Structural Evolution in the Galaxy-Halo Connection, and Halo Properties As a Function of Environment Density and Web Location

Quantifying and Understanding the Galaxy — Halo Connection July 7, 2017

Structural Evolution in the Galaxy-Halo Connection, and Halo Properties as a Function of Environment Density and Web Location

Joel Primack UCSC with collaborators including Aldo Rodriguez-Puebla, Christoph Lee, Peter Behroozi, Sandy Faber, Radu Dragomir, Tze Ping Goh, Miguel Aragon Calvo, Doug Hellinger, Anatoly Klypin, Viraj Pandya, Rachel Somerville, & Avishai Dekel Halo Demographics with Planck Parameters 17

Halo Demographics with Planck Parameters 15

Figure 18. Mean cumulative number of subhalos of maximum circular velocity Vsub for host halos with maximum velocities Vmax = 200, 500, 1000 and 1580 km /s as a function of Vsub/Vmax for (left panel) Vsub = Vacc,and(right panel) Vsub = Vpeak.Thedotted curve is the ﬁtting function Equation (47).

d Nsub(>Vsub Vmax) where Φsub(Vsub Vmax)= ⟨ | ⟩ . (48) | d log Vsub x f(x) ln(1 + x) . (53) Using this definition we can thus derive the maximum cir- ≡ − 1+x cular velocity function as: The Klypin concentration cvir,K can be found be solving Figure 21. Equation (52) numerically. It is more robustHalo than spin deter- distribution for the BolshoiP (upper left), SMDPL (bottom left) and MDPL (bottom right) simulations. Filled dnsub dnh grey circles show the λ distribution while the red circles show the λ distribution. Solid lines show the best fit to a Schechter-like = Φsub(Vsub Vmax) d log Vmax. (49) mining R by fitting the NFW profile, especially for halosP B d log Vsub | d log Vmax s function, Equation (57), while the dotted lines show the bestfitforalognormaldistribution,Equation(56).Theblack(blue) lines are ! with few particles, since halo profiles are not well deter- the best fits to the λB (λP )distributions.BothdistributionsarewellfitatlowvaluesbytheSchechter-likedistribution,whichalsoisa mined both at distances comparable to the simulation force good fit the the λP distribution at higher values, while λB is somewhat better fit by a log-normal distribution at higher values. 6 HALO CONCENTRATION AND SPIN resolution and also at large distances near Rvir.Figure19 shows that at high redshifts NFW concentrations are sys- 6.1 Halo concentrations tematically lower than Klypin concentrations.Table 7. Best Fitting fit parameters func- to the lognormal distribution func- which can be obtained from Equation (54) by assuming all High resolution N body simulations have shown that the tions for cvir,K are given in Klypin ettion al.P (2014)(log λ) ford log allλ. halos particles to be in circular orbits. Similarly to λP,thespin − density profile of dark matter halos can be well described by and for relaxed halos, for both Bolshoi-Planck/MultiDark- parameter λB correlates only weakly with halo mass espe- the Navarro, Frenk & White (1996, NFW) profile, Planck and Bolshoi/MultiDark simulations; fitting functions 4 cially at z = 0. We found that the median value for Milky 16 Simulation σP log λ0,P σB log λ0,B are also given there for concentrations of halos defined by Way mass halos at z =0isλ 0.035 and it decreases to 4ρ P s the 200c overdensity criterion.Halo DemographicsKey processes that drive with the PlanckTable Parameters 1. Numerical and cosmological parameters9 for the simulations analyzed in this paper. The columns give the simulation∼ ρNFW(r)= 2 . (50) BolshoiP 0.248 -1.423identifier 0.268 on the CosmoSim -1.459 website, the size of the simulatedλP box in0h−.1027Gpc, the at numberz =6.ForMilkyWaymasshalos,thedis- of particles, the mass per simulation −1 −1 (r/Rs)(1 + r/Rs) particle m in units h M⊙,thePlummerequivalentgravitationalsofteninglength∼ ϵ in units of physical h kpc, the evolution of halo concentration are also discussed there. p persion of λB is slightly larger than of λP;wefindthatitis SMDPL 0.249 -1.435adopted 0.268 values for -1.471ΩMatter, ΩBaryon, ΩΛ, σ8,thespectralindexns,andtheHubbleconstantH0 in km/s/Mpc. The The scale radius Rs is the radius where the logarithmic slope Diemer & Kravtsov (2015) discusses the relation between references for these simulations are (a) Klypin et al. (2014),0 (b).27 Klypin, dex Trujillo-Gomez at z =0anditdecreasesto & Primack (2011), (c) Prada et al. 0.2dexatz =6. (2012). of the density profile is -2. The NFW profile is completelyHalo haloand concentration, Subhalo the slopeDemographics of the fluctuation power with spec- Planck Cosmological ∼ ∼ Halo DemographicsMDPL 0.250 with –1.438 Planck 0.271 Parameters –1.443 9 The spin parameter λ slightly increases at high red- Simulation box particles mp ϵ ΩM ΩB ΩΛ σ8 ns H0 CodeB Ref. characterized by two parameters, for example ρs and Rs, trum and the peak height. < 12 Parameters: Bolshoi-Planck and MultiDark-PlanckBolshoiP 0Simulations.25 20483 1.5 × 108 1.00.shifts307 0.048 especially 0.693 0.823 for 0.96 low 67.8ART mass halos, aMvir 10 M⊙.Incon- The solid lines in the left panel of Figure 19 show the re- 3 7 or more usefully the halo mass, Mvir,anditsconcentration SMDPL 0.43840 9.6 × 10 1.50.307 0.048 0.693 0.829 0.96 67.8GADGET-2a ∼ 2 Aldo Rodrìguez-Puebla, Peter Behroozi, Joel Primack, Anatoly Klypin, ChristophMDPL 1Lee,.03840 Doug3 1.5 ×Hellinger109 50.trast,307 0.048 the 0.693 value 0.829 of 0.96 the 67. spin8GADGET-2a parameter λP shows a system- parameter, cvir.Theconcentrationparameterisdefinedas sulting Klypin concentrations byHalo solving Demographics Equation (52) with and Planck Parameters 9 Bolshoi 0.25 20483 1.3 MNRAS× 108 1.00.atic270 2016 0 decrease.047 0.730 as0.820 redshift 0.95 70.0ART increases. This b was previously noted the ratio between the virial radius R and the scale radius Cosmologicalusing the bestSimulations fitting values for the Vmax Mvir relation 3 9 vir deed, techniquesHalo− Mass such as Function subhalo abundance matchingMultiDark and 1.02048 8.7 × 10 7.00.over270 0. the047 0 interval.730 0.820z 0.=095 70.0ART2byHetznecker&Burkert(2006), c Rs: from Section 3.1, see Equation (5).halo At occupationz =0and distributionz =1the models require as inputs the Vmax(Mvir, z) − 2 the spin parameterand FitsλP correlates only weakly with halo mass

iue1. Figure ae ovle sue ncosmological in assumed values to pared h bevtospotdaea olw:WMAP5+BAO+SN follows: as are plotted observations The Hnhwe l 09,WMAP7+BAO+ 2009), al. et (Hinshaw who attribute the different evolution of the two spin param- 01,WMAP9+eCMB+BAO+ 2011), lnk3W+ih+A Pac olbrto ta.2014) al. et Collaboration (Planck Planck13+WP+highL+BAO n lnk5T,EE+oPlniget(lnkCollabo (Planck Planck15+TT,TE,EE+lowP+lensing+ext and aine l 2015a). al. et ration ie Wto ta.21) akk Sila ta.21) Q 2014), al. et (Skillman DarkSky 2013), al. et (Watson bilee otnu Himn ta.2015), al. et (Heitmann Continuum 05,adBlhiPac n utDr-lnk(Klypin MultiDark-Planck and Bolshoi-Planck and 2015), ta.21)smltos iue1sosteWMAP5/7/9 the shows 1 Figure simulations. 2014) al. et Hnhwe l 03)adPac 03(lnkCollabo- (Planck 2013 Planck and 2013b) al. et (Hinshaw aine l 04 n lnk21 Pac Collaboration (Planck 2015 Planck and 2014) al. et ration ta.21a omlgclparameters cosmological 2015a) al. et omlgclprmtr dpe o hs iuain.Th simulations. these for adopted parameters cosmological ilnimsmltosue h rtya WA1 pa- (WMAP1) first-year the used simulations Millennium aees(pre ta.20) h oso,QContinuum, Q Bolshoi, the 2003); al. et (Spergel rameters halo/subhalo number densities. Furthermore, simplified pre- n uie iuain sdteWA57cosmological WMAP5/7 the used simulations Jubilee and aaees hl the while parameters; sdtePac 03prmtr,adteDrSysimula- DarkSky the and parameters, 2013 Planck the used in sdprmtr ewe MP n lnk2013. Planck and WMAP9 between parameters used tions

Bhoz,Wcse u21)and 2013) Wu & Wechsler (Behroozi, Bhoz ta.21)t nlz eut o h re- the for results analyze to 2013) al. et (Behroozi etBlhiPac Blhi) ml MultiDark-Planck Small (BolshoiP), Bolshoi-Planck cent resulting concentrations are in very good agreement with SDL n utDr-lnk(DL simulations (MDPL) MultiDark-Planck and (SMDPL) ae nte21 lnkcsooia aaees(Planck parameters cosmological Planck 2013 the on based olbrto ta.21)adcmail ihtePlanck the with compatible and 2014) al. et Collaboration 05prmtr Pac olbrto ta.21a.The 2015a). al. et Collaboration (Planck parameters 2015 osoP MP n DLsmltosaentthe not are simulations MDPL and SMDPL BolshoiP, ags ftenwhg-eouinsmltos u hydo they but simulations, high-resolution new the of largest aeteavnaeta hyhv enaaye ngreat in analyzed been have they that advantage the have eal n l fteeaaye r en aepublicly made being are analyses these of all and detail, vial.I diin nti ae eso h e the show we paper this in addition, In available. h hnefo h MP/ otePac 03cosmo- 2013 Planck the to WMAP5/7 the from change the oia parameters. logical rlbschl rpris paigtersaigrelatio scaling their updating properties, halo basic eral af u n c t i o no fr e d s h i f tf o rt h eP l a n c kc o s m o l o g i c a lp a r a m e - esa ela h esiteouino aosbaonumbe halo/subhalo of evolution redshift the as well as ters este.Frtemjrt fteehl rprisw repo we properties halo these of majority the For densities. tigfntosta a evr sflntol ogi in- gain to only not useful very be can that functions fitting ih bu h aosbaopplto u lofrthe for also but population halo/subhalo the about sight aayhl oncinadtu o aayeouin In- evolution. galaxy for thus and connection galaxy-halo Rvir scriptionsespecially for the at z evolution=0.ThemedianvalueforMilkyWaymass of dark matter halo properties eters mainly to different effects of minor mergers on λP and cvir = . (51) what is found in the simulation with an accuracy of 3% 12 −1 4 2 halos (i.e., with M 10 h M⊙)atz =0isλ 0.036, Rs 10 −1 are ideal tools for people∼ interestedvir in understanding average P λ0B. for halos above Mvir =10 h M⊙.However,athigherred-∼ ∼ nti ae euethe use we paper this In properties of halos and the galaxies that they host. nti ae efcso h cln eain fsev- of relations scaling the on focus we paper this In and it decreases a factor of 1.8atz =6,thatis,λP 60.02. Figure 19 shows halo concentrations, cvir,asafunction ∼ ∼ shifts z =2, 4, 6, our predicted KlypinForHere concentrations Milky we analyze Way massall havedark halos, matter the halos dispersion and subhalos is approximately Figure 21 quantifies in more detail the distribution of of Mvir for redshifts z =0, 1, 2, 4, and 6. The left panel an accuracy of 10%. found by Rockstar,anddonotjustfocusonthosethatsat-z = 8 halo spins separately for the BolshoiP, SMDPL and MDPL ∼ isfy0 some.24 criteria dex at forz =0anditdecreasesto being “relaxed” or otherwise “good,”0.16 dex at z =6. of the figure shows halo concentrations calculated by find- ∼ ∼ simulations. In order to avoid resolution effects and to obtain ing the best scale on radius, constraints Observational R assuming a NFW profile for inNote contrast that to some the earlier dispersion studies of is dark not matter symmetric, halo prop- meaning that s erties (e.g., Bett et al. 2007; Macciòet al. 2007; Ludlow reliable statistics, we calculate the distribution of halo spins the distribution of λP is not a lognormal distribution. This 11 14 −1 each halo in the simulation. Instead, the right panel shows 6.2 Halo Spin et al. 2014). The reason is that all sufficiently massive halos ⊙ Figure 19. Halo concentration as a function of M at z =0, 1, 2, 4, and 6. The left panel in the figure shows halo concentrations in the halo mass range 10 10 h M for the BolshoiP vir areis expectedconsistent to host with galaxies previous or, for findings the more massive based ones, on highZero-point resolution − halo concentrations calculated by determining thecalculated scale ra by- finding the scale radius, R assuming a NFW profile in the simulation. Instead, the right panel shows Klypin halo (upper left panel) and SMDPL (bottom left panel) simula- The left panels of Figure 20 shows thegroupsN mediansbody or clusters simulations for of thegalaxies. spin (e.g., Bett et al. 2007). offset dius, Rs using the Vmax and Mvir relationship fromconcentrations the NFW from determining the scale radius, Rs using the Vmax and Mvir relationship from the NFW formulae (see text). Solid lines −This paper is an introduction to a series of papers tions, while for the MDPL (bottom right panel) simulation formulae, see Klypin, Trujillo-Gomez & Primack (2011)in the left and panel show theparameter resulting KlypinλP as concentrations a function bysolvingEquation(52)andusingthebestfittingvaluesfort of Mvir at zThe=0 right, 2, 4, panel6, and of 8. Figure 20 showshe Vmax the− M spinvir distribution 12 14 −1 relation from Section 3.1. presenting additional analyses of the Bolshoi-Planck and we do the same but for the mass range 10 10 h M⊙.

