Risa Wechsler - Astronomy and Astrophysics

Halo Occupation and Cosmology
from SDSS Clusters
Risa Wechsler
University of Chicago
Kavli Inst. for Cosmological Physics
Enrico Fermi Institute
Astronomy & Astrophysics Dept
Gus Evrard, Tim McKay, Ben Koester (Michigan)
Eduardo Rozo, Erin Sheldon, Sarah Hansen, Iro Tasitsiomi (University of Chic
Chris Miller (CTIO), Bob Nichol (Portsmouth)
Jim Annis (Fermilab) David Johnston (Princeton)

SDSS data now covers >8000 sq
degrees
Cluster finder (maxBCG), uses
photometric data to identify
BCGs and red sequence galaxies
More than 800,000 objects with at
least 2 bright red galaxies.
172000 with >=10 bright red
galaxies
dn/dlogN for 0.05

Cluster mass profiles from weak lensing
(the galaxy mass correlation function)
!" [h M O•
pc #2 ]
!" [h M O•
pc #2 ]
!" [h M O•
pc #2 ]
10 4
10 3
10 2
10
1
0.1
10 -2
10 4
10 3
10 2
10
1
0.1
10 -2
10 4
10 3
10 2
10
1
0.1
10 -2
10 -2
1 $ N gals $ 3
8 $ N gals $ 9
31 $ N gals $ 40
0.1 1 10
R [h #1 Mpc]
Sheldon et al 2005 (in prep)
10 -2
4 $ N gals $ 4
10 $ N gals $ 15
41 $ N gals $ 50
0.1 1 10
R [h #1 Mpc]
10 -2
5 $ N gals $ 5
16 $ N gals $ 20
51 $ N gals $ 75
0.1 1 10
R [h #1 Mpc]
10 -2
6 $ N gals $ 7
21 $ N gals $ 30
76 $ N gals $ 343
0.1 1 10
R [h #1 Mpc]
Based on a sample of ~100000 groups (DR3+)

M 200
Lensing Mass
Cluster Size
10 14
10 13
10 12
r 200 [h !1 Mpc]
S
M200 = A Ngal A= 2.1±0.4 ×10 11
S= 1.56±0.07
χ 2 = 11.1 DOF=10
1 10 100
2.0
1.0
0.9
0.8
0.7
0.6
0.5
Sheldon et al 2005 (in prep)
Hansen et al 2005,
ApJ in press
0.4
6 8 10 20 40 60 80 100
N gals
Sigma diff
Velocity Dispersion
1000
100
Real Data
McKay et al 2005 (in prep)
1 10 100 1000
N gals
several ways to measure the scaling
between cluster richness and “mass”
only problem: you don’t know what N is,
and you don’t know what M (or sigma or R) is!

M 200
Lensing Mass
r200 [h !1 Cluster Mpc] Size
10 14
10 13
10 12
2.0
1.0
0.9
0.8
0.7
0.6
0.5
S
M200 = A Ngal A= 2.1±0.4 ×10 11
S= 1.56±0.07
χ 2 = 11.1 DOF=10
0.4
6 8 10 20 40 60 80 100
N gals
lensing mass
Sigma diff
1000
several ways to
measure the
scaling between
cluster richness
and “mass”
Real Data
• need to understand velocity bias (as a function of radius & L)
1
Sheldon et al 2005 (in prep)
• can measure scatter
10 100
cluster sizes
100
1 10
McKay et al 2005 (in prep)
100 1000
Ngals Hansen et al 2005,
ApJ in press
Velocity Dispersion
• well understood theoretically
• selection biases and centering effects need to be understood
• no direct method to measure scatter
cluster velocity dispersions
• need additional data (spectra), which is typically redshift dependent
1000.0
• depends on galaxy background, degenerate with cosmology
cluster-cluster correlation function
• no direct method to measure scatter
ξ(r)
Cluster Correlation
Function
100.0
10.0
• uncertainties in redshifts can bias measurements
probably have more scatter than Lx, SZ,
1.0
but order of magnitude easier to find
0.1
1 10 100
r [Mpc/h]

how to predict cluster observables theoretically?
two-part question:
• how are galaxies connected to dark matter (bias/halo occupation)
• how are clusters observables connected to real groups/clusters of galaxies?
mock catalogs that connect theoretically understood quantities to the full
richness of the SDSS data set:
• need a large simulated volume: would like to have a method that can work
without high resolution simulations
• best cluster finders depend on galaxy luminosity and color; need galaxies with
realistic luminosities & colors and to match joint luminosity-color distribution as a
function of redshift & local density
• run identical analysis code used on data on simulations
basic method
1. populate the simulation with the measured luminosity function.
2. luminosity dependent bias: assign galaxies to dark matter particles based on
the local dark matter galaxy distribution by tuning P(δ dm |L) to match the
observed luminosity dependent 2-pt. correlation function
3. color based on the luminosity and local galaxy density: each mock galaxy gets
assigned a real SDSS galaxy from a volume-limited sample, based on its
luminosity and galaxy density

