The assembly bias of emission line galaxies
Esteban Jimenez, Nelson Padilla, Sergio Contreras, Idit Zehavi, Carlton Baugh, Alvaro Orsi
MMNRAS , 1–14 (2020) Preprint 19 October 2020 Compiled using MNRAS L A TEX style file v3.0
The assembly bias of emission line galaxies
Esteban Jim´enez , (cid:63) , Nelson Padilla , , Sergio Contreras , Idit Zehavi ,Carlton M. Baugh and ´Alvaro Orsi , Instituto de Astrof´ısica, Pontificia Universidad Cat´olica de Chile, Santiago, Chile International Centre for Radio Astronomy Research (ICRAR), University of Western Australia, Crawley, WA 6009, Australia Centro de Astro-Ingenier´ıa, Pontificia Universidad Cat´olica de Chile, Santiago, Chile Donostia International Physics Center (DIPC), Manuel Lardizabal pasealekua 4, 20018 Donostia, Basque Country, Spain Department of Physics, Case Western Reserve University, Cleveland, OH 44106, USA Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK Centro de Estudios de F´ısica del Cosmos de Arag´on. Plaza San Juan 1, planta 2, 44001 Teruel, Spain PlantTech Research Institute Limited. South British House, 4th Floor, 35 Grey Street, Tauranga 3110, New Zealand
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
The next generation of spectroscopic surveys will target emission-line galaxies (ELGs)to produce constraints on cosmological parameters. We study the large scale structuretraced by ELGs using a combination of a semi-analytical model of galaxy formation,a code that computes the nebular emission from HII regions using the propertiesof the interstellar medium, and a large-volume, high-resolution N-body simulation.We consider fixed number density samples where galaxies are selected by either theirH α , [OIII] λ λλ − β parameter related to the growth rate of overdensities. We find a slighttendency for the BAO peak to shift toward smaller scales for [OII] emitters and that β is scale-dependent at large scales. Our results suggest that ELG samples includeenvironmental effects that should be modelled in order to remove potential systematicerrors that could affect the estimation of cosmological parameters. Key words: galaxies: evolution – galaxies: formation – galaxies: statistic – cosmology:large-scale structure of the Universe
Mapping the Universe using photometric and spectroscopicsurveys allows us to measure the cosmic large-scale struc-ture which encodes valuable cosmological information. How-ever, since the galaxy distribution is not a direct tracer ofthe underlying density field it is essential to understand theconnection between galaxies and dark matter haloes to ob-tain an accurate interpretation of the Universe (for a reviewsee Wechsler & Tinker 2018). A relevant statistical prop-erty of the galaxy distribution is the clustering signal whichis often quantified using the two-point correlation function (cid:63)
E-mail: [email protected] (2PCF). Measuring galaxy clustering allows us to extracttwo pieces of information that can be used to constrain thecosmological model (Weinberg et al. 2013): (i) the scale ofstandard ruler features, such as the baryonic acoustic oscil-lation (BAO) peak, from which we can obtain the cosmicexpansion history, and (ii) the magnitude of redshift-spacedistortions (RSD) in the clustering signal, which are drivenby the rate at which structure grows. Both of these quanti-ties depend on the amount of dark matter and dark energy.Precise measurements of BAO and RSD are difficult toobtain because cosmic (sample) variance and shot noise aresignificant when the sampled volume is small (Kaiser 1986a).The Sloan Digital Sky Survey (SDSS) and the 2dF GalaxyRedshift Survey (2dFGRS) were the first to observe hun- © a r X i v : . [ a s t r o - ph . GA ] O c t Esteban Jim´enez et al. dreds of thousands of galaxies in large volumes, obtainingconvincing detections of the BAO (Eisenstein et al. 2005;Cole et al. 2005). Observations have continued throughoutthe last fifteen years mostly using massive luminous redgalaxies (LRGs) as the tracers of the large-scale structure(e.g Eisenstein et al. 2011; Zehavi et al. 2011; Dawson et al.2013; Bautista et al. 2018).Advances in wide field spectroscopy have opened up theopportunity to trace the large-scale structure using emission-line galaxies (ELGs). The nebular emission of these galaxiesis produced by gas in HII regions which is photoionized byradiation from young stars. Some emission line luminositieshave therefore been used to infer star formation rates, al-though in general the relation between line emission andSFR can be complicated as the emission depends on thelocal properties of the ISM such as gas metallicity, temper-ature and density (e.g Levesque et al. 2010; Gutkin et al.2016; Byler et al. 2017) and on the attenuation by dust ofthe line luminosity. Moreover, ELGs do not trace the fieldin the same way as LRGs; ELGs tend to reside in low masshaloes (Favole et al. 2016; Gonzalez-Perez et al. 2018) andlive in filaments and sheets rather than in the knots of thecosmic web occupied by LRGs (Gonzalez-Perez et al. 2020).Typically, given the depth of upcoming surveys withspectrographs that operate in the optical, ELG catalogueshave redshift distributions that peak around z ∼ α emitters at z (cid:38)
2, enables us to inves-tigate the history of cosmic expansion at previously unex-plored epochs. The SDSS-IV/eBOSS survey (Dawson et al.2016) provides one of the largest ELG catalogues to date,and the next generation of surveys like DESI (DESI Collab-oration et al. 2016) and Euclid (Laureijs et al. 2011) willdetect millions of ELGs. This will potentially enable us tomeasure cosmological parameters with exceptional precision.To fully exploit the future ELG data it is essential tounderstand any systematic effects that may influence theinferred cosmological constraints. Galaxy formation modelscan be used for this purpose, to provide insights into thegalaxy-halo connection with the by-product of testing dif-ferent prescriptions for the physical processes that regulategalaxy evolution. A useful approach to explore galaxy for-mation is to use semi-analytical models (SAMs Cole et al.2000; Baugh 2006; Somerville et al. 2008). These models usesimplified descriptions of physical processes that shape thefate of baryons within the dark matter halo merger treesextracted from N-body dark matter only simulations, ex-pressed in a set of coupled differential equations with pa-rameters to encapsulate “sub-grid” physics. SAMs can suc-cessfully reproduce, amongst other things, the observed lu-minosity and stellar mass functions (e.g Croton et al. 2006;Henriques et al. 2015; Croton et al. 2016; Stevens et al. 2016;Lagos et al. 2018; Baugh et al. 2019). Alternatively, hydro-dynamical simulations offer a complementary approach tofollow baryonic physics, which in general requires fewer as-sumptions and approximations than are needed in SAMs,but which nevertheless still appeal to using sub-grid recipesfor unresolved processes (e.g Vogelsberger et al. 2014; Schayeet al. 2015; Nelson et al. 2018). Due to the higher compu-tational overhead of hydrodynamical simulations comparedwith SAMs, the largest volumes probed by state-of-the-arthydrodynamical simulations are still 10-100 times smallerthan the typical SAM volume. Another approach used to connect galaxies with theirhost haloes is to employ an empirical model such as thehalo occupation distribution (HOD) framework (e.g Bensonet al. 2000; Scoccimarro et al. 2001; Berlind & Weinberg2002; Kravtsov et al. 2004; Zheng et al. 2005). The HODprovides an empirical relation between the average numberof galaxies N hosted by haloes with mass M. This relationis characterized by a probability distribution P(N | M) thatdepends on the redshift, number density and selection cri-teria of a galaxy sample. Here, the standard assumption isthat the galaxy content depends only on halo mass, but thismay not be true if the galaxy distribution correlates with theassembly history of haloes. N-body simulations have shownthat the clustering of dark matter haloes does depend onsecondary halo properties like formation time, concentrationand spin (e.g Gao et al. 2005; Gao & White 2007; Wechsleret al. 2006), an effect called halo assembly bias. Likewise,the manifestation of assembly bias in galaxy clustering, com-monly referred to as galaxy assembly bias, has been foundboth in SAMs (e.g Croton et al. 2007; Contreras et al. 2019;Zehavi et al. 2018, 