1994;Hudon &Lilly 1996;Woods &Fahlman 1997)our survey diﬀers primarily in its depth2McCracken et.al(B∼28)and broad wavelength coverage(in this analysis we consider samples selected in BRIK bandpasses).To interpret our results we use redshift distributions derived from the luminosity evolution models we have de-scribed in our previous papers((McCracken et al.2000;Met-calfe et al.1996).These models are able to reproduce all the observable quantities of the faintﬁeld galaxy popula-tion(counts,colours,redshift distributions),at least for low Ω0universes and within current observational uncertainties (Metcalfe et al.1996);it is these successes which give us con-ﬁdence in using our models as probe of the clustering his-tory of the Universe,rather than using our measurements of Aωas a probe of the underlying redshift distributions. In our models,highΩ0Universes can be accommodated by the model if we add an extra population of low luminosity galaxies with constant star-formation rates which boost the counts at faint(B>25m)magnitude levels(Campos1997). We also considerﬂat cosmologies withΛ=0.For reference, the scaling relation computed for a model with stable clus-tering and no luminosity evolution is also presented.Models such as those presented in this paper are rela-tively successful in describing clustering measurements per-formed on deep blank-ﬁeld surveys like the one detailed in this work(Roche et al.1993;Brainerd,Smail,&Mould 1994).However,observations of the clustering properties of Lyman-break galaxies(Madau et al.1996)indicate that these objects have comparable clustering properties(Gi-avalisco et al.1998)to some classes of locally observed galax-ies,making such objects initially diﬃcult to understand in terms of this monotonic scaling of r0with redshift.We will explain how these observations can be understood in the context of the results presented in this paper.Our paper is organised as follows:in Section2we de-scribe in outline the preparation of our datasets;in Section3 we describe the techniques we use to measure and analyse our data;in Section4we present our measurements of the projected correlation function inﬁve bandpasses in compar-ison with previous work and investigate if our errors esti-mates are realistic;in Section5we compare our correlation measurements with the predictions of our evolutionary mod-els;andﬁnally,in Section6we outline the main conclusions from this work.2OBSER V ATIONS AND CATALOGUESFull details of the optical observations comprising the WHDF will be presented in a forthcoming paper(Metcalfe et al2000).A subset of our infrared observations of the WHDF is described in McCracken et al.(2000)which com-prises the K<20UKIRT observations.Additional infrared observations at Calar Alto Observatory produced a second catalogue limited at H<22.5which will be fully described in a separate paper(McCracken et al,in preparation).In this section we will brieﬂy describe our object detection and photometry techniques which are very similar to that usedin our previous galaxy counts papers(Metcalfe et al.1991;Jones et al.1991;Metcalfe et al.1995;McCracken et al.2000).All our optical data discussed in this paper was takenat the William Herschel Telescope(WHT),with the excep-tion of a short I−band exposure made at the Isaac NewtonTelescope(INT).After bias subtraction andﬂat-ﬁelding,the sky back-ground is removed and isophotal image detection is carriedout.These images are then removed from the frame,replacedby a local sky value,and the resulting frame smoothed heav-ily before being subtracted from the original.This producesa veryﬂat background.The isophotal detection process isthen repeated.A Kron(1980)-type pseudo-total magnitudeis then calculated for each image,using a local value of sky.Table1shows the magnitude limits for ourﬁelds.As inour previous papers the minimum Kron radius is set to bethat for an unresolved image of high signal-to-noise,and thecorrection to total is the light outside this minimum radiusfor such an image.Our measurement limits give the totalmagnitudes of unresolved objects which are a3σdetectioninside the minimum radius(which is typically∼1.4′′forthe WHDF data).Star-galaxy separation was done on theB frame using the diﬀerence between the total magnitudeand that inside a1′′aperture,as described in Metcalfe et al.(1991).This enabled us to separate to B∼24m.Some addi-tional very red stars were identiﬁed from the R and I frames.As the WHDF is at high galactic latitude the stellar con-tamination should in any case be quite low.For the purposesof measuring the correlation function,masksﬁles were alsoconstructed to cover regions containing bright galaxies orstars.The area of theﬁeld aﬀected by such bright objects isless than10%of the total.Similar methods were also used to generate cataloguesfrom the north and south Hubble deepﬁelds(i.e.,we donot use any of the existing HDF catalogues but use ourown independently written object detection and photometrysoftware).One signiﬁcant diﬀerence between the HDF dataand our ground-based data is of course their much higherresolution.As described fully in Metcalfe et al(2000,inpreparation),we visually inspect all detections on our HDFN/S data in an attempt to reduce the number of spuriousentries in our catalogues.We also carry out a’reassembly’process in which multiple detections