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( J E 1/2 = | | GM 5/2 dM dM baryon = ✏(M ) DM dt halo dt dMgas = SFR(t)+ ⇤ (t) d+t Ewind + J E 1/2 = | | 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) 101 ) 1 p 10 (r p M !5log(h) 100 102 Simple Abundance Matching Abundance"Matching:"-1 101 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) 1 ) p 10 p §5foramoredetaileddiscussionoftheHODassociated(r (r p p M !5log(h) with this model. ! The good agreement between the observed galaxy cor- MB!5log(h)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) The projected two-point correlation function, ωp(rp), dition, Coilp et al. (2005b) has estimated the two-point §5foramoredetaileddiscussionoftheHODassociated (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) 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. Stellar0.2 mass- and color-dependent10 1* clustering2 as predictedRp [Mpc/h]10by our* age matching0.2 formalism. Top10 Row* 1 :Theprojected2 correlation function (multiplied by rp)predictedbyourmodel(blacksolidcurves)ascomparedtothe clustering of three SDSS stellar mass threshold samples: log (M∗) > [9.8, 10.2, 10.6]. Bottom Row:Correlationfunctionssplitbycolorforred(blue)mock ] 10 galaxies2 shown10.0 with red (blue) solid curves. Red (blue) points show the clustering of red (blue) SDSS galaxies. Solid bands in Behroozi+15 each panel show the error in our model prediction as described § 5.1. The slight under-prediction of abundance matching on small /pc Hearin+14 scales • O for the log10(M∗) > 10.2sample(top,centerpanel)propagatesthroughtothecolorsplit (bottom, center panel), though the relative clustering strength of red and blue galaxies is captured by the model at all stellar masses and over all scales. [M 1.0 ∆Σ RED group multiplicity 6.3 Galaxy-Galaxy Lensing 6.4BLUE Galaxy Group Environment 0.1 RSD multipolesIn addition to wp (rp)and∆Σ,weemployagroup-finder While the 2PCF encodes rich information about the galaxy-halo connection,200 measurements1000 of galaxy-galaxy200 to test1000 how well our200 model predicts the1000 scaling of central Reddick+13 lensing have been shown to break degeneracies between and satellite color with host halo mass. As our proxy for R [kpc] R [kpc] BCG R [kpc] galaxy-halo parameters that are present when model con- halo mass we use M∗ , the stellar mass of the group’s straintsFigure are 3. derived∆Σ as a from function clustering of stellar measurements mass and color. alone As was showncentral for the galaxy.projected In Fig. clustering 4, we in show Fig. the 2, the mean top rowg − isr thecolor BCG (e.g.,abundance More et matching al. 2013). result To for that all galaxies end, in and Fig. the 3 bottomwe com- rowshowsthepredictedcolorsplitfromouragematchingmodelof group galaxies as a function of M∗ .Weshowthe(red and blue solid curves) as compared to new SDSS galaxy-galaxy lensing measurements. Derived errors for the data and the model pare our model prediction to new measurements of the results for central galaxies and satellites from left to right, are described in § 2.4 & § 5.2, respectively. stellar mass- and color-dependent galaxy-galaxy lensing respectively. The dashed line is the mean g − r color of BCG signal, ∆Σ.Aswasthecaseforthe2PCFcomparison,we the mock galaxies in a given M∗ bin. The solid gray accurately predict ∆Σ at the abundance matching level region shows Poisson errors on the mean color in each bin. (black solid1.2 curves versus SDSS solid black data points 1.0 in the top row), though the amplitude of the model pre- Our predicted mean satellite color is in good agree- diction appears1.1 slightly boostedSDSS relative to the data for ment the data over the full host halo mass range probed 0.9 all three stellar mass thresholds.MOCK Red and blue filled cir- by our galaxy sample. This is also true for central galax- cles in all panels represent the red and blue SDSS galaxy ies, excepting some slight tension at the low M BCG end. 1.0 ∗ populations, respectively, while red and blue solid curves Again,0.8 we emphasize that we have not tuned any param- are