aa r X i v : . [ a s t r o - ph . C O ] J u l Mon. Not. R. Astron. Soc. , 1–6 (2013) Printed 26 September 2018 (MN L A TEX style file v2.2)
Detection of galaxy assembly bias
Lan Wang ⋆ , Simone M. Weinmann , Gabriella De Lucia , Xiaohu Yang , Partner Group of the Max Planck Institute for Astrophysics, National Astronomical Observatories,Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands INAF - Astronomical Observatory of Trieste, via G.B. Tiepolo 11, I-34143 Trieste, Italy Center for Astronomy and Astrophysics, Shanghai Jiao Tong University, Shanghai 200240, China Shanghai Astronomical Observatory, Nandan Road 80, Shanghai 200030, China
Accepted 2013 ???? ??. Received 2013 ???? ??; in original form 2013 ???? ??
ABSTRACT
Assembly bias describes the finding that the clustering of dark matter haloes dependson halo formation time at fixed halo mass. In this paper, we analyse the influenceof assembly bias on galaxy clustering using both semi-analytical models (SAMs) andobservational data. At fixed stellar mass, SAMs predict that the clustering of central galaxies depends on the specific star formation rate (sSFR), with more passive galax-ies having a higher clustering amplitude. We find similar trends using SDSS groupcatalogues, and verify that these are not affected by possible biases due to the groupfinding algorithm. Low mass central galaxies reside in narrow bins of halo mass, sothe observed trends of higher clustering amplitude for galaxies with lower sSFR isnot driven by variations of the parent halo mass. We argue that the clustering de-pendence on sSFR represent a direct detection of assembly bias. In addition, contraryto what expected based on clustering of dark matter haloes, we find that low-masscentral galaxies in SAMs with larger host halo mass have a lower clustering amplitudethan their counter-parts residing in lower mass haloes. This results from the fact that,at fixed stellar mass, assembly bias has a stronger influence on clustering than thedependence on the parent halo mass.
Key words: galaxies: formation – galaxies: haloes
Empirical models that link galaxy properties statisti-cally with their hosting dark matter (sub)halo massesinclude the Halo Occupation Distribution (HOD)method (Berlind & Weinberg 2002; Yang et al. 2003;Wang et al. 2006), and the abundance matching method(Vale & Ostriker 2006; Guo et al. 2010; Moster et al. 2010).The HOD method places galaxies into dark matter haloesby modeling the number and the spatial distribution ofgalaxies in haloes of given mass. The abundance matchingmethod assumes a one-to-one correspondence betweengalaxies and subhaloes, with higher mass galaxies residingin subhaloes of higher mass at the time of accretion. Bothmethods assume that galaxy properties depend only onhalo mass, and are independent of any other properties ofthe parent halo. This assumption, which also applies tothe excursion set (Extended Press-Schechter) formalism(Bond et al. 1991), however, is challenged by the discoveryof the assembly bias effect found by Gao et al. (2005) for ⋆ Email: [email protected] haloes less massive than about 10 h − M ⊙ . Assembly biasindicates the finding that at the same halo mass, earlierassembled haloes cluster more than the ones that assemblelate. Evidence that galaxy properties might depend on otherproperties than halo mass has also been found in differentgalaxy formation models (Zhu et al. 2006; Croton et al.2007).From an observational point of view, Yang et al. (2006)found that the clustering of galaxy groups of fixed halomasses depends on the star formation rate of the centralgalaxies which are located at the centres of dark mat-ter haloes. This is probably the first claim of observa-tional detection of halo assembly bias. Along this line,subsequent studies have also searched for a correlationbetween galaxy properties and halo properties at fixedhalo mass (Wang et al. 2008; Tinker et al. 2011, 2012).Kauffmann et al. (2012) have found interesting evidencethat central galaxy properties are correlated with the prop-erties of their neighbours beyond the virial radius of theirparent haloes (“galactic conformity” Weinmann et al. 2006).The existence of assembly bias in the real Universe is, how-ever, still debated (also because of uncertainties in esti- c (cid:13) Wang et al.
Figure 1.