2019; Jim´enez et al. 2019; Xu et al. 2020)and hydrodynamical simulations (e.g Artale et al. 2018; Xu& Zheng 2020; Montero-Dorta et al. 2020). Assessing the ex-istence of assembly bias in the real Universe is an importanttask; cosmological constraints from future surveys will mostlikely be limited by how well we can model the observationsrather than the precision of the measurements.In general, assembly bias enhances the clustering am-plitude on large scales for stellar mass selected samples andsuppresses it for SFR selections (Contreras et al. 2019, 2020).However, as we found in these studies, these trends canchange depending on the number density and redshift ofthe sample. So far, there are no direct measurements of theassembly bias signature in ELG catalogues, but, in princi-ple, the effect should be similar to that reported for SFRselections as ELGs are a subset of star-forming galaxies.Here we aim to study the large-scale structure of ELGsby measuring the clustering and galaxy assembly bias sig-nature of these samples. We employ galaxies from the SAGsemi-analytical model (Cora et al. 2018) run on the Multi-Dark Planck cosmological simulation (Klypin et al. 2016).The total simulated volume is (1 h − Gpc) , so the effect ofthe sample variance is greatly reduced. Thus, we can accu-rately sample the 2PCF up to scales of the BAO feature anddetermine whether or not the impact of assembly bias fromELG selections is significant. We calculate the nebular emis-sion in SAG galaxies using the GET_EMLINES code from Orsiet al. (2014), and then store the H α , [OIII] and [OII] lineemission luminosities. These emission lines at z ∼ β parameter, which quantifies the strength of anisotropiesproduced by the RSD, are shown in Section 6 for each sam-ple. We conclude in Section 7. Brief discussions about results MNRAS , 1–14 (2020) he assembly bias of ELGs from other SAMs, and ELG sample completeness, are pre-sented in Appendix A and B, respectively.Throughout the paper masses are measured in h − M (cid:12) ,the SFR is measured in h − M (cid:12) yr − and distances are mea-sured in h − Mpc and are in comoving units.
Here we use the Semi-Analytical Galaxies (SAG) modelof galaxy formation (Cora 2006). Semi-analytical modelsuse the merger trees extracted from N-Body simulations tomodel the main physical processes involved in the evolutionof a galaxy, such as the treatment of radiative cooling of hotgas, star formation, feedback effects from supernovae and ac-tive galactic nucleus (AGN) feedback, chemical enrichmentof the gas, the growth of supermassive black holes, and theimpact from galaxy mergers, among others.The version of SAG used in this work is the one pre-sented in Cora et al. (2018), which uses the outputs ofthe MultiDark2 cosmological simulation (hereafter MDPL2,Klypin et al. 2016, see section 2.2 for more details). Themain output of the simulation and the SAM are publiclyavailable as a part of the MultiDark comparison project(Knebe et al. 2018). The SAG SAM was originally presentedin Cora (2006) and is based on the model by Springel et al.(2001). Since then the code has been through several up-dates (Lagos et al. 2008; Tecce et al. 2010; Orsi et al. 2014;Padilla et al. 2014; Mu˜noz Arancibia et al. 2015; Gargiuloet al. 2015) and is capable of reproducing observations bothat low and high redshift. One of the key features of thismodel is the use of particle swarm optimization technique(PSO) to automatically set the model parameters by requir-ing the output to fit several observables (Ruiz et al. 2015).The galaxy properties produced by this model includestellar mass, cold gas, black hole and bulge masses, the av-erage and instantaneous star formation rates (SFR), wherethe latter corresponds to the SFR in the most recent timesub-step, which is a subdivision of the timestep between thesimulation snapshots. Sub-step sizes range from 5 and 15Myr, whereas the time between snapshots is of the orderof 100 Myr. These quantities are computed separately fordisks and bulges, where the former are the result of quies-cent star formation in cooled gas disks and the latter formvia starburst episodes. The gas-phase metallicity for bothcomponents is calculated by modelling the chemical enrich-ment of the ISM, which takes into account mass loss frommassive stars and supernovae. These two ways to computethe SFR are important when computing the emission linefluxes of the galaxies (see section 2.3 for more details). As mentioned in the previous section, SAG was run on thehalo merger trees from the
MULTIDARK simulation MDPL2(Klypin et al. 2016). The MDPL2 adopts a ΛCDM Universe,charaterized by Planck cosmological parameters (PlanckCollaboration et al. 2014): Ω m = 0 . b = 0 . Ω Λ = 0 . h = 0 .
678 and n s = 0 .
96. The simu-lation follows 3840 particles within a cubic box of co-moving side-length 1 h − Gpc, with a mass resolution ofm p = 1 . × h − M (cid:12) . The particles are followed from z = 120 until z=0 and their positions and velocities areoutput at 126 snaphots. The dark matter haloes are identi-fied with the ROCKSTAR halo finder (Behroozi et al. 2013a),and the
CONSISTENT TREES code (Behroozi et al. 2013b) isused to construct the merger trees. These halo finder andhalo merger tree algorithms identify objects in phase space,keeping a better track of the substructures after their infall.The large cosmological volume of the MDPL2 allows usto make accurate clustering measurements up to scale sepa-rations that encapsulate useful cosmological information.
To model the nebular emission of the star-forming galaxieswe use the
GET_EMLINES model introduced by Orsi et al.(2014) (hereafter O14) to post-process the output from theSAG model. The GET_EMLINES code uses the output of thephotoionisation code
MAPPINGS-III (Dopita & Sutherland1995; Groves et al. 2004), as tabulated by Levesque et al.(2010).
MAPPINGS-III predicts the nebular emission fromHII regions. The grid calculated by Levesque et al. (2010)tabulates the emission line fluxes as a function of the gas-phase metallicity and the ionization parameter of the HII re-gion, q . O14 uses the gas metallicities of the bulges and disksfrom the SAG galaxies, but it does not predict the ionizationparameter within individual HII regions due to a lack of res-olution to resolve the internal structure of galaxies. Instead,O14 advocated a model in which q could be inferred fromthe gas-phase metallicity, an assumption which is inspired byobservational results which suggest that q is anti-correlatedwith the metallicity of the cold star-forming gas (e.g Nagaoet al. 2006; Groves & Allen 2010; Shim & Chary 2013). O14show that parameters selected in their model to calculate q from the gas phase metallicity allowed the SAG model toreproduce the locus of star forming galaxies in the so-calledBPT diagram relating the line ratios [OIII λ β and[NII λ α (Baldwin et al. 1981).cNote that O14 showedthat the predictions were robust to substantial perturba-tions to the parameter values in the model for q . Ideally, the GET_EMLINES code uses the instantaneous SFR rather thana time-averaged SFR, as the instantaneous SFR is a bet-ter indicator of the number of Lyman continuum photonswhich make up the ionising radiation field and, as a con-sequence, of the H α luminosity. Nevertheless, Favole et al.(2020) used the averaged SFR predicted by the SAGE (Crotonet al. 2016) and
GALACTICUS (Benson 2012) SAMs to inferthe [OII] line emission, and found reasonable agreement withobservational data at z ∼ GET_EMLINES and instantaneous SFRs to com-pute the luminosities for the H α , [OIII] λ λλ − λλ − α ,[OIII], [OII] and [NII] respectively). As these values are cal-culated separately for the bulge and disk components of agalaxy, we sum these contributions to obtain the total nebu- https://github.com/aaorsi/get emlinesMNRAS000
GALACTICUS (Benson 2012) SAMs to inferthe [OII] line emission, and found reasonable agreement withobservational data at z ∼ GET_EMLINES and instantaneous SFRs to com-pute the luminosities for the H α , [OIII] λ λλ − λλ − α ,[OIII], [OII] and [NII] respectively). As these values are cal-culated separately for the bulge and disk components of agalaxy, we sum these contributions to obtain the total nebu- https://github.com/aaorsi/get emlinesMNRAS000 , 1–14 (2020) Esteban Jim´enez et al. lar emission for each galaxy. Note that we do not apply anyattenuation to the line luminosity.