on an individual galaxyare combined to produce a single detection.This admittedlysubjective procedure is unavoidable in the HDF cataloguesgiven the extremely high resolution of the data.3METHODS AND TECHNIQUES3.1Determining the angular correlation functionWe use the normal estimator of Landy&Szalay(1993),given in equation 1.Here we follow the usual notationwhere DD indicates the number of galaxy-galaxy pairs,DRgalaxy-random pairs and RR random-random pairs for agiven angular separation and bin width:ω(θ)=DD−2DR+RRGalaxy clustering in the Herschel deepﬁeld3Filter U B R I K HLimit(3σ)26.827.926.323.5/25.620.022.5Area(arcmin2)48.548.548.588.3/53.047.250Table1.Photometric limits of the WHDF.The two magnitude limits in I refer to two separate surveys,one carried out at the INT (and covering88.3arcmin2and the other based on WHT data.For a range of magnitude-limited samples of each cata-logue,ω(θ)is computed using equation1for a series of binsspaced in increments of0.2in log(θ),whereθis in degrees.As we have only observed oneﬁeld we cannot use theﬁeld-to-ﬁeld variance to estimate the errors in each bin;insteadwe implement a bootstrap-resampling technique(Barrow,Sonoda,&Bhavsar1984;Ling,Barrow,&Frenk1986).Inthis method,the error in each bin is computed from thevariance of the estimator as applied to a large(∼200)num-ber of bootstrap-resampled catalogues.As expected,thesebootstrap errors are larger(normally∼×2)than the normal√Ω2 θ−δdΩ1dΩ2(3)whereθis the angular separation of each galaxy pair and dΩ1and dΩ2the solid angle subtended by each pair.If we assume a power-law correlation function,ω(θ)∝θ−0.8we may calculate this quantity for ourﬁelds by direct integra-tion.Typically weﬁnd C∼13for the WHDF and∼40for the HDF(we must assume a slope for power-law correlation function as we cannot calculate it directly from this data;−0.8allows us to compare our work with similar studies in the literature).The error on Aω,the overallﬁt,is determined from the method of Marquardt(1963),as described in Press et al. (1986).This method combines errors on each bin in an in-dependent manner to calculate the total error of theﬁt. Figure1showsﬁts made for the B−band catalogue.We determine correlation amplitudes for the Hubble deepﬁeld data using a similar procedure.In this case we ﬁt ourﬁnal power law to an average of the correlation func-tion determined independently on each of the three WFPC2 chips.For our NICMOS correlation amplitude,we compute our correlation functions from the total numbers of pairs from both surveys.For all these space-based data sets the ﬁeld of view is extremely small,and consequently the re-quired integral constraint correction is very large.Addition-ally,the small numbers of pairs involved means thatﬁts are generally dependent on three or fewer bins,and for this rea-son our resulting correlation amplitudes determined from these data should be regarded as upper limits on theﬁttedamplitudes,rather than deﬁnitive measurements.In order to Figure1.ω(θ)as measured for samples limited at B<27m and B<28m.The solid line shows theﬁt toω(θ)=Aω(θ−0.8−C) where C is the“integral constraint”term described in the text and Aωis the value ofω(θ)at1◦try to reduce problems from“merged”objects as described in Section2we carry out ourﬁts at angular separation>1′′.3.2Modelling the correlation functionWe would like to compare our measured correlation ampli-tudes with those of model predictions.In order to do this we must assume a functional form for the spatial correlation function.From the results of large surveys(Groth&Peebles 1977;Davis&Peebles1983;Maddox et al.1990b)it is found thatξ(r)(the spatial correlation function)is well approxi-mated byξ(r)=(r0/r)γ,at least for scales<20h−1Mpc. Projecting a model forξ(r)onto the two-dimensional distri-bution of galaxies measured byω(θ)involves integrating this function over redshift space using Limber’s formula(Limber 1953).We must parametrise the scaling of the correlation func-tion with redshift.Early papers(Groth&Peebles1977; Phillipps et al.1978)assumed a scaling of the form ξ(r,z)=h(z) r04McCracken et.alwhereh(z)=(1+z)−(3+ǫ)(5) (in this case r is the proper distance);this relation has been used in many recent observationally-motivated studies inves-tigating the projected two-point function(Efstathiou et al. 1991;Roche et al.1993;Brainerd,Smail,&Mould1994; Infante&Pritchet1995a;Brainerd&Smail1998).To derive an expression forω(θ),the projected corre-lation function,we note that for small angles,the relation betweenω(θ)andξ(r)becomes(Efstathiou et al.1991)ω(θ)=√Γ(γ/2)Adz 2dz/∞dNdγ−1A(z)(dr(z)/dz)(8)where d A(z)is the angular diameter distance and dr(z)/dz is the derivative of the proper distance.Analysis of the aforementioned large local redshift sur-veys suggests thatγ=1.8,leading to three cases of interest to us:clusteringﬁxed in proper coordinates,in which case ǫ=0.0;clusteringﬁxed in co-moving coordinates which givesǫ=−1.2.Finally,the predictions of linear theory give ǫ=1.0.This formalism has been widely used in many papers which investigate the clustering of faintﬁeld galaxies:see, for example,Infante&Pritchet(1995b),Woods&Fahlman (1997).As we have already noted,in these“epsilon models”characterised by equation4the co-moving galaxy correla-tion length decreases monotonically with redshift(providing of courseǫ>−1.2,which