The Co-evolution of Galaxies and Dark Matter Halos

Charlie Conroy

(Princeton University)

with

Andrey Kravtsov, Risa Wechsler,

Martin White, & Shirley Ho.

Outline

• What we learn from:1. Observed clustering of galaxies2. Observed evolution in the stellar mass

function and the intracluster light (ICL)3. Observed multiplicity function of LRGs in

groups and clusters

• The Big Picture:– What does LCDM plus observations of galaxies tell us

about the relation between galaxies and dark matter?– Uncertanties in cosmology << Uncertainties in galaxy

formation/evolution

The Clustering of Galaxies and Halos from z=4 to z=0

• Luminosity dependent clustering

is a power-law, but why??

Galaxy Clustering: I

Davis et al ‘88

brighter

fainter

dP = n [1+(r)] dV

Definition of

Galaxy Clustering: II

• Galaxy clustering is a function of luminosity, confirmed in both SDSS and 2dF surveys (among others)

Zehavi et al. ‘05

b2 = galdm

Definition of galaxy bias: Mo

re c

lust

ere

d

Brighter galaxiesNote: bias measured at a particular scale

• Clustering at z~1

Galaxy Clustering: III

Brighter galaxies

Mo

re c

lust

ere

d

Coil et al ‘06Ouchi et al. ‘05

~1-10 Mpc/h

~50-70 kpc/h

• Clustering at z~4

Brighter galaxies

Dark Matter Clustering

• Galaxy clustering is ~ a power-law and evolves only weakly with redshift

• DM clustering is not a power law, and is a strong function of redshift

• How do we reconcile this with observed galaxy clustering?

Colin et al ‘99

CDM Simulation

Halo Clustering

• The clustering of dark matter halos is similar to the clustering of galaxies (i.e. power-law, slow function of redshift)

• (How) do galaxies correspond to dark matter halos?

Colin et al ‘99

The Big Question

The Model

CDM Cosmology: m=0.3, =0.7, =0.9, h=0.7

– ART N-body code (Klypin & Kravtsov)

• Box Sizes: 80 & 120 Mpc/h. Npart = 5123

• Particle Mass: 3.2 x 108 & 1.1 x 109 Msun/h hpeak=1-2 kpc/h

• Halos identified using BDM algorithm

Simulation Details

Distinct halos vs. Subhalos

“Distinct” halos

Subhalos: their centers are within the virial radii of larger “parent” halos Note: subhalos used to be

distinct halos!

Merger Trees

Time

Wechsler et al ‘02

(for a distinct halo)

Halo Evolution

Time

Accretion epoch

Vm

ax,

mas

s

Distinct Halo Evolution: Subhalo Evolution:

Vm

ax,

mas

s

Time

Constant increase

increase decrease

Connecting Halos to Galaxies: I

• Find a relation between galaxy luminosity and halo Vmax, the maximum of the circular velocity function: [GM(<r)/r]1/2, or, equivalently, Mvir.

• Why?– Tully-Fisher & Faber-Jackson relations

demonstrate a strong correlation between galaxy velocity and luminosity.

– Strong theoretical expectations that galaxy luminosity will correlate with halo mass (e.g. White & Rees ‘78)

– brighter galaxies live in more massive halos

Which Vmax Correlates with Luminosity?

• For distinct halos, we use Vmax measured at z = zobs.

• For subhalos we use Vmax at the epoch of accretion:

Time

Accretion epoch

Vm

ax,

mas

s

Why?

Vmax at accretion should more accurately reflect the build-up of stellar mass, and hence luminosity

Connecting Halos to Galaxies: II

ngal(>L) = nhalo(>Vmax)

A one-to-one mapping between luminosity and Vmax such that the observed luminosity function is preserved. The LF is the only input to the model.

z=0 L-Vmax relation

Note: no scatterr-ba

nd lu

min

osity

Vmax

Results:Comparing Galaxy Clustering to Halo Clustering

z ~ 0

Data = red points

Halos = blue lines

DM = dotted lines

SDSS data

Data: Zehavi ‘05

Projected correlation function:

Notice the “bump”

Vmax at accretion vs. Vmax today

accretion

today

• In order to match observed clustering at z=0, we must use accretion epoch Vmax for subhalos

• Using accretion epoch effectively increases the fraction of galaxies that are satellites

z ~ 1

Data = red points

Halos = blue lines

DM = dotted lines

DEEP2 data

Data: Coil ‘06

z ~ 4 Subaru data

Data: Ouchi ‘05

Notice strong linear bias: b~5

Notice strong “break” on small scales

• We have assumed that a satellite galaxy is destroyed when the subhalo is destroyed

• Are there satellite galaxies which have no counterparts in (our) simulations??

• No.• Significant fraction (>20%) of

“missing” subhalos ruled out observationally, for the mass ranges we probe

• In other words, subhalos in our simulations do not experience significant overmerging.

Are We Missing Satellites?

What About 8?

• The 2-pt auto-correlation of halos in this model does not depend on 8

• Large scale clustering of halos decreases, but Nsat increases for lower 8

Mr<-21 = dashed

Mr<-20.5 = solid

Implications

gal is a power-law because halo is a power-law– deviations from a power-law at high z and high

luminosity are due to the clustering of halos (incl subhalos).

• High-res dissipationless N-body simulations can completely describe & explain the dependence of galaxy clustering on luminosity, scale, and redshift with a simple assumption regarding the relation between galaxy luminosity and Vmax

• Understanding luminosity & scale dependent clustering is separable.

Build-up of stellar mass and the ICL since z=1

Evolution in the Stellar Mass Function

• Observations indicate mild/no evolution in the stellar MF since z=1 at the massive end

• Evolution in the LF also consistent with ~passive evolution at the bright end since z=1.

