Galaxy properties in the cosmic web of EAGLE simulation
Wenxiao Xu, Qi Guo, Haonan Zheng, Liang Gao, Cedric Lacey, Qing Gu, Shihong Liao, Shi Shao, Tianxiang Mao, Tianchi Zhang, Xuelei Chen
MMNRAS , 000–000 (2020) Preprint 17 September 2020 Compiled using MNRAS L A TEX style file v3.0
Galaxy properties in the cosmic web of EAGLE simulation
Wenxiao Xu, , Qi Guo, , (cid:63) Haonan Zheng, , Liang Gao, , † Cedric Lacey, Qing Gu, , Shihong Liao, Shi Shao, Tianxiang Mao, , Tianchi Zhang , and Xuelei Chen , Key Laboratory for Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012, China University of Chinese Academy of Sciences, Beijing, 100049, China Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We investigate the dependence of the galaxy properties on cosmic web environmentsusing the most up-to-date hydrodynamic simulation: Evolution and Assembly ofGalaxies and their Environments (EAGLE). The baryon fractions in haloes and theamplitudes of the galaxy luminosity function decrease going from knots to filaments tosheets to voids. Interestingly, the value of L ∗ varies dramatically in different cosmic webenvironments. At z = 0, we find a characteristic halo mass of h − M (cid:12) , below whichthe stellar-to-halo mass ratio is higher in knots while above which it reverses. Thisparticular halo mass corresponds to a characteristic stellar mass of . × h − M (cid:12) .Below the characteristic stellar mass central galaxies have redder colors, lower sSFRsand higher metallicities in knots than those in filaments, sheets and voids, while abovethis characteristic stellar mass, the cosmic web environmental dependences either re-verse or vanish. Such dependences can be attributed to the fact that the active galaxyfraction decreases along voids, sheets, filaments and knots. The cosmic web depen-dences get weaker towards higher redshifts for most of the explored galaxy propertiesand scaling relations, except for the gas metallicity vs. stellar mass relation. Key words:
Cosmology: Large-scale Structure of the Universe – galaxies: general –galaxies: evolution
The large scale structure (LSS) of the Universe exhibits aweb-like structure, which is usually categorized into fourcomponents: voids, sheets, filaments and knots. It originatesfrom small perturbations in the very early Universe and isshaped gradually by the large scale gravitational fields. Dif-ferent components correspond to different stages of gravi-tational collapse. Large sheets of matter form via gravita-tional collapse along one principal direction, filaments formvia gravitational collapse along two principal axes and knotsform via gravitational collapse along three principal axes.The relatively empty regions of the Universe between knots,filaments and sheets are referred to as cosmic voids, whosedensity is well below the cosmic mean value. Most mass iscontained in knots and filaments, while most volume is filledby voids. The relative mass fractions and filling factors ofeach component could evolve significantly from high to lowredshifts (Cui et al. 2019; Zhu & Feng 2017a). (cid:63)
E-mail: [email protected] † E-mail: [email protected]
The cosmic web environments have influences on thehalo formation history and the halo properties. Haloes inknots tend to be older than those in other web environ-ments, and massive haloes in knots have higher spin thanthose in filaments, sheets and voids (e.g. Hahn et al. 2007).The halo mass function strongly depends on the web envi-ronment such that it has a much higher amplitude in fil-aments than in voids (e.g. Ganeshaiah Veena et al. 2018).Recently, the large-scale cosmic web environment was alsofound to correlate with the orientation of haloes (e.g. Zhanget al. 2009; Codis et al. 2012; Ganeshaiah Veena et al. 2018).However, the role the cosmic web plays in galaxy formationis not clear. Recent work found that the blue galaxy fractionand the star formation rate of blue galaxies decline from thefield to knots at low redshift, but the dependence disappearsat higher redshifts (Darvish et al. 2017a; Kraljic et al. 2018).Similar trends are also found in the state-of-the-art hydro-dynamical simulation HORIZON-AGN (Dubois et al. 2014).Using the Sloan Digital Survey (SDSS), Chen et al. (2017)demonstrated that red, massive galaxies tend to reside infilaments more than blue, less-massive galaxies.It has been suggested that the cosmic web shapes the © a r X i v : . [ a s t r o - ph . GA ] S e p Wenxiao Xu et al. galaxy properties primarily through the strong dependenceof the galaxy properties on the mass of their host halo (e.g.Gay et al. 2010; Goh et al. 2019; Yan et al. 2013). This isalso supported by Eardley et al. (2015) who found in GalaxyAnd Mass Assembly survey (GAMA) that the strong varia-tion of galaxy properties in different cosmic web structuresvanishes when comparing at the same local density. How-ever, by using SDSS data, Poudel et al. (2017) found thatat a fixed halo mass, central galaxies in filaments have red-der colors, higher stellar mass, lower specific star formationrates and higher abundances of elliptical galaxies compareto those outside the filaments. Observationally it is hard tomeasure the halo mass for an individual galaxy while stack-ing methods could smear out the cosmic web dependence ifit is not strong enough. Theoretical work using cosmologicalhydro-dynamical simulations can provide more clues to suchstudies. Using IllustrisTNG, Martizzi et al. (2020) found ata given halo mass, galaxies with stellar masses lower thanthe median value are more likely to be found in voids andsheets, whereas galaxies with stellar masses higher than themedian are more likely to be found in filaments and knots.Liao & Gao (2019) found that haloes in filament have higherbaryon fractions and stellar mass fractions compare to thosein the field.In recent years, cosmological hydro-dynamical simula-tions have gained great success in reproducing many ob-served galaxy properties (e.g. Vogelsberger et al. 2014;Schaye et al. 2015). In such simulations the cosmic web effectis taken into account automatically. Here we use the state-of-art cosmological hydrodynamical simulation, Evolution andAssembly of Galaxies and their Environments (EAGLE) todisentangle the connections between galaxies, dark matterhaloes and the cosmic web and revisit the relation betweengalaxy properties and geometric cosmic web structures.This paper is organized as follows. We introduce theEAGLE simulation and describe the environmental classifi-cation method in Section 2. The cosmic-web dependence ofthe various baryonic components and the scaling relationsare presented in Section 3 and Section 4, respectively. InSection 5, we summarize our results.