ν The spin parameter for every halocalculated in the simulations using the was alternative deﬁnition (Bullock et al. Klypin et al. (2014); (see also, Behroozi, WechslerFigureFigure 7.& Left Wu 1. Observational Panel: The halo constraints mass function on σ8 fromand zΩ=0toM com-z =9.RightMultiDark-Planck Panel: Cumulative simulations. halo mass The function. statistics The and various physica solidl −

2 In all the panels the grey filled circles show the distribution pared to values assumedHalo in cosmologicalSpin ParametersN−body simulations. as2001a): a function of M CadBlhiPac simulations Bolshoi-Planck and GC 2013). For the NFW profile, the radius at whichlines the show circu- the fits to thecalculated simulations, Equation using the (25). definition (Peeblesmeaning 1969): of halo concentration are discussedvir in detail in Figure 7. Left Panel: The haloThe mass observations function plotted from arez as=0to follows: WMAP5+BAO+SNz =9.Right Panel: Cumulative halo mass function. The various solid for λP while the red filled circles show the distribution for Figure 7. Left Panel: The halo mass function from z =0toz =9.KlypinRight et al. Panel: (2014), whichCumulative is also an overview halo massFigure of the 3. function. Left Bolshoi Panel:- Maximum The various halo circular solidvelocity, Vmax,asafunctionofMvir at z =0, 2, 4, 6and8.Mediansareshownasthe lar velocity is maximized is Rmax =2.1626Rs (Klypin(Hinshaw et al. et al. 2009), WMAP7+BAO+1/2 H (Jarosik et al. lines show the fits to the simulations, Equation (25). J E 0 Planck and MultiDark-PlanckJ simulations,solid including lines for the Big- BolshoiP and MDPL simulations, filled cirλclesB are.Asanticipatedfromthe the medians of the SMDPL simulation. At λz =0thegreybandisMvir relationship, the log λ lines show the fits to the simulations, Equation (25). the 68% range of the maximum circular velocity. The dotted lines show the fits to the simulation. A single power law is able toreproduce 2011), WMAP9+eCMB+BAO+λP = | H0| (Hinshaw, et al. 2013a), λB = (54), −1 3 We have released(55) the − 2001; Behroozi, Wechsler & Wu 2013), and it can be shown 5/2 MultiDark simulations in (2.5h Gpc) volumesthe results from that the we simulation. The slopes are approximately independent of redshift with a value of ∼ 1/3. Right Panel: The highest Planck13+WP+highL+BAO (Planck Collaboration et al. 2014), √2MvirVvirRvir distributions are asymmetrical. This is more evident for λP H GMvir maximum circular velocity reached along the main progenitorbranch,Vpeak,asafunctionofMvir at z =0, 2, 4, 6and8.Similarlyto that and Planck15+TT,TE,EE+lowP+lensing+ext (Planck Collabo- do not discuss here since they are mainly useful forhalo statis- catalogs and the Vmax panel, medians are shown as the solid lines. At z =0thegreybandisthe1σ (68%) range of the maximum circular velocity. 0 ration et al. 2015a). where J and E are the total angulartics of momentum galaxy clusters. and The theStellar Halo AccretionThe dotted Rate linesmerger show Co- the fits trees to the simulation. from Also, the slopes are approximately independent of redshift with a value of ∼ 1/3. cvir 2 Rvir 2.1626 evolution⃝c 2016 (SHARC) RAS, MNRAS assumption—i.e.,000,1–?? that the star forma-

Hnhwe l 2013a), al. et = (Hinshaw Vmax (52) Rockstar f(cvir) GMvir f(2.1626) total energy of a halo of mass Mvirtion.Asothershavefound, rate of central galaxies on the main sequenceBolshoi-Planck of star and

ν ( 6.1 shows that for the NFW radial halo mass distribution, Distinct halos can lose mass due to stripping events as bilee (Watson et al. 2013), DarkSky (Skillman et al. 2014), Q formation is proportional to their host halo’s§ mass accretion 2 Rmax =2.1626MultiDark-PlanckRs.) Because Vmax characterizes the inner aresultofinteractionswithotherhalos.Inconsequence, 2 ×

N C(siaae al. et (Ishiyama GC Continuum (Heitmann et al. 2015), ν GC (Ishiyama et al. rate—was explored in Rodr´ıguez-Puebla ethalo, al. (2016), it may correlate which better with the properties of the cen- the maximum halo circular velocity Vmax can signiﬁcantly ossetTrees Consistent ⃝c 2016 RAS, MNRAS 000,1–??

8 H tral galaxy thancosmologicalMvir does. The left panel of Figure 3 shows decrease. This reduction in Vmax can introduce an extra − 2015), and Bolshoi-Planck and MultiDark-Planck (Klypin used abundance matching based on the Bolshoi-Planck sim- σ the medians of the maximum halo circular velocity, Vmax, source of uncertainty when relating galaxies to dark mat-

0 and

8 oysimulations. body et al. 2014) simulations. Figure 1 shows the WMAP5/7/9 ulation. That paper showed that SHARC is remarkably con- as a functionsimulations. of Mvir at z =0, 2, 4, 6and8,solidlines.The Our paper ter halos, since it is expected that stripping would aﬀect (Hinshaw et al. 2013b) and Planck 2013 (Planck Collabo- sistent with the observed galaxy star formationgrey band rate at outz = 0 to shows the 68% range of the maximum halos more signiﬁcantly than the central galaxies deep in-

Jrske al. et (Jarosik and Decreases with includes Appendices ration et al. 2014) and Planck 2015 (Planck Collaboration z 4andthatthe 0.3dexdispersioninthehalomasscircular velocity, i.e., the halo distribution between the 16th side them. Therefore, in the case of stripped halos, the cor-

Ω ∼ ∼ and 84th percentiles. We ﬁnd that the 68% range of the relation between the present Vmax of the halo and galaxy et al. 2015a) cosmological parameters σ8 and ΩM ,andthe accretion rate is consistent with the observed small disperwith- instructions for

aofinder halo distribution is approximately independent of redshift and stellar mass/luminosity is not trivial. Indeed, Moster et al. M increasing z cosmological parameters adopted for these simulations. The sion of the star formation rate about the main sequence. The halo mass, withreading a value of 0these.05 dex. In files. general, the Vmax– (2010) and Reddick et al. (2013) found that the highest Ω ∼ ,andthe Millennium simulations used the first-year (WMAP1) pa- clustering properties of halos and subhalosM isvir therelation subject follows of a power law-fit at all redshifts and over maximum circular velocity reached along the halo’s main

M the mass range where we can resolve distinct halos in the progenitor branch, Vpeak,isabetterhaloproxyforgalaxy ﬀ rameters (Spergel et al. 2003); the Bolshoi, Q Continuum, Rodriguez-Puebla et al. 2016b (in prep.). How properties ofhttp://hipacc.ucsc.edu/10.2 Bolshoi-Planck simulations, Mvir 10 M⊙.Toagood stellar mass/luminosity. For these reasons we ﬁnd it useful csof ects and Jubilee simulations used the WMAP5/7 cosmological dark matter halos vary with the density of their environment ∼ approximation, the Vmax–Mvir slope is given by α 1/3, to report the Vpeak–Mvir relation in this paper. com- Bolshoi/MergerTrees.html 2 −1 ∼ sas ns parameters; while the ν GC and Bolshoi-Planck simulations on length scales from 0.5 to 16 h Mpc isas discussed expected from in Lee spherical collapse. In reality, however, the The right panel of Figure 3 shows the redshift evolu- used the Planck 2013 parameters, and the DarkSky simula- Figureet al. (2016a, 9. Characteristic in prep.), which halo mass showsM amongC as aslope functionother depends things of redshift. slightly that on redshift as we will quantify below. Medians are shown as the solid lines. At z = 0 the grey area is the 68% range. tion of the highest maximum circular velocity reached along