M-4 ~ 0.2dex

Evolution in the Halo Mass Function

• Strong evolution in the Halo MF from z=1 to z=0 at the massive end

• Growth of halo does not track growth of central galaxy at z<1 in massive halos

• But halos accrete most of their mass in ~1/10 Mhalo size clumps

Log(Mvir)

Observations of the ICL

• BCG surface brightness profiles in excess of deVaucouleurs at large scales

• Best fit by a 2-compenent deV profile, rather than a generalized Sersic profile

• Associate 2nd deV profile with “ICL”

Gonzalez et al. 2005

Semi-major axis (kpc)

Su

rfa

ce b

righ

nes

s (m

ag/a

rse

c2)

deV

Modeling Stellar Mass Build-up

1) Use the observed z=1 galaxy stellar MF to connect stellar mass to halo mass at z=1

2) Follow the build-up of stellar mass with time using halo merger trees.

3) Ignore star-formation and other dissipative physics• Appropriate for the most massive galaxies where

zform,stars>2• Therefore a lower bound to stellar mass build-up

Fate(s) of Satellite Galaxies

• The evolution of satellite galaxies is tracked along with its dark matter subhalo until the subhalo dissolves. When the subhalo dissolves we have a decision to make:

1) Keep the satellite galaxy KeepSat2) Put the satellite’s stars into the BCG Sat2Cen3) Put the satellite’s stars into the ICL Sat2ICL4) Equally split between 2) and 3) Sat2Cen+ICL

model name

Evolution in the Galaxy Stellar MF

• Sample the observational uncertainties

• Model Sat2Cen ruled out by observed evolution in stellar MF.

• Other models OK.

Observationally allowed range

Sat2Cen

BCG Luminosity - Mass Relation

• Mstar / LK = 0.72

• Model Sat2Cen ruled out (again).

• Model Sat2Cen+ICL marginally ruled out.

• Implies that <50% of satellites from disrupted subhalos deposit their stars onto the central BCG

The Intracluster Light

• Model Sat2ICL (red points) reproduces observed total BCG+ICL luminosities.

• Model KeepSat (blue points) dramatically fails this test.

• We assumed that ICL is built-up at z<1 by major mergers, tidal stripping not important. – Validated by hydro-sims.

• Model Sat2ICL (red points) reproduces observed ICL light fraction better than model Sat2Cen+ICL (blue points).

• Depends on modeling of observed surface brightness profile and def’n of ICL.

Gonzalez et al. 2005

• Model Sat2ICL is the only model that matches an array of observations

• In massive halos (>1013.5 Msun), satellite galaxies dissolve when their associated subhalo dissolves, and the satellite stars are dumped primarily into the ICL.

• This explains the apparent contradiction between the lack

of evolution in the stellar MF and the strong evolution in the halo MF.

• This model predicts strong evolution in the total (BCG+ICL) light since z=1 (very hard to observe this at z=1!)

Implications

Implications for Star-formation

• Match z=0 stellar MF to the z=0 halo MF in the usual way

• Compare z=0 “true” stellar mass to the z=0 stellar mass predicted by our dissipationless models

• The difference should reflect the amount of star-formation since z=1

• Galaxies in halos above 1013.5 Msun have had little star-formation

• At lower masses, fraction of stars formed since z=1 decrease with increasing halo mass.

Evolution in Mstar-Mvir Relation: I

Evolution in galaxy stellar MF measured out to z~4 by Fontana et al. 2006

Evolution in Mstar-Mvir Relation: II

Log(Mvir)

Log

(Mst

ar)

Fra

ctio

n o

f b

aryo

ns

st

ars

• Match stellar MF to halo MF at various epochs.

• As Universe evolves, the peak conversion efficiency evolves to lower halo masses (“downsizing”)

• At low halo masses stellar mass and halo mass increase with time, whereas at higher halo masses only the halo mass increases with time.

• Simple model matches observations, and favors 8=0.75 (dashed line).

The LRG Multiplicity Function

Observed LRG Multiplicity Function

• 43 Clusters identified at 0.2<z<0.5 in Rosat/Chandra x-ray data that overlap SDSS footprint.

• Cluster masses determined from x-ray observations

• Mvir > 1014 Msun

• LRGs identified in SDSS with photo-z’s (dz~0.03)

Shirley Ho, et al. in prep

Modeling the LRG Multiplicity Fcn

Shape and normalization are important constraints

Data

MLRG>6E12

MLRG>1E13

t = 1.6 Gyr

t = 4.3 Gyr t = 5.9 Gyr

t = 3.2 Gyrt = time for LRG to merge once accreted

Conclusions

1) By utilizing the observed number density of galaxies and LCDM simulations we can learn a great deal about the relation between galaxies and halos and the evolution of this relation with time.

2) Observations which are thought to evolve dissipationlessly with time are particularly attractive because they are easy to model and yet much can be learned.

3) The ICL is built up by merging satellites at z<1. LRG multiplicity function provides information about merger/DF timescales.

What about scatter?

• We expect scatter between Mvir and Mstar, what effect does this have?

The Importance of Scatter: I

• Scatter strongly affects the clustering of bright galaxies, but does not affect fainter galaxies

• Use this sensitivity to constrain the amount of scatter for bright galaxies

• Work in progress

z = 0

• Scatter needed to match the observed galaxy-mass cross correlation function for bright galaxies

• Note: these plots were made using the current Vmax for subhalos. We have not yet investigated scatter using accretion epoch Vmax for subhalos

The Importance of Scatter: IITasitsiomi et al. 04

• bla

The Importance of Scatter: III