The EAGLE simulation consists of a series of cosmologi-cal simulations performed with a modified version of theN-body Tree-PM smoothed particle hydrodynamics (SPH)code GADGET-3 (Springel 2005). In this paper we use thelargest volume EAGLE simulation, labelled as L100N1504,which was carried out in a box of 100Mpc each side, tracing dark matter particles and an equal number of baryonicparticles. The initial mass of the gas particles is . × M (cid:12) and the dark matter particles mass is . × M (cid:12) . TheEAGLE simulations adopts the cosmological parameterstaken from the Planck results (Planck Collaboration et al.2014): Ω m = . , Ω Λ = . , Ω b = . , h = . , σ = . , n s = . and Y = . .The simulations used state-of-art numerical techniquesand subgrid physics including radiative cooling and photo-heating (Wiersma et al. 2009a), star formation law (Schaye & Dalla Vecchia 2008), stellar evolution and enrichment(Wiersma et al. 2009b), stellar feedback (Dalla Vecchia &Schaye 2012), and black hole seeding and growth (Springelet al. 2005; Rosas-Guevara et al. 2015). These models wereproven successful in reproducing many observed galaxyproperties including the galaxy stellar mass function, galaxysizes and the amplitude of the galaxy-central black holemass relation, etc. (Schaye et al. 2015). The friends-of-friends(FOF) method (Davis et al. 1985) was performed onthe particle data to generate FOF groups by linking particlesseparated by 0.2 times the average particle separation. Ineach FOF group, the SUBFIND (Springel et al. 2001; Dolaget al. 2009) algorithm was applied to identify the self-boundparticles as subhalos/substructures. M is adopted to referto the virial mass, which is the total mass within R withinwhich the average density is 200 times the critical density.Galaxies reside in the center of each substructure. The stellarmass is defined as the total mass of stellar particles within30 pkpc radii of the centre of each subhalo. The luminosityand color are calculated using a stellar population synthesismodel taking into account the SFR history and metallicityof each star particle (Trayford et al. 2015). In the publicEAGLE simulation catalog, it provides magnitudes in thefive rest-frame SDSS bands and 3 UKIRT bands. This sam-ple contains absolute rest-frame magnitudes for all galaxieswith M ∗ > . M (cid:12) . No dust attenuation has been included. The cosmic web present itself in large-scale surveys, as wellas in cosmological simulations. Many different approachesto classify the cosmic web elements have been developed inthe literature. The tidal tensor and the velocity shear tensorare two of the most popular quantities to identify the cosmicweb (see Libeskind et al. (2018) for a comparison of differentclassifications of the cosmic web). Here we follow Hahn et al.(2007) to use the tidal tensor to classify the four cosmic webelements.A region is identified as void, sheet, filament or knotaccording to the number of dimensions that this particularpatch collapses along. The tidal tensor T ij is given by theHessian matrix of the gravitational potential φ : T ij = ∂ φ∂ r i ∂ r j . (1)The gravitational potential φ from the matter density fieldis obtained using the Poisson’s equation: ∇ φ = δ, (2)where ρ denotes the mean mass density of the universe and δ = ρρ − denotes the density contrast. In practice, we splitthe simulation box into 256 cartesian cells and estimatethe density and density contrast by assigning the particlesto each cell using the cloud-in-cell method (Sefusatti et al.2016). We further smooth the discrete density field with aGaussian filter of width R s = . / h .There are three eigenvalues of the tidal tensor T i , j , λ ≥ λ ≥ λ . Hahn et al. (2007) used the number of pos-itive eigenvalues of T ij ( λ th = 0) to classify the four possi-ble environments. However, in reality, such criteria lead toan under-estimate of the filling factor of the voids. We fol-low Forero-Romero et al. (2009) to introduce an eigenvalue MNRAS , 000–000 (2020) alaxy properties in the cosmic web of EAGLE simulation x [ Mpc / h ] y [ M p c / h ] l o g ( + δ ) x [ Mpc / h ] y [ M p c / h ] VoidSheetFilamentKnot
Figure 1.
Left panel: Overdensity map of a slice of . / h thickness. The color bar denotes the values of logarithm of the overdensity.Right panel: The corresponding cosmic web elements generated using the method as described in Section 2.2. Red, cyan, blue and greenregions are for the knots, filaments, sheets and voids, respectively.Volume fraction Mass fractionRedshift Knot Filament Sheet Void Knot Filament Sheet Void0 0.010 0.168 0.416 0.406 0.279(0.268) 0.393(0.398) 0.239(0.244) 0.089(0.090)1 0.010 0.138 0.397 0.455 0.154(0.147) 0.355(0.358) 0.329(0.332) 0.162(0.163)3 0.007 0.083 0.331 0.579 0.042(0.042) 0.209(0.209) 0.392(0.392) 0.357(0.357)6 0.001 0.024 0.187 0.788 0.004(0.004) 0.057(0.057) 0.272(0.272) 0.667(0.667) Table 1.
Volume fraction and mass fraction in each cosmic web component in the EAGLE simulations at z ∼ , , , . Cols 1: redshifts;Cols 2, 3, 4, 5: volume fraction in knots, filaments, sheets and voids, respectively; Cols 6, 7, 8, 9: mass fraction in knots, filaments, sheetsand voids, respectively (numbers within brackets are for baryonic mass fraction only). threshold λ th , as a free parameter and define the cosmic webelements as following:(i) Void: all eigenvalues λ i below the threshold λ th ( λ th ≥ λ ≥ λ ≥ λ ).(ii) Sheets: two eigenvalues λ i below the threshold λ th ( λ ≥ λ th ≥ λ ≥ λ ).(iii) Filaments: one eigenvalues λ i below the threshold λ th ( λ ≥ λ ≥ λ th ≥ λ ).(iv) Knots: all eigenvalues λ i above the threshold ( λ ≥ λ ≥ λ ≥ λ th ).Here we adopt a fixed λ th = . at z = , , . , . .We test our results using different λ th at different redshiftsand find the results are in qualitative agreement with thosewith the fixed λ th . This is consistent with the conclusionsreached by Zhu & Feng (2017b). In Fig. 1, we show the mapof the overdensity and the corresponding cosmic web in aslice . / h thick at z = . The cosmic structures arewell captured by the tidal tensor method. Table 1 summarizes the volume fractions and mass fractionsin different cosmic web environments. At z =0 the volumefractions are . , . , . , . among the void, sheets,filaments and knots, while the total mass fractions locatedin each structure element are . , . , . , . . This is consistent with the results using Illustris simulation thatmost matter resides either in haloes or in filaments but verylittle in voids, though the voids contribute a significant frac-tion of the total volume (Haider et al. 2016). Both the vol-ume fraction and mass fraction of voids increase with red-shift, whilst they decrease in knots and filaments.For the baryon component, as expected, it is a goodtracer of the total matter at large scales across cosmic time(Cen & Ostriker 1999; Dav´e et al. 2001; Eckert et al. 2015).We find that the baryon fraction in knots and filaments de-creases dramatically with redshifts. Cui et al. (2019) reachedsimilar conclusions as ours, though their classification ofthe cosmic web adopted a different cell size and eigenvaluethreshold, indicating our results are qualitatively robustagainst the method of classification of the cosmic web. Inaddition, Cui et al. (2019) demonstrated that the baryonfraction in different components of the web and its evolu-tion depend only very weakly on the different physics imple-mented in the simulations.We further investigate the normalized baryon fraction( f bar / ¯ f = ( M bar / M )/( Ω b / Ω ) ) as a function of halo massin different cosmic web environments (Fig. 2), where ¯ f is theuniversal baryonic fraction 15.7%, f bar is the baryon fractionmeasured within R . It shows that the baryonic fractionis an increasing function of the halo mass in all web envi-ronments. The strong halo mass dependence of the baryonicfraction presents itself over all the redshifts from 0 to 6. Atz =0, only in massive clusters ( ∼ h − M (cid:12) ), the baryonicfraction does reach the universal value, while this fraction MNRAS , 000–000 (2020)
Wenxiao Xu et al. f b a r / ¯ f z = 0 . KnotFilamentSheetVoid z = 1 . M [h − M fl ] f b a r / ¯ f z = 3 . M [h − M fl ] z = 5 . Figure 2.