produces models with clustering constant in co-moving co-ordinates)However,several recent works have indicated that this may not be a realistic as-sumption.In theoretical studies,both N-body simulations (Colin et al.1999)and semi-analytic models(Baugh et al. 1999;Kauﬀmann et al.1999)indicate that the co-moving galaxy correlation length decreases until z∼1−2after which it increases again.These theoretical studies(Gover-nato et al.1998)also allow us to explain the high clustering amplitudes observed for Lyman break galaxies at z∼3(Gi-avalisco et al.1998;Adelberger et al.1998)as a consequence of their formation in highly biased environments.Further-more,the clustering growth is expected to be more rapid for less massive objects and and for clustering amplitudes measured on smaller scales(Baugh et al.1999).Motivated by these works we also model our correla-tion amplitudes using a modiﬁcation of equation4.In place of the normal epsilon parametrisation,we have used in the relativistic Limber’s equation a more general form for the evolution ofξ(r,z),namelyξ(r,z)= r com0(z)(1+z)r0 γ(10) To illustrate the possible eﬀect of modelling more exactlythe evolution of the correlation function,we have used the evolution seen in the large N-body simulation of Kravtsov &Klypin(1999);the semi-analytic models mentioned above produce a similar form for the evolution ofξ(r,z)in their simulations.As ourﬁeld sample is dominated by spirals, we have therefore considered the haloes of the simulation having velocity v>120km−1.Also,asω(θ)for these deep ﬁelds has,as usual,beenﬁtted to a−0.8power law,we have converted the Colin et al.data to provide the same correlation strength as a−1.8power law forξ(r,z)at a comoving separation of0.3h−1Mpc,which at the depths of our data here corresponds roughly to the angular scale of ourestimates forω(θ).Finally,to obtain the function,r com(z), a splineﬁt was made to the converted Colin et al.data points with a simple linear extrapolation to redshifts larger than the maximum redshift,z=5,for which they have estimated the correlation function for their simulation.Fig.2plots the resulting form of the evolution used for r com(z) normalised to r0.In using this in Limber’s equation,we have taken,as with Roche et al.(1993),r0=4.3h−1Mpc,which is little diﬀerent from the converted Colin et al.value of 4.2h−1Mpc.Galaxy clustering in the Herschel deepﬁeld53.3Calculating dn/dzFrom equation7we see that the amplitude ofω(θ)depends on the redshift distribution,dn/dz.To produce these red-shift distributions we employ a pure luminosity evolution (PLE)model in which star-formation increases exponen-tially with look-back time.Earlier versions of these models are discussed in our previous papers(Metcalfe et al.1991; Metcalfe et al.1995;Metcalfe et al.1996),and a full descrip-tion of the model used in this paper is given in(McCracken et al.2000).In this paper we assume H0=50kms−1Mpc−1, although changing the value of H0does not markedly af-fect our conclusions.Two values of the deceleration param-eter q0=0.05and q0=0.5,are adopted,corresponding to open andﬂat cosmologies respectively.The input parame-ters to our models consist of observed local galaxy param-eters(namely,rest-frame colours and luminosity functions) for each of theﬁve morphological types(E/S0,Sab,Sbc, Scd and Sdm)we consider in our models.These morpho-logical types are divided into early-type(E/S0/Sab)and spiral(Sbc/Scd/Sdm)and these two classes are each given a separate star-formation history,parametrised in terms of an e-folding timeτ.We compute the k+e corrections us-ing the models of Bruzual&Charlot(1993).We could,in principle,sub-divide the spirals into diﬀerent morphologi-cal types each with diﬀerent star formation histories but for simplicity we do not;(k+e)corrections for the diﬀerent types are fairly similar to each other in these models in any case.Instead,taking a Sbc model as representative of all types we produce the other types by normalising the Sbc track to the observed rest-frame colours.As in our earlier papers(Jones et al.1991;Metcalfe et al.1991;Metcalfe et al. 1995;McCracken et al.2000),the normalisations of our lu-minosity functions are chosen to match the galaxy counts at B∼18−20and we seek to explain the low number counts at bright magnitudes from a combination of photometric er-rors and anomalous galaxy clustering,rather than substan-tial and hence unphysical evolution at low redshift in the luminosity of galaxies.Our models also include the eﬀects of the Lyman-αforest,and,for spiral types,dust extinction corresponding to the Large Magellanic Cloud as described in Pei(1992).The model redshift distributions produced are in good agreement with the redshift distributions of the CFRS (Lilly et al.1995a)and from the Keck Hawaii redshift sur-vey(Cowie,Songaila,&Hu1996).To illustrate the eﬀect which the inclusion of the evolutionary corrections have on our computed correlation function scaling relation,we also calculate an non-evolving redshift distribution.This is pro-duced by applying k−corrections only to each galaxy type. 4MEASURED AMPLITUDESIn this Section we will present a comparison between our measurements of Aωand those in the literature.We defer an analysis of the implications these measurements have for the growth of galaxy clustering,as well as a discussion