- e , The red solid line shows the numerical solution to Equation (31). rt halos in low-density regions experience lower tidal forces Figuretions used 20. parametersSpin parameter between as a function WMAP9 of M and Planckat z =0 2013., 2, 4, 6, and 8. Medians are shown as the solid lines. At z =0thegreyareais r vir Rockstar Theand dashed have lower black spin line parameters, shows our numerical and that fit a largeto MC fractiongiven by ⃝c 2016 RAS, MNRAS 000,1–?? Figurethe 68% 8.InAmplitude range this of paper the of distribution. linear we use perturbations, the The left panelσ(Mvir of),halo this as afigur finderfunc-eshowsthespinparametercalculatedusingEquation(54)while the right Consistent Trees Equation (29). tionpanel(Behroozi, of M showsvir.Theredsolidlineshowsthenumericalsolutionto theWechsler spin parameter & Wu 2013) calculated and using Equation (55). of lower-mass halos in high-density regions are “stripped,” Equation(Behroozi (26). The et al. dashed 2013) black to line analyze shows results the fit to for the the ampli re-- i.e. their mass at z =0islessthanthatoftheirprogeni-

ed ehiussc ssbaoaudnemthn and matching abundance subhalo as such techniques deed, aoocpto itiuinmdl eur sipt the inputs as require models distribution occupation halo aosbaonme este.Frhroe ipie pr simpliﬁed Furthermore, densities. number halo/subhalo citosfrteeouino akmte aoproperties halo matter dark of evolution the for scriptions r da ol o epeitrse nudrtnigaver understanding in interested people for tools ideal are rpriso ao n h aaista hyhost. they that galaxies the and halos of properties

on by found sysm rtrafrbig“eae”o tews “good,” otherwise or “relaxed” being for criteria some isfy ncnrs osm ale tde fdr atrhl prop- halo matter dark of studies earlier some to contrast in ris(.. ete l 07 ac` ta.20;Ludlow 2007; al. Macciò et 2007; al. et Bett (e.g., erties ta.21) h esni htalsu all that is reason The 2014). al. et r xetdt otglxe r o h oemsieones, massive more the for or, galaxies host to expected are ruso lseso galaxies. of clusters or groups rsnigadtoa nlsso h oso-lnkand Bolshoi-Planck the of analyses additional presenting utDr-lnksmltos h ttsisadphysica and statistics The simulations. MultiDark-Planck enn fhl ocnrto r icse ndti in detail in discussed are concentration halo of meaning lpne l 21) hc sas noeve fteBolshoi the of overview an also is which (2014), al. et Klypin lnkadMliakPac iuain,icuigBig- including simulations, MultiDark-Planck and Planck utDr iuain n(2 in simulations MultiDark ontdsushr ic hyaemil sflfrstatis- for useful mainly are they since here discuss not do iso aaycutr.TeSelrHl crto aeCo- Rate Accretion Halo Stellar The clusters. galaxy of tics vlto SAC supinie,ta h trforma- star the that assumption—i.e., (SHARC) evolution inrt fcnrlglxe ntemi euneo star of sequence main the on galaxies central of rate tion omto spootoa oterhs aosms accreti mass halo’s host their to proportional is formation aewsepoe nRd´ge-ubae l 21) whic (2016), Rodr´ıguez-Puebla al. in et explored rate—was sdaudnemthn ae nteBlhiPac sim- Bolshoi-Planck the on based matching abundance used tors at higher redshifts. Another paper (Lee et al., 2016b, lto.Ta ae hwdta HR srmral con- remarkably is SHARC that showed paper That ulation. itn ihteosre aaysa omto aeotto out rate formation star galaxy observed the with sistent z cent Bolshoi-Planck (BolshoiP), Small MultiDark-Planck crto aei ossetwt h bevdsaldisper small observed the with consistent is rate accretion ino h trfrainrt bu h ansqec.The sequence. main the about rate formation star the of sion tude of perturbations given by Equation (29). lseigpoete fhlsadsbao stesbeto subject the is subhalos and halos of properties clustering orge-ubae l 06 i rp) o rprisof properties How prep.). (in 2016b al. et Rodriguez-Puebla akmte ao aywt h est fterenvironment their of density the with vary halos matter dark nlnt clsfo . o16 to 0.5 from scales length on ta.(06,i rp) hc hw mn te hnsthat things other among shows which prep.), in (2016a, al. et ao nlwdniyrgoseprec oe ia forces tidal lower experience regions low-density in halos n aelwrsi aaees n htalrefraction large a that and parameters, spin lower have and flwrms ao nhg-est ein r “stripped, are regions high-density in halos lower-mass of ..terms at mass their i.e. osa ihrrdhfs nte ae Lee l,2016b, al., et (Lee paper Another redshifts. higher at tors npe. tde h asso aosrpigadpropertie and stripping halo of causes the studies prep.) in fsc tipdhls ute aescmaigwt ob- with comparing papers Further halos. stripped such of evtosaeas npeaain ln ihmc galaxy mock with along preparation, in also are servations aaosbsdo Bolshoi-Planck. on based catalogs ltosadhww en h aomass. halo the define we how and ulations e cln eain o itnthls(.. hs hta that those (i.e., halos distinct for relations scaling key o uhls n ie grsadfitn omlsfrmax- for formulas fitting and figures gives and subhalos) not mmhl iclrvlct ( velocity circular halo imum ( uhl ( subhalo o safnto fterhs aoms ( mass halo host their of function a as los h aoadsbaovlct functions. velocity subhalo and halo the aetePac omlg aoms n eoiyfunctions velocity and mass halo cosmology Planck the pare ihtoefo h MP/ omlgclparameters. cosmological WMAP5/7 the from those with icse h eedneo aocnetainadsi on spin and concentration halo of dependence the discusses asadredshift. and mass ihradFbrJcsnrltosbtenhl circular halo between relations Faber-Jackson and Fisher velocity (SMDPL) and MultiDark-Planck (MDPL) simulations havein prep.) found studies slopes the between causesα of halo1.4 stripping1.6(Blantonetal.2005; and properties § Table 8. Best fit parameters to Schechter-like distribution functionforP (log λ)d log λ.

∼ ∼ − .)adms rwh( growth mass and 3.2) based on the 2013 Planck cosmological parameters (Planck Baldry,of such Glazebrook stripped halos. & Driver Further 2008; papers Baldry comparing et al. 2012) with mean- ob-

eew analyze we Here hsppri nitouto oasre fpapers of series a to introduction an is paper This ing that, for some reason, the star formation efficiency in low 4andthatthe Collaboration et al. 2014) and compatible with the Planck servations are also in preparation, along with mock galaxy hsppri raie sfollows: as organized is paper This halo mass function using the bestSimulation fit parametersα fromβ table log λ Figureα 9.β Characteristiclog λ halo mass MC as a function of redshift. P P 0mass,catalogsP halosB based hasB on been Bolshoi-Planck. suppressed0,B (e.g. Behroozi, Wechsler & 3. 2015 parameters (Planck Collaboration et al. 2015a). The The red solid line shows the numerical solution to Equation (31). BolshoiP, SMDPL and MDPLBolshoiP simulations 4.126 are not 0.610 the -2.919Conroy 3.488This 2013b; paper 0.6042 Moster, is organized -2.878 Naab as & follows: White2 2013). discusses Nevertheless, the sim- FigureRockstar 10 shows the ratio of the number densities nBP § largest of the new high-resolution simulations, but they do measurementsulationsThe dashed and how of we blackthe define baryonic line the shows halo mass mass. have our3describesthe found numerical slopes fit as to MC given by V

§ Figure 8. Amplitudeand nB between of linear the perturbations, Bolshoi-PlanckSMDPL andσ(M thevir 4.090), Bolshoi as a 0.612Figure func- sim- -2.917 9. Characteristic 4.121 0.611 -2.916 halo mass M § as a function of redshift.

.)nme este,adtenme fsubha- of number the and densities, number 4.2) max have the advantage that they have been analyzed in great steepkeyEquation scaling as α relations1. (29).9(Baldry,Glazebrook&Driver2008). for distinct halos (i.e.,C those that are ulations as a function of M from z =0toz =8.The tion of Mvir.Theredsolidlineshowsthenumericalsolutiontodetail, and all of these analysesvir are being made publicly not subhalos)∼ and gives figures and fitting formulas for max- different cosmological parameters implyMDPL that 4.047 at z =0,on 0.612The red -2.914 solid 3.468 line 0.591 shows -2.907 the numerical solution to Equation (31). Equation (26). Theavailable. dashed In addition,black line in this shows paper the we fit show to the the eff ampliects of- imum halo circular velocity ( 3.1), halo mass accretion rates average, there are 12% more Milky-Way mass halos inThe the dashed black line shows§ our numerical fit to M given by n h tla aso h eta galaxies central the of mass stellar the and C Figure 8. Amplitudetude of of linear perturbations perturbations,the change given from by∼σ the Equation(M WMAP5/7), as (29). to a the func- Planck 2013 cosmo- 4.2( 3.2) Subhalo and mass mass growth function ( 3.3). 4discusseshalo(4.1) and Bolshoi-Planck than in thevir Bolshoi simulation. This fraction § have found slopes§ between§ α 1.4 §1.6(Blantonetal.2005; logical parameters. 13Equationsubhalo (29). ( 4.2) number densities, and the number of subha- z tion of M .Theredsolidlineshowsthenumericalsolutiontoincreases to higher masses, 25% for Mvir 3 10 M⊙. Subhalos§ can lose a significant fraction∼ of their− mass due vir In,a n dd this on o tj u paper s tf o c u so we nt h o s focus et h a ts aon t - the scaling relations of sev- los as a function of their host halo mass ( 4.3). 5presents ∼ ∼ × Baldry, Glazebrook⃝c &2016 Driver RAS, 2008; MNRAS§ § Baldry000,1–?? et al. 2012) mean-

§ ∼ This fraction also increases with redshift, and we find that to tidal striping. Since tidal stripping affects the dark mat- =0i sl e s st h a nt h a to ft h e i rp r o g e n i - Equation (26). The dashed black lineeral basic shows halo properties,the fit to updating the ampli their scaling- relations as the halo and subhalo velocity functions. 4and 5alsocom-

7d i s c u s s e st h ee v o l u t i o no ft h eT u l l y - all § § at zafunctionofredshiftforthePlanckcosmologicalparame-=2, 4and6thereare 25, 40 and 60% more Milky- terpareing more the that, Planck than for the cosmology some stars of reason, halo the mass central the and galaxyvelocity star formation deep functions inside eﬃciency in low

0 tude of perturbationshalo given mass by function Equation using (29). the best ﬁt∼ parameters from table Wayters mass as well halos as the in the redshift Bolshoi-Planck evolution of than halo/subhalo in the Bolshoi number thewith halo, those this from means the WMAP5/7 that the cosmological correlation parameters. between galaxy6 . mass halos has been suppressed (e.g. Behroozi, Wechsler &

3d e xd i s p e r s i o ni nt h eh a l om a s s have found slopes between α 1.4 1.6(Blantonetal.2005;§ 3. simulation.densities. subhalos and halos matter At Fordark z the=8,thereareabout3timesasmany majority of these halo properties we report stellardiscusses mass the and dependence present subhalo of halo concentration mass is not trivial. and spin There- on § 11 Conroy 2013b; Moster,∼ Naab− & White 2013). Nevertheless, 3.3). Figure 10M showsvirﬁtting=10 functions theM⊙ ratiohalos that in of can Bolshoi-Planck the be very number useful as not densities in only Bolshoi. to gainBaldry,nBP in- fore Glazebrookmass in and approaches redshift. & for7discussestheevolutionoftheTully- Driver connecting 2008; galaxies Baldry to dark et matter al. 2012) mean- measurements§ of the baryonic mass have found slopes as . In the cold dark matter cosmology it is predicted that (sub)halos, such as the abundance matching technique, it § sight about the halo/subhalo population but also for the Fisher and Faber-Jackson relations between halo circular

⃝

5 c and nB between the Bolshoi-Planck and the Bolshoi sim- .) aoms crto rates accretion mass halo 3.1), ing that, for some reason, the star formation eﬃciency in low h thegalaxy-halo number density connection of dark and matter thus halos for galaxy is a strong evolution. function In- hasvelocitysteep beenVmax shownas αand that the1.9(Baldry,Glazebrook&Driver2008). stellarthe mass mass the of subhalo the central had galaxies when it h halo mass function using the best ﬁt parameters from table−1.8