Baryon fraction as a function of halo mass in different cosmic web environments. The shaded regions indicate the th - th percentile scatter in each corresponding halo mass bin. Red, cyan, blue and green curves donate the median values of the baryonicfractions in knots, filaments, sheets and voids, respectively. Error bars present errors on the median values estimated based on 1000bootstrap samples. Redshifts are indicated on the top right corner of each panel. drops dramatically towards lower masses. At low masses,the overall baryonic fraction increases significantly with red-shifts. For example, for haloes of M ∼ h − M (cid:12) thebaryon fraction increases from . at z ∼ to . at z ∼ . .In the MassiveBlack-II simulation, Khandai et al. (2015)found an even stronger redshift evolution of the baryon frac-tion. Peirani et al. (2012) found a similar trend of the meanbaryonic fraction in groups over cosmic time using hydro-dynamical zoom-in simulations. They claimed that it is dueto the lower accretion rate of dissipative gas onto the haloescompared to that of dark matter at low redshifts. Anotherreason for the high baryon fraction at high redshifts is thatthe potential well is deeper and it is thus harder to ex-pel baryons out even for haloes of relatively low masses.On the other hand, for the massive systems (more mas-sive than h − M (cid:12) ) their baryonic fractions hardly changewith redshifts. Haloes of such masses have potential wellsdeep enough to keep most of their baryons both at low andat high redshifts.The baryonic fraction increases from voids, sheets, fil-aments towards knots. For haloes of h − M (cid:12) , the bary-onic fraction in voids is lower than that in knots by 0.8 dexat z=0. It is much stronger dependence than that foundby Metuki et al. (2015) who used simulations with differentsubgrid physics. This cosmic web dependence gets weaker to-wards lower masses and almost vanishes at h − M (cid:12) . Fig.2 also shows that in general the cosmic web dependence getsstronger with redshifts up to z =3, especially at low masses. At the highest redshift, z ∼
6, the cosmic web dependence getsweaker again.
In this section, we focus on the stellar mass and its rela-tion to the cosmic web. The cosmic web dependences of thegalaxy properties vs. stellar masses relations are presentedin Sec. 4.We show the stellar mass-to-halo mass ratio for centralgalaxies ( M (cid:63), central / M ) at various redshifts in Fig. 3. Aspresented by Schaye et al. (2015), the trend of the full sam-ple is consistent with that inferred by the subhalo abundancematching methods (e.g. Guo et al. 2011; Moster et al. 2013)at z = 0. A similar analysis is applied to the total stel-lar mass fraction ( M (cid:63), group / M , dotted curves), wherethe total stellar mass referred to is the total stellar masseswithin R . It peaks at ∼ h − M (cid:12) and drops fast bothtowards the low mass and high mass ends. Different fromthe stellar-to-halo mass ratio for central galaxies, the slopeat high masses is much flatter for the total stellar masses. Atlow masses, the central and total stellar mass to halo massratios are almost identical, indicating that satellite galaxiesand intra-cluster lights contribute more to massive systemsthan to low mass systems. These trends are found at red-shifts up to z ∼
3. At z = 6 no high mass systems are formeddue to the limited box size. The amplitudes of the centraland total stellar-to-halo mass ratios decrease towards higherredshifts, consistent with the finding from the subhalo abun-
MNRAS000
MNRAS000 , 000–000 (2020) alaxy properties in the cosmic web of EAGLE simulation M / M c r i t z = 0 . M cen / M M group / M KnotFilamentSheetVoid M [h − M fl ] z = 1 . M [h − M fl ] M / M c r i t z = 3 . M [h − M fl ] z = 5 . Figure 3.
Stellar mass-to-halo mass relation as a function of cosmic web environments. The solid curves account for stellar mass incentral galaxies while the dashed curves account for the total stellar mass within the corresponding virial radius. The Shade regionsindicate the th - th percentile scatter in each corresponding halo mass bin. Red, cyan, blue and green curves donate the medianvalues of the ratios in knots, filaments, sheets and voids, respectively. Errors are estimated based on 1000 bootstrap samples. Redshiftsare indicated on the top right corner of each panel. dance matching method (Moster et al. 2013) that the galaxyformation efficiency decreases slightly with increasing red-shifts.At z = 0 the central and total stellar mass-to-halo massratios decrease from knots to filaments to sheets and tovoids for haloes below ∼ h − M (cid:12) . In haloes of h − M (cid:12) ,where most of the dwarf galaxies reside, the ratios drop bya factor of ∼
2. At high masses, it is at the opposite. Inknots the ratios are the lowest while in voids the ratios arethe highest. At the peak location ( ∼ h − M (cid:12) ), about themass of the Milky Way’s halo, the central and total stel-lar mass-to-halo mass ratios do not vary between differentcosmic web environments. Such environmental dependenciesare also found at z=1, though somehow weaker than that atz=0. At even higher redshifts( z > ), the cosmic web depen-dence vanishes at low masses, and no statistical results canbe obtained at high masses due to the limited number ofhigh mass systems. Most stars are locked in galaxies. The fraction of galaxiesas a function of stellar mass in different cosmic web envi-ronments are shown in Fig. 4. In a given stellar mass bin,the fraction of galaxies in any cosmic web environment iscalculated by dividing the number of galaxies in the corre-sponding web environment by the total number of galaxies.In the top left panel, it shows that at z = 0 most of the massive galaxies reside in knots, consistent with previousresults (Metuki et al. 2015; Eardley et al. 2015). For galax-ies of the Milky Way mass and dwarf galaxies, most residein filaments, though a comparable, yet slightly lower frac-tion reside in knots. This is also found by Eardley et al.(2015) using GAMA data and Metuki et al. (2015) usingsimulations. Only a very small fraction of galaxies reside invoids at all masses considered here. The fractions in differ-ent cosmic web environments are similar at z = 1. At higherredshifts, more galaxies are found in voids and sheets thanat lower redshifts, while less is found in knots and filaments,especially at low masses.The dependence on the cosmic web is more significantwhen converting the total number of galaxies to the volumenumber density (the stellar mass functions) as shown in Fig.5. At z =0, the number density drops by two orders of mag-nitude from knots to voids. Such strong dependences are alsofound by theoretical work (Metuki et al. 2015) and observa-tional work (Alpaslan et al. 2015). Interestingly, we find themass at the knee (corresponding to L ∗ ) decreases by a fac-tor of ∼
8, with the value of . h − M (cid:12) in the knots and . h − M (cid:12) in voids. This change is dramatic given thatthe corresponding mass for the global stellar mass functionbarely changes since z ∼ MNRAS , 000–000 (2020)
Wenxiao Xu et al. F r a c t i o n z = 0 . z = 1 . M [ h − M fl ] F r a c t i o n z = 3 . M [ h − M fl ] z = 5 . KnotFilamentSheetVoid
Figure 4.