We use galaxy samples characterised by fixed number den-sities of objects. We achieve this by ranking the galaxiesfrom the highest to lowest values of a given property (e.g.their emission line luminosity, averaged SFR or stellar mass),and then retaing only those galaxies above a threshold valuethat corresponds to the desired number density. The num-ber densities used in this work are n = 0 . h Mpc − , n = 0 . h Mpc − and n = 0 . h Mpc − .As the samples selected by line emission are star-forming galaxies, it is expected that they will have someoverlap with galaxies selected by their SFR. Hence, we alsoinclude SFR selected samples and perform the same analysison these as carried out for the ELG samples. We also con-sider stellar-mass selected samples to allow further compar-isons with assembly bias signatures which have been studiedin several galaxy formation models (e.g Artale et al. 2018;Zehavi et al. 2018; Contreras et al. 2019). The cumulativedistribution functions for the different selections are shownin Fig. 1. The number densities adopted to define our sam-ples are shown by the horizontal thin dashed lines. Note thatthe galaxies included in each sample are those to the right ofthe intersection between the cumulative functions with thehorizontal lines. We also include a selection based on thecombined luminosity of the H α +doublet [NII] λλ − α (see also Merson et al.2018).The data used here correspond to a subsample of SAG where galaxies were selected with a stellar-mass cut of5 × h − M (cid:12) . This cut affects the completeness of SFRand ELG selections. In Appendix B we explain that this hasa negligible impact on the trends and results we obtain. To assess the level of similarity between the ELG and star-forming galaxy samples we compare their two-point corre-lation functions (2PCF). The 2PCF measures the excessprobability of finding a pair of objects at a separation r compared to a homogeneously distributed sample. We mea-sure the 2PCF using the CorrFunc public code presented inSinha & Garrison (2017) . The resulting 2PCF are shownin the main panel of Fig. 2 for the SFR and ELG sampleswith number density n = 0 . h Mpc − ; the sub-panelshows the ratios between these measurements and the 2PCFof the SFR selected sample. The first impression is that theshapes of the 2PCFs are largely similar, irrespective of sep-aration, with variations within 10%. On large scales, thedifferences are mostly due to the different bias parametersof the samples, with the [OIII] and [OII] selected samples http://skiesanduniverses.org/ https://corrfunc.readthedocs.io/en/master/ showing weaker clustering than the H α and SFR samples.On small scales, the differences may be due to the additionaldependence on the physical conditions in the ISM; the H α emission mostly traces the SFR, but the [OIII] and [OII]emission also depends on the cold gas metallicity. Hence, dif-ferences in the one-halo terms suggest a possible connectionbetween the spatial distribution of ELGs and the propertiesof their ISM. As can be seen from Fig. 2, the difference inthe 2PCF compared with that measured for the SFR se-lected sample depends on which line is chosen to constructthe sample. Both the H α and H α + [NII] selections resultin an amplitude for the 2PCF that is similar to that foundfor the SFR selection. This is expected as the strength ofH α emission is almost an instantaneous measure of the starformation rate, with little dependence on the metallicity ofthe star forming gas. The 2PCFs measured for the [OIII]and [OII] selections show a bigger difference from that foundfor the star formation sample, with an amplitude reductionof ∼
20 and 30 per cent, respectively. This change in theeffective bias parameter of these samples is related to theselection of galaxies with specific combinations of SFR andgas metallicity, as we demonstrate below.One way to interpret the 2PCF is by using the halooccupation distribution (HOD) framework. The HOD char-acterises a galaxy population via the halo occupation func-tion, the average number of galaxies as a function of the hosthalo mass. Whereas HODs are typically used as an empiricalmodel with parameters which are set to reproduce the mea-sured abundance and 2PCF of a galaxy samples, SAMs pre-dict the form of the HOD. So, in the case of SAMs, the HODformalism produces a concise description of the model out-put that can be readily interpreted in relation to the 2PCF.In general, this function is separated into the contributionfrom central galaxies and from satellites with specific formsthat depend on the selection criteria (Zheng et al. 2005). Forexample, when samples are defined by luminosity or stellarmass cuts, the HOD for central galaxies follows a step-likeform. When samples are defined by SFR or colour cuts, onthe other hand, the HOD of centrals reaches a peak followedby a dip to values below unity as the halo mass increases(e.g Zehavi et al. 2011; Contreras et al. 2013; Gonzalez-Perezet al. 2018; Jim´enez et al. 2019). The output of a SAM forthese selections can be tabulated as an HOD, without hav-ing to adopt a particular parametric form, which is verypowerful when considering selections for which there is littleavailable data, such as ELGs.Fig. 3 shows the HODs predicted by the SAG modelfor SFR and ELG selections with a number density n =0 . h Mpc − . We also show results for a stellar massselected sample to illustrate the differences compared to thestar-forming and ELG samples. The stellar mass selectedsample in the figure shows the canonical step-like form forthe HODs of centrals, with the HOD for satellites exhibitinga power-law behaviour. In contrast, the ELG selections showa peak in the HOD of central galaxies, which shifts to lowermasses for the [OIII] and [OII] selections. This indicates thatmodel ELGs are mostly hosted by low halo masses, consis-tent with previous results from simulations (e.g Gonzalez-Perez et al. 2018). For large halo masses, the HODs of bothcentrals and satellites increase with halo mass.The overlap between the SFR and ELG-selected sam-ples can be quantified by analysing the similarities in their MNRAS , 1–14 (2020) he assembly bias of ELGs (cid:0) M ∗ / h − M (cid:12) (cid:1) − − − − − − − l og (cid:0) n ga l ( > x ) / h M p c − (cid:1) n = 0 .
01 h Mpc − n = 0 . Mpc − n = 0 .
001 h Mpc − − (cid:0) SFR / M (cid:12) yr − (cid:1)
41 42 43 44 45log (cid:0) L Line / erg s − (cid:1) H α [OIII][OII] Figure 1.
The cumulative distribution functions of SAG galaxies selected by stellar mass ( left ), SFR ( middle ) and H α , [OIII], [OII] lineluminosities ( right ). The horizontal dashed lines indicate the number densities used to define our galaxy samples. Note the plateau atlow SFR and L Line , which is due to a stellar mass cut in the parent catalogue, which is discussed further in Appendix B. − − l og ( ξ ) n = 0 . Mpc − SFRH α H α + [NII] [OIII][OII] − . − . − . − . . . . . / h − Mpc)0 . . . . ξ / ξ S F R Figure 2.
