Combine Observations of Galaxy Clusters to Constrain Cosmological Parameters

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Combine Observations of Galaxy Clusters to
Constrain Cosmological Parameters

• Heng Yu ( ?? )
• 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 gt 106 K , P 10431045 erg/s
• Extended source
• ß-model (Cavaliere et.al 1978)
• NFW (Navarro et.al 1997)
• double-ß (Mohr et.al 1999)
• Thermal Bremsstrahlung spectrum
• 7keV Fe emission line

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Bullet Cluster (2006) Direct Evidence of DM
arXivastro-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
ß-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 SgtScr 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
• ?arc () position of arcs Optical HST
• T (keV) gas temperature X-ray Spectrum
• ßpower index X-ray surface Brightness
• ?c core radius of X-ray cluster
• Zarc redshift of arcs Spectrum

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Arc Sample

• D.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
• ?arc

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Zd T

• Can be found directly at BAX
• BAX the X-Rays Clusters Database
• This database contains information on 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 gt 4keV
• Regular X-ray Morphology
• (no merging as A2218)
• 2) Dds / Ds lt 1
• Angular distance should have physical
  significance
• ? /?crgt1
• 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

Grid Direct Search --Powells UOBYQA
algorithm (using Numerical difference to
approach directional derivative) --CONDOR http//w
ww.applied-mathematics.net
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Grid-search
MCMC

• Multigrid

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 function

38 clusters 0.14 lt z lt 0.9 (Bonamente,2006)
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Combination Result
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Summary

• Lensing cluster, 9 points, sensitive to O?
• X-ray gas fraction,42 points, sensitive to OM
• 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