Fractions of galaxies in different web environments as a function of stellar mass at z ∼ , , . , . . Red, cyan, blue andgreen regions represent the fractions in knots, filaments, sheets and voids, respectively. Redshifts are indicated at the top right corner ofeach panel. -4 -3 -2 -1 d n / d L o g ( M ) [ ( M p c / h ) − ] z = 0 . z = 1 . M [h − M fl ] -4 -3 -2 -1 d n / d L o g ( M ) [ ( M p c / h ) − ] z = 3 . M [h − M fl ] z = 5 . KnotFilamentSheetVoidTotal
Figure 5.
The stellar mass functions in different cosmic web environments at different redshifts. Solid black curves are the overall stellarmass functions, while dashed ones are those for different environments with the same color coding as those in Fig. 4.MNRAS , 000–000 (2020) alaxy properties in the cosmic web of EAGLE simulation M , cen [h − M fl ] M c r i t [ h − M fl ] KnotFilamentSheetVoid
Figure 6.
The halo mass vs. stellar mass relation for centralgalaxies at z=0. The Shade regions indicate the th - th per-centile scatter in each corresponding stellar mass bin. Red, cyan,blue and green curves donate the median value of the ratios inknots, filaments, sheets and voids, respectively. Error bars aregenerated using the bootstrap method. The observed scaling relations are very important in reveal-ing the underlying physics of galaxy formation. In this sec-tion, we show how cosmic web environments affect the colorvs. stellar mass relation, specific star formation rate (sSFR)vs. stellar mass relation and stellar/gas metallicity vs. stel-lar mass relation. Since the environmental dependence ofsatellite galaxies are very much different from that of cen-tral galaxies (e.g. Peng et al. 2010), in this section we focuson central galaxies only.Previous work found that the cosmic web dependenceand the halo mass dependence are highly degenerate (e.g.Brouwer et al. 2016). Large scale web environments couldshape the galaxy properties through the halo mass for galax-ies properties depend strongly on halo mass (e.g. Metukiet al. 2015) and large scale structures affect halo masses sig-nificantly. We show in Fig. 6 that for a given stellar mass, thetypical halo mass varies in different cosmic environments.For galaxies with stellar mass below . × h − M (cid:12) , thehost haloes are less massive in knots, while for those withstellar mass above . × h − M (cid:12) , the host haloes are moremassive in knots. This is consistent with what we found inFig. 3. In order to disentangle the connections between thecosmic web, dark matter haloes and galaxies, we measurethe pure cosmic environmental effects by removing the darkhalo effects. In practice, for any quantity of interest, X , wecalculate R X as a function of the cosmic web environment,where R X is defined as: R X = X (cid:104) X | M (cid:105) − , (3)For each M at a given redshift, we calculate the averagevalue of X , (cid:104) X | M (cid:105) , in advance. R X quantifies the off-set of the property X that deviates from the expected values forgiven halo masses.For any quantity X that depends directly only on halomass, the mean of R X will equal 0 for any subsample, includ-ing one defined by stellar mass and environment, as below.By using R X , we can test whether an apparent dependence of X on environment at a given stellar mass is entirely driven bythe dependence of halo mass on environment at given stel-lar mass, or whether there is some remaining dependence onenvironment at fixed halo mass. Color is one of the most important observables for it is key tounderstand galaxies’ star formation history. Previous stud-ies found that galaxies on the color vs. stellar mass diagramcan be grouped into three categories, blue cloud (active),red sequence (passive) and green valley (those in between).Galaxies in low density environments (e.g. filaments, sheetsand voids) tend to be bluer, while those in high density en-vironments (knots) tend to be redder (Poudel et al. 2017).However, this could be caused by the fact that in low den-sity regions galaxies and their host haloes are smaller, whilesmaller galaxies are in general bluer (Cucciati et al. 2011;Baldry et al. 2006).Fig. 7 shows the g − r color vs. stellar mass relation as afunction of the environments and stellar mass. Observed col-ors can be influenced by dust extinction and we thus use theintrinsic color. For the color is a dimensionless quantity andcan be 0 in many cases, instead of using Eq. (3) we adopta slightly different quantity to remove the halo dependence.For each galaxy, we calculate R g − r = (g-r) - (cid:104)( g − r )| M (cid:105) .At z=0, for galaxies less massive than 1.8 × h − M (cid:12) , itshows a clear dependence on environments, especially forthose in knots. Galaxies in knots are redder than those invoids by 0.08 ma g (1.8 σ ). This is related to the fraction ofactive galaxies in different environments which we will dis-cuss in more detail in the next subsection. At stellar massesabove 1.8 × h − M (cid:12) , there is no clear cosmic web environ-mental dependence. The difference between voids and sheetsis weak across all the stellar mass ranges.The dependence on environments vanishes for galaxiesat high redshifts: z =1,3, and 6 at all masses. This is consis-tent with Darvish et al. (2017b) who found no cosmic webdependence of galaxy color in the COSMOS fields at z = 1. Colors are influenced by the star formation history, espe-cially the current star formation rate. Fig. 8 shows thespecific star formation rate (sSFR) as a function of stel-lar mass and cosmic environments. Similar to the color vs.stellar mass relation, at z=0, the cosmic environmental de-pendence is the strongest for galaxies with stellar mass lessthan . × h − M (cid:12) . The sSFR is lower by 50% in knotsthan that in voids. At higher masses, given the large scat-ters, we can not find clear environmental dependence. Thisis consistent with the observational results by Poudel et al.(2017) who found central galaxies in low-density environ-ments with higher sSFR compared to those in high-densityenvironments at a fixed group mass using group catalogs MNRAS , 000–000 (2020)
Wenxiao Xu et al. R g − r z = 0 . z = 1 . M [h − M fl ] R g − r z = 3 . M [h − M fl ] z = 5 . KnotFilamentSheetVoid
Figure 7.