the model predictions according to age matching. The eters in our model. The successful prediction for central 0.9 separationg - r in ∆Σ between red and blue samples is pre- andg - r satellite colors naturally emerges from the age distri- dicted reasonably well, excepting only blue samples on bution0.7 matching formalism. Specifically, at fixed stellar small scales,0.8 where measurement errors become large. mass, the colors of our mock galaxies are drawn from the 0.6 0.7 CENTRALS ⃝c 0000 RAS,SATELLITES MNRAS 000,000–000 0.6 0.5 10.0 10.5 11.0 11.5 12.0 10.0 10.5 11.0 11.5 12.0 BCG BCG log10(M* ) [MO •] log10(M* ) [MO •] BCG Figure 4. Mean g-r color as a function of stellar mass of the brightest central galaxy, M∗ ,forSDSSgalaxies(blackfilled circles) and the prediction from our mock catalog (dashed curves). Solid gray bands indicate Poisson error estimations.Results for central galaxies are shown in the left panelYamamoto+15 and satellitegalaxiesintheright. Hearin+12 ⃝c 0000 RAS, MNRAS 000,000–000 Simple Abundance Matching Formulation details significantly impact level of success Which subhalo property? How far down the mass function? Resolution requirements? Reddick+12 Garrison-Kimmel+13 Guo & White 2013 What do we learn from abundance matching? Whenever you get so much for so little, nature is telling you your assumptions must be reasonably correct Basic lesson: Depth of the gravitational potential well is the coarse-grained halo property with the dominant influence on galaxy mass What do we learn from abundance matching? BrightestModel Cluster parameters Galaxies in have Cosmological universal Simulations translation5 Provides boundary conditions for more fine-grained models 1014 1014 1013 1013 12 ⊙ ⊙ 10 M M / / 1012 25 tot , , ∗ ∗ M M 1011 Behroozi+ (2013) - z =0 1011 Moster+ (2013) - z =0 KVM 2014 - w/o scatter 1010 Hansen+ (2009) - z =0 KVM 2014 - w scatter z = 0 -AGN-ON z = 0 -AGN-ON z = 0 -AGN-OFF z = 0 -AGN-OFF 1010 1014 1015 1014 1015 M200c/M⊙ M200c/M⊙ Martizzi+14 Figure 2. Left: Results from our simulations versus the halo mass vs. stellar mass relation at redshift z =0fromHansenetal.(2009) (blue line, with its 1σ scatter), Moster et al. (2013) (green line), Behroozi et al. (2013) (red line, with its 1σ scatter). Our AGN-ON simulations are represented by the red triangles, whereas the AGN-OFF simulations are represented by black squares. TheBCGstellar −2 mass definition assumes a surface brightness limit µV =25mag/arcsec .Right:Halomassvs.stellarmassrelationatredshiftz =0 from Kravtsov et al. (2014) (cyan line) versus our simulations. Our AGN-ON simulations are represented by the red triangles, whereas the AGN-OFF simulations are represented by black squares. The stellar mass on the y axis is the total stellar mass associated to the BCG+ICL component. 15 z=0− AGN − OFF 0 z=0− AGN − ON 10 20 ] 2 tot 25 , ∗ arcsec M / / −1 ∗ 10 M mag [ v µ 30 35 z=0− AGN − OFF z=0− AGN − ON 10−2 10 100 20 22 24 26 28 30 32 34 36 2 R[kpc] µv[mag/arcsec ] Figure 3. Left: V-band surface brightness for all the BCGs in our sample. AGN-ON is shown in red, AGN-OFF is shown in black. The −2 green dashed line represents the surface brightness cut adopted to define galaxy masses µV =25mag/arcsec .Thebluedashedline −2 represents an alternative cut µV =27mag/arcsec which allows to include most of the Intracluster Light in the stellar mass estimate. Right: normalized stellar mass as a function of the adopted magnitude cut for all the BCGs. The mass distribution includesBCG+ICL. −2 −2 The green and blue lines represent µV =25mag/arcsec and µV =27mag/arcsec ,respectively. What do we learn from abundance matching? Model parameters have universal translation Provides boundary conditions for more fine-grained models Matthee+16 Halo Occupation Distribution Based on host halos only Parameterized form of P(Ncen|Mhalo) & P(Nsat|Mhalo) M1 HOD Model 100.00 All Galaxies M2 Red Galaxies Blue Galaxies 10.00 M3 1.00 0.10 Number of Galaxies 0.01 1011 1012 1013 1014 1015 Halo Mass Halo Occupation Distribution HOD functional forms physically motivated by hydro