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Combine Observations of Galaxy Clusters to Constrain
Cosmological Parameters
Heng Yu ( 余恒 )
& Zong-Hong Zhu
Beijing Normal University
2008. 12.12
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Outline
1. Background
2. Method 1: strong lensing cluster
3. Method 2: X-ray gas fraction
4. Method 3: S-Z effect
5. Results
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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
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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
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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
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Bullet Cluster (2006): Direct Evidence of DM
arXiv:astro-ph/0608407
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Method 1: Giant Arcs in Lensing clusters
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Gravitational lensing
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Isothermal model
β-model
Hydrostatic
density
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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
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Observational quantity• Finally, from observation we can get
• And model can tell us
• then
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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]
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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 :
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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/
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Beta & theta_c
• Can be choosen In the “Physical data” frame
• Then we got the ADS link of all refered literature
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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
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New Sample
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3-D Hubble Diagram
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Dashed line: Old sample (Sereno 2004)
Solid line: New sample
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Method 2: Gas fraction
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Gas mass
• X-ray gas mass fraction within r2500 is constant with redshift
• NFW model
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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
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Multigrid MCMCGrid-search
Number of parameters: n
Calculation amount:
102n 108 (fixed)
n x 104
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Method 3: S-Z effect
WMAP temperature map with diamonds representing the position of nearby galaxy clusters
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Precondition
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Angular distance
• SX0 : X-ray surface brightness
• dT0 : SZE decrement
• Lambda: X-ray cooling function38 clusters 0.14 < z < 0.9 (Bonamente,2006)
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Combination Result
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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 !
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Thanks!
The real world is always complex, but we are approaching the truth !
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A2218 Optical
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A2218 X-ray
Machacek, 2002 ApJ with Chandra