In the DLB07 (upper two panels) and the Guo11 (lower two panels) models, the halo formation redshift – M infall relation andthe fractional distribution (in unit of per Log( M infall ) dex) in M infall in different stellar mass bins, for central (blue lines) and satellite(red lines) galaxies. Error bars indicate the 68 percentile distributions. mates of halo masses), and it remains unclear if (and towhat extent) assembly bias influences the observed proper-ties of galaxies. In this paper, we analyse the dependence ofgalaxy clustering on different galaxy and halo properties inboth semi-analytic galaxy formation models (SAMs) and ina group catalogue based on the SDSS DR7. Our main resultis that central galaxies with lower specific star formationrate cluster more than the ones with more active star for-mation at fixed stellar mass, both in SAM and observations.As we argue below, this may provide evidence for assemblybias in the real Universe.The outline of our paper is as follows. In Section 2, weshow the dependence of galaxy clustering on halo mass, haloformation time, and specific star formation rate of galaxiesfor two SAMs. In Section 3, observational correlation func-tions for central galaxies split by specific star formation rateand halo mass are calculated using group catalogues, and arecompared with the predictions from mock galaxy cataloguesfrom the two SAMs we analysed. Conclusions and discus-sions are presented in Section 4. All model results shownbelow are based on dark matter halo trees from the Mil-lennium Simulation (Springel et al. 2005). The resolution ofthe simulation gives a lower limit in the dark matter halomass of around 10 h − M ⊙ , and a lower limit in the galaxystellar mass of around 6 × M ⊙ . In our previous study (Wang et al. 2013), we have shownthat the stellar masses of galaxies extracted from the semi-analytic models of De Lucia & Blaizot (2007, DLB07) andGuo et al. (2011, Guo11) depend not only on halo mass butalso on halo formation time. In this section, we investigatefurther the correlation between galaxy properties and thoseof their parent haloes, with the aim of identifying likely indi-cations of assembly bias. In the following, M infall is the mass of host halo when galaxy is/was last time a central objectof its hosting FOF group. For centrals, M infall = M halo .Fig. 1 shows the relation between the formation timeof host haloes (defined as the redshift when half of M infall was first assembled into a single object) and M infall in twoSAMs. For a satellite galaxy, we trace back its main pro-genitors to the time when it was for the last time a cen-tral galaxy, and record the mass of its parent FOF groupat this time as M infall . To define the corresponding forma-tion time, we then follow the main progenitor of the haloidentified at the infall time, up to the time when its massfirst reaches half of M infall . At all stellar masses, less mas-sive haloes assemble much earlier than more massive ones.We also show in Fig. 1 the distribution of M infall for thesegalaxies. At low stellar masses, the distributions are quitenarrow. We note that the bias varies very weakly as a func-tion of halo mass for haloes with M infall . . h − M ⊙ (e.g.Sheth, Mo, & Tormen 2001): for the two lowest stellar massbins considered, the maximum variation for the bias is atthe level of 10 − ∼ . h − M ⊙ the bias increases rapidly as a functionof halo mass. Therefore, for massive galaxies, one expects astronger clustering variation due to a wider range of hosthalo masses.In Fig. 2, we check the dependence of galaxy cluster-ing on halo formation time, sSFR, and M infall at fixed stel-lar mass in the models of DLB07 and Guo11 in two stel-lar mass bins. For each stellar mass bin, galaxies are splitinto different sub-samples according to the median value ofeach physical parameter considered. We show results bothfor the full population of galaxies, and for centrals and satel-lites separately. The top two panels show that galaxies re-siding in earlier formed haloes cluster more strongly thantheir counterparts residing in haloes that formed later, which c (cid:13) , 1–6 alaxy assembly bias Figure 2.
