Transcript Dark Ages - University of Chicago

Cosmology with Galaxy Clusters
Zoltán Haiman
Princeton University
Collaborators: Joe Mohr (Illinois)
Gil Holder (IAS)
Wayne Hu (Chicago)
Asantha Cooray (Caltech)
Licia Verde (Princeton)
David Spergel (Princeton)
Dark Energy Workshop, Chicago, 14 December 2001
} I.
} II.
} III.
Outline of Talk
1.
Cosmological Sensitivity of Cluster
Surveys
what is driving the constraints?
2.
Beyond Number Counts
what can we learn from dN/dM,
P(k), and scaling laws
Introduction
Era of “Precision Cosmology”:
Parameters of standard cosmological model
to be determined to high accuracy by CMB,
Type Ia SNe, and structure formation (weak
lensing, Ly forest) studies.
Future Galaxy Cluster Surveys:
Current samples of tens of clusters can be replaced
by thousands of clusters with mass estimates in
planned SZE and X-ray surveys
Why Do We Need Yet Another Cosmological Probe?
- Systematics are different (and possible to model!)
- Degeneracies are independent of CMB, SNe, Galaxies
- Unique exponential dependence
Power & Complementarity
Z. Haiman / DUET
Constraints using dN/dz
of ~18,000 clusters in a
wide angle X-ray survey

(Don Lamb’s talk)
Power comparable to:
Planck measurements
of CMB anisotropies
2,400 Type Ia SNe
from SNAP
M
-M to ~1%
- to ~5%
Galaxy Cluster Abundance
Dependence on cosmological parameters
# of clusters per
unit area and z:

dN
dV
dn

  dM
ddz
ddz M min
dM
comoving
volume
mass
limit
mass
function
mass function:
 0  1 d M
dn
 0.315 
dM
M   M dM

 exp  [0.61  log( g z M )]3.8


overall
normalization
power
spectrum (8, M-r)
(  M h 2 )
(M  M h2 r 3 )
growth
function

Jenkins
et al. 2001
Hubble volume
N-body simulations
in three cosmologies
cf: Press-Schechter
Observables in Future Surveys
SZ decrement:
M virTvir
ΔT
σT
ΔS 
 2
dl ne k BTe   f ICM
2 
2
TCMB
me c
dA
X-ray flux:
1
LX
2
FX 
dV ne Λ(Te )  2
2 
4πd L
dL
Predicting the Limiting Masses
• Overall value of Mmin: determines expected
yield and hence statistical power of the survey
• Scaling with cosmology: effects sensitivity of
the survey to variations in cosmic parameters
• To make predictions, must assume:
SZE: M-T relation (Bryan & Norman 1998)
c (z)
(top-hat collapse)
(r)
(NFW halo)
X-ray: L-T relation (Arnaud & Evrard 1999;
assuming it holds at all z)
Mass Limits and Dependence on w
log(M/M⊙)
X-ray survey
XR: flux=5x10-14 erg s-1 cm-2
SZ: 5 detection in mock SZA
observations (hydro sim.)
• X-ray surveys more
sensitive to mass limit
w = -0.9
w = -0.6
SZE survey
sensitivity amplified in the
exponential tail of dN/dM
• w, M non-negligible
sensitivity
•  dependence weak
redshift
• H0 dependency:
M ∝ H0-1
Which Effect is Driving Constraints?
• Fiducial CDM cosmology:
M = 0.3
 = 0.7
w = -1 (= )
H0 = 72 km s-1 Mpc-1
8 = 1 n = 1
• Examine sensitivity of dN/dz to five parameters
M, w, , H0 , 8
by varying them individually.
• Assume that we know local abundance N(z=0)
Sensitivity to M in SZE Survey
M effects local abundance: N(z=0) ∝ M → 8 ∝ M-0.5
12 deg2 SZE survey
M=0.27
M=0.30
M=0.33
dN/dz shape
relatively
insensitive to M
Sensitivity driven
by 8 change
Haiman, Mohr & Holder 2001
Sensitivity to w in SZE Survey
Haiman, Mohr & Holder 2001
12 deg2 SZE survey
w=-1
w=-0.6
w=-0.2
dN/dz shape
flattens with w
Sensitivity
driven by:
volume (low-z)
growth (high-z)
Sensitivity to M,w in X-ray Survey
Haiman, Mohr & Holder 2001
104 deg2 X-ray survey
w=-1
w=-0.6
w=-0.2
w
Sensitivity
driven by
Mmin
M=0.27
M=0.30
M=0.33
M
Sensitivity
driven by
8 change
Sensitivities to  , 8 , H0
• Changes in  and w similar
change redshift when dark energy kicks in
combination of volume and growth function
• Changes in 8 effect (only the) exponential term
not degenerate with any other parameter
• H0 dependence weak, only via curvature in P(k)
dN/dz(>M/h) independent of H0 in power
law limit P∝kn
When is Mass Limit Important?
in the sense of driving the
cosmology-sensitivity
0
w
H0