sims, SAMs, and subhalo occupations Berlind et al. (2003) Kravtsov et al. (2004) Halo Occupation Distribution Occupation statistics ==> galaxy clustering M1 M2 M3 Halo Occupation Distribution Successful fits to galaxy clustering, including dependence on Mr brightness Zehavi+11 Halo Occupation Distribution Successful fits to galaxy clustering and lensing, including dependence on g-r color Zehavi+11 Zu & Mandelbaum (2016) Halo Occupation Distribution Successful fits to galaxy clustering, including dependence on redshift COSMOS PRIMUS Leauthaud, Tinker et al. (2011) Skibba, Coil et al. (2015) Halo Occupation Distribution Cosmological parameter estimation Cosmological Constraints from Clustering and Lensing 11 Tinker+11 Reid+14 Figure 4. Cosmological constraints for the Fiducial model. Histograms show the marginalized posterior distributions, while the blue contour show the 68% and 95% CLs of the joint, two-dimensionalmarginalizedposteriordistributions.Forcomparison,the corresponding CLs from WMAP7 are shown as green contours, while the red, solid curves show the marginalized WMAP7 prior distributions used for Cacciato+122 the secondary cosmological parameters, ns, h and Ωb h . σ8 inherent in our analysis runs perpendicular to that in- two-dimensional (contour plots) marginalized posterior dis- herent in the CMB data. This indicates that a combined tributions on all five cosmological parameters. Solid con- analysis will be able to significantly tighten the constraints tours indicate the 68% and 95% CLs obtained from the on Ωm and σ8 (see also Paper II). Finally, Fig. 3 suggests analysis presented here, while the dotted contours are the that our constraints are even tighter than those from the 68% and 95% CLs from the WMAP7 analysis, shown for WMAP7 analysis. However, we emphasize that this is not a comparison. The strongest parameter degeneracies are be- fair comparison since we have used priors from WMAP7 on tween Ωm and σ8 (cross-correlation coefficient r = 0.81), 2 2 − the secondary cosmological parameters ns, h and Ωb h ,but between Ωb h and ns (r =0.79), and between Ωm and h not on Ωm or σ8 (see Paper II for the case with no priors on (r = 0.74). All other combinations are only weakly corre- 2 − ns, h and Ωb h ). lated with r < 0.5. | | Fig. 4 shows the one-dimensional (histograms) and joint Overall, there is good agreement between our con- ⃝c 2008 RAS, MNRAS 000,1–21 What do we learn from the HOD? Whenever you get so much for so little, nature is telling you your assumptions must be reasonably correct Basic lesson: Depth of the gravitational potential well has the dominant influence on galaxy mass and color/SFR Halo Occupation Distribution Quantitative constraints on the strength of assembly bias with the Decorated HOD Hearin+15 Zentner+16 (see Halotools for python implementation) Halo Occupation Distribution Central assembly bias well-constrained away from zero Mr < -20 Central galaxy Zero assembly bias assembly bias strength parameter constraints Zentner+16 See also Vakili & Hahn 2016 Halotools Open-source python library for galaxy—halo modeling of large-scale structure halotools.readthedocs.io Simple Age Matching Construction of the Halo--SFR map Formulation has direct mathematical analogy to simple abundance matching high-mass low-mass galaxies Ingredient 1: Halo mass galaxies regulates available SFR high-mass low-mass halos halos Simple Age Matching Construction of the Halo--SFR map Ingredient 2: Galaxy SFR ∝ Halo “age” at fixed halo mass old, slow-accreting, young, fast-accreting, early-forming actively-forming halos halos Mhalo Mhalo Mhalo Hearin & Watson 2013 Simple Age Matching Many different successful predictions with few parameters and two simple ingredients galaxy clustering & lensing satellite quenching profiles Watson et al. 2015 RSD multipoles Central & satellite color vs. group mass Yamamoto et al. 2016 Hearin et al. 2014 Simple Age Matching Formulation details significantly impact level of success Red/blue SHMR Galactic Conformity Mandelbaum et al. 1014 (2015) More et al. ] (2011) age-matching M 1 13