The evolution of galaxy clustering since z = 3 using the UKIDSS Ultra Deep Survey: the divergence of passive and star-forming galaxies
William Hartley, Omar Almaini, Michele Cirasuolo, Sebastien Foucaud, Chris Simpson, Christopher Conselice, Ian Smail, Ross McLure, Jim Dunlop, Rob Chuter, Steve Maddox, Kyle Lane, Emma Bradshaw
aa r X i v : . [ a s t r o - ph . C O ] M a y Mon. Not. R. Astron. Soc. , 1–11 (2010) Printed 4 November 2018 (MN L A TEX style file v2.2)
The evolution of galaxy clustering since z = 3 using the UKIDSSUltra Deep Survey: the divergence of passive and star-forminggalaxies W. G. Hartley ⋆ , O. Almaini , M. Cirasuolo , S. Foucaud , , C. Simpson ,C. J. Conselice , I. Smail , R. J. McLure , J. S. Dunlop , R. W. Chuter ,S. Maddox , K. P. Lane , E. J. Bradshaw School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ Department of Earth Sciences, National Taiwan Normal University, No. 88, Section 4, Tingzhou Road, Wenshan District, Taipei 11677, Taiwan Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Wharf, Birkenhead CH41 1LD Institute for Computational Cosmology, Department of Physics, Durham University, Durham DH1 3LE Department of Astrophysics, University of Oxford, OX1 3RH
ABSTRACT
We use the UKIDSS Ultra-Deep Survey to trace the evolution of galaxy clusteringto z = 3 . Using photometric redshifts derived from data covering the wavelength range . − . µ m we examine this clustering as a function of absolute K-band luminosity, colourand star-formation rate. Comparing the deprojected clustering amplitudes, we find that redgalaxies are more strongly clustered than blue galaxies out to at least z = 1 . , irrespective ofrest-frame K-band luminosity. We then construct passive and star-forming samples based onstellar age, colour and star-formation histories calculated from the best fitting templates. Theclustering strength of star-forming galaxies declines steadily from r ≃ h − Mpc at z ≃ to r ≃ h − Mpc at z ≃ , while passive galaxies have clustering strengths up to a factorof two higher. Within the passive and star-forming subsamples, however, we find very littledependence of galaxy clustering on K-band luminosity. Galaxy ‘passivity’ appears to be thestrongest indicator of clustering strength. We compare these clustering measurements withthose predicted for dark matter halos and conclude that passive galaxies typically reside inhalos of mass M > M ⊙ while luminous star-forming galaxies occupy halos an order ofmagnitude less massive over the range . < z < . . The decline in the clustering strength ofstar-forming galaxies with decreasing redshift indicates a decline in the hosting halo mass forgalaxies of a given luminosity. We find evidence for convergence of clustering in star-formingand passive galaxies around z ∼ , which is consistent with this being the epoch at which thered sequence of galaxies becomes distinct. Key words:
Infrared: galaxies – Cosmology: large-scale structure – Galaxies: High Redshift– Galaxies: Evolution – Galaxies: Formation.
The origin of the red sequence of galaxies, and more gen-erally the bimodality in the colour-absolute magnitude plane(Visvanathan & Sandage 1977), have become increasingly impor-tant questions in extragalactic astronomy. Since Dressler (1980)first identified the trend for elliptical galaxies to be preferentiallyfound in the denser regions of clusters, evidence has grown to ⋆ E-mail: [email protected] suggest that there are crucial differences in the evolutionary his-tories of red and blue galaxies at low redshift. Present day mas-sive, passive galaxies are claimed to be largely in place by z=1 orearlier (e.g. Yamada et al. 2005; Cimatti, Daddi, & Renzini 2006;Conselice et al. 2007), implying an extremely rapid period of star-formation. The luminosity and mass functions of lower-mass andstar-forming galaxies, however, evolve significantly over the sametime period (Bundy et al. 2006; Cirasuolo et al. 2010).The early formation of stars in the most massive galaxies hasbecome known as downsizing (Cowie et al. 1996) and is in contrast c (cid:13) W. G. Hartley et al. to the well-established hierarchical growth of the underlying darkmatter distribution. These massive, quiescent galaxies dominatepresent-day groups and clusters and are thought to have formedat the highest peaks of the dark matter density field. The expectedclustering of the dark matter is well understood (e.g. Mo & White2002), and at any given epoch the real-space clustering ampli-tude over mid to large scales is a monotonically increasing func-tion of dark matter halo mass. Measuring the clustering propertiesfor galaxy samples therefore provides a direct link from the visi-ble galaxies to the invisible dark matter in which they are found.Furthermore, the growth of dark matter halos over time is alsowell modelled, and so the evolution of the most massive systemsthroughout cosmic history can be traced through the use of cluster-ing statistics.Over the last few years the clustering technique has beenapplied to complete samples of optically-selected galaxies, sep-arated by luminosity and colour. Zehavi et al. (2005) computedthe angular auto-correlation functions of red and blue volume-limited sub-samples of galaxies from the Sloan Digital Sky Sur-vey (SDSS; York et al. 2000) for separations < h − Mpc andredshifts, z < . They found that the population of galaxies redin g − r colour are more strongly clustered than those with bluercolours ( r = 5 . . h − Mpc for red and blue populations re-spectively). Moreover, they show that this difference remains whenthe samples are further broken down into absolute R-band magni-tude sub-samples.Meneux et al. (2006) split the VIMOS-VLT Deep Survey(VVDS; Le