The deviation of g − r color from the expected values as a function of stellar mass for central galaxies in different environments.Red, cyan, blue and green curves donate the median value of the deviation in knots, filaments, sheets and voids, respectively. Scatters arefor each galaxy with the same color coding as the curves. Error bars are generated using the bootstrap method. Redshifts are indicatedat the top right corner of each panel. R s S F R z = 0 . z = 1 . M [h − M fl ] R s S F R z = 3 . M [h − M fl ] z = 5 . KnotFilamentSheetVoid
Figure 8.
The deviation of specific star formation rate from the expected values as a function of stellar mass for central galaxies indifferent environments. Red, cyan, blue and green curves donate the median value of the deviation in knots, filaments, sheets and voids,respectively. Scatters are for each galaxy with the same color coding as the curves. Error bars are generated using the bootstrap method.Redshifts are indicated at the top right corner of each panel. MNRAS , 000–000 (2020) alaxy properties in the cosmic web of EAGLE simulation M [h − M fl ] R s S F R sSFR > − [ yr − ] M [h − M fl ] sSFR < − [ yr − ] z = 0 Figure 9.
The deviation of the sSFR from the expected values as a function of stellar mass in different environments for active(sSFR > − / yr , left panel) and passive (sSFR < − / yr , right panel) galaxies at z=0. Red, cyan, blue and green curves donate themedian value of the deviation in knots, filaments, sheets and voids, respectively. Error bars are generated using the bootstrap method. (Tempel et al. 2014) extracted from the SDSS DR10. Thecosmic environmental dependence is much weaker at highredshifts, broadly consistent with the results of Scoville et al.(2013) and Darvish et al. (2016). Different from the color vs.stellar mass relation, at z = 3 the sSFR is slightly higher inknots compared to that in other environments.Corresponding to the red sequence and blue cloud,galaxies can be separated into passive and active sub-populations using their specific star formation rates. Unlikegalaxy colors, sSFR is not affected by metallicity and starformation history. Here we adopt log (sSFR[/yr]) = -11 as thethreshold: galaxies with log (sSFR[/yr]) < -11 are referred toas passive galaxies, while those with log (sSFR[/yr]) > -11are taken to be active (star-forming) galaxies. The thresh-old value is fixed over cosmic time as its evolution is notvery strong (Matthee & Schaye 2019).The left panel in Fig. 9 shows the environmental de-pendence of the sSFR for active galaxies at z=0. For activegalaxies, no environmental dependences present themselvesexcept for those with masses ∼ . × h − M (cid:12) where thesSFR of central galaxies is lower in voids than in other cos-mic web environments. At higher masses, such dependencevanishes. For passive galaxies, as shown in the right panel,there is no environmental dependence over all the stellarmass ranges considered.The rather low sSFR in knots in the first panel of Fig. 8might be explained by their low fraction of active galaxies.The average active galaxy fraction increases from knots, fila-ments to sheets and voids, ranging from . , . , . , . ,respectively. When taking into account the expected ac-tive galaxy fraction for any given halo mass and the num-ber of haloes of the given mass in each cosmic web envi-ronment, the derived expected active galaxy fractions are . , . , . , . in knots, filaments, sheets, voids, respec-tively. To make it more clear, we redo this analysis in eachstellar mass bin and subtract the direct measurement of theactive galaxy fraction from the correspondingly expected ac-tive galaxy fraction. The results are presented in Fig. 10. It M [h − M fl ] R A c t i v e Figure 10.
The deviation of active fraction from the expectedvalues as a function of stellar mass for central galaxies in differentenvironments at z=0. Red, cyan, blue and green curves are for theknots, filaments, sheets and voids, respectively. shows that at masses below . × h − M (cid:12) , there are lessactive galaxies in knots than in filaments, sheets and voids. Itis the low fraction of active galaxies in knots that leads to thelow sSFR in knots. It also explains the redder color in knotsas shown in Fig. 7. Sobral et al. (2011) have also argued thatthe environment is responsible for star-formation quenchingin dense environments. In other words, denser environmentsincrease the possibility of galaxies to become quenched. Athigh masses, on the other hand, there is instead not muchdifference in the active fraction in different environments.As a consequence, the cosmic web dependences of the colorand sSFR also vanish.At high redshifts, most galaxies are star-forming andthere is almost no environmental dependence of the active MNRAS , 000–000 (2020) Wenxiao Xu et al. R Z S t a r z = 0 . z = 1 . M [h − M fl ] R Z S t a r z = 3 . M [h − M fl ] z = 5 . KnotFilamentSheetVoid
Figure 11.
The deviation of the stellar metallicity from the expected values as a function of stellar mass for central galaxies indifferent environments. Red, cyan, blue and green curves donate the median values of the deviation in knots, filaments, sheets and voids,respectively. Scatters are for each galaxy with the same color coding as the curves. Errors are generated using the bootstrap method.Redshifts are indicated at the top right corner of each panel. fraction: at z > , the active fraction approaches 1 in allcosmic web environments. The environmental dependenceof the sSFR thus vanishes. Metal enrichment is one of the most important processes ingalaxy evolution which involves the gas cooling, star forma-tion, supernova feedback, etc. Schaye et al. (2015) found thegas and stellar metallicity vs. stellar mass relations in EA-GLE are in broad agreement with observations for galaxiesmore massive than M (cid:12) , though at the low mass end therelations are not as steep as the observed ones.Fig. 11 shows the stellar metallicity vs. stellar mass rela-tion in the different cosmic web environment. At low masses( M (cid:63) ∼ . × h − M (cid:12) ) the metallicity is higher in knotsthan in other environments. This is related to the relationbetween stellar mass, metallicity and star formation rate, asdiscovered in previous works (e.g. Ellison et al. 2008; Man-nucci et al. 2010; Yates et al. 2012; De Rossi et al. 2015).Specifically, De Rossi et al. (2017) found that in EAGLEsimulations the metallicity of low-mass systems decreaseswith SFR for a given stellar mass. The high metallicity inknots is thus consistent with their low star formation ratesas shown in Fig. 8. Such environmental dependence is muchweaker at high redshifts.Different