−

06RS MNRAS RAS, 2016 ulations as a function of Mvir from z =0toz =8.The § of halo mass at low masses dnh/dMvir M .Incontrast, was still a distinct∼ halo correlates better with the stellar − vir mass halos has been suppressed (e.g. Behroozi, Wechsler &

4discusseshalo( 1 ∝ ⃝c 2016 RAS, MNRAS 000,1–?? 1 3. diﬀerent cosmologicalthe observed parameters galaxy stellar mass imply function, that as at wellz =0,on as the lu- mass of the galaxy it hosts. This comes from the fact that

Gpc) minosity function, has a slope that is ﬂatter. Recent analysConroyis when 2013b; assuming Moster, identical Naab stellar-to-halo & White mass relations2013). fo Nevertheless,r p sdsusdi Lee in discussed is Mpc Figure 10 showsaverage, theﬃ thereratio are of the12% number more Milky-Way densities massn halos in the ∼ BP 4.2 Subhalo mass function inl asv halos massive ciently measurements of the baryonic mass have found slopes as and nB between theBolshoi-Planck Bolshoi-Planck⃝c 2016 than RAS, in and the MNRAS Bolshoi the000,1– Bolshoi simulation.?? sim- This fraction

3 § 13steep as α 1.9(Baldry,Glazebrook&Driver2008). icse h sim- the discusses 2

§ increases to higher masses, 25% for Mvir 3 10 M⊙. Subhalos can lose a signiﬁcant fraction of their mass due

oue htwe that volumes ulations as a function of M from z =0toz =8.The 4and vir ∼ ∼ × ∼ § This fraction also increases with redshift, and we ﬁnd that to tidal striping. Since tidal stripping aﬀects the dark mat-

4.3). § diﬀerent cosmological parameters imply that at z =0,on

3describesthe at z =2, 4and6thereare 25, 40 and 60% more Milky- ter more than the stars of the central galaxy deep inside average, there are 12% more Milky-Way∼ mass halos in the Way mass halos in the Bolshoi-Planck than in the Bolshoi4.2 Subhalothe halo, mass this function means that the correlation between galaxy § ∼

5alsocom- § Bolshoi-Planck thansimulation. in the Bolshoi At z =8,thereareabout3timesasmany simulation. This fraction stellar mass and present subhalo mass is not trivial. There-

5presents

§ 13

000,1– 11

.)and 4.1) increases to higherM masses,=10 M⊙25%halos for inM Bolshoi-Planckvir 3 10 asM in⊙ Bolshoi.. Subhalosfore can in lose approaches a significant for connecting fraction galaxies of their to mass dark matterdue vir ∼ ∼ × This fraction also increasesIn the cold with dark redshift, matter and cosmology we find it isthat predictedto that tidal striping.(sub)halos, Since such tidal as the stripping abundance affects matching the dark technique, mat- it the number density of dark matterage halos is a strong function has been shown that the mass the subhalo had when it e- on at z =2, 4and6thereare 25, 40 and 60% more Milky- ter more than the stars of the central galaxy deep inside −1.8 h

re § - ?? l

” - ∼ f of halo mass at low masses dnh/dMvir M .Incontrast, was still a distinct halo correlates better with the stellar s 6 Way mass halos in the Bolshoi-Planck than in the∝ Bolshoivir the halo, this means that the correlation between galaxy the observed galaxy stellar mass function, as well as the lu- mass of the galaxy it hosts. This comes from the fact that simulation. At z =8,thereareabout3timesasmany stellar mass and present subhalo mass is not trivial. There- 11 minosity function, has a slope that is ﬂatter. Recent analysis when assuming identical stellar-to-halo mass relations for Mvir =10 M⊙ halos in Bolshoi-Planck as in Bolshoi. fore in approaches for connecting galaxies to dark matter In the cold dark⃝c 2016 matter RAS, cosmology MNRAS 000,1– it is?? predicted that (sub)halos, such as the abundance matching technique, it the number density of dark matter halos is a strong function has been shown that the mass the subhalo had when it −1.8 of halo mass at low masses dnh/dMvir M .Incontrast, was still a distinct halo correlates better with the stellar ∝ vir the observed galaxy stellar mass function, as well as the lu- mass of the galaxy it hosts. This comes from the fact that minosity function, has a slope that is ﬂatter. Recent analysis when assuming identical stellar-to-halo mass relations for

⃝c 2016 RAS, MNRAS 000,1–?? Constraining the Galaxy Halo Connection: 8 Star Formation Histories, Galaxy10 Mergers, and Structural Properties

Table 1. Observational data on the galaxy stellar mass function Aldo Rodriguez-Puebla, Joel Primack,Table Vladimir 2. Observational data Avila-Reese, on the star formation rates Sandra Faber MNRAS 2017

a 2 Author Redshift Ω [deg ]Corrections Author Redshifta SFR Estimator Corrections Type Bell et al. (2003) z ∼ 0.1462I+SP+C Chen et al. (2009) z ∼ 0.1Hα/Hβ SAll Yang, Mo & van den Bosch (2009a) z ∼ 0.14681I+SP+C Salim et al. (2007) z ∼ 0.1UVSEDSAll Li & White (2009) z ∼ 0.16437I+P+C Noeske et al. (2007) 0.2