The 2PCFs for SAG samples selected according to dif-ferent properties, as indicated by the key; in each case the numberdensity is n = 0 . h Mpc − . The bottom panel shows theratio of the correlation functions measured for each sample withrespect to the SFR-selected sample. galaxy properties. Fig. 4 shows the distribution of galaxiesin the instantaneous SFR vs. gas metallicity plane for theSFR, H α and [OII] selections, in all cases with a numberdensity n = 0 . h Mpc − . As can be seen, the distri-bution of the H α selected sample is in very good agreementwith that of the SFR selection, as expected. In contrast, thedistribution for the [OII]-selected sample is shifted to lowerinstantaneous SFR and cold gas metallicity. Still, an impor-tant fraction of [OII] emitters overlap with the SFR and H α selections. Table 1 shows the fraction of overlap between the . . . . . . . . h / h − M (cid:12) ) − . − . − . − . . . . . . l og h N i n = 0 . Mpc − All Centrals SatellitesStellar massSFRH α H α + [NII][OIII][OII] Figure 3.
The HODs predicted by the SAG model for all galax-ies (solid), centrals (dotted) and satellites (dashed), with dif-ferent colours indicating different galaxy selections, as shownby the figure key. All samples have a number density of n =0 . h Mpc − . ELG and SFR selections. Note that ELG and SFR selectedsamples have less overlap at lower number densities.
Measurements from N-body simulations have shown thatin order to fully determine the clustering of dark matterhaloes one needs, in addition to their masses, knowledge ofsecondary halo properties such as formation time, concen-tration, subhalo occupation and spin (e.g Gao et al. 2005;Wechsler et al. 2006; Gao & White 2007). This effect, termed
MNRAS000
MNRAS000 , 1–14 (2020)
Esteban Jim´enez et al. n/h Mpc − H α [OIII] [OII]0 .
001 0 .
81 0 .
57 0 . . .
91 0 .
71 0 . .
01 0 .
96 0 .
91 0 . Table 1.
Fraction of SFR-selected galaxies that also satisfy theELG selection criteria. Different rows indicate the number densityof the samples as shown in the first column. Columns 2, 3 and4 give the fraction of objects that also meet the H α , [OIII] and[OII] selections, respectively. − (cid:0) SFR inst / M (cid:12) yr − (cid:1) − . − . − . − . l og ( Z d i s k ) − . − . − . − . disk )n = 0 . Mpc − SFRH α [OII] Figure 4.
Distributions of instantaneous SFR (SFR inst ) and coldgas metallicity of the disk (Z disk ) for SAG samples with fixednumber density n = 0 . h Mpc − . Different colours corre-spond to different selections as shown by the key; the densitycontours enclose 68% and 99% of the distribution of galaxies.The corner panel shows the bivariate distributions, whereas thetop and right panels show the marginalised distributions of in-stantaneous SFR and cold gas metallicity, respectively. halo assembly bias, may potentially have an impact on thegalaxy content of haloes, producing variations in the halooccupation functions and therefore affecting the large-scalegalaxy clustering amplitude (e.g Artale et al. 2018; Zehaviet al. 2018; Contreras et al. 2019). Hence, it is important tomodel this effect when interpreting the correlation functionusing the standard HOD framework.SAM samples that are obtained using halo merger his-tories extracted from N-body simulations are affected byassembly bias because the growth histories of dark matterhaloes, and therefore the level of assembly bias that haloesare subject to, also affect the galaxies that evolve withinthem. To measure the impact of assembly bias on the clus-tering of our galaxy samples we compare their 2PCFs withthat of “shuffled” galaxy samples. The shuffling removes in-formation about the assembly history of haloes by randomlyexchanging the galaxy populations between haloes of thesame mass (Croton et al. 2007; Xu et al. 2020). The standardapproach preserves the central-satellites distances, thereforethe one-halo terms of the shuffled catalogues are the same as those of the original SAM samples. The assembly biassignature can be obtained by comparing the 2PCF of theSAM samples to that of the shuffled samples.The impact of assembly bias on galaxy clustering de-pends on the selection criteria, number density and redshiftof the sample (e.g Contreras et al. 2019). As the ELG se-lection shows substantial overlap with selection by SFR (seeFig. 4), we can estimate how much of the effect of assemblybias on the clustering of ELGs comes from the SFR selection.We do this by looking at the assembly bias effect present ina purely SFR-selected sample. Even though nebular emis-sion traces SFR, some properties of the gas in the ISM, suchas metallicity, can introduce additional effects that are notincluded when selecting by SFR alone. The assembly biassignatures for SFR-, stellar mass- and ELG-selected sam-ples are shown in Fig. 5 for the three number densities. Itcan be seen from Fig. 5 that the assembly bias in the H α and H α + [NII] selections is similar to that seen in the SFRselection. In contrast, assembly bias suppresses the galaxyclustering of [OIII] and [OII] selections by up to 30 per cent.Table 1 shows that the H α sample has a high overlap withthe SFR selected sample for all number densities consid-ered. For [OIII] emitters, the overlap with the SFR-selectionis high for the highest number density sample, explainingtheir similar clustering in the top panel of Fig. ?? . For theother number densities considered, the overlap between the[OIII] and SFR selected samples is much smaller and theirclustering is different.Furthermore, the assembly bias is scale-dependent, par-ticularly in the case of [OII]. This steepness in the ratio ofthe 2PCF to the shuffled samples is also present in the SFR,H α and H α +[NII] selections but only for the lowest numberdensities and, in any case, it is not as scale-dependent asin the [OIII] and [OII] cases. Moreover, there is a “bump”feature in the ratio that is present only for the latter twoselections around the transition from the one-halo to thetwo-halo term (log( r/h − Mpc) ∼ − . ξ mm , and the 2PCF of the galaxy sample ξ gal we compute the large scale bias of each sample using b ( r ) = (cid:115) ξ gal ξ mm . (1)The value of the bias parameter is expected to be constant MNRAS , 1–14 (2020) he assembly bias of ELGs . . . . . . . .
01 h Mpc − Stellar massSFR H α H α + [NII] [OIII][OII]0 . . . . . . . ξ / ξ Shu ffl e d n = 0 . Mpc − − . − . − . . . . . / h − Mpc)0 . . . . . . . .
001 h Mpc − Figure 5.
