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Galaxy—Halo Modeling of Large-Scale Structure

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Galaxy—Halo Modeling of Large-Scale Structure Andrew Hearin, Argonne National Lab Theory overview, lessons from previous successes, Galaxy—Halo Modeling and guidelines for a future of forward-modeling diverse of Large-Scale Structure datasets Galaxy Formation Theory “Fundamental” theory has been complete for decades LQCD + LEW LQCD + LEW LQCD + LEW LQCD + LEW LQCD + LEW LQCD + LEW LQCD + LEW Coarse Grained Models “Fundamental” theory is hopeless Hydro sims, SAMs, empirical models are coarse-grained models of the fundamental theory Mapping Simulated to Real Quantities An extremely high-dimensional problem High-dimensional space of possible functions F1 F2 F3 Simulated density field Galaxy distribution F1 F2 F3 Simplifying the Problem Dark Matter Halos: Fundamental building blocks of large-scale structure e.g. White & Rees 78 Dark Matter Halos Host halos and subhalos Host halo Subhalo Subhalo Host halo boundary (aka “virial radius”) Subhalo Coarse Grained Models Three complementary approaches 1 Hydro Semi-analytic model Empirical model Vmax = GM(<R)/R J E 1/2 λ = | | GM 5/2 dM dM baryon = ✏(M ) DM dt halo dt dMgas = SFR(t)+ ⇤ (t) d+t − Ewind + J E 1/2 λ = | | GM 5/2 dM dM baryon = ✏(M ) DM dt halo dt dMgas = SFR(t)+ ⇤ (t) dt − Ewind ... = ... c 0000 RAS, MNRAS 000,000–000 Mapping Simulated to Real Quantities Basic Approach: Determine map from (sub)halos —> galaxies Building a Galaxy—Halo Model Simple abundance matching ansatz Host halo Central galaxy Subhalo Satellite galaxy Satellite galaxy Subhalo Satellite galaxy Subhalo Building a Galaxy—Halo Model Simple abundance matching ansatz Bigger (sub)halos Bigger galaxies Smaller (sub)halos Smaller galaxies MODELING GALAXY CLUSTERING THROUGH COSMIC TIME 7 3 10 102 Mr!5log(h)<!21.0 Mr!5log(h)<!20.0 Mr-5log(h)<-21 Mr-5log(h)<-20 Mr-5log(h)<-19 Mr-5log(h)<-18 102 101 ) 1 p 10 (r p M !5log(h)<!19.0 M !5log(h)<!18.0 ! r r <N(M)> 100 102 Simple Abundance Matching Abundance"Matching:"-1 1 10 10 1011 1012 1013 1014 -1 0.1 1.0 0.1 1.0 10.0 Mass (h MO •) r (h!1 Mpc) QuantitativeSuccessful"prediction"of"galaxy"clustering7p level of success is (should be) startling! Fig. 5.— Left: Comparison between the SDSS projected correlation function(points)andthecorrelationfunctionderivedfromhalos (solid lines) for various luminosity threshold samples. Forcomparisonweincludethecorrelationfunctionofdarkmatter particles (dotted lines) at the median redshift of the sample. Right: The first moment of the halo occupation distribution (HOD) forthefourhalosamples. For all four samples, the gradual roll-off at small mass is due to scatter in the Vmax -mass relation. The fan (dotted lines) corresponds to slopes of 0.4, 0.7, and 1.0. SDSS"(z~0.1)7MODELING GALAXY CLUSTERING THROUGH COSMIC TIME 7 3 DEEP2"(z~1)7 the halo samples10 corresponding to brighter galaxy 102 Mr!5log(h)<!21.0 Mr!5log(h)<!20.0 samples reside preferentially in more massive distinct Mr-5log(h)<-21 MB!M5log(h)<-5log(h)<-20!20.5 MB!5log(h)<!20.0 halos. The halo sample corresponding to the brightest r Mr-5log(h)<-19 galaxies (Mr − 5logh<−21) rarely has more than one 2 Mr-5log(h)<-18 2 10 halo per distinct10 halo. All three halo samples display a gradual roll-off in ⟨N(M)⟩ at low mass which is simply 101 due to scatter in the Vmax -mass relation, as we select 1 samples using Vmax ,butplotasafunctionofmass.See 10 ) 1 ) p p 10 §5foramoredetaileddiscussionoftheHODassociated(r (r p p M !5log(h)<!19.0 M !5log(h)<!18.0 ! r r <N(M)> with this model. ! The good agreement between the observed galaxy cor- MB!5log(h)<!19.5 MB!5log(h)<!19.0 0 relation function and samples of halos with our L−Vmax 10 102 model, over a range102 of luminosities and scales, suggests that the luminosity dependence of galaxy clustering is due primarily to how galaxies form within dark matter halos. This implies that galaxy properties vary as a func- 1 10 -1 tion of larger scale1 environment only insofar as the halos 10 10 11 12 13 14 in which the galaxies reside vary. 10 10 10 10 0.1 1.0 0.1-1 1.0 10.0 0.1 1.0 0.1 1.0 10.0 Mass (h MO •) !1 !1 r (h Mpc) rp (h Mpc) 4.2. Clustering at pz ∼ 1 Conroy"et"al."20067 The DEEP2Fig. 5.— GalaxyLeft: Comparison Redshift between Survey the SDSS (Davis projected et al. correlation function(points)andthecorrelationfunctionderivedfromhalos (solid lines) for various luminosity threshold samples. ForcomparisonweincludethecorrelationfunctionofdarkmatFig. 6.— Projected two-point correlation functionter particles at z (dotted∼ 1for 2004) haslines) gathered at the median optical redshift spectra of the for sample.∼ 50Right:, 000The galaxies first momentDEEP2 of the halo galaxies occupation (solid distributioncircles) and (HOD) halos (solid forthefourhalosamples. lines), at four differ- at z ∼ 1usingtheDEIMOSspectrographontheKeckIIFor all four samples, the gradual roll-off at small mass is due to scatterent luminosity in the Vmax thresholds.