from the relation with sSFR and color, thestellar metallicity vs. stellar mass relation shows a strongdependence on cosmic environments at high masses. The metallicity increases from knots, filaments, sheets towardsvoids. This is consistent with the increasing central stel-lar mass-to-halo mass ratios along knots, filaments, sheetsand voids, i.e. more metals are generated if more stars areformed. Such dependence persists up to z=3. At even higherredshifts, there are not enough samples to make solid con-clusions.As for the sSFR, we split the galaxies into active andpassive subsamples at z = 0. The transition mass at M (cid:63) ∼ . × h − M (cid:12) presents itself both for the active and pas-sive galaxies, below which the metallicity is higher in knotswhile above which the metallicity is lower in knots. The en-vironmental dependence is stronger for passive galaxies thanfor active galaxies.The cosmic web dependences of the gas metallicity as afunction of stellar mass and redshift are presented in Fig. 13.Since there is very little gas in passive galaxies, here wefocus on active galaxies. At z=0, at stellar masses below . × h − M (cid:12) the gas metallicity is higher in knots, whileat high masses the difference between different web envi-ronments disappears. Different from other scaling relations,this cosmic web dependence of gas metallicity gets strongerat higher redshifts for massive galaxies. The gas metallicityis the lowest in knots and gets higher along filaments, sheetsand voids. MNRAS000
The deviation of the stellar metallicity from the expected values as a function of stellar mass for central galaxies indifferent environments. Red, cyan, blue and green curves donate the median values of the deviation in knots, filaments, sheets and voids,respectively. Scatters are for each galaxy with the same color coding as the curves. Errors are generated using the bootstrap method.Redshifts are indicated at the top right corner of each panel. fraction: at z > , the active fraction approaches 1 in allcosmic web environments. The environmental dependenceof the sSFR thus vanishes. Metal enrichment is one of the most important processes ingalaxy evolution which involves the gas cooling, star forma-tion, supernova feedback, etc. Schaye et al. (2015) found thegas and stellar metallicity vs. stellar mass relations in EA-GLE are in broad agreement with observations for galaxiesmore massive than M (cid:12) , though at the low mass end therelations are not as steep as the observed ones.Fig. 11 shows the stellar metallicity vs. stellar mass rela-tion in the different cosmic web environment. At low masses( M (cid:63) ∼ . × h − M (cid:12) ) the metallicity is higher in knotsthan in other environments. This is related to the relationbetween stellar mass, metallicity and star formation rate, asdiscovered in previous works (e.g. Ellison et al. 2008; Man-nucci et al. 2010; Yates et al. 2012; De Rossi et al. 2015).Specifically, De Rossi et al. (2017) found that in EAGLEsimulations the metallicity of low-mass systems decreaseswith SFR for a given stellar mass. The high metallicity inknots is thus consistent with their low star formation ratesas shown in Fig. 8. Such environmental dependence is muchweaker at high redshifts.Different from the relation with sSFR and color, thestellar metallicity vs. stellar mass relation shows a strongdependence on cosmic environments at high masses. The metallicity increases from knots, filaments, sheets towardsvoids. This is consistent with the increasing central stel-lar mass-to-halo mass ratios along knots, filaments, sheetsand voids, i.e. more metals are generated if more stars areformed. Such dependence persists up to z=3. At even higherredshifts, there are not enough samples to make solid con-clusions.As for the sSFR, we split the galaxies into active andpassive subsamples at z = 0. The transition mass at M (cid:63) ∼ . × h − M (cid:12) presents itself both for the active and pas-sive galaxies, below which the metallicity is higher in knotswhile above which the metallicity is lower in knots. The en-vironmental dependence is stronger for passive galaxies thanfor active galaxies.The cosmic web dependences of the gas metallicity as afunction of stellar mass and redshift are presented in Fig. 13.Since there is very little gas in passive galaxies, here wefocus on active galaxies. At z=0, at stellar masses below . × h − M (cid:12) the gas metallicity is higher in knots, whileat high masses the difference between different web envi-ronments disappears. Different from other scaling relations,this cosmic web dependence of gas metallicity gets strongerat higher redshifts for massive galaxies. The gas metallicityis the lowest in knots and gets higher along filaments, sheetsand voids. MNRAS000 , 000–000 (2020) alaxy properties in the cosmic web of EAGLE simulation M [h − M fl ] R Z s t a r sSFR > − [ yr − ] M [h − M fl ] sSFR < − [ yr − ] Figure 12.
The deviation of the stellar metallicity from the expected values as a function of stellar mass in different environments foractive (left panel) and passive (right panel) galaxies. Red, cyan, blue and green curves donate the median values of the deviation inknots, filaments, sheets and voids, respectively. Errors are generated using the bootstrap method. R Z S F , ga s z = 0 . sSFR > − [ yr − ] z = 1 . M [h − M fl ] R Z S F , ga s z = 3 . M [h − M fl ] z = 5 . KnotFilamentSheetVoid
Figure 13.
Similar to Fig. 11 but for gas metallicity of active galaxies.
We remove the halo effect from the cosmic web dependencein previous sections. However, it is difficult to obtain halomass observationally. Here we present the apparent cosmicweb dependence (including halo effects, hereafter we refer toit as combined dependence) on the scaling relations. Sincethe cosmic environmental effect is weak at high redshifts formost of the scaling relations, we focus on results at z=0. The top left panel of Fig. 14 shows the g-r color vs.stellar mass relations for galaxies in different environments.Galaxies are redder in knots compared to other environ-ments at all masses. This is different from the results shownin Fig. 7 that when removing halo effects at stellar massabove . × h − M (cid:12) galaxies in knots have similar colorsas those in filaments, sheets and voids. Such dependencesare also found in the sSFR vs. stellar mass relations (middleleft panel). These can be explained by the fact that there aremore massive haloes in high density regions and galaxies in MNRAS , 000–000 (2020) Wenxiao Xu et al. g − r KnotFilamentSheetVoid Z s t a r -12 -11 -10 -9 s S F R M [h − M fl ] Z S F , g a s M [h − M fl ] A c t i v e F r a c t i o n Figure 14.