The assembly bias signature in the SAG samples. Eachpanel shows a different number density as labelled. Note that theassembly bias for the [OIII] and [OII] selections exhibits a clearscale-dependent signature for the two lowest number densities. to first-order on linear scales and to vary with the galaxyselection.The main panels of Fig. 6 show the 2PCFs of thedark matter and the SAG and shuffled samples for theH α , [OIII] and [OII] selections, for the number density of n = 0 . h Mpc − . For clarity, we show results for thetwo-halo term only (log( r/h − Mpc) (cid:38) . b ( r ), for each sample is shown as acoloured line in the bottom panels. We average these valuesbetween 25 and 50 h − Mpc to obtain a constant large-scalebias, which is shown by the gray horizontal lines for com-parison with b ( r ). For the H α selection the bias parameter isroughly constant over the range 25 < r /h − Mpc <
50, forboth the SAG and shuffled samples. In contrast, the biasparameters for the SAG [OIII] and [OII] selections show ascale-dependence. The bias for the shuffled samples is seento be roughly constant. For the lowest number density sam-ple (not shown here), we find that the bias parameter has aneven steeper scale dependence for [OII] and [OIII] selections.The larger value found for the bias of the H α selected sam-ple indicates that, in this case, galaxies trace higher peaksin the density field than galaxies in the other ELG-selectedsamples.The prediction of a scale-dependent bias parameter forthe SAG [OIII]- and [OII]-selected samples indicates that there are additional features which shape the large scaleclustering of these tracers. This suggests that the gas metal-licity, which has an impact on the [OII] and [OIII] emissionfor a given amount of star formation, has some dependenceon environment. This is confirmed by the much weaker scaledependence found for the bias on large scales in the shuffledsamples. In this section we investigate the origin of the scale-dependence of the galaxy assembly bias signature in galax-ies selected by their [OIII] and [OII] line emission. As justnoted, the scale-dependent bias is only present in the orig-inal SAG samples and not in their shuffled counterparts.This suggests that the preference for the environment thatcharacterises galaxies with strong line emission, that couldcause this scale dependence, is removed when shuffling thesesamples. Gonzalez-Perez et al. (2020) analyzed how modelELGs trace the large scale structure in an N-Body simula-tion. They found that about half of [OII] emitters live infilaments while one-third live in sheets. This indicates thatthe galaxies selected using [OII] line luminosity will be pref-erentially located in low density regions. Hence, quantifyingthe effect that the shuffling procedure has of moving ELGsto random locations in the cosmic web can provide an insightinto the relation between the environment of [OII] emit-ters and the scale-dependent assembly bias. Whilst there issome overlap between the SFR and [OII] selected samples,the SFR-selected sample shows little sign of scale dependentbias. Hence, the source of the scale dependence is likely tobe found in the galaxies that are not in common betweenthe two samples. Indeed, Table 1 shows that the overlap be-tween the SFR and [OII] emitters is less than 50 per centfor the two lowest density samples. This indicates that theorigin of the scale dependence is encoded in the selection by[OII] luminosity.One approach to quantifying the environment of agalaxy sample is to compute the local number density ofmain haloes around each galaxy. We use the main halos as weassociate galaxies with their host dark matter haloes ratherthan with subhaloes; not all of the satellite galaxies may beassociated with a resolved subhalo. We define the numberdensity, n local , using the distance to the fifth nearest mainhalo in the MDPL2 simulation, r , as n local = 5 /V ( r ),where V ( r ) is the volume of a sphere of radius r = r .To count neighbouring haloes we use those with masses M h > . h − M (cid:12) for all galaxy selections.We now consider the contribution of different halos tothe sample bias and their environment. Following Kim et al.(2009), we compute the effective clustering bias as a functionof halo mass for each galaxy sample, and show the results inthe top panel of Fig 7. This parameter quantifies the contri-bution of galaxies in haloes of a given mass to the large scalegalaxy clustering amplitude of the sample. The effective biasis simply computed as b ( M ) × Φ( M ) × (cid:104) N ( M ) (cid:105) where b ( M )is the bias function, Φ( M ) is the halo mass function and (cid:104) N ( M ) (cid:105) is the halo occupation function of the galaxy sam-ple. For each selection, the effective bias reaches a peak atdifferent halo masses, close to the location of the “knee” ofthe occupation function (i.e. when the highest fraction of MNRAS000
50, forboth the SAG and shuffled samples. In contrast, the biasparameters for the SAG [OIII] and [OII] selections show ascale-dependence. The bias for the shuffled samples is seento be roughly constant. For the lowest number density sam-ple (not shown here), we find that the bias parameter has aneven steeper scale dependence for [OII] and [OIII] selections.The larger value found for the bias of the H α selected sam-ple indicates that, in this case, galaxies trace higher peaksin the density field than galaxies in the other ELG-selectedsamples.The prediction of a scale-dependent bias parameter forthe SAG [OIII]- and [OII]-selected samples indicates that there are additional features which shape the large scaleclustering of these tracers. This suggests that the gas metal-licity, which has an impact on the [OII] and [OIII] emissionfor a given amount of star formation, has some dependenceon environment. This is confirmed by the much weaker scaledependence found for the bias on large scales in the shuffledsamples. In this section we investigate the origin of the scale-dependence of the galaxy assembly bias signature in galax-ies selected by their [OIII] and [OII] line emission. As justnoted, the scale-dependent bias is only present in the orig-inal SAG samples and not in their shuffled counterparts.This suggests that the preference for the environment thatcharacterises galaxies with strong line emission, that couldcause this scale dependence, is removed when shuffling thesesamples. Gonzalez-Perez et al. (2020) analyzed how modelELGs trace the large scale structure in an N-Body simula-tion. They found that about half of [OII] emitters live infilaments while one-third live in sheets. This indicates thatthe galaxies selected using [OII] line luminosity will be pref-erentially located in low density regions. Hence, quantifyingthe effect that the shuffling procedure has of moving ELGsto random locations in the cosmic web can provide an insightinto the relation between the environment of [OII] emit-ters and the scale-dependent assembly bias. Whilst there issome overlap between the SFR and [OII] selected samples,the SFR-selected sample shows little sign of scale dependentbias. Hence, the source of the scale dependence is likely tobe found in the galaxies that are not in common betweenthe two samples. Indeed, Table 1 shows that the overlap be-tween the SFR and [OII] emitters is less than 50 per centfor the two lowest density samples. This indicates that theorigin of the scale dependence is encoded in the selection by[OII] luminosity.One approach to quantifying the environment of agalaxy sample is to compute the local number density ofmain haloes around each galaxy. We use the main halos as weassociate galaxies with their host dark matter haloes ratherthan with subhaloes; not all of the satellite galaxies may beassociated with a resolved subhalo. We define the numberdensity, n local , using the distance to the fifth nearest mainhalo in the MDPL2 simulation, r , as n local = 5 /V ( r ),where V ( r ) is the volume of a sphere of radius r = r .To count neighbouring haloes we use those with masses M h > . h − M (cid:12) for all galaxy selections.We now consider the contribution of different halos tothe sample bias and their environment. Following Kim et al.(2009), we compute the effective clustering bias as a functionof halo mass for each galaxy sample, and show the results inthe top panel of Fig 7. This parameter quantifies the contri-bution of galaxies in haloes of a given mass to the large scalegalaxy clustering amplitude of the sample. The effective biasis simply computed as b ( M ) × Φ( M ) × (cid:104) N ( M ) (cid:105) where b ( M )is the bias function, Φ( M ) is the halo mass function and (cid:104) N ( M ) (cid:105) is the halo occupation function of the galaxy sam-ple. For each selection, the effective bias reaches a peak atdifferent halo masses, close to the location of the “knee” ofthe occupation function (i.e. when the highest fraction of MNRAS000 , 1–14 (2020)
Esteban Jim´enez et al. − − − l og ( ξ ) n = 0 . Mpc − H αξ from SAG ξ from Shuffled ξ mm − MDPL2 [OIII] [OII] . . . / h − Mpc)1 . . . b ( r ) . . . / h − Mpc) 0 . . . / h − Mpc)
Figure 6. ( Top ) The 2PCFs of the SAG samples (solid) and the shuffled samples (dashed-dotted) for the H α ( left panel ), [OIII] ( middlepanel ) and [OII] ( right panel ) selections. The black dashed lines correspond to the 2PCF of the dark matter distribution of the MDPL2simulation. ( Bottom ) The bias parameter, as a function of scale-separation, for the SAG and shuffled samples. The horizontal solid(dashed) grey line corresponds to the bias parameters of the SAG (shuffled) samples averaged between 25 and 50 h − Mpc. haloes of a given mass contain a central). The middle panelshows the average n local for the SAG and shuffled samples;the bottom panel shows the ratios between the n local of theSAG and shuffled samples for each galaxy selection. Notethat a ratio higher than unity indicates that galaxies in theSAG samples are in higher density regions than their shuf-fled counterparts.The SAG galaxy samples exhibit different average n local , which suggest that these different galaxy popula-tions live in different environments. In contrast, the aver-aged n local for the shuffled samples are largely the samefor all selections. Therefore, it appears that the shufflingprocedure removes correlations between the selection andenvironment. For example, for the [OII]-selected galaxiesfrom SAG, the shuffling removes the strong environmen-tal preference for [OII] emitters to reside in filaments andsheets. As the shuffling procedure moves galaxies betweenhaloes of the same mass, the resulting HODs of the shuf-fled samples are similar to those of their SAG counterparts,which in turn are notably different between selections (seeFig. 3). Thus, their b ( M ) and 2PFCs are also different evenwhen their averaged n local are similar. For the stellar mass-selected sample, we see that the ratio of n local in the SAGmodel to that in the shuffled counterpart is close to unitywhich indicates that the shuffling procedure does not modifythe environment for this particular selection. For the SFR-and ELG-selected samples, on the other hand, the ratiosin the bottom panel of Fig. 7 show clear departures fromunity. Moreover, these ratios depend on halo mass, whichsuggests that the mass of the host haloes is related to thestrength of the environmental selection of SAG galaxies.Even though all selections show this dependence on mass,in principle, its impact on galaxy clustering only appears tobe important when this dependence is seen at halo massesaround the peak of the contribution to the effective clus-tering bias for each selection. In particular, for the [OII] selection, there is an overlap between the peak of the ef-fective bias and the mass dependence of the density ratioin the halo mass range 11 . < log( M h /h − M (cid:12) ) <
12. Incontrast, for the SFR and H α selections, we find no depen-dence on halo mass around the peak of the effective bias inlog( M h /h − M (cid:12) ) ∼
12. For the [OIII]-selected sample, theratio also depends on halo mass but in a narrower range11 . < log(M h /h − M (cid:12) ) < .