SZ
no
no
no
no
XR
no
yes
no
no
overwhelmed by 8-sensitivity
if local abundance held fixed
(M vs w) from 12 deg2 SZE survey
Haiman, Mohr & Holder 2001
3
2
1
Constraints using
~200 clusters
M
vs
1% measurement of
CMB peak location
or
1% determination
of dl(z=1) from SNe
w
Clusters alone: ~4% accuracy on 0; ~40% constraint on w
Outline of Talk
1.
Cosmological Sensitivity of Cluster
Surveys
what is driving the constraints?
2.
Beyond Number Counts
what can we learn from dN/dM,
P(k), and scaling laws
Beyond Number Counts
• Large surveys contain information in addition
to total number and redshift distribution of clusters
Shape of dN/dM
Power Spectrum
• Scaling relations
Advantages of combining S and Tx
• Goal: complementary information provides an
internal cross-check on systematic errors
Degeneracies between “cosmology” and
“cluster physics” different for each probe
(e.g. for dN/dz and for S - Tx relation)
Shape of dN/dM
work in progress
Change in dN/dM
under 10% change
in M (0.3 →0.33)
Consider seven
z-bins, readjust 8
2  significance
for DUET sample
of 20,000 clusters
[encouraging, but must explore full degeneracy space]
Cluster Power Spectrum
• Galaxy clusters highly biased:
Large amplitude for PC(k) = b2 P(k)
Cluster bias (in principle) calculable
• Expected statistical errors on P(k)
FKP (Feldman, Kaiser &Peacock 1994)


Pk
1
1 / 2

 nk 1 
2

Pk
n
b
P
k 

“signal-to-noise” increased by b2 ~25
rivals that of SDSS spectroscopic sample
Cluster Power Spectrum - Accuracies
Z. Haiman / DUET
~6,000 clusters in each
of three redshift bins
P(k) determined to
roughly the same
accuracy in each z-bin
Accuracies:
k/k=0.1 → 7%
k<0.2
→ 2%
NB: baryon “wiggles”
are detectable at ~2
Effect on the Cluster Power Spectrum
Pure P(k) “shape test”
Courtesy W. Hu / DUET
Neutrino Mass
example m=0.2eV
h2≈ 0.002
CMB anisotropies
3D power spectrum
(M vs  ) from Cluster Power Spectrum
Cooray, Hu & Haiman, in preparation
Use 3D power spectrum
M h2
DUET improves CMB
neutrino limits:
factor of ~10 over MAP
factor of ~2 over Planck
(because of degeneracy
breaking)
DUET+Planck Accuracy
 h2
h2 ~ 0.002
Angular Power Spectrum
Cooray, Hu & Haiman, in preparation
To apply geometric dA(z)
test from physical scales
of P(k) Cooray et al. 2001
Mh2
Matter-radiation
equality scale keq ∝ Mh2
“standard rod” when
calibrated from CMB
(m vs w) from Angular Power Spectrum
Cooray, Hu & Haiman, in preparation
with ~12,000 clusters
Using geometric dA(z)
test from physical scales
of P(k) Cooray et al. 2001
M h2
Projected 2D angular
power spectrum in 5
redshift bins between
0<z<0.5.
clusters break CMB
degeneracies & shrink
confidence regions
w
DUET+Planck: w ~ to 5%
Cluster Power Spectrum - Summary
• High bias of galaxy clusters enables accurate
measurement of cluster P(k):
k/k=0.1 → P(k) to 7% at k=0.1
k<0.2
→ P(<k) to 2%
(rivals SDSS spectroscopic sample)
• Expected statistical errors from DUET+Planck:
h2 ~ 0.002
- shape test
w ~ to 5% - dA(z) test
• Enough “signal-to-noise” to consider 3-4 z- or M-bins:
evolution of clustering
peak bias theories / non-gaussianity
SZE and X-ray Synergy
Using scaling relations, we can simultaneously
Probe cosmology and test cluster structure
S - TX scaling relation expected to have small scatter:
(1) SZ signal robust (2) effect of cluster ages
SZ decrement vs Temperature
SZ decrement vs Angular size
Verde, Haiman & Spergel 2001
Fundamental Plane: (S ,TX, )
Verde, Haiman & Spergel 2001
Plane shape
sensitive to
cosmology
and cluster
structure

Tests the
origin of
scatter
(S ,TX) scaling relations + dN/dz test
work in preparation
Using a sample
of ~200 clusters
Different Mmin - 0
degeneracies
 can check on
systematics
Conclusions
1.
Clusters are a tool of “precision cosmology”
a unique blend of cosmological tests, combining
volume, growth function, and mass limits
2.
Using dN/dz, P(k) complementary to other probes
e.g.: (M,w) , (M,  ), (M,  ) planes vs CMB and SNe
3.
Combining SZ and X-rays can tackle systematics
solving for cosmology AND cluster parameters?