F`evre et al. 2005) galaxies into red and blue spectraltypes by the method of Zucca et al. (2006) and computed their clus-tering out to z ≃ . . They found that the deprojected clusteringscale length of the red spectral type galaxies ( r ∼ h − Mpc)was greater than that of the blue type galaxies ( r ∼ h − Mpc)at all redshifts investigated. Carlberg et al. (1997) find similar re-sults for their sample at z ≃ . . More recently Coil et al. (2008)used the DEEP2 galaxy redshift survey to address the same ques-tion at z = 1 . They also found that red-sequence galaxies are morestrongly clustered ( r ∼ h − Mpc for red and blue sam-ples), but additionally showed that those galaxies with intermedi-ate colours had an intermediate clustering strength. They computedthe relative bias between their sub-samples, finding a smoothly in-creasing bias with rest-frame (U-B) colour up to the red sequence.Recently, two further deep surveys have been used to studythe clustering of galaxies in the range . < z < . : the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS, Ilbert et al.2006) and the zCOSMOS field (Lilly et al. 2007). McCracken et al.(2008) used the CFHTLS, splitting the galaxy sample by template-fit spectral type and B-band luminosity. Based on photometric red-shifts, they find that the difference in clustering strength betweengalaxies fit by early type and late type templates is roughly constantacross all redshifts studied. The luminosity dependence at a givenredshift, however, is minimal. Intriguingly, the early type popula-tion at z ∼ . shows hints of an inverse dependence of lumi-nosity on clustering strength. The authors attribute this behaviourto fainter red galaxies being preferentially located in cluster envi-ronments. Meneux et al. (2009) meanwhile, use the spectroscopiczCOSMOS data, finding a weak dependence on luminosity whichremains when stellar mass is used instead.Each of these studies has been based upon an optical colourselection, which limits these studies to z . Beyond this red-shift optical studies become increasingly biased against passive anddusty galaxies and so are only able to probe the clustering of unob-scured star-forming galaxies. The relative clustering strengths for complete samples of passive and star-forming galaxies are there-fore poorly understood beyond z ∼ . Infrared survey data are notbiased in this way and in addition, at z < , the K-band luminos-ity is a reasonable proxy for the stellar mass of a galaxy. Infrared-selected samples are therefore vital in the study of high redshiftgalaxy clustering.Utilising infrared data, the high redshift progenitors ofnearby high-mass, passive systems have been suggested as be-ing passively-selected BzK galaxies (Daddi et al. 2004; Kong et al.2006; Hartley et al. 2008), ultra-compact z=2 red galaxies (e.g.Zirm et al. 2007; Toft et al. 2007; Cimatti et al. 2008), sub-mmgalaxies (Lilly et al. 1999; Swinbank et al. 2006), µ m sourcesselected at z > (e.g. Magliocchetti et al. 2008), distantred galaxies (DRGs) (Franx et al. 2003; Conselice et al. 2007;Foucaud et al. 2007), extremely red objects (EROs) (Roche et al.2002; McCarthy et al. 2004) and Ultra-luminous infrared galax-ies (ULIRGS) (e.g. Farrah et al. 2006). Each of these populationshave been found to cluster very strongly, with r values in therange < r < h − Mpc (Roche et al. 2002; Blain et al. 2004;Farrah et al. 2006; Foucaud et al. 2007; Magliocchetti et al. 2008;Weiß et al. 2009).In Hartley et al. (2008) (henceforth H08) we used the colourselection criteria of Daddi et al. (2004) to investigate the clusteringproperties of passive and star-forming galaxies at . < z < . .We showed that, when limiting the samples to K AB < , the pas-sive galaxies were significantly more clustered than star-forminggalaxies. This result was found in angular clustering and also whendeprojected to find the real-space clustering strength; with cluster-ing scale lengths of ∼ h − Mpc for the passive sample (pBzK)and ∼ h − Mpc for the star-forming sample (sBzK).Although all of these different galaxy populations overlap tosome extent (Lane et al. 2007), their biases differ and they are sen-sitive to different epochs. It is therefore difficult to compare thesesamples with low redshift samples or to study global galaxy evo-lution. The analysis in H08 in particular left some open questions.We established that passive galaxies are more clustered even at suchhigh redshifts, but the passive population is exclusively bright andthe star-forming galaxies exhibited a strong limiting-magnitude de-pendence on clustering strength. It is therefore not clear whether itis luminosity or passivity that is more significantly correlated withclustering strength. Even at low-redshift debate remains over sucha distinction (Norberg et al. 2002), complicated by the dominanceof passive systems at the bright end of the luminosity function.Williams et al. (2009) used a two-colour rest-frame selectionto select a quiescent cloud and star-forming track over the range < z < . Using this novel selection, they compute the cluster-ing scale lengths of their two samples, finding very similar lengthsto those of the BzK selections in H08. They also report evidencefor a mild evolution in clustering with luminosity for the star-forming galaxies by splitting their samples into two luminositybins. Coil et al. (2006) also find, at z = 1 , only a modest depen-dence for clustering strength to increase with B-band luminosity,covering . L ∗ < L < . L ∗ .A remaining open question is to determine when the passivepopulation is built up. Though we found in H08 that this build-upoccurs over . < z < . , and Williams et al. (2009) find similarevidence for their sample at < z < , these ranges in redshift arevery broad. Can we identify a narrow epoch at which the cluster-ing strengths of passive and star-forming galaxies of a given lumi-nosity are equal? At this epoch passive and star-forming galaxieswould occupy the same mass of dark matter halos and differencesin their internal processes could be clearer. In this paper we attempt c (cid:13) , 1–11 lustering of passive galaxies to disentangle the effects on clustering strength due to passivityand luminosity and to further refine the redshift range over whichthe passive population of galaxies is first established.Where relevant, we adopt a concordance cosmology inour analysis; Ω M = 0 . , Ω Λ = 0 . , h = H /
