The Masses of Galaxies from the Galaxy-Halo Connection

Transcription

1 with Charlie Conroy (Princeton) Peter Behroozi (KIPAC/Stanford) R isa Wechsler The Masses of Galaxies from the Galaxy-Halo Connection

2 The Basic Idea Theory: We now have a reasonable accounting for the distribution of mass in the Universe, and how this mass assembles over time, from numerical simulations. Observations: We now have statistically well-measured galaxy populations at various epochs. Use these two sets of information to get empirical constraints on the connection between stellar masses of galaxies and total masses of dark halos at given epochs. This can be extended to infer how galaxies grow and form stars over time. the galaxy-halo connection: methods & constraints what can the galaxy-halo connection teach us about how galaxies are assembled and how they form stars? current uncertainties in the galaxy-halo connection

3 galaxy/halo abundance (mass function) galaxy/halo abundance galaxy/halo clustering (bias function) galaxy / halo mass galaxy bias halo bias Mo & White 1996 Seljak & Warren 2004 galaxy luminosity Zehavi et al 2004 halo mass

4 The halo counting approach SubHalo Abundance Matching (SHAM) similar to the HOD approach, but instead assume that each galaxy lives in a / halo/subhalo, go from directly to galaxies using some mass-connected property luminosity/stellar mass function Cumulative luminosity function velocity/halo mass v function max Cumulative circular velocity function Kravtsov N-body prediction V max [km/s] 200 Sheth-Tormen prediction M r 5logh assign luminosities to subhalo circular velocities by matching n(>v max ) to n(>l) clearly motivated by tightness in FP & TF v max e.g. Kravtsov, Berlind, RW, et al 2004; Conroy, RW & Kravtsov 2006; Conroy & Wechsler 2008 also Vale & Ostriker 2006, 2007; Wang et al 2006; Kim et al 2008; Moster et al 2008; etc etc.

5 Wechsler et al 2002 Distinct Halo Evolution Subhalo Evolution Accretion epoch V max, mass 1/3 Constant increase V max, mass 1/3 increase decrease Time Time

6 galaxy-galaxy correlation function at higher redshift SDSS, z=0 data: Zehavi et al 2004 Subaru, z=4-5 data: Ouchi et al 2005 the scale of typical halos dark matter Conroy, Wechsler, & Kravtsov 2006 the scale & luminosity dependence of galaxy clustering at high z are very well explained by this simple approach!

7 additional clustering statistics provide further tests model makes predictions for a variety of statistics, e.g.: 1. galaxy-mass correlations (Tasitsiomi et al 2004) 2. close pair statistics & evolution (Berrier et al 2006) 3. 3pt statistics (Marin et al 2008) 4. high redshift galaxy clustering (Lee et al 2009) 5. properties of galaxies in clusters (RW et al in prep, Vale & Ostriker) (related model in talk by Cacciato) fiducial model described by one (well-constrained) parameter! (for a given cosmology) What can we learn from this? What are the uncertainties?

8 Connection between galaxy mass and halo mass integrated star formation efficiency average stellar mass η M star / M vir / f b log[m star (M sun )] stellar mass growth dominates z=0 z=0 z=2 z=2 halo growth dominates inputs: HMF(z) & GSMF(z) Mhalo ~12.5 or M* ~11 marks the transition between dominant halo growth and dominant stellar mass growth peak of integrated star formation efficiency shifts to lower mass with time peak of integrated star formation efficiency increases by ~ 4x from z=2 to z=0. (uncertain by a factor of ~2) halo log[m mass (z) at (M redshift )] z Conroy & Wechsler 08

9 Connection between galaxy mass and today s halo mass average stellar mass log[m star (M sun )] z=0 z=2 additional inputs: MAH(M) this the only additional ingredient needed to infer the average stellar mass growth of galaxies! as we saw previously, virtually no room for growth at the massive end (stellar mass is in place early for massive galaxies) integrated star formation efficiency!" M star / M vir / f b 0.10 z=0 z=2 very rapid mass growth for low mass galaxies vertical lines in this plot give you the evolution along trajectories halo l [M mass ( 0) (M at z=0 )] Conroy & Wechsler 08

10 Growth of Stellar Mass vs. Growth of Halo Mass formation redshift mass builds-up hierarchically: small halos get more fractional mass earlier than larger mass halos stellar mass build-up proceeds the other way: stars in massive galaxies in place by z=1; still rapidly forming in small galaxies

