Combine Observations of Galaxy Clusters to Constrain

Cosmological Parameters

Heng Yu ( 余恒 )

& Zong-Hong Zhu

Beijing Normal University

2008. 12.12

Outline

1. Background

2. Method 1: strong lensing cluster

3. Method 2: X-ray gas fraction

4. Method 3: S-Z effect

5. Results

Brief history

• 1901 Max Wolf discover Coma cluster

• 1933 Zwicky perceive the existence of dark matter from Coma cluster

• 1958 Abell published first galaxy cluster catalogue according to the Palomar Observatory Sky Survey (POSS)

• 1961-1968 Zwicky give his catalogue with different criteria

X-ray satellite History

• 1962 Aerobee Rocket USAF 2 -10 keV • 1970-1973 Uhuru NASA 2-20 keV (1st)• 1978-1981 Einstein NASA 0.2-3.5 keV• 1990-1999 ROSAT Ge/US/UK 0.1 - 2.5 keV • 1993-2000 ASCA Japan 0.4 -12 keV (CCD)• 1999 Chandra NASA 0.1-10 keV• 1999 XMM-Newton ESO 0.1-15 keV• 2005 Sukuza Japan

X-ray Clusters

• Luminonious X-ray radiation

T > 106 K ， P ≈ 1043 ～ 1045 erg/s• Extended source

β-model (Cavaliere et.al 1978)

NFW (Navarro et.al 1997)

double-β (Mohr et.al 1999)• Thermal Bremsstrahlung spectrum• 7keV Fe emission line

Bullet Cluster (2006): Direct Evidence of DM

arXiv:astro-ph/0608407

Method 1: Giant Arcs in Lensing clusters

Gravitational lensing

Isothermal model

β-model

Hydrostatic

density

Arcs

• Integrate to 2-D• Critical surface mass density

Here D is angular diameter

distance, subscript s stands for

source, and d the lens

So when Σ>Σcr clusters can generate arcs

• The position of tangential critical curve

Observational quantity• Finally, from observation we can get

• And model can tell us

• then

What we need?

• Zd : redshift of cluster [Spectrum]

• θarc (”) : position of arcs [Optical HST]

• T (keV) : gas temperature [X-ray Spectrum]

• β： power index [X-ray surface Brightness]

• θc: core radius of X-ray cluster• Zarc: redshift of arcs [Spectrum]

Arc SampleD.J.Sand

ApJ 2005 arXiv 0502528:

find 104 tangential arcs and 4 radial arcs out of 128 GCs from HST WFPC2 Archive

zarc : only 58 arcs out of 27 clusters have redshift value

θarc :

Zd & T• Can be found directly at BAX

BAX: the X-Rays Clusters Database This database contains information o

n 1579 groups and clusters of galaxies, and 298 clusters with available temperature measurements http://bax.ast.obs-mip.fr/

Beta & theta_c

• Can be choosen In the “Physical data” frame

• Then we got the ADS link of all refered literature

Criteria

1) T > 4keV

Regular X-ray Morphology

(no merging as A2218)

2) Dds / Ds < 1

Angular distance should have physical significance

3) ∑ /∑cr ＞ 1

surface mass can genarate arcs

New Sample

3-D Hubble Diagram

Dashed line: Old sample (Sereno 2004)

Solid line: New sample

Method 2: Gas fraction

Gas mass

• X-ray gas mass fraction within r2500 is constant with redshift

• NFW model

Optimization Algorithm

• Popular MCMC

(Markov chain Monte Carlo)

--CosmoMC

2/

11

2

,1min),(

eP

P

P

n

nnn

Grid + Direct Search--Powell’s UOBYQA algorithm (using Numerical difference to approach directional derivative)--CONDORhttp://www.applied-mathematics.net

Multigrid MCMCGrid-search

Number of parameters: n

Calculation amount:

102n 108 (fixed)

n x 104

Method 3: S-Z effect

WMAP temperature map with diamonds representing the position of nearby galaxy clusters

Precondition

Angular distance

• SX0 : X-ray surface brightness

• dT0 : SZE decrement

• Lambda: X-ray cooling function38 clusters 0.14 < z < 0.9 (Bonamente,2006)

Combination Result

Summary

• Lensing cluster, 9 points, sensitive to ΩΛ

• X-ray gas fraction,42 points, sensitive to ΩM

and Direct Search algorithm is effective

• S-Z effect , 38 points, not big enough

to do such constrain

So Galaxy cluster is an expecting independent object for cosmological constrain !

Thanks!

The real world is always complex, but we are approaching the truth !

A2218 Optical

A2218 X-ray

Machacek, 2002 ApJ with Chandra