100 =0 . − Mpc − and σ = 0 . . All magnitudes are given in theVega system unless otherwise stated. The remainder of the paperis organised in the following way: in the following section we pro-vide details of the data sets used, derived quantities and method ofselecting passive galaxies. In section 3 we compute the clusteringstrengths of these samples and then discuss their implications insection 4. We conclude in section 5. The analysis we present in this work is based primarily on thethird data release (DR3) of the ongoing UKIRT (United King-dom Infra-Red Telescope) Infrared Deep Sky Survey, Ultra-DeepSurvey (UKIDSS UDS, Lawrence et al. 2007). UKIDSS comprisesfive complementary sub-surveys with the UDS being the deepest,targeting a depth of K = 23 over a single, 4-pointing mosaic ofthe Wide-Field Camera (WFCAM, Casali et al. 2007): an area of . × . degrees. UKIDSS began in the spring of 2005 and theUDS has seen several data releases: an early release of the first fewweeks of data (EDR, Dye et al. 2006), a one-year release (DR1,Warren et al. 2007), which we used in Hartley et al. (2008), and themore recent three-year data release (DR3).The principle improvement from the DR1 to the DR3 is theaddition of H-band data. Additional data in the K-band also pro-vides an incremental improvement in depth. The σ depths within ′′ diameter apertures for the DR3 in J, H and K-bands are . (AB . ), . (AB . ) and . (AB . ) respectively. Thesedepths make it the deepest single-field near infrared survey of itsarea to date. For details of the stacking procedure, mosaicing, cat-alogue extraction and depth estimation we refer the reader to Al-maini et al. (in prep.) and Foucaud et al. (2007).In addition to near infrared data, the field is covered by ex-tremely deep optical data in the B, V, R, i ′ and z ′ -bands fromthe Subaru-XMM Deep Survey (SXDS, Sekiguchi et al. 2005;Furusawa et al. 2008), Spitzer data reaching σ depths of 24.2and 24.0 (AB) at . µ m and . µ m respectively from a re-cent Spitzer
Legacy Program (SpUDS, PI:Dunlop) and U-banddata taken with CFHT Megacam. The SXDS utilised Suprime-cam on the Subaru telescope, achieving depths of B AB =28 . , V AB = 27 . , R AB = 27 . , i ′ AB = 27 . and z ′ AB = 26 . (Furusawa et al. 2008, σ , ′′ ). Border regions, areas around brightstars and obvious cross-talk artifacts were masked and any sourceswithin such regions were discarded. The co-incident area with theUDS taking masking into account is . deg .The world-public DR3 catalogue extracted from the K-bandimage is used as the basis for our selection, upon which we imposea cut at K = 21 . ( K AB = 23 ) within ′′ diameter apertures.This cut was made to minimise photometric errors and the numberof spurious sources and to ensure a high level of completeness androbust photometric redshifts (see below). This limit is fainter than M ∗ K , the characteristic luminosity of the K-band luminosity func-tion (Cirasuolo et al. 2010 and fig. 1). We are therefore probing theproperties of ‘normal’ galaxies out to z = 3 . Corresponding ′′ magnitudes for each object were extracted directly from the optical, J and H-band images at the position of the source after a detailedastrometric re-alignment to the UDS K-band image.From our combined catalogue we remove stars in the follow-ing way: bright ( K < . ) stars were removed by excludingthose with K-band aperture magnitudes within ′′ and ′′ satisfying K ′′ − K ′′ > − . , where the stars are clearly separated fromthe galaxies. The remaining, fainter stars form a stellar locus in the ( B − z ′ ) − ( z ′ − K ) plane (as noted by Daddi et al. 2004) and caneasily be removed by the criterion ( z ′ − K ) < . B − z ′ ) − . (Cirasuolo et al. 2010). Saturated stars and the surrounding con-taminated regions were carefully masked out during the analysis.These cuts left galaxies from which we made our selections,as detailed in the following section.The magnitudes obtained from the images were then used todetermine photometric redshifts (photo-zs) and stellar ages by a χ minimisation over a large suite of model templates, constructed us-ing Bruzual & Charlot (2003) with a Salpeter initial mass function,and including a treatment of dust content (see Cirasuolo et al. 2007,2010 for a full account). These templates cover nine values of theexponential star-formation decay rate ( τ = 0 . , . , . , , , , and Gyrs, and an instantaneous burst), and allow stellar ages upto the age of the Universe at any given redshift. The dust reddeningis allowed to vary between < A V < , following the Calzettilaw (Calzetti et al. 2000), and line of sight neutral Hydrogen ab-sorption, calculated from Madau (1995), is also taken into account.We remove from our catalogue any source with an unaccept-able fit ( χ > , . of the galaxy sample) as they will likely bemis-assigned when we break up our sample by redshift, and the de-rived stellar ages are unlikely to be reliable for such objects. Uponinvestigation, the majority of these discarded sources were foundto be