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Risa Wechsler - Astronomy and Astrophysics

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Halo Occupation <strong>and</strong> Cosmology<br />

from SDSS Clusters<br />

<strong>Risa</strong> <strong>Wechsler</strong><br />

University of Chicago<br />

Kavli Inst. for Cosmological Physics<br />

Enrico Fermi Institute<br />

<strong>Astronomy</strong> & <strong>Astrophysics</strong> Dept<br />

Gus Evrard, Tim McKay, Ben Koester (Michigan)<br />

Eduardo Rozo, Erin Sheldon, Sarah Hansen, Iro Tasitsiomi (University of Chic<br />

Chris Miller (CTIO), Bob Nichol (Portsmouth)<br />

Jim Annis (Fermilab) David Johnston (Princeton)


SDSS data now covers >8000 sq<br />

degrees<br />

Cluster finder (maxBCG), uses<br />

photometric data to identify<br />

BCGs <strong>and</strong> red sequence galaxies<br />

More than 800,000 objects with at<br />

least 2 bright red galaxies.<br />

172000 with >=10 bright red<br />

galaxies<br />

dn/dlogN for 0.05


Cluster mass profiles from weak lensing<br />

(the galaxy mass correlation function)<br />

!" [h M O•<br />

pc #2 ]<br />

!" [h M O•<br />

pc #2 ]<br />

!" [h M O•<br />

pc #2 ]<br />

10 4<br />

10 3<br />

10 2<br />

10<br />

1<br />

0.1<br />

10 -2<br />

10 4<br />

10 3<br />

10 2<br />

10<br />

1<br />

0.1<br />

10 -2<br />

10 4<br />

10 3<br />

10 2<br />

10<br />

1<br />

0.1<br />

10 -2<br />

10 -2<br />

1 $ N gals $ 3<br />

8 $ N gals $ 9<br />

31 $ N gals $ 40<br />

0.1 1 10<br />

R [h #1 Mpc]<br />

Sheldon et al 2005 (in prep)<br />

10 -2<br />

4 $ N gals $ 4<br />

10 $ N gals $ 15<br />

41 $ N gals $ 50<br />

0.1 1 10<br />

R [h #1 Mpc]<br />

10 -2<br />

5 $ N gals $ 5<br />

16 $ N gals $ 20<br />

51 $ N gals $ 75<br />

0.1 1 10<br />

R [h #1 Mpc]<br />

10 -2<br />

6 $ N gals $ 7<br />

21 $ N gals $ 30<br />

76 $ N gals $ 343<br />

0.1 1 10<br />

R [h #1 Mpc]<br />

Based on a sample of ~100000 groups (DR3+)


M 200<br />

Lensing Mass<br />

Cluster Size<br />

10 14<br />

10 13<br />

10 12<br />

r 200 [h !1 Mpc]<br />

S<br />

M200 = A Ngal A= 2.1±0.4 ×10 11<br />

S= 1.56±0.07<br />

χ 2 = 11.1 DOF=10<br />

1 10 100<br />

<br />

2.0<br />

1.0<br />

0.9<br />

0.8<br />

0.7<br />

0.6<br />

0.5<br />

Sheldon et al 2005 (in prep)<br />

Hansen et al 2005,<br />

ApJ in press<br />

0.4<br />

6 8 10 20 40 60 80 100<br />

N gals<br />

Sigma diff<br />

Velocity Dispersion<br />

1000<br />

100<br />

Real Data<br />

McKay et al 2005 (in prep)<br />

1 10 100 1000<br />

N gals<br />

several ways to measure the scaling<br />

between cluster richness <strong>and</strong> “mass”<br />

only problem: you don’t know what N is,<br />

<strong>and</strong> you don’t know what M (or sigma or R) is!