The g − r color, sSFR, active fraction, stellar metallicity and star forming gas metallicity as a function of stellar mass forcentral galaxies in different environments. Red, cyan, blue and green curves donate the median values in knots, filaments, sheets andvoids, respectively. Each dot represent an individual galaxy with the same color coding as the curves. Errors are generated using thebootstrap method. massive haloes are usually redder/with lower sSFR. The ac-tive fraction increases with stellar mass up to ∼ × h − M (cid:12) and decreases towards higher masses. This variations withstellar mass are similar to each other between voids, sheetsand filaments. For those in knots, the amplitude is lower,the turn-over mass is higher, and at low masses the slope issteeper.For a given stellar mass, the halo mass is lower in knotsfor those with stellar mass below . × h − M (cid:12) (Fig. 6).In low mass haloes the feedback is usually more effectiveand it is thus easier for new formed heavy elements to es-cape. This compensate with the cosmic web dependence ofstellar metallicity as shown in Fig. 11, resulting in the ab-sence of variance between different environments as shown in the right top panel of Fig. 14. At high masses, the stellarmetallicity decreases with environmental densities, similarto those without halo effects (Fig. 11). For the gas metalli-cally vs. stellar mass relation (right bottom panel of Fig. 14),there is almost no difference between voids, sheets and fil-aments. On the other hand, the scaling relation in knots isvery different. It increases rapidly with stellar masses below . × h − M (cid:12) and also decreases towards high masses.The absolute values are lower in knots both at low and highmasses compared to other environments, but is higher at theturn over mass.In summary, for the color vs. stellar mass relation andsSFR vs. stellar mass relation, the combined dependence fol-lows the pure cosmic web dependence at low masses quanti- MNRAS000
The g − r color, sSFR, active fraction, stellar metallicity and star forming gas metallicity as a function of stellar mass forcentral galaxies in different environments. Red, cyan, blue and green curves donate the median values in knots, filaments, sheets andvoids, respectively. Each dot represent an individual galaxy with the same color coding as the curves. Errors are generated using thebootstrap method. massive haloes are usually redder/with lower sSFR. The ac-tive fraction increases with stellar mass up to ∼ × h − M (cid:12) and decreases towards higher masses. This variations withstellar mass are similar to each other between voids, sheetsand filaments. For those in knots, the amplitude is lower,the turn-over mass is higher, and at low masses the slope issteeper.For a given stellar mass, the halo mass is lower in knotsfor those with stellar mass below . × h − M (cid:12) (Fig. 6).In low mass haloes the feedback is usually more effectiveand it is thus easier for new formed heavy elements to es-cape. This compensate with the cosmic web dependence ofstellar metallicity as shown in Fig. 11, resulting in the ab-sence of variance between different environments as shown in the right top panel of Fig. 14. At high masses, the stellarmetallicity decreases with environmental densities, similarto those without halo effects (Fig. 11). For the gas metalli-cally vs. stellar mass relation (right bottom panel of Fig. 14),there is almost no difference between voids, sheets and fil-aments. On the other hand, the scaling relation in knots isvery different. It increases rapidly with stellar masses below . × h − M (cid:12) and also decreases towards high masses.The absolute values are lower in knots both at low and highmasses compared to other environments, but is higher at theturn over mass.In summary, for the color vs. stellar mass relation andsSFR vs. stellar mass relation, the combined dependence fol-lows the pure cosmic web dependence at low masses quanti- MNRAS000 , 000–000 (2020) alaxy properties in the cosmic web of EAGLE simulation tatively, while at high masses, the combined dependence isstronger. For the stellar metallicity vs. stellar mass, the com-bined dependence mimic the pure cosmic web dependenceat high masses, but vanish at low masses. The gas metalli-cally vs. stellar mass relation behaves significantly differentin knots compared to other environments, and the combineddependence deviate from the pure cosmic web dependenceat all masses. In this paper, we investigate the dependence of galaxy prop-erties on different cosmic web environments and their evo-lution, using the EAGLE cosmological hydrodynamical sim-ulations. We split the simulation box into cells andgenerate the web elements adopting the web classificationmethod of Hahn et al. (2007). Here we summarize our re-sults as follows.We find the baryon fraction increases with halo massin all environments, and the fraction is higher in denser re-gions, i.e. increasing along the sequence voids, sheets, fila-ments and knots. This environmental dependence persists upto redshift 6. The cosmic web dependence becomes slightlystronger at higher redshifts up to z ∼ and then becomesweaker towards even higher redshifts. The central and totalstellar mass-to-halo mass ratios both peak at halo masses ∼ h − M (cid:12) . At low masses, more stars are formed in knotsthan in other web environments, while at high masses, lessstars are formed in knots. The cosmic web dependence of thegalaxy stellar mass functions is very strong at all redshifts,with the amplitude decreasing along the sequence knots,filaments, sheets and voids. Interestingly, though the aver-age characteristic stellar mass corresponding to L ∗ does notevolve much since z=1, it changes by an order of magnitudegoing from knots to voids at z =0.We remove the halo mass dependence and investigatethe relation between the cosmic web and various scaling re-lations for central galaxies. We find a characteristic stellarmass of . × h − M (cid:12) , below and above which the cosmicweb dependence behaves oppositely. Galaxies with stellarmass below the characteristic mass are redder, with loweractive fraction, lower sSFR, and higher stellar metallicity inknots than in voids, while at stellar masses above the char-acteristic mass the dependences on the cosmic web eitherreverse or vanish. At low masses, the relatively strong webdependences of the color vs. stellar mass relation and of thesSFR vs. stellar mass relation can be attributed to the cos-mic web dependence of the active galaxy fraction, i.e. theactive fraction is higher in voids than in knots. For activegalaxies, the stellar metallicity is higher in knots comparedto other web environments for those with stellar mass belowthe characteristic mass.The cosmic web dependences are weaker at higher red-shifts for almost all the galaxy properties and scaling re-lations we explored, including the central (total) stellar-to-halo mass ratio, color vs. stellar mass relation, sSFR vs. stel-lar mass relation and stellar metallicity vs. stellar mass rela-tion. But this is not the case for the gas metallicity vs. stel-lar mass relation. For galaxies above the characteristic stel-lar mass, this cosmic web dependence gets even stronger at high redshifts, decreasing along the sequence voids, sheets,filaments and knots.The combined halo + cosmic web dependence follow thecosmic web dependence at low masses for the color/sSFRvs. stellar mass relations, but is stronger at high masses. Itreverses for the stellar metallicity at high masses, the com-bined dependence mimic the cosmic web dependence, whileat low masses, the combined dependence almost vanish. Onecan not use the combined dependence of gas metallicity rela-tion vs. stellar mass relation to explore the pure cosmic webdependence at all for they behave different at all masses. DATA AVAILABILITY
The data presented in this article are available at the EA-GLE simulations public database ( http://icc.dur.ac.uk/Eagle/database.php ). ACKNOWLEDGEMENTS
We thank Yingjie Jing and Marius Cautun for helpful dis-cussion. This work is supported by the National Key R & D Program of China (Nos 2018YFA0404503, 2016YFA0400703and 2016YFA0400702) and the National Natural ScienceFoundation of China(NSFC)(11573033, 11622325, 11133003,11425312, 11733010, 11633004). L.G. also acknowledges theNational Key Program for Science and Technology Re-search Development (2017YFB0203300). C.G.L was sup-ported by the Science and Technology Facilities Coun-cil [ST/P000541/1]. X.C. also acknowledges the NSFC-ISFjoint research program No. 11761141012, the CAS Fron-tier Science Key Project QYZDJ-SSW-SLH017, ChineseAcademy of Sciences (CAS) Strategic Priority ResearchProgram XDA15020200, and the MoST 2016YFE0100300,2018YFE0120800. Q.G., L.G. and C.G.L acknowledge sup-port from the Royal Society Newton Advanced Fellow-ships. This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capitalgrant ST/H008519/1, and STFC DiRAC Operations grantST/K003267/1 and Durham University. DiRAC is part ofthe National E-Infrastructure.