cross-talk artifacts ( ), QSOs ( ) or the minor mem-bers of pairs or mergers ( ). The majority of the remaining dis-carded objects were of very low surface brightness and many ofthem would not have made it into the volume-limited sub-samples.The fraction of otherwise useful objects rejected by this χ > criterion is therefore < . . Rest-frame magnitudes and colourswere computed by integrating the appropriate filter over the best-fitting template of each object. In this work we make use of the ab-solute rest-frame K-band magnitude and rest-frame ( U − B ) colour. In this section we outline our definition of the passive galaxysample. At low redshift, passive galaxies form a well-definedred sequence in a diagram of rest-frame U − B colour ver-sus absolute magnitude. The red sequence is not exclusivelycomposed of passive systems, however, and typically containsa contamination from dusty star-forming galaxies (e.g.Wolf, Gray, & Meisenheimer 2005). At high redshifts ( z > )contamination by dusty star-forming objects becomes increasinglyproblematic (Daddi et al. 2004). In addition, a simple U − B cutdoes not make full use of all the available photometry. For thesereasons, we define our passive sample with two criteria: (a) thegalaxy must be ‘red’ in rest-frame U − B colour and (b) the best-fitting galaxy template must imply a very low level of residual starformation. These criteria are further detailed below.Our rest-frame U − B colours are computed from the best-fitting template used to find the photometric redshift. The templatescover two possible star-formation histories: either an instantaneousburst parameterised by an age, or an exponentially decaying star-formation rate parameterised by an age and the e-folding time, τ .Hence, c (cid:13) , 1–11 W. G. Hartley et al.
Figure 1.
The distribution of UDS galaxies used in this work in the pho-tometric redshift – M K plane. The dot-dashed lines show the sub-sampleregions for which we compute clustering lengths, provided they contain > galaxies. Also plotted, as the dashed-line curve, is the fit for theevolution of the characteristic luminosity, M ∗ K , of the K-band luminosityfunction, as given in Cirasuolo et al. (2010). Figure 2.
Colour-luminosity density plot of the full galaxy sample (light,red contours) and of those used to define the red sequence (heavy contours).The red sequence was defined by fitting a line of the form U − B = a × M K + b to the galaxies which were best fit by a burst template with age > Gyr . This fit is shown by the dot-dashed line, while the dotted line isthe σ lower envelope. Galaxies redder than the dotted line are defined as‘red’ for the purposes of our sample selections. SF R obs = SF R initial × e − age/τ (1)where SF R obs is the SFR at the time of observation.We wish to define our red sequence initially using the mostconservative and clean sample of passive galaxies drawn from ourcatalogue. We construct this sample to be those galaxies which aresimultaneously old (age > Gyr) and are fit with a burst template,as these values imply a strong ˚ A break. We then perform a χ minimisation to fit an equation of the form U − B AB = a × M K + b to these galaxies. The ‘red’ sample is then taken to include allgalaxies within σ scatter of this fit (or redder). In Figure 2 we plotcontours showing where galaxies lie in the ( U − B ) AB vs. absoluteK-band magnitude plane. Overlaid in black are the contours for the burst galaxies described above, the associated best fit (dashed-dotted line) and red/blue selection criterion (dotted line).The red sequence is known to evolve with time, with reddercolours at lower redshifts (e.g. Brammer et al. 2009). Accuratelyaccounting for this evolution with photometric redshifts is prob-lematic. The typical errors on our U-B colours are . magni-tudes, which is of the same order as the expected colour evolution.For simplicity, we choose not to treat the red sequence in such de-tail and instead use a fixed colour selection boundary. We note thatour ‘red’ sample includes part of the green valley, and so we areunlikely to miss many intrinsically red galaxies at high redshift.In order to remove the galaxies that are red due to dust ratherthan age we make use of the star-formation histories obtained fromthe templates. To be selected as a passive galaxy we require thegalaxy to be red, as defined above, older than Gyr and to have abest-fit SFR (from the photo-z template fits) below some cut-offvalue (as given by equation 1, where τ = 0 for a burst model). Byvarying this SFR cut-off criterion we can study how the inclusionof galaxies with greater recent star formation rates influences theclustering strengths of the sub-samples.We require, for our primary passive sample, a highly con-servative limit to residual star-formation rate: SF R o . of SF R initial (in addition to being red in rest-frame U − B and witha stellar age > Gyr). We choose this strict limit to minimise thecontamination by dusty star-forming objects whilst retaining suffi-cient objects with which to compute meaningful clustering lengths.There are well-known degeneracies between age, metallicity anddust content. We cannot completely overcome them, even with themultiple bands of deep photometry at our disposal. However, theseparameters imply a strong break in the galaxy SED and hence onlythe most extreme dusty contaminants will be included. The num-ber of objects satisfying these selection criteria is 3991 ( of the‘red’ sample). The vast majority of passive galaxies selected in thisway also lie within the ‘pERO’ colour selection boundaries (seesection 4).We choose, as a baseline against which to compare our pas-sive sample, an actively star-forming sample with a single criterion:
SF R o > of SF R initial . This star-forming sample consists of22856 objects of which are ‘blue’ according to our (U-B) cri-terion and are ‘red’. We then construct three further passivesamples by relaxing the SFR criterion used in our primary passivesample to include galaxies with SF R o . , SF R o and SF R o of SF R initial . In each of these three additionalsamples the requirements for red U − B colour and stellar age arekept the same as the primary sample. The number of objects ineach of these expanded passive samples are 6111, 7677 and 10032respectively. We will occasionally refer to these samples in the textby the SFR limit imposed during selection. The real-space correlation length of a sample of galaxies is inti-mately related to the mass of dark matter halos in which they arefound. The value of this clustering scale-length is therefore of greatinterest in the study of galaxy formation and evolution. In this workwe determine the angular correlation function of the galaxies asthey are seen in projection, and then use the redshift distributionto deproject to find the real-space scale length ( r ). This process isdetailed below.The 2-point angular correlation function, w ( θ ) is defined by c (cid:13) , 1–11 lustering of passive galaxies the joint probability of finding two galaxies in solid angle elements δ Ω and δ Ω at a given separation (Peebles 1980), δP = n δ Ω δ Ω (1 + w ( θ )) . (2)To estimate the correlation function we use the estimator ofLandy & Szalay (1993), w ( θ ) = DD − DR + RRRR (3)where DD, DR and RR are the counts of data-data, data-randomand random-random pairs respectively at angular separation θ , nor-malised by the total number possible. Although this estimator is rel-atively robust against systematic errors, there remains a small biasdue to the finite field size. This bias is corrected by an integral con-straint, constant C. We follow the method of Roche & Eales (1999)by using the random–random counts to estimate the size of thisbias: C = Σ N RR ( θ ) θ − . Σ N RR ( θ ) , (4)where the sums extend to the largest separations within the field.The angular correlation functions are fit by χ minimisationwith a power law of fixed slope, δ = − . . The fit is made over midto large scales to avoid biases arising from multiple halo occupa-tion. The small-scale limit corresponds to . h − Mpc , where pre-vious w ( θ ) measurements of galaxies over < z < begin to di-verge from the large scale power law (H08). The large scale cut offis at . degrees where survey area limits our measurements. Thismethod is the same as that presented in H08. Correlation functionuncertainties are determined using bootstrap resampling, which aretypically 2-3 times the Poisson errors.The real space clustering and projected clustering arelinked by the relativistic Limber equation (Limber 1954). Ifthe redshift distribution of a sample is known, the Lim-ber equation can be inverted and the correlation length, r , can be calculated in a robust manner (Peebles 1980;Magliocchetti & Maddox 1999; Roche, Dunlop, & Almaini 2003).Following Magliocchetti & Maddox (1999) and adjusting to takeinto account our known photometric redshift distributions we de-termine r as r = " cAH H γ ( R ∞ n ( z ) dz ) R ∞ n ( z ) x ( z ) − γ P (Ω , z ) F ( z ) dz ! /γ (5)where n ( z ) is the redshift distribution of the sub-sampleand all other symbols have the same meanings as inMagliocchetti & Maddox (1999).Below we present the resulting measurements for r as a func-tion of redshift and K-band luminosity. This is first determinedfor all galaxies and then further subdivided by colour and star-formation history. Using the method outlined above we computed the galaxy cluster-ing scale lengths, r , for each of the volume limited sub-samplesshown in Figure 1, provided that each subsample contained at least150 galaxies. These measurements are shown in Figure 3. The first This value was chosen to maximise the fitting range, though we have alsotried . h − Mpc and . h − Mpc, finding consistent results.
Figure 3.
Upper.
The global evolution of clustering in the UDS field. Galax-ies are split into the volume-limited sub-samples shown in Figure 1 andthe real-space correlation lengths are computed (see text). The evolutionof clustering strength with redshift is mild for most luminosity ranges.
Lower.
The sub-samples are further separated into red and blue in rest-frame ( U − B ) colour and the clustering computed once again. Globally,red galaxies are slightly more strongly clustered than blue galaxies. The in-crease in r found for bright galaxies at low-redshift is clearly seen to bedominated by red galaxies. thing of note in these measurements is the lack of strong evo-lution of r with redshift at a given M K . Furthermore, there isvery little luminosity segregation, consistent with the findings ofCoil et al. (2008), although the most luminous galaxies are slightlymore strongly clustered at z ∼ . In much of the literature concerning the evolution of galaxy cluster-ing, populations are separated by colour, rather than star-formationproperties. Rest-frame colours are simpler to compute and there-fore allow more straightforward comparisons with previous work.In Figure 3 we again compute r values for the subsamples in Fig-ure 1, but this time we also separate red and blue galaxies, usingour rest-frame ( U − B ) colours defined in Section 2.1 (Figure 2).At z < , red galaxies are significantly more clustered thanblue galaxies, similar to the result of Coil et al. (2008) at z ≃ .This difference is particularly pronounced for the brightest sub-samples, where the strong clustering observed in the full sample is c (cid:13) , 1–11 W. G. Hartley et al.
Figure 4.