of our evolutionary models,to Section5;here we present com-parisons only with the non-evolving,ǫ=0,q0=0.05model.In panels a–d of Figure3we plot ourﬁtted correlation amplitudes extrapolated to one degree(ﬁlled symbols,cir-cles for WHDF and squares for HDF)as a function of sam-ple limiting magnitude for BRIK bandpasses in comparison with measurements from the literature(open symbols).The solid line shows the predictions of the stable clustering,ǫ=0non-evolving(i.e.,no luminosity evolution)model,com-puted assuming r0=4.3h−1Mpc and q0=0.05(This value of r0was chosen to produce the correct clustering ampli-tude at brighter magnitudes as measured from early Schmidtplate surveys(Jones,Shanks,&Fong1987;Stevenson et al. 1985).We adopt the same value of r0for all bandpasses;inSection5.4we discuss if this is an appropriate assumptionfor our data.)Starting with the B−band,we note that here ourWHDF sample reaches extremely high galaxy surfacedensity—approaching∼106gal deg−2at B=28m,and furthermore it probes to the highest redshift;our low-q0evolutionary models indicate that by B∼28we reachingz med∼2.Moreover,our measurements of the B−band cor-relation function are signiﬁcantly deeper than any previouslypublished work.Our brightest bin,at B<27.0,is in agree-ment with the correlation amplitude measured by Metcalfe et al.(1995).Faintwards of B=27,our correlation am-plitudes remainﬂat.The errors on ourﬁtted correlations in B are relatively low in comparison with our other band-passes because at B<28we detect∼6000galaxies,more than in any other bandpass.Our HDF-N/S clustering mea-surements are in agreement with the measurement from the much larger area of the WHDF.Our non-evolving models have some important diﬀer-ences with those used in the earlier works of Roche et al. (1993)and Metcalfe et al.(1995).Firstly,our models in-clude the eﬀects of internal extinction by dust(correspond-ing to A B=0.3mag,using the dust model of Pei(1992)) and reddening by the Lyman alpha forest(as modelled in Madau(1995)).Both of these eﬀects may become signiﬁcant at the very faintest magnitudes we reach,where z med>2. Secondly,our k−corrections are computed from the mod-els of Bruzual&Charlot(1993)for both our evolving and non-evolving models,whereas Roche et al.(1993)and Met-calfe,Fong,&Shanks(1995)used polynomialﬁts to the spectral energy distributions of Pence(1976)for their non-evolving models.Theseﬁts extend only to z∼2and are held constant at higher redshifts.Thirdly,the redshift dis-tributions in these earlier papers were artiﬁcially truncated at z=3.The sum eﬀect of these diﬀerences is that in Roche et al.(1993)and Metcalfe et al.(1995)the slope of the Aω–magnitude limit scaling relation remains constant whilst our slope begins to decrease at B∼26.By this magnitude limit the diﬀerence between our predictions and these previous works is∼0.2in log(Aω).Our R−band correlations plotted in panel(b)of Fig-ure3reach R<26,although the number of galaxies in this catalogue is much smaller(∼300)than in B−and consequently our errors are larger.Our measured clustering amplitude at R<25.5agrees well with the faintest data point of Brainerd,Smail,&Mould(1994);unfortunately, our survey area is too small to permit us to check our clus-tering amplitudes with values from the literature measured at brighter magnitudes such as the large,∼2deg2CCD survey of Roche&Eales(1999).Our measured clustering amplitudes in R−in the WHDF are much lower than the predictions of the non-evolving,stable clustering model.Our HDF clustering measurements are in good agreement with6McCracken et.alFigure3.The logarithm of the amplitude of the angular correlation functionω(θ)at one degree(Aω)in the WHDF(ﬁlled circles), HDF-N(ﬁlled squares)and HDF-S(ﬁlled pentagons)shown as a function of apparent magnitude for BRIK selected samples(panels a–d).For I,correlations are plotted as a function of sample median magnitude.Open symbols show points from the literature.The solid line shows the predictions a non-evolving model withǫ=0and with r0=4.3h−1Mpc and q0=0.05.Error bars on our measurements are calculated by a bootstrap resampling technique,as described in Section3.1.Galaxy clustering in the Herschel deepﬁeld7the HDF clustering measurements of Villumsen,Freudling, &Da Costa(1997).For our I−band measurements,shown in panel(c)of Figure3,we follow the practice in the literature and show correlation amplitudes as a function of sample median mag-nitudes and not limiting magnitudes.We follow the same procedure for our model correlation amplitudes which are plotted at the median magnitude of each magnitude lim-ited slice.In addition to our I<26WHT data,we have a second,larger image taken at the INT which overlaps the WHDF.This covers a total of∼80arcmin2to I<23.5and allows us to determine Aωfrom I med=20to I med=22(the three brightest WHDF bins on the graph).The faintest bin in this INT dataset is in agreement with our measurements from the brightest bin of the WHT dataset.Furthermore, the preliminary result from the large-area0.2deg2survey of Woods et al.