M 200<br />

Lensing Mass<br />

r200 [h !1 Cluster Mpc] Size<br />

10 14<br />

10 13<br />

10 12<br />

2.0<br />

1.0<br />

0.9<br />

0.8<br />

0.7<br />

0.6<br />

0.5<br />

S<br />

M200 = A Ngal A= 2.1±0.4 ×10 11<br />

S= 1.56±0.07<br />

χ 2 = 11.1 DOF=10<br />

0.4<br />

6 8 10 20 40 60 80 100<br />

N gals<br />

lensing mass<br />

Sigma diff<br />

1000<br />

several ways to<br />

measure the<br />

scaling between<br />

cluster richness<br />

<strong>and</strong> “mass”<br />

Real Data<br />

• need to underst<strong>and</strong> velocity bias (as a function of radius & L)<br />

1<br />

Sheldon et al 2005 (in prep)<br />

• can measure scatter<br />

10 100<br />

cluster sizes<br />

100<br />

1 10<br />

McKay et al 2005 (in prep)<br />

100 1000<br />

Ngals Hansen et al 2005,<br />

ApJ in press<br />

Velocity Dispersion<br />

• well understood theoretically<br />

• selection biases <strong>and</strong> centering effects need to be understood<br />

• no direct method to measure scatter<br />

cluster velocity dispersions<br />

• need additional data (spectra), which is typically redshift dependent<br />

1000.0<br />

• depends on galaxy background, degenerate with cosmology<br />

cluster-cluster correlation function<br />

• no direct method to measure scatter<br />

ξ(r)<br />

Cluster Correlation<br />

Function<br />

100.0<br />

10.0<br />

• uncertainties in redshifts can bias measurements<br />

probably have more scatter than Lx, SZ,<br />

1.0<br />

but order of magnitude easier to find<br />

0.1<br />

1 10 100<br />

r [Mpc/h]


how to predict cluster observables theoretically?<br />

two-part question:<br />

• how are galaxies connected to dark matter (bias/halo occupation)<br />

• how are clusters observables connected to real groups/clusters of galaxies?<br />

mock catalogs that connect theoretically understood quantities to the full<br />

richness of the SDSS data set:<br />

• need a large simulated volume: would like to have a method that can work<br />

without high resolution simulations<br />

• best cluster finders depend on galaxy luminosity <strong>and</strong> color; need galaxies with<br />

realistic luminosities & colors <strong>and</strong> to match joint luminosity-color distribution as a<br />

function of redshift & local density<br />

• run identical analysis code used on data on simulations<br />

basic method<br />

1. populate the simulation with the measured luminosity function.<br />

2. luminosity dependent bias: assign galaxies to dark matter particles based on<br />

the local dark matter galaxy distribution by tuning P(δ dm |L) to match the<br />

observed luminosity dependent 2-pt. correlation function<br />

3. color based on the luminosity <strong>and</strong> local galaxy density: each mock galaxy gets<br />

assigned a real SDSS galaxy from a volume-limited sample, based on its<br />

luminosity <strong>and</strong> galaxy density


Adding Density Determined GAlaxies to Light-cone Simulations<br />

(ADDGALS)<br />

assign galaxies to dark matter particles<br />

based on their local dark matter, with<br />

some probability P(δm|Mr)<br />

a useful measure of local mass density:<br />

radius enclosing M=M* (~2x10 13 Msun/<br />

h)--for dm, distribution is a lognormal<br />

+gaussian<br />

assume that at every luminosity, the<br />

galaxy population has a local density PDF<br />

with this form, for some choice of<br />

parameters<br />

as a function of luminosity, constrain the<br />

values of the PDF with the two-point<br />

correlation function wp(r, L)<br />

use an MCMC approach to constrain the<br />

five parameters of the distribution as a<br />

function of luminosity<br />

probability<br />

0.6<br />

0.5<br />

0.4<br />

0.3<br />

0.2<br />

0.1<br />

Mr


slope of this fraction R_delta at L*<br />

slope of R_delta<br />

fraction of “field”galaxies<br />

probability<br />

0.6<br />

0.5<br />

0.4<br />

0.3<br />

0.2<br />

0.1<br />

Mr


the recipe<br />

1. populate the simulation with a given luminosity function. was<br />

using SDSS r-b<strong>and</strong> LF with 1.6mag evolution per unit redshift.<br />