Evolution of the clustering strengths with redshift for our four passive samples with the single comparison star-formingsample. With the most conservative passive definition (requiring red rest-frame U − B colour, stellar age > Gyr and
SF R o . SF R initial ), the passive galaxy sub-samples are significantly more strongly clustered than the star-forming sub-samples for z < . . Above z = 2 the number of passive galaxies becomes too small to make robust clustering measurements. As the passivegalaxy selection criterion of SFR (given in each panel) is relaxed, the clustering strengths of star-forming and passive sub-samplesbecome more similar. Each point is plotted at the mean redshift of the sub-sample it represents. clearly a result of the clustering of red galaxies. Above z = 1 . theclustering strengths of the blue and red subsamples appear to con-verge, indicating that this may be the principle epoch at which thered sequence is populated. The red population is inhomogeneous,however, containing both passive and dusty star-forming objects.We therefore use our template fits to separate the passive and star-forming galaxies (Section 2.1).We plot the deprojected clustering lengths of our passive andstar-forming samples in Figure 4 with the SFR limits described insection 2.1 shown in each panel. For the most conservative passivesample (SFR . ) the clustering strengths of the passively-selected galaxies are greater than those of the equivalent star-forming galaxies for almost all sub-samples up to z = 1 . . Ourresult, shown in the upper left panel of Figure 4, shows that the clus-tering length is more strongly dependent on passivity than on lumi-nosity, with very little luminosity segregation in the star-formingsample. This difference continues to at least the median redshift ofBzK-selected galaxies (Hartley et al. 2008). Above z ∼ . , how-ever, the respective clustering strengths of passive and star-forminggalaxies appear to converge. Further survey data will be required toconfirm this finding, which is discussed in section 4. As we relaxthe SFR requirement to allow galaxies with higher residual star-formation rates into the passive selection, we find that the strengthof clustering of the passive sub-samples decreases, which confirmsthat truly passive galaxies are more strongly clustered among the‘red’ population. For illustration, in Figure 5 we show the angular clusteringmeasurements for passive and star-forming galaxies over all sub-samples in the two redshift ranges, < z . and . < z .The passive samples use our conservative definition ( SF R o . SF R initial ) described in section 2.1. The solid lines are thebest power-law fits and, in agreement with our earlier measure-ments for BzK-selected galaxies (H08), the passive galaxies arefound to cluster more strongly.
We use the formalism given in Mo & White (2002) to find theclustering strengths of dark matter halos of given masses as afunction of redshift. These models gather together previous work(Press & Schechter 1974; Bond et al. 1991; Mo & White 1996;Jing 1998; Sheth, Mo, & Tormen 2001) and use the ellipsoidal col-lapse model which has been calibrated against dark-matter only N-body simulations. Their aim is to provide the abundances and clus-tering of dark matter halos as functions of redshift and mass acrossa wide dynamic range.In Figure 6 we plot these models for halos of mass M ⊙ to M ⊙ together with the results from our conservative pas-sive sample (see section 2.1) and star-forming sample. At z < ,star-forming galaxies generally occupy halos of mass M ⊙ orsmaller, while passive galaxies occupy halos of mass M ⊙ to × M ⊙ . The general trend for star-forming galaxies is for c (cid:13) , 1–11 lustering of passive galaxies Figure 5.
Angular clustering measurements for conservative passive galax-ies (
SF R o . SF R initial ) and star-forming galaxies within theredshift ranges < z . (upper) and . < z (lower)with the star-forming points off set for clarity. Subsamples in luminos-ity have been combined for illustrative purposes. Solid lines show thebest power-law fits, using a constant slope of − . , over large-scales: . h − Mpc (Dashedline) − . deg. In both cases the passive samplesare more strongly clustered, consistent with the measurements of pBzK andsBzK-selected galaxies (e.g. H08). Errors are determined from a bootstrapanalysis. galaxies of a given luminosity to occupy halos of greater massat higher redshift. This is a manifestation of halo downsizing(Cowie et al. 1996; Foucaud et al. 2010, in press). This downsiz-ing in host halo mass for star-forming galaxies appears to extendbeyond z=2. At these very early times bright star-forming galax-ies are hosted by massive dark matter halos ( M ∼ × M ⊙ ).Presumably these are among the progenitors of low redshift group-dominant galaxies.The passive galaxies occupy halos up to an order of magni-tude more massive than the star-forming galaxies. In contrast to thestar-forming galaxies, the brightest passive galaxies appear to showconstant clustering strength over the range . < z < . . If con-firmed by future survey data, this result suggests that bright passivegalaxies are hosted by similar mass halos across this redshift range. We have shown that passive galaxies, defined by fitting templatesover 11 bands from the UV to
Spitzer ’s IRAC bands, are morestrongly clustered than star-forming galaxies at z < . . Clusteringstrength is intimately linked with the minimum mass of dark matterhalo that can host a galaxy of a given type. Passive galaxies there-fore on average occupy more massive dark matter halos than theirstar-forming counterparts. These results indicate that at z < . the passivity of a galaxy sample is a strong indicator of the typicalmass of dark matter halo that host them.The K-band luminosity is a reasonable proxy for the stellarmass of a galaxy, though galaxies may dim by approximately onemagnitude after they stop forming stars (e.g Lilly & Longair 1984;Cowie et al. 1996). Even taking this dimming into account, the con-servative passive sub-samples ( SF R .
1% SFR initial ) are typ-ically more strongly clustered than the star-forming samples for agiven stellar mass.
Figure 6.