Correlation functions (CFs) of galaxies split by halo formation time, sSFR and M infall in two stellar mass bins oflog( M star /M ⊙ )=[9.77,10.27] and [10.77,11.27] in the two SAMs. For each stellar mass bin, results are shown for all galaxies in themass bin, as well as for central and satellite galaxies separately. In each panel, a black line is used to show the CF for all galaxies in thecorresponding mass bin, while coloured lines correspond to sub-samples with values of the considered physical property smaller or largerthan the median. reflects the halo assembly bias (Gao et al. 2005; Zhu et al.2006; Croton et al. 2007).When split by sSFR, we find that galaxies with lowersSFR cluster more. This is consistent with observations thatold and red galaxies cluster more even at fixed stellar masses(Li et al. 2006; Bamford et al. 2009; Weinmann et al. 2011)and is mainly due to the higher clustering of satellites vs.centrals. However, we find that the result is still presentwhen considering only central galaxies, or only satellitegalaxies at scales smaller than 1 h − Mpc in the Guo11model. In both SAMs, for the small stellar mass bin con-sidered, the clustering of central galaxies depends on theirsSFR. We will show later that this trend is not driven bytrends as a function of parent halo mass.In Fig. 3, we show the relation between galaxy sSFRand galaxy assembly time, defined as the time when halfof the galaxy stellar mass of the present day is assembledin a single progenitor of the galaxy. In general, for galaxieswith stellar mass lower than 10 . M ⊙ , galaxies with lower sSFR assemble earlier. Combining this result with the find-ing that low-mass central galaxies with lower sSFR clustermore, we find that the clustering of low-mass central galax-ies in SAMs depends on the galaxy assembly time, i.e. thereis an assembly bias.The result that galaxies with low sSFR cluster morethan their counter-parts with higher sSFR could be due toa dependence of galaxy clustering on halo mass: the clus-tering amplitude increases with increasing halo mass, so ifgalaxies with lower sSFR are sitting in more massive haloes,this would explain the trends found. However, this is notthe case for low mass galaxies. In the bottom two rows ofFig. 2, we show the galaxy correlation functions (CFs) splitby M infall . For low mass galaxies, those with smaller M infall actually cluster more strongly in both SAMs, for both cen-trals and satellites. This can be understood as follows: asshown in Fig. 1, at fixed stellar mass, less massive haloesform earlier. And earlier formed haloes cluster more due tohalo assembly bias. In addition, the bias of the host haloes of c (cid:13) , 1–6 Wang et al. low mass galaxies varies little as mentioned before, which re-sults into little variations of galaxy clustering amplitude dueto varying host halo mass. Therefore, for the lower stellarmass bin considered, the dependence of clustering on haloformation time has a larger influence than the dependence ofclustering on halo mass. For the higher stellar mass bin, thedependencies on halo mass and halo formation time com-pensate, and CFs of galaxies with different M infall are quitesimilar, with only slight differences for satellites on smallscales. Can we find assembly bias as seen in the SAMs also in re-ality? While it is impossible to measure the halo formationtime for observational results, we can check galaxy cluster-ing as a function of halo mass and sSFR, which could beaffected by assembly bias, as shown in Section 2.For satellite galaxies, besides the possible effect of as-sembly bias on their clustering property, there are othercomplications due to the fact that they can be accreted overa range of cosmic epochs. Therefore, in the following, wefocus only on central galaxies.
We make use of the galaxy (Blanton et al. 2005) and group(Yang et al. 2007) catalogues extracted from the SDSS DR7data, and use these catalogues to distinguish between centraland satellite galaxies. For central galaxies within differentstellar mass bins, we split galaxies into two subsamples withequal numbers of galaxies, according to the median value ofsSFR and M halo respectively in this mass bin, and calculatethe projected CFs for each subsample. The details of howto get the projected 2PCFs of SDSS DR7 galaxies can befound in Appendix A of Yang et al. (2012).In Fig. 4, CFs of subsamples in observation are shownfor four different stellar mass bins. At low stellar masses,central galaxies with lower sSFR cluster more than thosewith higher sSFR, which is consistent with the trends foundin the SAM. As argued in Section 2, this trend possibly indi-cates a signature of galaxy assembly bias in the data. Fig. 4also shows that there is no significant difference betweenthe clustering properties of sub-samples split by M halo inthe group catalogues. Note, however, that in the SDSS ob-servations (as well as in the mock catalogues that we willuse in the next subsection), halo masses are estimated froma simple ranking of the group stellar masses. In this way,splitting the sample as a function of halo mass just reflectstrends as a function of stellar mass. Any possible formationtime information associated with the mass of haloes in thereal Universe will be erased due to the halo mass measure-ment adopted in the data. To ensure a fair comparison with SAMs, we build mock cata-logues for both DLB07 and Guo11 models, to mimic volumesand apparent magnitude limits of the observational data andto take into account the observational selection effects. The mock redshift