(switch to 1.3mag per unit z?)<br />

2. luminosity dependent bias: assign galaxies to dark matter particles<br />

based on the local dark matter galaxy distribution by tuning P<br />

(δ dm |Mr) to match the observed luminosity dependent 2-pt.<br />

correlation function<br />

3. each mock galaxy gets assigned a real SDSS galaxies, based on<br />

its luminosity <strong>and</strong> local galaxy<br />

measure the 5th/10th nearest neighbor galaxy for a volume<br />

limited sample. for 0.4L* (Mr = -19.78), this is ~z=0.05-0.1.<br />

measure this same density estimator for each of the mock<br />

galaxies<br />

bin galaxies in L <strong>and</strong> dg, choose a real galaxy from the<br />

appropriate bin<br />

4. apply simple target selection algorithm, main + LRGs


probability<br />

probability<br />

this mock catalog matches the<br />

data in several key respects<br />

1.2<br />

1.0<br />

0.8<br />

0.6<br />

0.4<br />

M z<br />

M r<br />

M g<br />

M u<br />

0.2<br />

0.0<br />

-23 -22 -21 -20 -19 -18 -17 -16<br />

M-5logh<br />

color distribution & evolution<br />

6<br />

5<br />

4<br />

3<br />

2<br />

1<br />

0<br />

luminosity function & evolution<br />

r-z<br />

g-i<br />

0 1 2 3<br />

color<br />

u-r<br />

!<br />

g-r color<br />

hv_2c_nn4/<br />

1000.0<br />

100.0<br />

10.0<br />

1.0<br />

0.1<br />

!23


halo occupation this method<br />

N gals<br />

100.00<br />

10.00<br />

1.00<br />

0.10<br />

0.01<br />

10 12<br />

M r < -20<br />

subhalo vf (KBW04)<br />

galaxy-mass (TKWP 04)<br />

ξ gg; bias(W05)<br />

ξ gg; CLFWW05<br />

M r


halo occupation: cosmological dependence<br />

fraction of<br />

“field”galaxies<br />

1.0<br />

0.9<br />

0.8<br />

σ 8<br />

0.7<br />

2.0 2.5 3.0 3.5 4.0<br />

denser regions<br />

σ 8<br />

fixed galaxy clustering (now well measured!) + cosmologically dependent dark matter <strong>and</strong> halo<br />

clustering --> changing bias model.<br />

lower normalization + same galaxy clustering -- same galaxies in more massive halos<br />

--> higher halo occupation, same galaxies live in denser regions


First thing to calibrate in the cluster finder:<br />

P(Ngals, obs| Ng, true)<br />

number of galaxies identified by cluster finder<br />

(within 1Mpc)<br />

number of galaxies within Rvir<br />

Turns out the problem is<br />

basically separable into<br />

two parts:<br />

1) for a given cosmology,<br />

how do the galaxies<br />

populate the dark matter?<br />

2) for a given cluster finder,<br />

how does Ntrue relate to<br />

Nobserved?<br />

**not dependent on<br />

cosmology or the relation<br />

between galaxies <strong>and</strong> dark<br />

matter**


cluster abundance alone<br />

number of halos<br />

10000<br />

1000<br />

100<br />

10<br />

10 13<br />

1<br />

10 14<br />

halo mass<br />

σ 8 =0.77, 0.9<br />

10 15<br />

number of clusters<br />

10000<br />

1000<br />

100<br />

10<br />

for ~5000 sq degrees to z~0.3<br />

with cluster richness<br />

as the “mass” measurement<br />

1<br />

10 100<br />

Ngals


M 200<br />

Lensing Mass<br />

Cluster Size<br />

10 14<br />

10 13<br />

10 12<br />

r 200 [h !1 Mpc]<br />

S<br />

M200 = A Ngal A= 2.1±0.4 ×10 11<br />

S= 1.56±0.07<br />

χ 2 = 11.1 DOF=10<br />

Sigma diff<br />

1000<br />

Real Data<br />

Sheldon et al 2005 (in prep) McKay et al 2005 (in prep)<br />

100<br />

1 10 100<br />

<br />

2.0<br />

1.0<br />

0.9<br />

0.8<br />

0.7<br />

0.6<br />

0.5<br />

Hansen et al 2005,<br />

ApJ in press<br />

0.4<br />

6 8 10 20 40 60 80 100<br />

N gals<br />

Velocity Dispersion<br />

1 10 100 1000<br />

N gals<br />

Now we know what the x-axis is.<br />

Since we have realistic clusters, we can now<br />

measure each of the y-axes for these plots in<br />

the same way in the models as they are<br />

measured in the data.<br />

Combining these constraints with the cluster<br />

abundance will provide powerful constraints on<br />

both cosmology <strong>and</strong> the true halo occupation.<br />

This extremely rich data set requires<br />

realistic simulations to make the most of it!


Thanks to S<strong>and</strong>y, Joel & George!

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