The clustering of our conservative passive sample and star-forming sample (symbols have the same meanings as in Figure 4) are com-pared with the clustering predictions of dark matter halos from Mo & White(2002). Lines of constant halo mass (in M ⊙ ) are shown, with additionaldashed-dotted lines for × M ⊙ (upper) and × M ⊙ (lower).Downsizing in the star-forming population is evident with the same lumi-nosity galaxies found in less massive halos towards z=0. The same can-not be said of the passive galaxies, which typically occupy halos of mass M > M ⊙ . Furthermore, there is an absence of a strong luminosity depen-dence on the clustering strength of the star-forming samples. Wehave therefore found that of the two effects that we set out to dis-entangle, passivity and luminosity, passivity is the more significantindicator of clustering strength at z < . . However, we note thatwe are unable to probe the most extreme high luminosity galaxies(M K < − ) due to our limited survey area.Above z = 1 . we are unable to significantly distinguishstar-forming and passive galaxy clustering. The correlation lengthsof passive and star-forming galaxies apparently converge at thisepoch. If this behaviour is confirmed it would suggest that theepoch z ∼ is the epoch in which the passive and star-formingsamples are first becoming distinct. Hence, it is likely to be the ma-jor epoch at which the red sequence is being populated. This findingmakes the further study of the . < z < . range critical and weintend to return to and improve upon this work as the UDS datapush deeper and spectroscopic samples become available.In the hierarchical formation of structure the first halos to col-lapse are those which eventually merge to form the most massivehalos at low redshifts. Our result then points towards a time se-quence: passive galaxies formed earlier in those first halos whilethose of similar stellar mass, but still forming stars, developed inlower mass halos that collapsed later. Galaxy and halo evolutionis accelerated at the earliest epochs with respect to the presentday. The galaxies formed at these strongly clustered, high densitypeaks of the matter distribution are therefore likely to become fullyevolved, passive galaxies more rapidly than the general population.Discounting mergers, the stellar mass of a galaxy is limited by theavailable gas reservoir so a passive galaxy could have formed sig-nificantly earlier than a star-forming galaxy, but end up with verysimilar stellar masses at the epoch of observation. Their respectivehalos, however, will have built-up mass since they first collapsedand so those of the earlier formers will be more massive. In thisway the difference in clustering strength is a natural result of hi- c (cid:13) , 1–11 W. G. Hartley et al. erarchical mass assembly in halos and downsizing in galaxies (c.f.Foucaud et al. 2010, in press).In addition to the relative differences in clustering strength at afixed redshift, we also find a potential difference in how the passiveand star-forming samples evolve with redshift. The star-formingsamples follow the behaviour we would expect as a result of thedownsizing scenario for galaxy evolution. Sub-samples of a givenK-band luminosity (stellar mass) taken from this population exhibita decline in clustering strength towards z = 0 . The most lumi-nous passive galaxies show tentative evidence for constant cluster-ing strength across . < z < . . A constant value of r of suchmagnitude indicates that the hosting dark matter halos are no lessmassive at lower redshift.Direct comparison with the results of previous work is ex-tremely difficult as the UDS is currently unique and this studyis the first of its type utilising K-band selection. Qualitatively,our results agree very well with the findings of Coil et al. (2008),McCracken et al. (2008) and Meneux et al. (2006): each of thesestudies finds a longer clustering lengths for red or passive galaxiesover blue or star-forming galaxies below z = 1 . We furthermoreagree with previous works that any luminosity dependence on clus-tering in the sample is minimal in comparison with that of passivityover the range of galaxy properties that we have investigated.McCracken et al. (2008) find that at intermediate redshifts( . < z < ), galaxies fit by an early-type template possiblyhave a inverse luminosity dependence, with less luminous galaxieshaving slightly longer correlation lengths. This behaviour is wellknown at low redshift, where passive dwarf galaxies exhibit strongclustering and are found to be associated with clusters of galaxies(Conselice et al. 2003; Zehavi et al. 2005). Our measurements forred galaxies at z < are not inconsistent with these findings. Throughout this work there are uncertainties that are extremely dif-ficult to quantify. Though dust attenuation is taken into accountduring template fitting, there is a well-established degeneracy be-tween the stellar age and dust content. Even with the wide range ofphotometry available, we cannot fully overcome this degeneracy.In addition, the typical redshift uncertainties are ∼ . z ) and typical uncertainties in U-B colour are . magnitudes. Weuse the ERO definitions of Pozzetti & Mannucci (2000) to examinewhether our passive selection method is robust. Each of the passiveobjects with best-fit redshifts within the range < z meetsthe i − K > (Vega) ERO criterion, with 1423 of the 1457 objectslying in the passive ERO (pERO) region, defined by i,J,K colours.In addition, when plotted in the ( B − z ) AB − ( z − K ) AB plane,our conservative passive sample populates the areas in which wewould expect to find passive galaxies (see the Appendix, Figure 7and Lane et al. 2007). We are therefore confident that the SED-fitstar formation properties we use are relatively robust, in compari-son with previous broad band techniques.Even with robust colours and selection criteria, the photomet-ric redshift technique can introduce uncertainties into our measure-ments by causing a galaxy to be assigned to the wrong sub-samplein redshift. Passive galaxies have a strong break implied by our se-lection process and hence the