Millennium-II high resolution N-body simulations (Fakhouri et al. and 2010). γ (z) 0.917 0.845 a 0.532 a2. (17) The dotted lines in Fig. 5 show power-law fits to the simulations = + × − × for the halo mass accretion rates, given by The dashed lines in Fig. 4 show this fit to the simulations. Finally, based on the above definitions of halo accretion rates, dMvir α(z) β(z)Mvir,12 E(z), (11) the rate at which the cosmological baryonic inflow material is ac- dt = creted into the dark matter halo is calculated as dMc,b/dt fc,b where Constraining thedM Galaxy/dt, where the cosmic Halo baryon fractionConnection: is f $ /=$ × vir c, b ≡ B, 0 M,0 = 2 0.156 for our cosmology. The rate dM /dt is an important quan- Starlog β(z) βFormation0 β1a β2a , Histories,(12) Galaxy Mergers,c, band Structural Properties The Galaxy-Halo Connection= + Over+ The Last 13.3 Gyrs 11 tity; it equals the star formation rate plus the gas outflow rate if the andAldo Rodriguez-Puebla, Joel Primack,galaxy Vladimir is in ‘equilibrium’ Avila-Reese, in bathtub model terms Sandra (e.g. Mitra, Dav Fabere´ MNRAS 2017 2 &Finlator2015,andreferencestherein). Complete samples, however, for all galaxies are only avail- α(z) α0 α1a α2a . (13) = + + Galaxies can be divided into two main groups: star-forming able at z<3. Therefore, here we decided to include SFRs Table 2 lists the best-fitting parameters for the dMvir/dt Mvir and quiescent. Star-forming galaxies are typically blue young disc − samples from star-forming galaxies, especially at high z>3. StarDownloaded from Formation 14 relations. Power-law fits can provide an accurate description for galaxies,Average while many quiescent Stellar galaxies Mass are red old spheroids. These Using only star-forming galaxies at high redshift is not a big both dMvir,dyn/dt and dMpeak/dt for the three simulations. properties are partially determined by the mass of the dark matter Rate Density source of uncertainty since most of the galaxies at z>3 are As can be observed in the upper panel of Fig. 4,however,a halo in whichHalo they Mass reside but, Relation due to complexity of the galaxy actually star forming, see e.g. Figure 2. The last column of power-law fit is a poor description of the instantaneous halo mass formation process, a dependence on other halo and/or environmen- Table 2 indicates the type of the data, namely, if the sam- accretion rates, especially for the BolshoiPand MDPL simulations tal properties is expected. For example, star-forming galaxies at a at low masses and low redshifts. In order to find a better description given redshift are known to show a tight dependence of star forma- ple is for all galaxies or for star-forming galaxies, and the http://mnras.oxfordjournals.org/ of the instantaneous halo mass accretion rates forQuenched the BolshoiP and tion rates on stellar mass, which is known as the ‘main sequence’ of redshift range. MDPL simulations we use a double power-law fit galaxy formation. The slopes and dispersions of halo mass accre- In addition to the compiled sample for z>3, here we Fraction tion ratescosmic reported baryon above fraction are very similar to the observed dispersion dMvir α(z) γ (z) calculate average SFRs using again the UV LFs described in β(z) Mvir,12 Mvir,12 E(z), (14) dt = + and slope of the star formation rates on the main sequence. This Appendix D. We begin by correcting the UV rest-frame ab- naturally suggests that the halo mass accretion rate is controlling where the normalization! is given by " solute magnitudes for extinction using the Meurer, Heckman not only the baryon fraction that is entering the galaxies, but also 2 & Calzetti (1999) average relation log β(z) 2.437 1.857 a 0.685 a , (15) their star formation efficiency. The galaxy stellar-to-halo mass re- = − × + × lation is known to be nearly independent of redshift from z 0out and the powers α(z)andγ (z) are given respectively by = AUV =4.43 + 1.99 , (41) to z 4 (Behroozi, Wechsler & Conroy 2013a), so the galaxy star Stellar Mass ∼ at University of California, Santa Cruz on August 23, 2016 h i h i α(z) 1.120 0.609 a 0.097 a2, (16) formation rate is determined on average by the mass accretion rate = − × + × where is the average slope of the observed UV con- of the halo in which it resides: dM /dt (dM /dMvir)(dMvir/dt). Density h i ∗ ∗ tinuum. We use the following relationship independent of Arecentpaperbysomeofus,Rodr´ıguez-Puebla= et al. (2016), made redshift: = 0.11 (MUV +19.5) 2, which is consis- Figure 2. The stellar mass M (z)atwhichthefractionsofblue the stronger assumption that this is true halo by halo for star-forming h i ⇥ 50 tent with previous determination of the slope (see e.g., star-forming and red quenched galaxies are both 50%. The open galaxies, which we called Stellar-Halo Accretion Rate Coevolution Bouwens et al. 2014). Then we calculate UV SFRs using the square with error bars shows the transition mass for local galaxies (SHARC). We showed that the SHARC assumption predicts galaxy star formation rates on the main sequence that are in good agreement as derived in Bell et al. (2003) based on the SDSS DR2, while Kennicutt (1998) relationship Median Halo with observationscosmic up to zbaryon4, and fraction that in addition it approximately the filled triangles show the transition mass derived in Bundy ∼ 1 1 matches the small observed dispersion of 0.3 dex of the galaxy SFR LUV/erg s Hz et al. (2006) based on the DEEP2 survey. DroryGrowth & Alvarez (2008) ∼ 1 (LUV)= 27 . (42) star formation rates about the main sequence. M yr 13.9 10 based on the FORS Deep Field survey is indicated with the long ⇥ dashed line; observations from Pozzetti et al. (2010) based on the We subtract -0.24 dex to be consistent with a Chabrier COSMOS survey are indicated with the x symbols; observations 3.3 Halo assembly (2003) IMF. Finally, we calculate the average SFR as a func- from Baldry et al. (2012) based on the GAMA survey are shown Fig. 5 presents the medians of the halo mass growth for progen- tion of stellar mass as 11 12 13 14 with a filled square; and observations from Muzzin et al. (2013) itors at z 0 with masses of Mvir 10 , 10 , 10 , 10 and based on the COSMOS/ULTRAVISTA survey are shown as filled 15 1 = = 1 Figure 5. Upper Panel: Cosmic star formation rate, CSFR. 10 h− M , for the BolshoiP (black solid line) SMDPL (red solid log SFR (M ,z) = (M ,z) P (M MUV,z) ⊙ h ⇤ i ⇤ ⇤ ⇤| ⇥ Thecircles. solid black The line empirical shows the results resulting based best on fit abundance model to the matching by line) and MDPL (blue solid line) simulations. In order to avoid res- Z CSFRFirmani as described & Avila-Reese in Section (2010) 2.4. Filled are red shown and withviolet the circles short dashed olution effects and thus obtain reliable statistics we require that at log SFR(MUV)UV(MUV,z)dMUV. (43) showlines. a set The of compiled solid black observations line shows by Madau the relation& Dickinson log( (2014)M50(z)/M )= every redshift at least 90 per cent of the haloes can be resolved with Both the probability distribution function P (M MUV,z) from10 FUV+IR.2+0.6z restemployed frame luminosities. in this paper, UV luminosities which is consistent are dust- with most at least 100 particles. The first thing to note is that the three simu- ⇤| corrected. Black solid circles show the results from the UV dust- and the function (M ,z) are described in detail in Ap- of the above studies. The gray solid lines show the results when lations agree with each other at all redshifts. From the figure it is ⇤ ⇤ corrected luminosity functions described in Appendix D. Lower shifting (M50(z)/M )0.1dexhigherandlower.Thered(blue)Figure 6.evident Upper that panel: high massEvolution haloes assembledof the mean more stellar-to-halo rapidly at later epochs pendix D. We use the following intervals of integration: Panel: CosmicFigure stellar 5. Median mass halo density. mass growth The solid for progenitors black linez shows0withmassesof curves show the11 stellar12 13 mass vs.14z where1 75% (25%)= of the galaxiesmass relationthan from lowerz mass=0.1to haloes.z =10asindicatedinthelegends. This is consistent with the fact the slopes M [ 17, 22.6] at z =4;M [ 16.4, 23] at z =5; the predictionsMvir for10 our, 10 best, 10 fit, and model. 10 Filledh− M black,solidlines.Fitstosimulations circles show UV UV = In our modelobtained we assume for halo that mass these accretion relations rates are valid are slightlyboth for greater cen- than 1. 2 2 theare data quenched. pointsare shown compiled with the in dotted Madau lines. & The Dickinson shaded⊙ area (2014). shows Allthe dispersion data around MUV [ 16.75, 22.5] at z =6;MUV [ 17, 22.75] at tral and satelliteFor the Planckgalaxies cosmology as explained we find in the that text. 1012 Theh 1 M relationshaloes formed 2 2 was adjustedthe medians.to the IMF of Chabrier (2003). In both panels, the − z =7andMUV [ 17.25, 22] at z =8. are shownhalf only of up their to themass largest by z halo1.2. mass Progenitors that will of M be observed⊙1013, 1014,and 2 light grey shaded area shows the systematic assumed to be of 0.25 ∼ vir = Table 2. Best-fitting parameters for the dMvir/dt Mvir relationships.using the solid1015 h angles1 M andhaloes redshift reached bins the of the mass surveys of 1012 fromh 1 M Tableat z 2.5, dex.Section 7). For the fraction of quiescent− galaxies f we use − − Q 1. Table 33.9, lists and thez range⊙5, respectively. over which Theoretically, our mass relations the characteristic can⊙ be ∼ mass 5 the followingdM /dt [h relation:1 M /yr] α α α β β trust.β Middle12 panel:1∼ 1 confidence intervals from the 3 10 4.3 Cosmic Star Formation Rate vir − 0 1 2 0 1 2 of 10 h− M is expected to mark a transition above⇥ which the ⊙ MCMC trials. Bottom⊙ panel: Evolution of the stellar-to-halo the virialInstantaneous shocks form and heat1 0.975 the 0.300 incoming0.224 gas 2.677 increases1.708 0.661 formation of stars in galaxies becomes increasingly inefficient. The We use the CSFR data compilation from Madau & Dickin- − − mass ratios M /Mvir for the same redshifts as above. The12 dotted1 (e.g.,fQ Dekel(M ,z &)= Birnboim 2006). Additionally,↵ , in such massive (44) reasons⇤ for this are that at halo masses above 10 h− M the ef- Dynamical⇤ 1+( averagedM /M 1.00050(z)) 0.329 0.206 2.730 1.828 0.654lines in both panels show the limits corresponding to the cosmic son (2014). This data was derived from FUV and IR rest galaxies the gas can be kept⇤ from cooling− by the feedback− ficiency at which the virial shocks can heat the gas increases⊙ (e.g. Peak 0.997 0.328 0.200 2.711 1.739 0.672baryon fraction ⌦B/⌦M 0.16. ⇡ frame luminosities by deriving empirical dust corrections to fromwhere activeM galactic50 is the nuclei transition (Croton stellar et al.− 2006;mass Cattaneo at which− the frac- Dekel & Birnboim 2006), and the gas can be kept from cooling by the FUV data in order to estimate robust CSFRs. We ad- et al.tions 2008; of Henriques blue star-forming et al. 2015; Somerville and red quenched & Davé2015, galaxies are and references therein). Central galaxies in massive halos that M50(z) roughly coincides with where ⌘ is maximum, justed their data to a Chabrier (2003) IMF by subtracting bothMNRAS 50%. Figure462, 893–916 2 shows (2016)M50 as a function of redshift 0.24 dex from their CSFRs. Finally, for z>3wecalculate are therefore expected, in a first approximation, to become especially at low z. This reflects the fact that halo mass passivefrom systems observations roughly andat the previous epoch when constraints. the halo reaches The solid blackquenching is part of the physical mechanisms that quench the CSFR using again the UV dust-corrected LFs and SFRs 12 1 theline mass shows of 10 theh relationM , thus log( theM term50(z halo)/M mass)=10 quench-.2+0.6zgalaxiesthat in massive halos. We will come back to this point described above and using the same integration limit as in ing.we On will the employ other hand, in this the less paper, massive and the the halos, gray the solid less linesin show Section 8.2. Madau & Dickinson (2014). We find that our CSFR is con- ecientthe results their growth when in shifting stellar mass (M50 is( expectedz)/M )by0.1dexabove to be due Finally, Figure 8 shows the trajectories for the M /Mvir ⇤ sistent with the compilation derived in Madau & Dickinson to supernova-drivenand below. We gas will loss use in their this lower shift gravitational as our uncertainty po- ratios in of progenitors of dark matter halos with masses be- 11 15 (2014) over the same redshift range. tentials. tween Mvir =10 M and Mvir =10 M at z =0.Note the definition for log(M50(z)/M ). The red (blue) curves 12 The right panel of Figure 7 shows the stellar conversion that galaxies in halos above Mvir =10 M had a maximum in the figure show the stellar mass vs. redshift where 75% eciency for the corresponding stellar mass growth histories followed by a decline of their M /Mvir ratio, while this ratio (25%) of the galaxies are quenched. Finally, we will as- ⇤ 4.4 The Fraction of Star-Forming and Quiescent of the halo progenitors discussed above. The range of the for galaxies in less massive halos continues increasing today. sume that ↵ = 1.3. The transition stellar mass is such Galaxies transition stellar mass M50(z), defined as the stellar mass at whichthat the at fractionz =0log( of star formingM50(z is)/ equalM )=10 to the fraction.2andat of z =2 6.2 Galaxy Growth and Star-Formation Histories In this paper we interchangeably refer to star-forming galax- quenchedlog(M galaxies50(z)/M (see)=11 Figure.4. 2 and Section 7), is shown by ies as blue galaxies and quiescent galaxies as red galaxies. We the dashedWe lines. note Below that these our lines statistical galaxies treatment are more likely of quenched to Figure vs. 9 shows the predicted star formation histories for utilize the fraction of blue/star-forming and red/quenched be starstar-forming forming. Note galaxies that the is ratherright panel di↵erent of Figure from 7 shows a commonprogenitors ap- of average dark matter halos at z =0with galaxies as a reference to compare with our model and thus proach in the literature, in which a given galaxy is considered c 20?? RAS, MNRAS 000,1–?? gain more insights on how galaxies evolve from active to to be quenched based on its specific star formation rate and passive as well as on their structural evolution (discussed in redshift. For example, Pandya et al. (2016) defines transi- c 20?? RAS, MNRAS 000,1–?? 16

Constraining the Galaxy Halo Connection: Star Formation16 Histories, Galaxy Mergers, and Structural Properties Aldo Rodriguez-Puebla, Joel Primack, Vladimir Avila-Reese, Sandra Faber MNRAS 2017

SFR vs. M*, Mvir, and z Stellar Mass-Halo Mass Relation

Galaxy Radial Stellar Mass Distribution

Solid lines show the redshift dependence for blue and red galaxies of the local relation by Mosleh, Williams & Franx (2013) based on the MPA-JHU SDSS DR7. The black solid lines show the average circularized effective radius as a function of stellar mass. The crosses show the effective radius at M50, the stellar mass at which the quenched fraction of galaxies is 50%. We utilize the plotted redshift dependences as an input to derive the average galaxy’s radial mass distribution as a function of stellar mass by assuming that blue/star-forming galaxies have a Sersic index n = 1 while red/quenched galaxies have a Sersic index n = 4.

Figure 16. Circularized effective radius for blue star-forming galaxies and red quiescent galaxies for six different redshift bins.The filled circles show the circularized effective radius as a function of stellar mass and redshift from van der Wel et al. (2014) based on multiwavelength photometry from the 3D-HST survey and HST/WFC3 imaging from CANDELS. Solid lines show the redshift dependence for blue and red galaxies of the local relation by Mosleh, Williams & Franx (2013) based on the MPA-JHU SDSS DR7. The black solid lines show the average circularized effective radius as a function of stellar mass. The crosses show the effective radius at M50,i.e.,the stellar mass at which theFigure observed 9. star-formingPanel a): fraction Galaxy of galaxies SFRs as is equal a function to the quenched of redshift, fraction halo of galaxies. mass, andNote stellarthat the mass. effective The solid lines indicate the average trajectories radius at M50 evolves very little with redshift and is ∼ 3kpc.Weutilizetheplottedredshiftdependencesasaninpu11 11.5 12 13 ttoderivethe14 15 corresponding to progenitors at z =0withMvir =10 , 10 , 10 , 10 , 10 and 10 M .ThecolorcodeshowstheSFRs.Panel average galaxy’s radial mass distribution as a function of stellar mass by assuming that blue/star-forming galaxies have a Sèrsic index n =1whilered/quenchedgalaxieshaveaSèrsicindexb): Galaxy growth trajectoriesn =4(seetextfordetails). in the stellar-to-halo mass plane (this is a projection of Panel a) when collapsing over the redshift axis). Panel c): Galaxy SFRs along the halo mass trajectories (this is a projection of the Panel a) when collapsing over the M axis). Panel ⇤ d): Galaxy SFRs along the stellar mass trajectories (this is a projection of the Panel a) when collapsing over the Mvir axis). The dotted lines show M50(z)abovewhich50%ofthegalaxiesarestatisticallyquenched,andtheupper(lower)long-dashcurvesshowthemassvs. z where 75% (25%) of the galaxies are quenched.