-mass relation. We The include fan (dotted jack-knife lines) errors, corresponds computed to 10-m telescope.slopes of 0.4, The 0.7, survey, and 1.0. recently completed, spans a using the eight octants of the simulation cube, on the model pre- 6 −3 3 2 diction for the brightest sample to demonstrate that they agree comoving volume of ∼ 10 h Mpc ,covering3deg over within 1σ.Theexcellentagreementonallscalesforthesefour four widely separated fields. We use the DEEP2 B-band samples suggests that luminosity-dependent clustering is aresult luminositythe function halo samples of Willmer corresponding et al. (2005) to tobrighter compute galaxy of two effects: a simple relation between galaxy luminositiesand samples reside preferentially in more massive distinct dark matter halos, and the spatial clustering of the halos. For com- the L−Vmax relation at z ∼ 1. A Schechter fit to the M !5log(h)<!20.5 M !5log(h)<!20.0 halos. The halo sample corresponding∗ to the brightest parison, we include the correlationB function of darkB matter particles overall luminosity function yields MB − 5logh = −20.73 (dotted lines). and φ∗ =8galaxies.7×10 (M−3rh−−35logMpch<3 with−21)α rarelyfixed has at α more= −1 than.30. one 102 Adetailedcomparisonhasshownthatthesevaluesarehalo per distinct halo. All three halo samples display a gradual roll-off in ⟨N(M)⟩ at low mass which is simply consistent with other estimates of the global luminosity due to scatter in the Vmax -mass relation, as we select function at z ∼ 1(Faberetal.2005). luminosity and1 color (Coil et al. 2004, 2005b,a). In ad- samples using Vmax ,butplotasafunctionofmass.See 10 ) The projected§5foramoredetaileddiscussionoftheHODassociated two-point correlation function, ωp(rp), dition, Coilp et al. (2005b) has estimated the two-point (r has been measured for DEEP2 galaxies as a function of cross correlationp between galaxies and groups, and be- with this model. ! The good agreement between the observed galaxy cor- MB!5log(h)<!19.5 MB!5log(h)<!19.0 relation function and samples of halos with our L−V max 2 model, over a range of luminosities and scales, suggests 10 that the luminosity dependence of galaxy clustering is due primarily to how galaxies form within dark matter halos. This implies that galaxy properties vary as a func- 101 tion of larger scale environment only insofar as the halos in which the galaxies reside vary. 0.1 1.0 0.1 1.0 10.0 !1 rp (h Mpc) 4.2. Clustering at z ∼ 1 The DEEP2 Galaxy Redshift Survey (Davis et al. Fig. 6.— Projected two-point correlation function at z ∼ 1for 2004) has gathered optical spectra for ∼ 50, 000 galaxies DEEP2 galaxies (solid circles) and halos (solid lines), at four differ- at z ∼ 1usingtheDEIMOSspectrographontheKeckII ent luminosity thresholds. We include jack-knife errors, computed 10-m telescope. The survey, recently completed, spans a using the eight octants of the simulation cube, on the model pre- 6 −3 3 2 diction for the brightest sample to demonstrate that they agree comoving volume of ∼ 10 h Mpc ,covering3deg over within 1σ.Theexcellentagreementonallscalesforthesefour four widely separated fields. We use the DEEP2 B-band samples suggests that luminosity-dependent clustering is aresult luminosity function of Willmer et al. (2005) to compute of two effects: a simple relation between galaxy luminositiesand dark matter halos, and the spatial clustering of the halos. For com- the L−Vmax relation at z ∼ 1. A Schechter fit to the ∗ parison, we include the correlation function of dark matter particles overall luminosity function yields MB − 5logh = −20.73 (dotted lines). and φ∗ =8.7×10−3h−3 Mpc3 with α fixed at α = −1.30. Adetailedcomparisonhasshownthatthesevaluesare consistent with other estimates of the global luminosity function at z ∼ 1(Faberetal.2005). luminosity and color (Coil et al. 2004, 2005b,a). In ad- The projected two-point correlation function, ωp(rp), dition, Coil et al. (2005b) has estimated the two-point has been measured for DEEP2 galaxies as a function of cross correlation between galaxies and groups, and be- Simple Abundance Matching Large-scale structure success is diverse satellite fractions 8 Hearingalaxy-galaxy et al. lensing Distribution of close pairs log10(M*) > 9.8 log10(M*) > 10.2 log10(M*) > 10.6 ] 2 [Mpc p 100 r × ) p (r p w SDSS Galaxies ALL zGALAXIES ~ 0.1 10 The Dark Side of Galaxy Color 9 0.1 1 10 Rp [Mpc/h] 0.1 1 10 log10(M*) > 9.8 log10(M*) > 10.2 log10(M*) > 10.6 ] 2 100.0 log10(M*) > 9.8 log10(M*) > 10.2 log10(M*) > 10.6 [Mpc p 100 ] r 2 × 10.0 ) p /pc (r • O p RED w [M BLUE 1.0 ∆Σ 10 0.1 1.0 10.0 ALL GALAXIES1.0 10.0 1.0 10.0 0.1 rp [Mpc] rp [Mpc] rp [Mpc] 100.0 log (M ) > 9.8 log (M ) > 10.2 log (M ) > 10.6 Figure 2.
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