catalogues are constructed in a way similarto that described in Yang et al. (2004), where the detailedsky coverage of the SDSS DR7 including the angular varia-tions in the magnitude limits and completeness of the data istaken into account (see e.g. Li et al. 2007). Then, we adoptthe same method used for the SDSS galaxies to define centraland satellite galaxies, and to compute their CFs. The resultsfrom these models are also shown in Fig. 4. Similar to whatshown in Fig. 2, for SAMs, central galaxies with lower sSFRcluster more than the ones with higher sSFR. The trend isconsistent with SDSS measurements. Note that for centralgalaxies, the ratios between subsamples split in sSFR in theGuo11 model are closer to the observational data, with re-spect to predictions from the DLB07 model. When satellitegalaxies are also taken into account, however, the CFs in theGuo11 model over-predicts the observational measurementsfor low-mass galaxies (Guo et al. 2011; Wang et al. 2013).Comparing SAM mock catalogues and the results aspresented in Fig. 2, we find some discrepancies. At smallscales, the clustering in mock catalogues is somewhat en-hanced which might due to a small fraction of mis-classifiedcentrals. Nevertheless, for the low-mass bin, at intermediatescales of r p =[0.5, 20] h − Mpc, results are quite consistentbetween the mock group catalogue and the original SAMcatalogues, and the dependence of clustering on sSFR is notaffected by the algorithm used to detect groups and iden-tify central and satellite galaxies. Thus, we conclude thatthe finding that low sSFR centrals in the SDSS cluster morethan their more active counterparts of the same stellar massis real, and not due to spurious effects introduced by thegroup finding algorithm.When splitting galaxies by host halo masses, resultsfrom the SDSS and those from mock catalogues based onthe SAMs used in our studies are consistent for galaxies lessmassive than 10 . M ⊙ . However, the assembly bias trendsassociated with M infall shown in the lower-left panels of Fig.2 do not show up in the mock catalogues. The reason isalready mentioned in previous subsection that in assigninghalo masses to groups, no additional information like forma-tion time is kept. In this paper, we find indications that the strong assemblybias of low-mass galaxies in the semi-analytic galaxy for-mation models of De Lucia & Blaizot (2007) and Guo et al.(2011) leaves a signature on galaxy clustering as a func-tion of halo mass and sSFR. In particular, we find that cen-tral galaxies with low sSFR galaxies cluster more than theircounterparts with the same stellar mass but higher sSFR.A similar trend is found in group catalogues based onthe SDSS DR7. For low mass galaxies, this is likely a sig-nature of assembly bias in the real Universe. Alternativeexplanations are possible: for example, the central galaxieswith lower sSFR could be associated with a ‘back-splash’population of galaxies that have been satellites in the past.These galaxies are found to form earlier than central galax-ies that did not experience such an event (Wang et al. 2009,Li et al., in preparation), which may contribute to assemblybias. However, the fraction of central backsplash galaxies is c (cid:13) , 1–6 alaxy assembly bias Figure 3.
The sSFR – galaxy assembly time relation in different stellar mass bins in the two SAMs, for central (blue lines) and satellite(red lines) galaxies. Error bars indicate 68 percentile distribution.
Figure 4.
CFs of central galaxies split by sSFR (upper two rows) and M halo (lower two rows) in the mock group catalogues of DLB07and Guo11 (solid/dashed lines), compared with the results of SDSS group catalogue (filled/open circles), in four different stellar massbins. The ratios of CFs of subsamples with lower and higher sSFR (second row) and the ratios of CFs of subsamples with higher andlower M halo (fourth row) are also presented, where error bars are the relative errors of the CFs for subsamples with higher sSFR andlower M halo , respectively. lower than 10 per cent, and therefore does not dominate theassembly bias effect, as shown by Wang et al. (2009).In SAMs, low mass central galaxies show a halo massdependence that seems to contradict the halo model pre-dictions: here, low mass haloes cluster stronger than highmass haloes. The reason is that, for these low mass centralgalaxies, there is a strong correlation between host halo massand halo formation time, with less massive haloes forming earlier. Haloes that form early cluster more than haloes ofsimilar mass that form later (assembly bias). In addition, theclustering amplitude of the parent haloes of low-mass cen-tral galaxies varies very little. Therefore, the dependence ofthe clustering amplitude on halo formation time has a largerimpact than the dependence due to variations of parent halomass.More generally, we have found evidence that the clus- c (cid:13) , 1–6 Wang et al. tering of central galaxies does not only depend on host halomass, but additionally on secondary parameters like the spe-cific star formation rate. While the physical reason for thesetrends remains unclear – it may be solely assembly bias or acombination of different effects – our results show that thesimple picture that galaxy properties depend only on halomass is incomplete. This has to be taken into account in em-pirical models like HOD and abundance matching that arebased on this assumption, and for precision measurementsof cosmological parameters using clustering studies.
ACKNOWLEDGMENTS
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