Figure 9. Panelwe plot a): Galaxy the ratio SFRs between as the a function specific star of formation redshift, rate halo mass,in time and steps stellar of 100 mass. Myrs. The Note solid that lines halo star indicate formation the average trajectories 11 11.5 12 13 14 15 corresponding(sSFR to progenitors = SFR/M ) at andz the=0with specific haloM massvir =10 accretion, 10 rate , 10eciencies, 10 , of10 theand order 10 of unityM .ThecolorcodeshowstheSFRs.Panel imply that the assembly ⇤ b): Galaxy growth(sMAR trajectories = (dMvir/dt) in/M thevir), i.e., stellar-to-halo sSFR/sMAR, as mass a function plane (thistime is for a projection galaxies is similar of Panel to that a) for when their darkcollapsing matter ha- over the redshift axis). 6 Panel c): Galaxyof halo SFRs mass. alongHereafter, the halo we refer mass to the trajectories ratio sSFR/ (thissMAR is a projectionlos – in other of words, the Panel a direct a) coevolution when collapsing between galaxies over the M axis). Panel as the instantaneous halo star formation eciency.7 Simi- and dark matter halos. In contrast, values that are in ei- ⇤ d): Galaxy SFRslarly along to our the definition stellar of mass SFRs, trajectories halo MARs were (this measured is a projectionther directions of the Panel much above a) when and below collapsing unity imply over that the theMvir axis). The dotted lines show M50(z)abovewhich50%ofthegalaxiesarestatisticallyquenched,andtheupper(lower)long-dashcurvesshowthemassvs.galaxy stellar mass growth is disconnected from the growth of its host dark matter halo. Recall that this discussion is z where 75% (25%)6 of the galaxies are quenched. Observe that the sSFR and the sMAR have units of the inverse valid only for galaxies in the centers of distinct dark matter of time. One can interpret them as the characteristic time that halos. it will take galaxies and halos to double their mass at a constant The main result from Figure 10 is that there is not a assembly rate. Therefore the ratio sSFR/sMAR = th/tg measures we plot the ratiohow fast between galaxies are thegaining specific stellar mass star compared formation to their halos rate in time steps of 100 Myrs. Note that halo star formation (sSFR = SFRgaining/M ) total and mass. the specific halo mass accretion rate eciencies of the order of unity imply that the assembly 7 Do not⇤ confuse the instantaneous halo star formation eciency mer is an instantaneous quantity while the latter is an integral (sMAR = (dMvir/dt)/Mvir), i.e., sSFR/sMAR, as a function time for galaxies is similar to that for their dark matter ha- with the halo stellar conversion eciency ⌘ = f /fb.Thefor- (cumulative) quantity. 6 ⇤ 11 11.5 12 13 Figure 17. Average evolution of the radial distribution of stellar massforgalaxiesinhaloprogenitorswithMvir =10 , 10 , 10 , 10 , of14 halo15 mass. Hereafter, we refer to the ratio sSFR/sMAR los – in other words, a direct coevolution between galaxies 10 and 10 M⊙at z =0.Theseradialdistributionscanbeimaginedasstackingall the density profiles of galaxies at a given virial 7 c 20?? RAS, MNRAS 000,1–?? massas theand z,nomatterwhethergalaxiesarespheroidsordisksoracombi instantaneous halo star formationnation e ofciency. both. Simi- and dark matter halos. In contrast, values that are in ei- larly to our definition of SFRs, halo MARs were measured ther directions much above and below unity imply that the

⃝c 20?? RAS, MNRASgalaxy000,1– stellar?? mass growth is disconnected from the growth of its host dark matter halo. Recall that this discussion is 6 Observe that the sSFR and the sMAR have units of the inverse valid only for galaxies in the centers of distinct dark matter of time. One can interpret them as the characteristic time that halos. it will take galaxies and halos to double their mass at a constant The main result from Figure 10 is that there is not a assembly rate. Therefore the ratio sSFR/sMAR = th/tg measures how fast galaxies are gaining stellar mass compared to their halos gaining total mass. 7 Do not confuse the instantaneous halo star formation eciency mer is an instantaneous quantity while the latter is an integral with the halo stellar conversion eciency ⌘ = f /fb.Thefor- (cumulative) quantity. ⇤

c 20?? RAS, MNRAS 000,1–?? Constraining the Galaxy Halo Connection: Star Formation Histories, Galaxy Mergers, and Structural Properties Aldo Rodriguez-Puebla, Joel Primack, Vladimir Avila-Reese, Sandra Faber MNRAS 2017 24 We infer galaxy merger rates from halo mergers

Change in slope in Reff - M✷ diagram after quenching, consistent with uptick in minor merger rate and galaxy minor merger simulations

ing

quench ing

quench

11 11.5 12 13 14 15 Figure 20. Trajectories for progenitors of halos with Mvir =10 , 10 , 10 , 10 , 10 and 10 M⊙ at z =0inthesize-massrelation (upper left panel) and for the minor (bottom left) and major (bottom right) merger rates. As in Figure 19, the symbols show diﬀerent redshifts as indicated by the labels. The dashed lines show the transition below which most galaxies are quiescent, and the upper (lower) dot-dashed curves show where 25% (75%) of the galaxies are quenched. Progenitors of quenched galaxies went through two phases, initially they grew in parallel trajectories as star formersinthesize-massrelation,butafterquenchingtheyevolvedmuchfasterinsize than in mass, resulting in a steeper relation at low z.Presumablythehighrateofminormergersisresponsibleforthisrapidsizegrowth.

We now discuss some implications and interpretations of our 8.1.1 Stellar-to-halo mass relationship results. We begin by comparing mean stellar masses as a function of virial mass, i.e., the SHMR. This is shown in Figure 21 for seven different redshift bins. Our resulting SHMRs are shown with the solid black lines. The grey areas in the upper panels show the standard deviations from the set of 3 105 × MCMC models described in Section 5 – in other words, they 8.1 Comparison with Previous Studies represent the 1σ confidence level of our inferences. System- atic errors are usually of the order of 0.25 dex and may In this section we compare to previous works that derived ∼ the SHMR at different redshifts. We divide our discussion increases with redshift. into two main comparisons: those studies that reported stel- In Figure 21 we compare our results with those reported lar mass as function of halo mass, SHMR, and those that in Guo et al. (2010, constrained only at z 0.1, violet ∼ have estimated the inverse of this relation, Mvir M∗.The solid line), Behroozi, Wechsler & Conroy (2013b, blue solid − former is typically reported in studies based on statistical lines) and Moster, Naab & White (2013, red solid lines). approaches, namely indirect methods, as in our case, while These authors used subhalo abundance matching to derive the latter is more natural for studies based on direct deter- the SHMRs. Guo et al. (2010) and Moster, Naab & White minations (e.g., weak gravitational lensing). All results were (2013) used only the GSMF as a constraint, while Behroozi, adjusted to a Hubble parameter of h =0.678 and to virial Wechsler & Conroy (2013b) included the observed specific halo masses. When required, we adjusted stellar masses to SFRs and the CSFR for constraining the best fit parame- aChabrierIMF. ters in their model. The filled circles with error bars show

⃝c 20?? RAS, MNRAS 000,1–?? \ quenching is correlated with ing sSFR/sSMR ing quench

quench

This ﬁgure shows that quenching is correlated with sSFR/sSMR = thalo/t✷, since sSFR/sSMR and quenching curves are nearly parallel. sSFR/sSMR - ﬁrst rises, reaching a peak ~2 at z ~ 3 for 1013 halos, a peak ~7 for 1012 halos at z~1.5, and 1011 halos are still at peak sSFR/sSMR ~ 10 - then declines along all Mvir and M* progenitor tracks toward z=0.

) )

vir vir average galaxies

/dM /dM obey SHARC until ✷ ✷ they quench ing quench ing

quench

= (SFR/MAR) / (dM = (SFR/MAR) / (dM

SHARC SHARC

R R

This ﬁgure shows that the SHARC approximation is rather well satisﬁed until quenching, the SHARC ratio RSHARC = (SFR / MAR) / (dMvir/dlog M*) having a value of about 1 to 2 along the progenitor trajectories, and then dropping after quenching. This shows quenching is correlated with RSHARC :

- the fraction of quenched galaxies is ~ 50% when RSHARC ~ 1 to 1.5, and the quenched fraction is > 75% when RSHARC drops to ~1 - like sSFR/sSMR, RSHARC ﬁrst rises along all progenitor curves, reaches a peak at higher z for higher mass (Mvir or M*), and then declines - unlike sSFR/sSMR, the peak SHARC ratio is nearly constant between 1.5 and 2 (the SHARC ratio peaks at about 2 for both 1011.5 halos at z ~ 0.5 and 1015 halos at z ~ 3, and at about 1.5 for intermediate mass halos).

Note: the SHARC formula is SFR = (dM✷/dMvir) MAR where MAR = dMvir/dt. Deﬁne RSHARC = (SFR / MAR) / (dM✷/dMvir), so SHARC ==> RSHARC = 1. Constraining the Galaxy Halo Connection: Star Formation Histories, Galaxy Mergers, and Structural Properties Aldo Rodriguez-Puebla, Joel Primack, Vladimir Avila-Reese, Sandra Faber MNRAS 2017

ing

ing quench

quench

This ﬁgure (and the left panel below) shows that ∑1 reaching a maximum correlates with quenching: - ∑1 at the quenching transition rises steadily with Mvir and reaches maximum at lower z for lower Mvir — “quenching downsizing” - That the progenitor tracks are parallel to the trajectory curves shows that ∑1 remains constant after it reaches its maximum

log Mvir/M⦿ 15 14 13 12 11.5 11

The right panel shows that Reff steadily rises along halo trajectories, and quenching typically occurs when Reff ≈ 3 kpc. Although ∑1 is ﬂat after quenching, the middle panel shows that ∑eff declines after quenching as Reff increases. https://132.248.1.39/galaxy/galaxy_halo.html Constraining the Galaxy Halo Connection: Star Formation Histories, Galaxy Mergers, and Structural Properties Aldo Rodriguez-Puebla, Joel Primack, Vladimir Avila-Reese, Sandra Faber (RP17) MNRAS 2017 Corresponding 2-point correlation fcns - Rodriguez-Puebla et al. in prep.