photometric redshift determinationis more reliable for these galaxies than for star-forming galaxies.There is an ongoing ESO Large Programme, the UDSz survey, toobtain ∼ redshifts of galaxies at z > in the UDS field.Early indications suggest that the photometric redshifts for our pas-sive galaxies are indeed highly reliable, with error estimates of δ z ∼ . z ) (though at the time of writing the majority ofthese are at z < . ).Photometric redshifts are particularly difficult to obtain at z > . . It is precisely beyond this point that the red and blue sam-ples converge, due in part to a decrease in the red galaxy clustering.On the other hand, the blue and star-forming samples’ clusteringstrengths increase over this range. Sub-sample misassignment, par-ticularly in redshift, will tend to dilute the clustering signal. Forthe observed convergence to be driven by errors in the photomet-ric redshifts would therefore require the clustering signal from ourred sample to be washed out, while that from the blue sample isnot. This in turn would require the redshifts of our blue and star-forming galaxies to be much more accurate than our red galaxies.We suggest that such a case is highly unlikely, but await a substan-tial sample of redshifts to confirm this.Of greater concern is the possibility that due to photometricredshift errors, star-forming galaxies are more likely to be assignedto the wrong redshift bins. This would dilute the clustering of theblue galaxies and artificially enhance the difference between pas-sive and star-forming samples. If dilution due to redshift errors issignificant we might expect that our clustering measurements forstar-forming galaxies are smaller than other studies of star-forminggalaxies at these redshifts. In H08 the clustering strength of sBzK-selected galaxies for a sample of median redshift ∼ . cut at K = 23 was found to be ∼ . h − Mpc. This value is simi-lar to the star-forming sub-samples of similar redshifts presentedhere. Although selections in other bands are not directly compara-ble we have found that clustering strength is only weakly dependenton K-band luminosity. Any moderately bright star-forming samplecan therefore be used as a comparison. Coil et al. (2008) found thatstar-forming galaxies at z = 1 have modest clustering strengthsof ∼ h − Mpc, with similar values found by Adelberger et al.(2004) (BM/BX-selected galaxies, z = 1 ) and McCracken et al.(2008) ( z = 0 . ). The z = 1 , UV-selected galaxies in Heinis et al.(2007) have a slightly larger correlation length ( . h − Mpc WGH would like to extend his thanks to Alfonso Arag´on-Salamanca for an extremely useful discussion during the prepara-tion of this work. WGH and SF would also like to acknowledgethe support of the STFC during the preparation of this work. IRSacknowledges support from STFC. RJM acknowledges Royal So-ciety funding through the award of a University Research Fellow-ship. JSD acknowledges the support of the Royal Society througha Wolfson Research Merit award. Finally, we would like to thankthe anonymous referee for their very thorough reading of our workand their insightful comments. APPENDIX In this appendix we re-visit the 2-colour selection of Daddi et al.(2004). We aim to derive a series of simple boundaries which can beused to approximate the passive samples used earlier in this work.Our purpose here is to facilitate the reproduction of our results incomplementary fields rather than create a robust definition for apassive sample. We choose the ( B − z ′ ) AB − ( z ′ − K ) AB plane be-cause the pBzK selection of Daddi et al. (2004) is well understood,and also because of the track identified in Lane et al. (2007). Thistrack has colours consistent with the SED of an E/S0 type galaxy,evolved through redshift, and is well separated from the rest of thedistribution. It suggests that it may be possible to separate passiveand star-forming galaxies over all redshifts with relative ease.The use of such simple photometric sample definitions maybe preferable to full star-formation history fitting when comparingdifferent data sets. In minimising the complexity of selection, theintrinsic differences in the samples should be more apparent andhence a better estimate for cosmic sample variance can be obtained.The colour boundaries outlined below are defined using the Subaruand UKIRT filters. Conversion to other filter sets can be made withreference to Hewett et al. (2006) and Furusawa et al. (2008). Samples in the ( B − z ′ ) − ( z ′ − K ) plane The plane is split into cells, . × . in colour, and within eachcell the fraction of galaxies that are in the passive sample is com-puted. Boundaries are chosen to provide a simple selection tech-nique which includes those cells with > passive galaxies. c (cid:13) , 1–11 W. G. Hartley et al. Figure 7. ( B − z ′ ) AB − ( z ′ − K ) AB colour-colour plot for actively star-forming sample (blue points), our ‘conservative’ passive galaxies (red) andthose which fall between these criteria (black). Also shown are the com-monly used BzK selection criteria of Daddi et al. (2004) and the bordersdefined in the appendix. Only half of the star-forming points are plotted forclarity. Table 1. Values for the boundary criteria defined in the text.Co-eff . SF R i . SF R i SF R i SF R i α β -1.0 -1.3 -2.5 ... γ δ -1.4 -1.2 -0.8 -1.0 ǫ These borders are shown in Figure 7 together with the conservativepassive sample and star-forming samples used in the main body ofthis paper. The boundaries for each sample are: ( z ′ − K ) AB < α ( B − z ′ ) AB + β or ( B − z ′ ) AB > γ or ( z ′ − K ) AB > δ ( B − z ′ ) AB + ǫ ; (6)where the values for α, β, γ, δ and ǫ are given in table 1.These 2-colour-defined passive samples include all galaxiesin the relevant region regardless of their best-fit age, U-B colouror SFR. The number of objects in each sample are 5438, 7287,8986 and 12242 respectively, and the number of objects in the star-forming sample is 20645.The clustering properties of the these galaxy samples weretreated in the same way as those in the main body of thispaper. 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