Adding Density Determined GAlaxies to Light-cone Simulations
(ADDGALS)
assign galaxies to dark matter particles
based on their local dark matter, with
some probability P(δm|Mr)
a useful measure of local mass density:
radius enclosing M=M* (~2x10 13 Msun/
h)--for dm, distribution is a lognormal
+gaussian
assume that at every luminosity, the
galaxy population has a local density PDF
with this form, for some choice of
parameters
as a function of luminosity, constrain the
values of the PDF with the two-point
correlation function wp(r, L)
use an MCMC approach to constrain the
five parameters of the distribution as a
function of luminosity
probability
0.6
0.5
0.4
0.3
0.2
0.1
Mr

slope of this fraction R_delta at L*
slope of R_delta
fraction of “field”galaxies
probability
0.6
0.5
0.4
0.3
0.2
0.1
Mr

the recipe
1. populate the simulation with a given luminosity function. was
using SDSS r-band LF with 1.6mag evolution per unit redshift.
(switch to 1.3mag per unit z?)
2. luminosity dependent bias: assign galaxies to dark matter particles
based on the local dark matter galaxy distribution by tuning P
(δ dm |Mr) to match the observed luminosity dependent 2-pt.
correlation function
3. each mock galaxy gets assigned a real SDSS galaxies, based on
its luminosity and local galaxy
measure the 5th/10th nearest neighbor galaxy for a volume
limited sample. for 0.4L* (Mr = -19.78), this is ~z=0.05-0.1.
measure this same density estimator for each of the mock
galaxies
bin galaxies in L and dg, choose a real galaxy from the
appropriate bin
4. apply simple target selection algorithm, main + LRGs

probability
probability
this mock catalog matches the
data in several key respects
1.2
1.0
0.8
0.6
0.4
M z
M r
M g
M u
0.2
0.0
-23 -22 -21 -20 -19 -18 -17 -16
M-5logh
color distribution & evolution
6
5
4
3
2
1
0
luminosity function & evolution
r-z
g-i
0 1 2 3
color
u-r
!
g-r color
hv_2c_nn4/
1000.0
100.0
10.0
1.0
0.1
!23

halo occupation this method
N gals
100.00
10.00
1.00
0.10
0.01
10 12
M r < -20
subhalo vf (KBW04)
galaxy-mass (TKWP 04)
ξ gg; bias(W05)
ξ gg; CLFWW05
M r

halo occupation: cosmological dependence
fraction of
“field”galaxies
1.0
0.9
0.8
σ 8
0.7
2.0 2.5 3.0 3.5 4.0
denser regions
σ 8
fixed galaxy clustering (now well measured!) + cosmologically dependent dark matter and halo
clustering --> changing bias model.
lower normalization + same galaxy clustering -- same galaxies in more massive halos
--> higher halo occupation, same galaxies live in denser regions

First thing to calibrate in the cluster finder:
P(Ngals, obs| Ng, true)
number of galaxies identified by cluster finder
(within 1Mpc)
number of galaxies within Rvir
Turns out the problem is
basically separable into
two parts:
1) for a given cosmology,
how do the galaxies
populate the dark matter?
2) for a given cluster finder,
how does Ntrue relate to
Nobserved?
**not dependent on
cosmology or the relation
between galaxies and dark
matter**

cluster abundance alone
number of halos
10000
1000
100
10
10 13
1
10 14
halo mass
σ 8 =0.77, 0.9
10 15
number of clusters
10000
1000
100
10
for ~5000 sq degrees to z~0.3
with cluster richness
as the “mass” measurement
1
10 100
Ngals

M 200
Lensing Mass
Cluster Size
10 14
10 13
10 12
r 200 [h !1 Mpc]
S
M200 = A Ngal A= 2.1±0.4 ×10 11
S= 1.56±0.07
χ 2 = 11.1 DOF=10
Sigma diff
1000
Real Data
Sheldon et al 2005 (in prep) McKay et al 2005 (in prep)
100
1 10 100
2.0
1.0
0.9
0.8
0.7
0.6
0.5
Hansen et al 2005,
ApJ in press
0.4
6 8 10 20 40 60 80 100
N gals
Velocity Dispersion
1 10 100 1000
N gals
Now we know what the x-axis is.
Since we have realistic clusters, we can now
measure each of the y-axes for these plots in
the same way in the models as they are
measured in the data.
Combining these constraints with the cluster
abundance will provide powerful constraints on
both cosmology and the true halo occupation.
This extremely rich data set requires
realistic simulations to make the most of it!

Thanks to Sandy, Joel & George!