9, which is close to the peakof the effective bias.Another approach to explore the origin of the scale-dependent assembly bias signature is to analyse the distri-bution of the gas-phase metallicity in the SAG samples. Asthe
GET_EMLINES code uses this property as an input to pre-dict the [OIII] and [OII] emission line luminosities, we ex-pect that it is correlated to some extent with the spatialdistribution of the [OIII] and [OII] selections. Fig. 8 showsthe distributions of SAG galaxies in the stellar mass-L[OII]and L(H α )-L[OII] planes. The points are colour-coded bymetallicity averaged weighting by the mass of cold gas inboth disks and bulges. We divide the galaxies into foursubsamples separated by cuts in stellar mass, L(H α ) andL[OII] (dashed lines) that correspond to a number density n = 0 . h Mpc − . Galaxies to the right (above) of thevertical (horizontal) dashed lines are contained in the [OII]-selected sample (stellar mass and H α selections). In this way,the overlap between the galaxy samples can be easily seen;for the L(H α )-L[OII] plane we see that about half of [OII]-selected galaxies are contained in the H α selection, whilefor the stellar mass-L[OII] comparison, the [OII] emittersaccount for 25 per cent of galaxies in the stellar mass se-lection. Moreover, galaxies in the [OII] selection tend to bemore metal-poor than for their H α or stellar mass counter-parts, which is consistent with the metallicity distributionsin Fig. 4. Indeed, it is clear that a large fraction of the [OII]-selected galaxies, in the bottom-right sectors, are the mostmetal poor. MNRAS , 1–14 (2020) he assembly bias of ELGs . . . b ( M h ) N ga l / N t o t ga l n = 0 . Mpc − . . . . . . h n l o c a l i / h M p c − Stellar massSFR H α [OIII] [OII]Shuffled11 . . . . . . . h / h − M (cid:12) )0 . . . n S A M / n Shu ffl e d Figure 7. ( Top ) The contribution to the effective clustering biasfrom halos as a function of halo mass. (
Middle ) the average localnumber densities for the SAG samples (solid) and their shuffledsamples (dashed) as a function of halo mass, defined as describedin the text. (
Bottom ) The ratio between the SAG and shuffleddensity measurements. Different colours indicate different galaxyselections as labelled in the middle panel.
We compute the auto-correlation functions of galaxiesin each sector of the stellar mass-L[OII] plane to look forinteresting features in their spatial clustering. We apply theshuffling procedure to these subsamples and measure the2PCF of the resulting shuffled samples. We also computethe ratios of the 2PCF measured from the SAG subsamplesto those of their shuffled counterparts to obtain the assem-bly bias signatures. The top right panel in Fig. 9 shows theassembly bias signatures for each subsample, colour-codedby its location in the stellar mass-L[OII] plane, as indicatedin the left panel. There is a remarkable difference betweenthe assembly bias signatures of the H α subsamples; the red-coded galaxies, which are not included in the [OII] selection,show almost no assembly bias, but the blue-coded ones showa prominent scale-dependence. Moreover, the assembly biasfor the grey-coded subsample (which mostly contains metal-poor galaxies), exhibits a steeper dependence on separation.These two results suggest that galaxies with low gas-phasemetallicity are driving the scale-dependent assembly bias.To connect this information with the environment of hosthaloes, we show, in the bottom-right panel of Fig. 9, the dis-tribution of local number densities for galaxies in each sub-sample. There is a subtle preference for grey-coded galaxiesto live in less dense regions than galaxies in the other sub-samples. These results suggest that the gas-phase metallicityis the property of the [OIII] and [OII] selections that pro-duces the scale-dependent assembly bias. Specifically, galax-ies with low metallicity, that live in low-density regions, ap- pear to account for most of the scale-dependence. Nevethe-less, further studies are needed to fully understand the cor-relation between metallicity and the spatial distribution ofgalaxies. In the previous sections we analyzed the scale-dependent as-sembly bias in the [OIII] and [OII] selected samples and itsrelation to the gas-phase metallicity and the environment ofthe galaxies. The scale dependence was found to be drivenby low metallicity galaxies in underdense environments. Thescale dependence may have important implications for cos-mological analyses.In this section we focus on the baryon acoustic oscilla-tion (BAO) feature and the β parameter. These quantitiesare measured from each of the SAG samples to check if theELG selection introduces any systematic effects into the in-ference of cosmological parameters. This analysis is partic-ularly important for the [OIII] and [OII] selections, as theycontain particular features such as a non constant bias anda galaxy assembly bias signal driven by the environment ofthese galaxies.Fig. 10 shows the 2PCFs of the SAG (top panels) andshuffled samples (bottom panels) for different selection crite-ria and number densities. Note that, in order to focus on theBAO peak, we display r × ξ ( r ). For comparison, we showthe z ∼ ∼ § ∼ β parameter for the SAG samples.This parameter is a function of the logarithmic growth rate, MNRAS000
We compute the auto-correlation functions of galaxiesin each sector of the stellar mass-L[OII] plane to look forinteresting features in their spatial clustering. We apply theshuffling procedure to these subsamples and measure the2PCF of the resulting shuffled samples. We also computethe ratios of the 2PCF measured from the SAG subsamplesto those of their shuffled counterparts to obtain the assem-bly bias signatures. The top right panel in Fig. 9 shows theassembly bias signatures for each subsample, colour-codedby its location in the stellar mass-L[OII] plane, as indicatedin the left panel. There is a remarkable difference betweenthe assembly bias signatures of the H α subsamples; the red-coded galaxies, which are not included in the [OII] selection,show almost no assembly bias, but the blue-coded ones showa prominent scale-dependence. Moreover, the assembly biasfor the grey-coded subsample (which mostly contains metal-poor galaxies), exhibits a steeper dependence on separation.These two results suggest that galaxies with low gas-phasemetallicity are driving the scale-dependent assembly bias.To connect this information with the environment of hosthaloes, we show, in the bottom-right panel of Fig. 9, the dis-tribution of local number densities for galaxies in each sub-sample. There is a subtle preference for grey-coded galaxiesto live in less dense regions than galaxies in the other sub-samples. These results suggest that the gas-phase metallicityis the property of the [OIII] and [OII] selections that pro-duces the scale-dependent assembly bias. Specifically, galax-ies with low metallicity, that live in low-density regions, ap- pear to account for most of the scale-dependence. Nevethe-less, further studies are needed to fully understand the cor-relation between metallicity and the spatial distribution ofgalaxies. In the previous sections we analyzed the scale-dependent as-sembly bias in the [OIII] and [OII] selected samples and itsrelation to the gas-phase metallicity and the environment ofthe galaxies. The scale dependence was found to be drivenby low metallicity galaxies in underdense environments. Thescale dependence may have important implications for cos-mological analyses.In this section we focus on the baryon acoustic oscilla-tion (BAO) feature and the β parameter. These quantitiesare measured from each of the SAG samples to check if theELG selection introduces any systematic effects into the in-ference of cosmological parameters. This analysis is partic-ularly important for the [OIII] and [OII] selections, as theycontain particular features such as a non constant bias anda galaxy assembly bias signal driven by the environment ofthese galaxies.Fig. 10 shows the 2PCFs of the SAG (top panels) andshuffled samples (bottom panels) for different selection crite-ria and number densities. Note that, in order to focus on theBAO peak, we display r × ξ ( r ). For comparison, we showthe z ∼ ∼ § ∼ β parameter for the SAG samples.This parameter is a function of the logarithmic growth rate, MNRAS000 , 1–14 (2020) Esteban Jim´enez et al.