Two point correlation function in ﬁve stellar mass bins. Solid lines indicate the results of the SHAM result from RP17 while ﬁlled circles with error bars is for the SDSS analysis from Yang+12. Note that RP17 used Mvir for distinct halos and Mpeak for subhalos in their SHAM analysis. The correlation function is known to be underestimated when using Mvir and Mpeak rather than Vmax and Vpeak in SHAM (e.g., Reddick et al. 2013). Abundance Matching LF and MF Are Independent of Density Radu Dragomir, Aldo Rodríguez-Puebla, Joel R. Primack, Christoph T. Lee, Peter Behroozi, Doug Hellinger, Avishai Dekel (in preparation)

exception

4 ≤ δ8

0.7 ≤ δ8 ≤ 1.6 -0.4 ≤ δ8 ≤ 0 -1 ≤ δ8 ≤ -0.75 Abundance Matching LF and MF Are Independent of Density Radu Dragomir, Aldo Rodríguez-Puebla, Joel R. Primack, Christoph T. Lee, Peter Behroozi, Doug Hellinger, Avishai Dekel (in preparation)

Two point correlation function in ﬁve r-band luminosity bins. Solid lines indicate the results of the SHAM result from Radu Dragomir et al. in prep., while ﬁlled circles with error bars are for the SDSS analysis from Zehavi+2011. Dragomir et al. in prep. uses Vmax for distinct halos and Vpeak for subhalos. Abundance Matching LF and MF Are Independent of Density Radu Dragomir, Aldo Rodríguez-Puebla, Joel R. Primack, Christoph T. Lee, Peter Behroozi, Doug Hellinger, Avishai Dekel (in preparation)

PRELIMINARY Abundance Matching LF and MF Are Independent of Density Radu Dragomir, Aldo Rodríguez-Puebla, Joel R. Primack, Christoph T. Lee, Peter Behroozi, Doug Hellinger, Avishai Dekel (in preparation)

Two point correlation function in five stellar mass bins. Solid lines indicate the results of the SHAM result from Radu in prep. while filled circles with error bars is for the SDSS analysis from Yang+12. In this case Dragomir et al. in prep. uses Vmax for distinct halos and Vpeak for subhalos in the SHAM analysis. Note that this SHAM reproduces the two point correlation function and the stellar mass function in various environments at the same time. Causes & Consequences of Halo Mass Loss Christoph T. Lee, Joel R. Primack, Peter Behroozi, Aldo Rodríguez-Puebla, Doug Hellinger, Austin Tuan, Jessica Zhu, Avishai Dekel in final prep. 20-80% Dispersion 95% CI

loglog1010 MMvirvir/(h-1=M 11⦿). 2= 11.20.375 ± 0.375M 11.95 12.7 13.45 160 ± 8

Concentration CNFW Spin λB 80 4 40 ] 2 [10 NFW

B 0

C 20 2

95% C.L. 10 20%-80%

1 5 z=0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

Mvir/Mpeak Mvir/Mpeak • Most low mass halos in dense regions are signiﬁcantly stripped

• Halos that have lost 5-15% of their mass relative to Mpeak have lower CNFW, higher λB

• Halos that have lost more than ~20% of their mass have higher CNFW and lower λB Dark Matter Halos: Causes & Consequences of Halo Mass Loss Christoph T. Lee1, Joel R. Primack1, Peter Behroozi2, Aldo Rodríguez-Puebla3, Doug Hellinger1, Jessica Zhu1, Austin Tuan1, Avishai Dekel4 1 Physics Department, UC Santa Cruz; 2 Astronomy Department, UC Berkeley; 3 Instituto de Astronomía, UNAM; 4 Racah Institute of Physics, The Hebrew University

1 ABSTRACT 2 Is halo mass loss common? 3 Why do halos lose mass? We study the properties of distinct dark matter 1 log10 µ = 11.2 11.95 12.7 13.45 halos that have a virial mass Mvir at z = 0 less than 1 1 µ = Mvir/(h M ) their peak mass Mpeak and identify two primary causes 0.9

peak Neither of halo mass loss: evaporation after a major merger 0.3 M and tidal stripping by a massive neighboring halo. 0.8 0.2 5%

Major mergers initially boost Mvir and typically cause > 0.7 90% of Halos the ﬁnal halo to become more prolate and less 0.1 * relaxed and to have higher spin and lower NFW 10% 0.6 + 375 concentration. As the halo relaxes, high energy 2 0. Evaporation 0.05 µ = 11. ± 0.5 material from the recent merger gradually escapes, log10 temporarily resulting in a net negative accretion rate 11.95 0.4 peak

that reduces the halo mass by 5-15% on average. 7 M 12. 0.3 Halos that experience a major merger around z = 0.5

0.01 5%

typically reach a minimum mass around z = 0. Tidal > 0.2

stripping occurs mainly in dense regions, and it Cummulative Distribution Function Both 45 0.1 causes halos to become less prolate and have lower 13. Lost Negligible Mass Loss Fraction of halos that have lost spins and higher NFW concentrations. Tidally * + stripped halos often lose a large fraction of their peak 40 30 20 10 0 Tidal Stripping mass (> 20%) and most never recover (or even re- Percent Mass Lost (Relative to Mpeak at z = 0) attain a positive accretion rate). Low mass halos are Most halos lose mass via evaporation after a major (or often strongly affected by both evaporative mass loss At z = 0, 22% of low mass halos (log μ =11.2) have minor) merger. Pure tidal stripping accounts for 23% and tidal stripping, while high mass halos are lost more than 5% of their peak mass, and 7% have of low mass halos that have lost mass, but very few predominantly inﬂuenced by evaporative mass loss lost more than 20%. Only 12% of high mass halos high mass halos. Some halos experience both and show few signs of signiﬁcant tidal stripping. (log μ =13.45) have lost > 5% of their peak mass. evaporation and tidal stripping. Around 22% of halos that have lost mass neither had a recent major merger nor experienced tidal stripping (rather, these typically 4 WhatCauses happens & Consequences when Examples of individual halo evolution experienced evaporation after a minor merger). halos lose mass? of Halo Mass Loss ] Major Merger

11 1.2 Christoph Lee 1.0 high TF Tidal Stripping: ) [10 Median evolution

Extending this analysis to all halos GalHalo17-Conference Poster 0.8 of all halos with

Strong tidal force from a nearby M same 5

1 0.6 M 5 massive halo removes loosely bound h vir at / ( 0.4 z Evaporation Dominated particles from a halo. 40% of tidally =0 Tidal vir Stripping 0.2 Evaporation stripped low mass halos lose more M than 20% of their peak mass. Tidally 13.45 stripped halos develop: 60 ]

2 4 • Low NFW scale radius (high

40 [10

concentration) due to steepening B 7 outer proﬁle 20 12. • Low spin parameter due to 375 0. NFW Scale Radius [kpc] 3 95 preferential removal of high Extending this analysis to all11 .halos 2 ± angular momentum material 16 = 11. peak µ M • Low prolateness (they become ] 10 2 12 Spin parameter log 5% [10

rounder) due to preferential >

B 8 removal of particles on highly 2 Tidal Stripping Lost Spin Parameter Dominated elliptical orbits. 4 *

60 40 20 0 Evaporation: 1 = needle 0.6 0 = sphere Percent Mass Lost (Relative to Mpeak at z = 0) Major mergers typically cause temporary jumps in NFW scale 0.4 Low mass halos (log μ =11.2) that have lost 5-15% of radius, spin parameter, and

Prolateness their peak mass most commonly experienced shape. As halos relax after a 0.2 evaporative mass loss (temporarily high spin merger, they shed high energy parameters). material (evaporate) and settle | 0.7 Low mass halos that have lost greater than 20% of U back to lower values of scale | T/ their peak mass typically are actively being tidally radius, spin parameter, shape, 0.5 stripped (low spin parameters). More heavily and viral ratio. After a major stripped halos have lower spin parameters. merger, halos typically lose Some low mass halos are strongly aﬀected by tidal

Virial Ratio 0.3 5-15% of their peak mass stripping, while high mass halos predominantly through evaporation. 1 2 3 4 1 2 3 4 5 experience evaporative mass loss. 1+z 1+z

6 Connection to environment density The median accretion rate of halos in high density environments is dramatically lower than in average density environments. A majority of low mass halos (log μ =11.2) in high density environments have negative accretion rates — they are losing mass via tidal stripping (see Lee et al. 2017 doi:10.1093/mnras/stw3348 for a full discussion of how halo properties depend on environment density). Tidal stripping rarely occurs in low density environments, since halos typically do not have massive neighbors nearby (tidal force strength correlates strongly with environment density). Evaporative mass loss is not as constrained by environment density, and is common at all environment densities. Causes & Consequences of Halo Mass Loss Christoph T. Lee, Joel R. Primack, Peter Behroozi, Aldo Rodríguez-Puebla, Doug Hellinger, Austin Tuan, Jessica Zhu, Avishai Dekel in ﬁnal prep. Tidal Stripping Post-Merger Relaxation z = SubHalo Properties of Dark Matter Haloes: Local Environment Density Christoph8 T. Lee, Joel R. Primack, Peter Behroozi, Aldo Rodríguez-Puebla, Doug Hellinger, Avishai DekelMNRAS 2017 Low Mass Intermediate Mass High Mass log M /M-1 = 1.5 0.375 0.75 0 0.75 log10 Mvirvir/(h CM⦿) = 11.200±0.375 11.95±0.375 12.70±0.375 13.45±0.375 log M = 11 .20± 0.375 11.95 12.70 13.45 10 vir ± 1 Concentration =1/2[h Mpc] 1 4 16 30 95% CI 2 8

NFW 20 C

10 Spin Parameter 4.0 ]

2 3.5

[10 3.0 B 2.5 ] 1

yr 2

11 Mass [10 -2 Accretion

/M -6 Rate

dyn z=0 ⌧ ˙ M 0 1 2 0 1 2 0 1 2 0 1 2 log10 ⇢/⇢avg log10 ⇢/⇢avg log10 ⇢/⇢avg log10 ⇢/⇢avg

Figure 5. Medians of scatter in ⇢ C , ⇢ ,and⇢ M˙ /M relationships at z = 0,where⇢ is the local environment density smoothed on NFW B di↵erent scales and ⇢avg is the average density of the simulation. Di↵erent coloured lines represent di↵erent smoothing scales. The shaded grey ﬁlled curve represents the 95% conﬁdence interval on the median, shown only for the characteristic smoothing length s,char = 1, 2, 4, and 8Mpc/h for mass bins from left to right, respectively, and provides an indication of sample size at di↵erent densities. Mass bins are 12.7 selected relative to the non-linear mass (log10 MC = 10 M at z = 0)tofacilitatecomparisonbetweenhalosabove,at,orbelowMC.We see that lower mass halos occupy regions with a wide range of local densities, while higher mass halos are restricted to higher density regions. Note also that larger smoothing scales will shift the range of densities towards the average density, so equal smoothing lengths should be used to compare density ranges for halos of di↵erent masses. See Fig. 6 for a discussion of the trends seen in this plot.

curves on each panel to facilitate comparison between dif- median density regions. More massive halos, however, tend ferent smoothing scales and halo masses. We also provide to have spin parameters that scale monotonically with local Fig. A3 as a means of translation between Figs. 5 and 6, density. Lastly, all halos tend to accrete less in higher density by relating actual values of halo properties to corresponding environments, though low mass halos exhibit far stronger percentile ranks. This percentilized form of correlations be- accretion suppression than massive halos. Interestingly, this tween halo properties and local density will be the basis for indicates that halos in low density regions (bottom 20% of much of our ensuing discussion. densities) accrete more rapidly than halos in higher density regions. In Fig. 6, we see that except in the lowest density regions, low mass halos (Mvir < MC) have median concentrations that scale monotonically with increasing local density. 5.2 Redshift evolution of halo properties at Surprisingly, we also find that low mass halos in the lowest di↵erent densities 15% of local densities have higher concentrations than halos in the roughly 20 40th percentile range. So, for halo masses One of the principal analysis methods we’ve used to inves- less than the characteristic mass MC, we find halo concen- tigate the origins of the trends in Fig. 6 is to examine the tration scales strongly with local density, with the caveat median evolution of halo properties along the most massive that concentrations go up in very low density regions. Halos progenitor branch (MMPB) of halos in regions of di↵erent at or above MC display a much weaker correlation between density at z = 0. In Figs. 7 and 8, for a given mass bin, we’ve density and concentration, though massive halos tend to be selected all halos in the 0 10th, 45 55th, and 90 100th per- more concentrated in lower density regions. For B, we find centile ranges of characteristic local density s,char at z = 0 to that halos less massive than MC in both high and low den- represent halos in low, median, and high density regions, re- sity regions have lower spin parameter compared to halos in spectively. Using the halo merger trees, we follow the MMPB

c 2016 RAS, MNRAS 000,1–20 Halo Properties Independent of Web Location at the Same Density Tze Ping Goh, Christoph T. Lee, Joel R. Primack, Miguel Aragon Calvo, Peter Behroozi, Aldo Rodríguez-Puebla, Doug Hellinger, Avishai Dekel, Kathryn Johnston (in preparation)

Speciﬁc Mass Accretion Rate

[h-1M⦿]

Bullock+2001 Spin Parameter λB

Concentration CNFW = Rvir/Rs

Scale Factor of Last Major Merger Halo Properties Independent of Web Location at the Same Density Tze Ping Goh, Christoph T. Lee, Joel R. Primack, Miguel Aragon Calvo, Peter Behroozi, Aldo Rodríguez-Puebla, Doug Hellinger, Avishai Dekel, Kathryn Johnston (in preparation)

Speciﬁc Mass Accretion Rate

[h-1M⦿]

Bullock+2001 Spin Parameter λB

Concentration CNFW = Rvir/Rs

Speciﬁc Mass Accretion Rate

[h-1M⦿]

Bullock+2001 Spin Parameter λB

Concentration CNFW = Rvir/Rs

0 1 2

At the same environmental density, halo properties are independent of cosmic web location. It doesn’t matter whether a halo is in a cosmic void, wall, or ﬁlament, what matters is the halos’s environmental [h-1M⦿] density. The properties studied are mass accretion rate, spin, halo concentration, scale factor of the last major merger, and prolateness. We had expected that a web’s cosmic web location would matter for at least some of these halo properties. That it does not is a signiﬁcant discovery.