(in preparation),shown as an open square, is agreement with our WHT measurement.At I med∼26, measurement from the HDFﬁelds appear to favour the lower values found in the WHDF.We note also that fainter I med∼21,our measurement are below the predictions of the non-evolvingǫ=0model.Faintwards of I med∼23a discrepancy emerges be-tween our measurements and two previously published stud-ies.At I med∼24,our WHDF clustering measurements are ∼5times lower than the measurements made by Brain-erd&Smail(1998)over two slightly smallerﬁelds of area ∼30arcmin2at a similar limiting magnitude.At brighter magnitudes,our points are also below the faintest bins of Postman et al.(1998).This work is a large-area CCD survey covering a contiguous16deg2area and is currently the most reliable determination of galaxy clustering over wide angles and at intermediate(z∼1)depths.We defer a detailed analysis of these diﬀerences until Section4.1where we will attempt to quantify if the discrepancies between our survey and the works of Postman et al.and Brainerd&Smail could be explained in terms of cosmic variance eﬀects.Finally,we turn to an investigation of galaxy correla-tions for K−selected samples.Until very recently measuring ω(θ)at near-infrared wavelengths was time-consuming and diﬃcult as typical detectors covered only∼1arcmin2.How-ever,wide-format IR arrays are becoming available making it now possible to conduct wide,deep surveys of the near-infrared sky.Theﬁlled circles in panel(d)of Figure3shows clustering amplitudes determined from our faint,H<22.5, wide area(∼50arcmin2)Calar Alto Survey are shown, which will be described fully in a forthcoming paper(Mc-Cracken et al2000,in preparation).Similarly,also plotted are clustering measurements from our6′×6′UKIRT IR-CAM3mosaic(McCracken et al.2000).At K∼27we have computed a single point from NICMOS data taken as part of the north and south Hubble deepﬁelds program(we trans-form from H to K using a model(H−K)colour).We note that all our measurements are in agreement with the predic-tions of our stable clustering,no luminosity evolution model.In plotting the H−limited Calar Alto points on our K−limited scaling relation we make two assumptions:ﬁrstly,at K∼22,(H−K)∼0.3;and secondly,for a given surface density,the clustering properties of H−selected and K−se-lected galaxies is identical.Theﬁrst assumption seems rea-sonable,given that at K∼20,galaxies in our survey have (H−K)∼0.3and it is unlikely that they become signiﬁ-cantly bluer by K∼22.The K−selected(I−K)histogramsshown in McCracken et al.(2000)support this.Also given that our Calar Alto H<20Aωagrees with our UKIRT K<19.5point,we conclude that our second assumption isalso valid.Our points at K=19−20agree with the survey of Roche,Eales,&Hippelein(1998)and Roche&Eales(1999);however at fainter magnitudes there is a discrepancy between our amplitudes and the measurement of Carlberg et al.(1997).Once again,we defer a detailed discussion ofthe possible explanation of these diﬀerences until the follow-ing section.4.1Quantifying errors in the correlation function In this Section we will investigate if we have estimated the magnitude of our correlation function error bars correctly.The small size of ourﬁeld means our integral constraint (equation(3)corrections are large,and consequently accu-rate measurements ofω(θ)are dependent on an accurate de-termination of this quantity.Our main motivation is to see if we can explain the discrepancies between our measurements of Aωat I<25and K∼21.5with those of Brainerd&Smail(1998)and Carlberg et al.(1997).There are already indications that such“extra”variance could be signiﬁcant at the depths of our survey.Postman et al.(1998)directlyaddress this question at shallower depths in their work which covers∼16deg2.By extracting250independent16′×16′ﬁelds from their survey(each of which isﬁve times larger than the WHDF but at a brighter limiting magnitude)theyﬁnd that the variance onω(1′)is comparable to its mean value of∼0.045,with extreme values reaching×3this.Fur-thermore,they suggest that as the error distribution for Aωis non-Gaussian,and skewed positively,there could be many more areas in which Aωis below the mean value,rather than above it.To quantify the amount of“extra”variance which could aﬀect clustering measurements in a very deepﬁeld like the WHDF we adopt a simple approach and generate large mock catalogues using the method of Soneira&Peebles(1978). This is an purely empirical approach to generate a hierar-chically clustered distribution of points.We start by placing within a sphere of radius R a random distribution of sub-spheres each of radius R/λ.Within each of these a further n spheres of radius Rλ2are added.This continues through L levels;in our simulation we adopt L=9.The amplitude of the correlation function isﬁxed by the number of centres used and the fraction of the total number of points which are retained;these quantities must be determined by trial and error.We measure the variance on the correlation functionfor many subsamples of this catalogue.We start by gen-erating a catalogue covering6.25deg2with the same sur-face density of objects as in our real catalogue at I<25 (corresponding to∼7.5×105galaxies).Next,we mea-sureω(θ)over the full simulated catalogue area.Our aim is to produce a catalogue for which theﬁtted correlation amplitude log(Aω)at I<25is midway between the re-sult of Brainerd&Smail(log(Aω)=−2.93+0.05−0.06)and ourown(log(Aω)=−3.61+0.16−0.26).Once a catalogue with the de-sired correlation amplitude is produced it is randomly sub-sampled to produce200sub-areas each of which has the。