Figure 8. ( Left ) The H α emission as a function of [OII] emission colour-coded by the cold mass-weighted metallicity of the disks andbulges. The cyan (green) dashed line indicates the cut in H α ([OII]) for a sample of number density n = 0 . h Mpc − . The fractionof galaxies with [OII] emission below and above the [OII] cut are included in both sectors. ( Right ) Same as the left but for stellar massas a function of [OII] emission.
Figure 9. ( Left ) Same as the right panel of Fig. 8 but with galaxies colour-coded by their location in the stellar mass-L[OII] plane.(
Top-right ) the assembly bias signatures for the three colour-coded subsamples. (
Bottom-right ) The local density distribution for galaxiesin the color-coded subsamples, where dashed vertical lines correspond to the mean of each distribution. which depends on the matter density parameter, and thebias parameter of the galaxy sample. Following Padilla et al.(2019), we compute β for shuffled samples where the relativevelocities of the galaxies within haloes – in addition to theirpositions – are maintained when shuffling satellites betweenhaloes. The β parameter can be obtained from the ratio between the monopoles of the correlation functions in realand redshift space (Kaiser 1986b): ξ ( s ) = (cid:18) β + 15 β (cid:19) ξ ( r ) . (2)The main panel of Fig. 11 shows the β parameter, cal-culated from Eq. 2, as a function of scale for the SAG (solid)and shuffled samples (dashed) with a number density of n = 0 . h Mpc − . For the SAG samples, we see that MNRAS , 1–14 (2020) he assembly bias of ELGs − − r ξ ( r ) n = 0 .
001 h Mpc − Stellar massSFR ξ mm − MDPL2 n = 0 . Mpc − H α [OIII][OII] n = 0 .
01 h Mpc −
80 90 100 110 120 130 140 150r / h − Mpc − − r ξ ( r ) Shuffled 80 90 100 110 120 130 140 150r / h − Mpc 80 90 100 110 120 130 140 150r / h − Mpc
Figure 10.
The baryon acoustic oscillation (BAO) feature for the SAG samples ( top ) and their shuffled counterparts ( bottom ) with numberdensities n = 0 . h Mpc − ( left , n = 0 . h Mpc − ( middle ) and n = 0 . h Mpc − ( right ). Colours correspond to the differentselections adopted, as shown in the keys. The vertical lines are included to guide the eye and indicate the position of the BAO peak forthe dark matter, according to the linear theory prediction (black dot-dashed line). the β parameter is roughly constant for the stellar mass se-lection, and it is scale-dependent for the other selections.However, for the shuffled samples, the scale dependence of β remains. The bottom panel of Fig. 11 shows the ratios be-tween the β parameter of the SAG samples to that of theirshuffled counterparts. For the stellar mass selection, the ratiois almost constant for all scales. For SFR- and ELG-selectedsamples, the ratio is more affected by noise, but it appears tobe consistent with a constant value, with the SFR and ELGselected samples returning a higher value of beta than theirshuffled counterparts. In principle, the steepness of β couldbe so slight that it falls below our noise level, even thoughwe do find a scale-dependent bias for the ELG SAG sam-ples, and a roughly constant one for the shuffled catalogues,especially for the [OIII] and [OII] selections (see Fig. 6). The next generation of galaxy surveys such as DESI andEuclid will map the sky by measuring redshifts to unprece-dented numbers of emission-line galaxies. To fully exploitthis upcoming data we need to understand how these galax-ies trace the underlying density of the Universe and to estab-lish if there are any systematic effects which might impairour ability to extract unbiased cosmological information.To investigate the potential of ELGs to constrain cos-mological parameters, we study the clustering and halo oc-cupation of the model galaxies from the SAG semi-analyticalmodel (Cora et al. 2018) applied to the MDPL2 simulationoutputs (Klypin et al. 2016). We use the instantaneous SFRand gas-phase metallicities of galaxies as the inputs to the
GET_EMLINES code to obtain the nebular line emission of thegalaxies. To mimic the selection criteria of future surveys, weuse fixed number density samples where galaxies are rankedaccording to their [OIII], [OII], H α and H α +[NII] line lumi-nosities. For comparison, we also include SFR- and stellarmass-selected samples.We measure the two-point correlation functions(2PCFs), the halo occupation distributions (HODs) and thegalaxy assembly bias signatures for each galaxy sample. Thegalaxy assembly bias is measured via the ratio between the2PCF of a SAG sample with that of a shuffled version of thesample, which, by construction, does not contain assemblybias. We also compute the absolute large scale bias of ELGsto look for correlations between assembly bias, large-scalebias, the environment of the galaxies, and the gas-phasemetallicity of the ELG-selected samples. Finally, we mea-sure the BAO feature and the β parameter for the SAG andshuffled samples to investigate the implications for cosmo-logical studies using ELGs. Our results can be summarisedas follows: • ELG-selected samples have 2PCFs and HODs that aresimilar to those of SFR selected galaxies. However, the[OIII]- and [OII]-selected samples are less clustered than ei-ther the SFR or H α samples. Moreover, their HODs indicatethat most of the selected galaxies live in low mass haloes.These differences explain why selecting by the luminosity ofthe [OIII] or [OII] lines does not reproduce the behaviour ofa SFR selected sample. • The assembly bias signature (i.e. the ratio between the2PCFs measured for the SAG and shuffled samples) for the[OIII] and [OII] selected samples is scale-dependent, with asteepness which becomes more pronounced for lower density
MNRAS000
MNRAS000 , 1–14 (2020) Esteban Jim´enez et al. s / h − Mpc0 . . . . β ( s ) n = 0 . Mpc − Stellar massSFRH α [OIII][OII]Shuffled20 30 40 50s / h − Mpc0 . . . β / β Shu ffl e d Figure 11. ( Top ) The β parameter as a function of separationfor the SAG (solid) and shuffled samples (dotted) with numberdensity n = 0 . h Mpc − . Different colours correspond todifferent selection criteria as indicated by the keys. ( Bottom ) theratio between the β parameters of the SAG and shuffled samples.The gray dashed line indicates unit ratio. samples (higher [OIII] and [OII] thresholds). For the SFRand H α selections, the assembly bias is scale-dependent forsamples with the lowest number density. In the case of galax-ies selected by stellar mass, the assembly bias is roughlyconstant for all number densities. • The large-scale bias, defined as the ratio between the2PCF of a galaxy sample and that of the dark matter, isscale-dependent for the [OIII]- and [OII]-selected samples inthe SAG model. For the shuffled samples, in contrast, thelarge-scale bias is roughly constant for all selections. Thissuggests that the shuffling procedure