SDSS galaxy mass and size are independent of web environment at fixed density (Yan, Fan, White 2013). GAMA data show that the galaxy luminosity function is also independent of web environment at fixed density (Eardley et al. MNRAS 2015). This contrasts with the finding that the halo mass function is dependent on web location at the same density using the v-web (Metuki, Liebeskind, Hoffman 2016). The Astrophysical Journal Letters,792:L6(6pp),2014September1 van der Wel et al.

0.75

0.5

0.25

0 1

Prolate Galaxies0.75 Dominate at High Redshifts & Low Masses

0.5

Prolate 0.25 Spheroidal Oblate 0

Figure 3. Reconstructed intrinsic shape distributions of star-forming galaxies in our 3D-HST/CANDELS sample in four stellar mass bins and five redshift bins. The model ellipticity and triaxiality distributions are assumed to be Gaussian, with the mean indicated by the filled squares, and the standard deviation indicated by the open vertical bars. The 1σ uncertainties on the mean and scatter are indicated by the error bars. Essentially all present-day galaxies have large ellipticities, and small triaxialities—they are almost all fairly thin disks. Toward higher redshifts low-mass galaxies become progressively more triaxial. High-mass galaxies always have rather low triaxialities, but they become thicker at z 2. ∼ (A color version of this figure is available in the online journal.)

van der Wel+2014 Figure 4. Color bars indicate the fraction of the different types of shape deﬁned in Figure 2 as a function of redshift and stellar mass. The negative redshift bins representSee the also SDSS Morphological results for z<0.1; the Survey other bins of are Galaxies from 3D-HST z=1.5-3.6/CANDELS. Law, Steidel+ ApJ 2012 (A color version of this ﬁgure is available in the online journal.) When Did Round Disk Galaxies Form? T. M. Takeuchi+ ApJ 2015 Letter allows us to generalize this conclusion to include earlier Despite this universal dominance of disks, the elongatedness epochs. of many low-mass galaxies at z ! 1impliesthattheshapeof At least since z 2moststarformationisaccountedforby agalaxygenerallydiffersfromthatofadiskatearlystages 10 ∼ !10 M galaxies (e.g., Karim et al. 2011). Figures 3 and 4 in its evolution. According to our results, an elongated, low- show that⊙ such galaxies have disk-like geometries over the same mass galaxy at z 1.5 will evolve into a disk at later times, or, redshift range. Given that 90% of stars in the universe formed reversing the argument,∼ disk galaxies in the present-day universe over that time span, it follows that the majority of all stars in the do not initially start out disks.13 universe formed in disk galaxies. Combined with the evidence As can be seen in Figure 3, the transition from elongated that star formation is spatially extended, and not, for example, to disky is gradual for the population. This is not necessarily concentrated in galaxy centers (e.g., Nelson et al. 2012;Wuyts et al. 2012)thisimpliesthatthevastmajorityofstarsformedin 13 This evolutionary path is potentially interrupted by the removal of gas and disks. cessation of star formation.

4 Our cosmological zoom-in simulations often produce elongated galaxies like observed ones. The elongated stellar distribution follows the elongated inner dark matter halo. MNRAS 453, 408–413 (2015) doi:10.1093/mnras/stv1603 Formation of elongated galaxies with low masses at high redshift Formation of elongated galaxies with low masses at high redshift Daniel Ceverino, Joel Primack and Avishai Dekel DanielABSTRACT Ceverino,1,2‹ Joel Primack3 and Avishai Dekel4 1WeCentro report de Astrobiolog the identiﬁcation´ıa (CSIC-INTA), of elongated Ctra de Torrej (triaxialon´ a Ajalvir, or prolate) km 4, E-28850 Torrejon´ de Ardoz, Madrid, Spain 2galaxiesAstro-UAM, in Universidad cosmological Autonoma simulations de Madrid, at Unidadz ~ 2. AsociadaThese are CSIC, E-28049 Madrid, Spain 3 Department of Physics, University of California, Santa9.5 Cruz, CA 95064, USA 4preferentiallyCenter for Astrophysics low-mass and Planetary galaxies Science, (M∗ ≤ Racah 10 InstituteM⊙), residing of Physics, in The Hebrew University, Jerusalem 91904, Israel Dark matter halos are elongated, especially ! near their centers. Initially stars follow the ! dark matter (DM) haloes with strongly elongated inner parts, a gravitationally dominant dark matter, as shown.! common feature of high-redshift DM haloes in the cold dark But later as the ordinary matter central density Acceptedmatter cosmology. 2015 July 14. A Received large population 2015 June 26; of in originalelongated form galaxies 2015 April 20 grows and it becomes gravitationally dominant, produces a very asymmetric distribution of projected axis ratios, the star and dark matter distributions both Downloaded from become disky — as observed by Hubble as observed in high-z galaxy surveys. This indicates that the Space Telescope (van der Wel+ ApJL Sept majority of the galaxies at high redshiftsABSTRACT are not discs or spheroids 2014).! but rather galaxies with elongatedWe morphologies report the identiﬁcation of elongated (triaxial or prolate) galaxies in cosmological simulations at z 2. These are preferentially low-mass galaxies (M 109.5 M ), residing in dark ≃ ∗ ≤ matter (DM) haloes with strongly elongated inner parts, a common feature⊙ of high-redshift

Nearby large galaxies are mostly disks and spheroids — but they start out looking more like pickles. http://mnras.oxfordjournals.org/ DM haloes in the ! cold dark matter cosmology. Feedback slows formation of stars at the centres of these haloes, so that a dominant and prolate DM distribution gives rise to galaxies elongated along the DM major axis. As galaxies grow in stellar mass, stars dominate the total mass within the galaxy half-mass radius, making stars and DM rounder and more oblate. A large population of elongated galaxies produces a very asymmetric distribution of projected axis ratios, as observed in high-z galaxy surveys. This indicates that the majority of the galaxies at high redshifts are not discs or spheroids but rather galaxies with elongated morphologies. Key words: galaxies: evolution – galaxies: formation. at University of California, Santa Cruz on October 16, 2015

cluded that the majority of the star-forming galaxies with stellar 1INTRODUCTION masses of M 109–109.5 M are elongated at z 1. At lower The intrinsic, three-dimensional (3D) shapes of today’s galaxies redshifts, galaxies∗ = with similar⊙ masses are mainly oblate,≥ disc-like can be roughly described as discs or spheroids, or a combination of systems. It seems that most low-mass galaxies have not yet formed the two. These shapes are characterized by having no preferential a regularly rotating stellar disc at z ! 1. This introduces an interest- long direction. Examples of galaxies elongated along a preferential ing theoretical challenge. In principle, these galaxies are gas-rich direction (prolate or triaxial) are rare at z 0(Padilla&Strauss and gas tends to settle in rotationally supported discs, if the angular 2008;Weijmansetal.2014). They are usually= unrelaxed systems, momentum is conserved (Fall & Efstathiou 1980;Blumenthaletal. such as ongoing mergers. However, at high redshifts, z 1–4, we 1986;Mo,Mao&White1998;Bullocketal.2001). At the same may witness the rise of the galaxy structures that we see= today at time, high-mass galaxies tend to be oblate systems even at high-z. the expense of other structures that may be more common during The observations thus suggest that protogalaxies may develop an those early and violent times. early prolate shape and then become oblate as they grow in mass. Observations trying to constrain the intrinsic shapes of the stellar Prolateness or triaxiality are common properties of dark mat- components of high-z galaxies are scarce but they agree that the ter (DM) haloes in N-body-only simulations (Jing & Suto 2002; distribution of projected axis ratios of high-z samples at z 1.5–4 Allgood et al. 2006; Bett et al. 2007;Maccioetal.` 2007;Maccio,` is inconsistent with a population of randomly oriented disc= galaxies Dutton & van den Bosch 2008;Schneider,Frenk&Cole2012, (Ravindranath et al. 2006;Lawetal.2012;Yuma,Ohta&Yabe and references therein). Haloes at a given mass scale are more pro- 2012). After some modelling, Law et al. (2012) concluded that late at earlier times, and at a given redshift more massive haloes the intrinsic shapes are strongly triaxial. This implies that a large are more elongated. For example, small haloes with virial masses 11 population of high-z galaxies are elongated along a preferential around Mv 10 M at redshift z 2areasprolateastoday’s direction. galaxy clusters.≃ Individual⊙ haloes are= more prolate at earlier times, van der Wel et al. (2014) looked at the mass and redshift de- when haloes are fed by narrow DM ﬁlaments, including mergers, pendence of the projected axis ratios using a large sample of star- rather than isotropically, as described in Vera-Ciro et al. (2011). The forming galaxies at 0

C ⃝ 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society FormationIn hydro of sims, elongated dark-matter galaxies dominated with low galaxies masses are at Daniel Ceverino, Joel Primack and Avishai Dekel MNRAS 2015 high redshift prolateCeverino, Primack, DekelMNRAS 453, 408 (2015) 10 Stars M* <10 M☉ at z=2

Dark matter

Also Tomassetti et al. 2016 MNRAS Simulated elongated galaxies are aligned with cosmic web ﬁlaments, become round after compaction 20 kpc (gas inﬂow fueling central starburst) Quantifying and Understanding the Galaxy — Halo Connection July 7, 2017

Structural Evolution in the Galaxy-Halo Connection, and Halo Properties as a Function of Environment Density and Web Location

Joel Primack

● Abundance matching with radii & mergers ⇒ R*~M*⅓ goes to R*~M*2 after quenching, &

quenching downsizing: ∑1 grows till quenching, ∑1,quench larger & at higher z for higher M*

● 2-pt Correlation Functions for SHAM with Mvir & Mpeak (OK) and Vmax & Vpeak (better)

● Halo properties Ṁ/M, λ, CNFW, aLMM, shape don’t depend on web location at fixed density

● Spin λ 30% smaller at low density tests whether galaxy R* is determined by host halo λ

● Halo Mass Loss: Evaporation after Merger ⇒ CNFW ⬇ & λ⬆, Tidal Stripping ⇒ CNFW ⬆ & λ⬇

● Galaxy Luminosity-Halo Mass, Stellar Mass-Halo Mass relations are independent of density

● Forming galaxies are elongated & oriented along filaments, become round after compaction