11 The star formation rate as a function of stellar mass additional model inputs: (1) amount stellar mass buildup due to merging (2) stellar mass loss specific star formation rate log[ssfr (Gyr -1 )] z=0.1 z=0.5 z=1.0 z=0.1, Salim et al. log[ssfr (Gyr!1 )] 1 0!1!2 z=0.1 z=0.5 z=1.0 star formation rate log(sfr (M sun yr -1 )] N07, z=0.5 N07, z=1.0 Noeske et al 2007; Zheng et al l [M (M )] log stellar mass Z07, z=0.5 Z07, z=0.9 log(sfr (M sun yr!1 )] 1 0! log[m (z) (M )]

12 Sources of error in the galaxy mass-halo mass relation Behroozi, Conroy & RW 2009 halo mass function cosmology dependence uncertainty in mass function for a given cosmology stellar mass function measurement error (poisson + sample variance) systematic errors in stellar masses random errors in stellar masses (Conroy et al 08) matching assumption scatter in M*-M for central galaxies assignment scheme for satellite galaxies

13 Sources of error in the galaxy mass-halo mass relation: stellar mass function statistical errors Behroozi, Conroy & RW 2009 Li & White z = 0.1 (WM5) z = 0.5 (WM5) z = 1.15 (WM5) z = 1.7 (WM5) M h / M * log 10 (M h ) [M ] O Marchesini et al 2009 z=0 Li & White 2009 z=0.5, 1 Perez-Gonzalez et al 2008 z= 1.7 Marchesini et al 2009 (converted to Chabrier IMF) statistical errors only.

14 Sources of error in the galaxy mass-halo mass relation: the halo mass function 1000 z = 0.1 (Wmap5) z = 0.1 (Wmap5,! 8 =0.912) z = 0.1 (Wmap5,! 8 =0.712) z = 0.1 (Wmap1) M h / M * log 10 (M h ) [M ] O (remove other s8, add z=1) errors include statistical errors on the SMF + error on the HMF

15 Sources of error in the galaxy mass-halo mass relation: systematics in matching galaxies to halos scatter in central galaxy mass assignment of satellite galaxies 1000 z = 0.0,! log M* = 0.32dex z = 0.0,! log M* = 0.16dex z = 0.0,! log M* = 0.00dex M h / M * log 10 (M h ) [M ] O Scatter no longer unknown! measurements from: maxbcg clusters (Wechsler et al in prep: σloglc (M)= 0.16) satellite dynamics: σloglc (M)= 0.16 galaxy clustering/hod e.g. Zheng et al 2008: σloglc (M)= 0.15 weak lensing (see Tasitsiomi et al 04, Cacciato talk)

16 Sources of error in the galaxy mass-halo mass relation: stellar mass function systematic errors 1000 z = 0.1 (WM5) z = 0.5 (WM5) z = 1.15 (WM5) z = 1.7 (WM5) add comparion of Li & White with statistical errors. M h / M * log 10 (M h ) [M ] O

17 Sources of error in the galaxy mass-halo mass relation: stellar mass function random errors M h / M * z = 0.1 (Wmap5) z = 0.5 (Wmap5) z = 1.15 (Wmap5) z = 1.7 (Wmap5) log 10 (M h ) [M ] O maybe show (1) this plot to the left but modified with the random scatter (if possible to make? perhaps can be done with old data?) (2) a demonstration of the effect of adding it onto the shape of the mass function (probably at high z so that it s visible) (change axes. is the plot still readable with errors on all 4 lines?)

18 Sources of error in the (central) galaxy mass-halo mass relation halo mass function cosmology dependence uncertainty for a given cosmology stellar mass function measurement error (poisson + sample variance) systematic errors in stellar masses random errors in stellar masses (Conroy et al) matching assumption scatter in M*-M for central galaxies assignment scheme for satellite galaxies subdominant subdominant subdominant at low z; important at z>1 IMPORTANT important at high mass as z increases impacts high mass end, but measurable. subdominant if other constraints used. neglibible (for central galaxies)

19 At high mass: Additional constraints from clusters maxbcg: SDSS clusters 0.1 < z < 0.3 (Koester et al 2007) Hansen et al 2009; RW et al 2009 cluster mass profiles Sheldon et al 2007 mass/light profiles cosmology analysis from maxbcg clusters (Rozo, RW et al 2009) constrains the distribution of P(M N) can turn this around now to get cluster properties as a function of halo mass

20 At low mass: Model appears to work for dwarf galaxies...with same M*-M scaling Busha et al 2009 add plot

21 Summary there are several powerful, complementary ways to connect galaxies and their histories to the distribution and assembly of dark matter halos. subhalo Abundance Matching: a very simple (one parameter) model The HALO MASSES of galaxies of a given number density (above a given stellar mass) are very well constrained in the context of LCDM To the extent that the true stellar masses of these galaxies are well known, the galaxy mass-halo mass relation is very well constrained. It is still difficult to produce this well-constrained relation in galaxy formation models and simulations (as we also heard from White, Steinmetz, Navarro)