removes an encodeddependence between the galaxy properties of [OIII] and [OII]selections with the environment. • For a fixed halo mass the local number density - that weuse to quantify the environment of host haloes - is roughlythe same for all shuffled samples. This indicates that theshuffling procedure eliminates the correlation between theselection and the environment of host haloes. In contrast,for the SAG samples the local number densities are notablydifferent between the selection criteria which indicates thatin some cases the selected galaxies live in special regions ofthe cosmic web. Moreover, the change of the environment ofthe [OII]-selected sample has a strong dependence with halomass (see Fig. 7). • Galaxies with low gas-phase metallicities are the onesthat produce the scale-dependent assembly bias signature.Indeed, for the SAG sample, a larger fraction of metal-poorgalaxies results in a steeper scale-dependent assembly biassignature (see Fig. 9). Moreover, these galaxies tend to livein low-density regions, which is more common for the ELGselected samples. • The scale of the BAO feature in the [OII]-selected sam- ple with number density n = 0 . h Mpc − , differs atthe 3 per cent level from that recovered using the other se-lections. Interestingly, this shift in the BAO peak is not seenfor the shuffled counterpart of the [OII] sample. Conversely,for the other selected samples, the BAO feature is locatedat the same position for both the SAG and shuffled samples.There is no clear shift in the position of the BAO feature forthe [OII] selections with lower and higher number densities. • The β parameter for the SFR- and ELG-selected sam-ples is non-constant as a function of scale for the SAG andthe shuffled samples. This is clearer for the [OII] and [OIII]selections and can be explained as a combination of the scale-dependent large scale bias and a possible non-constant log-arithmic growth rate. For the stellar mass case, in contrast, β is roughly constant.Our results show that care must be given when usingfuture galaxy samples from Euclid and DESI, which will beselected by their emission line luminosities. We find thatthis type of selection can produce samples that lie in spe-cial environments, and because of this their clustering canshow a different slope than that of the underlying matterdensity field. This type of environment selection needs to bemodelled and marginalised over in cosmological parameterconstraints from such samples in order to avoid systematiceffects in their analysis. ACKNOWLEDGEMENTS
DATA AVAILABILITY STATEMENT
The data underlying this article will be shared on reasonablerequest to the corresponding author.
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APPENDIX A: ASSEMBLY BIAS OF ELGS IN
L-GALAXIES
To assess if the scale-dependent assembly bias can be foundin other semi-analytical models, we select galaxy samples atz=0 from the Guo et al. (2013) model (hereafter G13) whichis a version of the
L-GALAXIES code from the Munich group(De Lucia et al. 2004; Croton et al. 2006; De Lucia & Blaizot2007; Guo et al. 2011; Henriques et al. 2013). G13 is a semi-analytic model, and as such it models a set of physical pro-cesses that shape the formation and evolution of galaxies,applied to halo merger trees drawn from the Millennium-WMAP7 simulation. This simulation was carried out in abox of 500 h − Mpc a side, and is the same as the originalMillennium simulation (Springel et al. 2005) but with up-dated cosmological parameters that match the results fromthe WMAP7 observations.We use the
GET_EMLINES code to obtain the nebularemission for G13 galaxies. The instantaneous SFR is not adirect output of G13, hence, we use the average
SFR insteadto infer line emission luminosities. This is motivated by theresults of Favole et al. (2020); they demonstrate that usingaverage SFRs as inputs for
GET_EMLINES produces good pre-dictions to study average populations of [OII] emission-linegalaxies. We then define new stellar mass, SFR, H α , [OIII]and [OII] selected samples following the procedure in § α and SFR selections are the same, which is a con-sequence of H α luminosity having a simple dependence onthe SFR, with little variation with the cold gas metallicity.Even though the clustering measurements are noisier at verylarge scales, we still find that the [OIII] and [OII] selectionshave a clear scale-dependent assembly bias. In contrast, forthe SFR and H α selections, the scale-dependence is therefor the lowest number density sample alone, while for thestellar mass-selected samples the signature is roughly flat inall cases. APPENDIX B: COMPLETENESS OF ELG SELECTEDSAMPLES
Selecting by emission line luminosities produces samplesthat trace the amplitude of SFR but also other additionalproperties, such as the cold gas metallicity. Thus, in princi-ple, a low-SFR galaxy may be included in an ELG-selectedsample. Because of this we analyze the effect of the mod-erate stellar mass cut imposed on the SAG data, which ispresent in the subsamples analyzed in this work; this mod-erate cut is M ∗ > . h − M (cid:12) which is slightly lower thanthe resolution of the MDPL2 and Millennium simulations( ∼ h − M (cid:12) ).As SAG and G13 show similar trends for assembly bias(see Fig. A1), we expect that the effect of the completenessstellar mass cut on these trends should be also similar forboth models. Fig. B1 displays the cumulative SFR functionfor subsamples of G13, defined by different stellar mass cuts.As expected from the stellar mass-SFR relation, we see thatthe larger the cut, the smaller the number of low-SFR galax-ies. . . . . . . . .
01 h Mpc − G13 z = Stelar massSFR H α [OIII] [OII]0 . . . . . . . ξ / ξ Shu ffl e d n = 0 . Mpc − − . − . − . . . . . / h − Mpc)0 . . . . . . . .
001 h Mpc − Figure A1.
Same as Fig. 5 but for galaxy samples extracted fromthe Guo et al. (2013) SAM.
We define a subsample of G13 by selecting galaxies withstellar mass above the cut imposed for SAG. Then, follow-ing the procedure in § . 2.4, we define our galaxy sampleswith this new cut. We measure the assembly bias signaturesfor these samples, and we compare them with the assemblybias of G13 samples with no previous cuts in stellar mass.We find that the assembly bias signatures are almost identi-cal for all selections and number densities. Noticeable differ-ences only arise at very large scales(log(r / h − Mpc) > . MNRAS , 1–14 (2020) he assembly bias of ELGs − − − / M (cid:12) yr − ) − − − − − − l og ( n ga l / h M p c − ) G13
AllM ∗ > h − M (cid:12) M ∗ > . h − M (cid:12) M ∗ > h − M (cid:12) Figure B1.
The cumulative SFR function of subsamples of theGuo et al. (2013) model defined by different stellar mass cutsindicated by the colors and labels. Horizontal lines indicate thedifferent number densities used to define the galaxy samples.MNRAS000