REFERENCES
Alpaslan M., et al., 2015, MNRAS, 451, 3249Baldry I. K., Balogh M. L., Bower R. G., Glazebrook K., NicholR. C., Bamford S. P., Budavari T., 2006, MNRAS, 373, 469Beare R., Brown M. J. I., Pimbblet K., Taylor E. N., 2019, ApJ,873, 78Brouwer M. M., et al., 2016, MNRAS, 462, 4451Cen R., Ostriker J. P., 1999, Astrophys. J., 514, 1Chen Y.-C., et al., 2017, MNRAS, 466, 1880Codis S., Pichon C., Devriendt J., Slyz A., Pogosyan D., DuboisY., Sousbie T., 2012, MNRAS, 427, 3320Correa C. A., Schaye J., Clauwens B., Bower R. G., Crain R. A.,Schaller M., Theuns T., Thob A. C. R., 2017, MNRAS, 472,L45Cucciati O., Iovino A., Kovaˇc K., 2011, Astrophysics and SpaceScience Proceedings, 27, 171Cui W., et al., 2019, MNRAS, 485, 2367Dalla Vecchia C., Schaye J., 2012, MNRAS, 426, 140MNRAS , 000–000 (2020) Wenxiao Xu et al.
Darvish B., Mobasher B., Sobral D., Rettura A., Scoville N.,Faisst A., Capak P., 2016, ApJ, 825, 113Darvish B., Mobasher B., Martin D. C., Sobral D., Scoville N.,Stroe A., Hemmati S., Kartaltepe J., 2017a, The Astrophysi-cal Journal, 837, 16Darvish B., Mobasher B., Martin D. C., Sobral D., Scoville N.,Stroe A., Hemmati S., Kartaltepe J., 2017b, ApJ, 837, 16Dav´e R., et al., 2001, ApJ, 552, 473Davis M., Efstathiou G., Frenk C. S., White S. D. M., 1985, ApJ,292, 371De Rossi M. E., Theuns T., Font A. S., McCarthy I. G., 2015,MNRAS, 452, 486De Rossi M. E., Bower R. G., Font A. S., Schaye J., Theuns T.,2017, MNRAS, 472, 3354Dolag K., Borgani S., Murante G., Springel V., 2009, MNRAS,399, 497Dubois Y., et al., 2014, Mon. Not. Roy. Astron. Soc., 444, 1453Eardley E., et al., 2015, MNRAS, 448, 3665Eckert D., et al., 2015, Nature, 528, 105Ellison S. L., Patton D. R., Simard L., McConnachie A. W., 2008,AJ, 135, 1877Forero-Romero J. E., Hoffman Y., Gottl¨ober S., Klypin A., YepesG., 2009, MNRAS, 396, 1815Ganeshaiah Veena P., Cautun M., van de Weygaert R., TempelE., Jones B. J. T., Rieder S., Frenk C. S., 2018, MNRAS, 481,414Gay C., Pichon C., Le Borgne D., Teyssier R., Sousbie T., De-vriendt J., 2010, MNRAS, 404, 1801Goh T., et al., 2019, MNRAS, 483, 2101Guo Q., et al., 2011, MNRAS, 413, 101Hahn O., Porciani C., Carollo C. M., Dekel A., 2007, MNRAS,375, 489Haider M., Steinhauser D., Vogelsberger M., Genel S., SpringelV., Torrey P., Hernquist L., 2016, Monthly Notices of theRoyal Astronomical Society, 457, 3024ˆa ˘A¸S3035Khandai N., Di Matteo T., Croft R., Wilkins S., Feng Y., TuckerE., DeGraf C., Liu M.-S., 2015, MNRAS, 450, 1349Kraljic K., et al., 2018, MNRAS, 474, 547Lange R., et al., 2015, MNRAS, 447, 2603Liao S., Gao L., 2019, MNRAS, 485, 464Libeskind N. I., et al., 2018, MNRAS, 473, 1195Mannucci F., Cresci G., Maiolino R., Marconi A., Gnerucci A.,2010, MNRAS, 408, 2115Martizzi D., Vogelsberger M., Torrey P., Pillepich A., HansenS. H., Marinacci F., Hernquist L., 2020, MNRAS, 491, 5747Matthee J., Schaye J., 2019, MNRAS, 484, 915Metuki O., Libeskind N. I., Hoffman Y., Crain R. A., Theuns T.,2015, MNRAS, 446, 1458Metuki O., Libeskind N. I., Hoffman Y., 2016, MNRAS, 460, 297Moster B. P., Naab T., White S. D. M., 2013, MNRAS, 428, 3121Peirani S., Jung I., Silk J., Pichon C., 2012, MNRAS, 427, 2625Peng Y.-j., et al., 2010, ApJ, 721, 193Planck Collaboration et al., 2014, A&A, 571, A1Poudel A., Hein¨am¨aki P., Tempel E., Einasto M., Lietzen H.,Nurmi P., 2017, A&A, 597, A86Rosas-Guevara Y. M., et al., 2015, MNRAS, 454, 1038Schaye J., Dalla Vecchia C., 2008, MNRAS, 383, 1210Schaye J., et al., 2015, MNRAS, 446, 521Scoville N., et al., 2013, The Astrophysical Journal SupplementSeries, 206, 3Sefusatti E., Crocce M., Scoccimarro R., Couchman H. M. P.,2016, Monthly Notices of the Royal Astronomical Society,460, 3624ˆa ˘A¸S3636Sobral D., Best P. N., Smail I., Geach J. E., Cirasuolo M., GarnT., Dalton G. B., 2011, MNRAS, 411, 675Springel V., 2005, MNRAS, 364, 1105Springel V., White S. D. M., Tormen G., Kauffmann G., 2001,MNRAS, 328, 726 Springel V., Di Matteo T., Hernquist L., 2005, MNRAS, 361, 776Tempel E., Kipper R., Saar E., Bussov M., Hektor A., Pelt J.,2014, A&A, 572, A8Trayford J. W., et al., 2015, MNRAS, 452, 2879Vogelsberger M., et al., 2014, MNRAS, 444, 1518Wiersma R. P. C., Schaye J., Smith B. D., 2009a, MNRAS, 393,99Wiersma R. P. C., Schaye J., Theuns T., Dalla Vecchia C., Tor-natore L., 2009b, MNRAS, 399, 574Yan H., Fan Z., White S. D. M., 2013, MNRAS, 430, 3432Yates R. M., Kauffmann G., Guo Q., 2012, MNRAS, 422, 215Zhang Y., Yang X., Faltenbacher A., Springel V., Lin W., WangH., 2009, The Astrophysical Journal, 706, 747ˆa ˘A¸S761Zhu W., Feng L.-L., 2017a, ApJ, 838, 21Zhu W., Feng L.-L., 2017b, ApJ, 838, 21This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000