英语人类的故事从宇宙到地球

The birth of nebulae and stars
Gravity and form particle swarm on each particle, which attract more particles, gas ball under appropriate conditions, in the center of the hot, dense enough, can generate burning helium and hydrogen producing stars. Born in the right as the stars in the Eagle nebula.
The formation and early history of the earth
4.6 billion years ago, the primitive earth, dead frozen world, through three effect to gain energy and began to evolution and development. • 1 ° impact effect: interstellar dust high-speed collision, the kinetic energy to heat energy • 2 ° compression effect: interstellar dust landing on the surface, increase external quality, internal squeezed, compression can be converted into heat energy. • 3 ° radioactive decay effect: radioactive elements in the interior of the earth (uranium, thorium, rubidium, etc.). Release huge energy • Evolution results: composition of the molten iron flows to the center of the earth, the formation of iron core, it is a rocky composition form structures (silicate).

高三英语科学前沿单选题30题

高三英语科学前沿单选题30题1.The discovery of a new planet is a major breakthrough in the field of_____.A.astronomyB.biologyC.chemistryD.physics答案：A。

本题考查名词词义辨析。

A 项“astronomy”天文学，发现新行星是天文学领域的重大突破；B 项“biology”生物学，与发现新行星无关；C 项“chemistry”化学，也不符合题意；D 项“physics”物理学，同样不涉及发现新行星。

2.The study of the human brain belongs to the field of_____.A.psychologyB.neuroscienceC.geologyD.mathematics答案：B。

A 项“psychology”心理学，主要研究心理现象；B 项“neuroscience”神经科学，研究人类大脑；C 项“geology”地质学，与大脑无关；D 项“mathematics”数学，也不涉及大脑研究。

3.The development of new materials is an important area in_____.A.engineeringB.literatureC.historyD.art答案：A。

A 项“engineering”工程学，涉及新材料的开发；B 项“literature”文学，不相关；C 项“history”历史，不符合；D 项“art”艺术，与新材料开发无关。

4.The research on climate change is mainly carried out in the field of_____.A.geographyB.economicsC.politicsD.music答案：A。

A 项“geography”地理学，气候变化的研究主要在地理学领域进行；B 项“economics”经济学，与气候变化研究的关系不大；C 项“politics”政治学，不是主要领域；D 项“music”音乐，完全不相关。

外太空的10大奥秘

条评论文：mtarmymanSince the beginning of life, man has looked to the stars with a sense of wonder. Between then and now, many advances have been made in the fields of astronomy, mathematics, and physics in an attempt to explain the things we see above, yet the more we believe we understand, the less we really seem to know. In something as big as the universe, there are bound to be unexplainable phenomena, and things we truly can’t grasp. The universe shows us how small we really are, and in a plac e so big, is it really plausible to believe that we are alone? And is there any reason someone might not want us to know? This is a list of what I believe to be some of the best mysteries and conspiracy theories of outer space.自从有生命开始，人类就怀着好奇心仰望星空。

从那时起到现在，天文、数学和物理等领域取得了许多进展，试图解释我们所看到的头顶上的世界。

但我们越是相信自己懂得的多，我们实际所知道的似乎就越少。

上海市浦东新区2021届高三上学期一模英语试题含解析

D. Because he had to attend a business meeting.
18. A. His flight number and arrival time.
B. The cause of the flight's late arrival.
C. The number of his luggage check.
D. It can create smells and give them off to any scene.
15. A. It helps shoppers locate the right brand of perfume.
B. It helps shoppers check out the perfumes before they buy.
阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。
Since astronomers confirmed the presence of planets beyond our solar system, called exoplanets, humans_________1_________(wonder) how many could harbor life.
Our galaxy holds at least an______4______(estimate) 300 million of these potentially habitable worlds, based on even the most conservative interpretation of the results in a new study to be published in The Astronomical Journal.

the galaxy翻译

the galaxy翻译"the galaxy"可以翻译为"银河系"或"星系"，它是指地球所在的星际空间中的巨大星球系统。

以下是一些关于"the galaxy"的用法和中英文对照例句：1. The galaxy is home to billions of stars and other celestial objects.银河系是亿万颗恒星和其他天体的家园。

2. Our solar system is located in the Milky Way galaxy.我们的太阳系位于银河系中。

3. Astronomers have discovered many exoplanets outside our galaxy.天文学家在我们的银河系外发现了许多系外行星。

4. The Andromeda galaxy is the closest spiral galaxy to the Milky Way.安德洛美达星系是离银河系最近的螺旋星系。

5. The Hubble Space Telescope has captured stunning images of distant galaxies.哈勃太空望远镜捕捉到了遥远星系的惊人图像。

6. Scientists are still studying the formation and evolution ofgalaxies.科学家们仍在研究星系的形成和演化。

7. The galaxy is estimated to be about 13.6 billion years old.银河系估计有大约136亿年的历史。

8. The center of our galaxy contains a supermassive black hole.我们银河系的中心包含一个超大质量黑洞。

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.。

The evolution of clustering and bias in the galaxy distribution

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

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

a rXiv:as tr o-ph/61363v112Oct26Studying Galaxy Evolution with Spitzer and Herschel CUP Conference Series,Vol.**VOLUME**,2006V.Charmandaris,D.Rigopoulou,N.Kylaﬁs Biased galaxy formation in the ﬁelds of high-redshift AGN J.A.Stevens,1M.J.Page,2F.J.Carrera,3R.J.Ivison,4and Ian Smail 51Centre for Astrophysics Research,University of Hertfordshire,College Lane,Herts AL109AB,UK 2Mullard Space Science Laboratory,University College London,Holmbury St.Mary,Dorking,Surrey RH56NT,UK 3Instituto de Fisica de Cantabria (CSIC-UC),Avienida de los Castros 39005Santander,Spain 4UK Astronomy Technology Centre,Royal Observatory,Blackford Hill,Edinburgh EH93HJ,UK 5Institute for Computational Cosmology,Durham University,South Road,Durham DH13LE,UK Abstract.We discuss preliminary results from our programme to map the ﬁelds of high-redshift AGN.In the context of the hierarchical models such ﬁelds are predicted to contain an over-density of young,luminous galaxies destined to evolve into the core of a rich cluster by the present epoch.We have thus imaged from submillimetre to X-ray wavelengths the few-arcmin scale ﬁelds of a small sample of high-redshift QSOs.We ﬁnd that submillimetre wavelength data from SCUBA show striking over-densities of luminous star-forming galaxies over scales of ∼500kpc.Whilst many of these galaxies are undetected even in deep near-IR imaging almost all of them are detected by Spitzer at 4.5,8.0and 24µm,showing that they have extremely red colours.However,they are not detected in our XMM-Newton observations suggesting that any AGN must be highly obscured.Optical-through-mid-IR SEDs show the redshifted 1.6µm bump from star-light giving preliminary evidence that the galaxies lie at the same redshift,and thus in the same structure,as the QSO although this ﬁnding must be conﬁrmed with photometric and/or spectroscopic redshifts.1.IntroductionThe popular hierarchical model of galaxy formation predicts that elliptical galax-ies found today in the cores of rich clusters formed at high redshifts and at rare high-density peaks of the dark matter distribution.Within these regions,gas rich proto-galaxies merge together rapidly and form stars at a high rate.The same reservoir of gas used to build the stellar mass can also fuel the growth of the supermassive black holes (SMBH)found dormant in the centre of the galaxies at low redshift (Kauﬀmann &Haehnelt 2000).Since massive star formation is known to be a dusty phenomenon,the light from such young galaxies may well be highly obscured rendering the population inaccessible to optical techniques.Dust enshrouded star formation is,however,a luminous phenomenon in the submillimetre (hereafter submm)through far-IR waveband where the star-light absorbed by dust grains is re-emitted.12Stevens,Page,Carrera,Ivison and SmailUnfortunately,it is not currently feasible at submm/far-IR wavelengths to perform a survey of a randomly selected region of sky over an area suﬃciently large to ensure that rare structures in the early universe are contained within it. However,one method of locating such structures is to target theﬁelds of high-redshift AGN.Given their huge luminosities,such objects must already contain a SMBH,and therefore must represent some of the most massive objects in exis-tence at their epochs.They should thus act as signposts to the rare high-density peaks that we wish to study and can target with existing technology at submm wavelengths(Ivison et al.2000;Stevens et al.2003).This paper presents pre-liminary results from such a programme.We concentrate on two QSOﬁelds at 1<z<3,presenting submm results obtained with SCUBA on the JCMT and follow-up imaging at near-IR(UKIRT)and mid-IR(Spitzer)wavelengths.2.Over-densities of luminous,extremely red star-forming galaxies The two targets discussed here are the X-ray absorbed QSOs RX J094144.51+ 385434.8(z=1.82)and RX J121803.82+470854.6(z=1.74).The importance of these objects has been discussed extensively in the literature(Page et al.2004; Stevens et al.2005).See also the contribution by Page et al.in this volume.Figure 1.Submm,mid-and near-IR imaging of the RX J121803.82+470854.6ﬁeld.Left-hand panel shows850µm contours(2,3,4,5σ)on a deepK-band image whilst the right-hand panel shows the same contours on an8.0µm image.Note that dust peaks lacking K-band counterparts often dohave detections at8.0µm.Each panel is∼1arcmin square.Submm,near-and mid-IR images of the RX J121803.82+470854.6ﬁeld are shown in Fig.1.The850µm data reveal a large over-density of sources, particularly pronounced in the close vicinity(∼30arcsec)of the QSO.Results from blank-ﬁeld surveys predict,at most,one≥3σsource in addition to the QSO.The near-and mid-IR imaging gives an indication that many of these submm sources are indeed real and have extremely red colours.Many of the them are detected by Spitzer even when they are not seen in deep(K∼20.5)near-IR imaging;e.g.the two most signiﬁcant dust peaks in Fig.1.Star-formationHigh-redshift AGNﬁelds3 rates computed in the standard manner are at least several100M⊙yr−1.It can thus be concluded that we have discovered a large over-density of star-forming galaxies in the few hundred kpc-scale environment of the QSO.Figure2.Submm and mid-IR imaging of the RX J094144.51+385434.8ﬁeld.450µm contours on the850µm image(left),450µm contours on the4.5µm image(centre)and450µm contours on the24µm image(right).Submm contours start at2σand increase in1σsteps.Panels are∼1.0×1.5arcmin.The structure of galaxies is∼400kpc in extent(Stevens et al.2004).Fig.2shows submm and mid-IR data for the RX J094144.51+385434.8ﬁeld.Here we see a similar over-density of luminous star-forming galaxies to that discussed above.For this dataset the observing conditions were suﬃciently transparent that we were able to collect good data at450µm.These data show that the large-scaleﬁlamentary structure seen at850µm breaks up into individual star-forming galaxies when observed at higher resolution(∼8cf.∼14arcsec).Such datasets were very rarely obtained with SCUBA at450µm because of the diﬃculty of observing at short submm wavelengths from Mauna Kea.However,the increased sensitivity andﬁeld-of-view aﬀorded by SCUBA-2 will go a long way to alleviating this problem and we can look forwards to higher resolution images of distant galaxies.A second result is that the submm-selected galaxies are detected by Spitzer with both IRAC and MIPS(Fig.2)verifying their reality and,with the addi-tion of optical and near-infrared imaging,allowing us to construct SEDs of the individual galaxies(see Fig.3).Weﬁnd that the SEDs are quite similar to that of the local ULIRG Arp220if it is moved to the redshift of the QSO(z=1.82) suggesting that the bump we see in the spectra,peaking roughly in the4.5µm band is the redshifted1.6µm bump from star-light.This result provides the ﬁrst evidence that the luminous star-forming galaxies discovered by SCUBA are at the same redshift and in the same structure as the QSO.We are currently working to conﬁrm thisﬁnding with photometric and spectroscopic redshifts.2.1.Buried AGN?If these galaxies are to evolve into cluster elliptical galaxies then the SMBHs found at their centres at the current epoch should be active at z∼2.Our50ks XMM-Newton observations detect the QSOs but not the star-forming galaxies in4Stevens,Page,Carrera,Ivison and SmailFigure3.Optical through mid-IR spectra of the QSO RX J094144.51+385434.8(top dotted line and points)and the submm galaxies in its vicinity.The solid line is the spectrum of the local ULIRG Arp220redshifted toz=1.82and scaled arbitrarily(Silva et al.1998).theirﬁelds.If we assume that these galaxies contain an AGN with a luminosity L(2−10keV)=1044erg s−1and a photon indexΓ=2then the non-detections imply a column density N H>5×1023cm−2.Therefore,if these galaxies contain reasonably powerful AGN they must be highly obscured.3.Looking ahead to SCUBA-2and HerschelThe next year will see major new facilities operating at far-IR and submm wave-lengths.Both Herschel and SCUBA-2will provide much faster mapping speeds than those currently available allowing us to map an area of sky around the QSOs large enough to observe the wholeﬁlamentary structure of the collapsing proto-cluster rather than just the core region.Simulations show that this will require a map of at least20Mpc square at z=2(comoving units).At present a signiﬁcant amount of telescope time is required to map one hundredth of this area but SCUBA-2can map a region this large in only a few hours.ReferencesIvison,R.J.,Dunlop,J.S.,Smail,Ian,Dey,Arjun,Liu,M.C.,&Graham,J.R.,2000, ApJ,542,27Kauﬀmann,G.,&Haehnelt,M.,2000,MNRAS,311,576Page,M.J.,Stevens,J.A.,Ivison,R.J.,&Carrera,F.J.,2004,ApJ,611,L85 Page,M.J.,Carrera,F.J.,Ebrero,J.,Stevens,J.A.,&Ivison R.J.,this issue Silva,L.,Granato,G.L.,Bressan,A.,&Danese,L.,1998,ApJ,509,103Stevens,J.A.et al.2003,Nat,425,264Stevens,J.A.,Page,M.J.,Ivison,R.J.,Smail,Ian,&Carrera,F.J.,2004,ApJ,604, L17High-redshift AGNﬁelds5 Stevens,J.A.,Page,M.J.,Ivison R.J.,Carrera,F.J.,Mittaz,J.P.D.,Smail,Ian,& McHardy,I.M.,2005,MNRAS,360,610。