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Using Galaxy Clusters forCosmology and the XCS
Ben Hoyle, Bob Nichol, David Bacon, Ed Lloyd-Davies, Kathy Romer & the XCS
Cape Town April ‘08
OverviewOverview Clusters Clusters & Cosmology Cluster collapse; cosmology Cluster surveys X-ray cluster catalogues The XMM Cluster Survey [XCS] Detecting clusters Cluster classification Redshift estimates High redshift cluster Mass estimate 1; Scaling relations Mass estimate 2; Weak lensing The magnification bias The future
Clusters Clusters & Cosmology Cluster collapse; cosmology Cluster surveys X-ray cluster catalogues The XMM Cluster Survey [XCS] Detecting clusters Cluster classification Redshift estimates High redshift cluster Mass estimate 1; Scaling relations Mass estimate 2; Weak lensing The magnification bias The future
Clusters Clusters
Properties of clusters of galaxies: Size ~ few Mpc Mass Emit broad range of EM Galaxies -> optical ICM -> X-rays
Properties of clusters of galaxies: Size ~ few Mpc Mass Emit broad range of EM Galaxies -> optical ICM -> X-rays
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>1012MΘ
Clusters & cosmologyClusters & cosmologyThe number density and mass of clusters, the mass function, n(M,z), are related to by:
The number density and mass of clusters, the mass function, n(M,z), are related to by:
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n(M,z)dM =2
π0
ρM
d lnσ (M)
d lnMexp(−
ν 2
2)dM
M 2
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ν =δsc
D(z)σ (M)
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δec = δsc (z) 1+ βσ 2
δsc2
⎡
⎣ ⎢
⎤
⎦ ⎥
γ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
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Ωm,ΩΛ ,σ 8,ω
• Sheth & Tormen, ellipsoidal collapse
Press & Schechter, spherical collapse
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σ(M)
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δec
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δsc
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D(z)
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σ 8
Parameter Descritption
Function of
Barrier value
Varience of density field
Normalisation Of den. field
Growth of strtucture
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σ 8
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Ωm,ΩΛ ,ω€
Ωm,ΩΛ
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Ωm,ΩΛ
Cluster collapse; cosmologyCluster collapse; cosmologyEllipsodial collapseSpherical collapse
Vary mattercontent
Vary w=const
ModifyGravity
Schaefer & Koyama
Cluster surveysCluster surveysCluster cosmology checklist: Lots of clusters Broad redshift range Mass estimates
Cluster cosmology checklist: Lots of clusters Broad redshift range Mass estimates
Optical cluster catalogues • Large numbers• Redshifts• No masses
X-ray cluster catalogues• Mass estimates:Cavaliere & Fusco-Femiano ’78, Dai et al ’06• Small numbers• Redshifts difficult
X-ray cluster cataloguesX-ray cluster catalogues
X-ray identified cluster catalogues are mainly taken from the literature.
X-ray identified cluster catalogues are mainly taken from the literature.Catalogue Clusters Redshifts? P.I.
XCS ~1800 <10% Romer ‘01
BCS 206 Yes Ebling ‘98
eBCS 107 Yes Ebling ‘02
R400D 242 Yes Burenin ‘02
OverviewOverview Clusters Clusters & Cosmology Cluster collapse; cosmology Cluster surveys X-ray cluster catalogues The XMM cluster survey [XCS] Detecting clusters Cluster classification Redshift estimates High redshift cluster Mass estimate 1; Scaling relations Mass estimate 2; Weak lensing The magnification bias The future
Clusters Clusters & Cosmology Cluster collapse; cosmology Cluster surveys X-ray cluster catalogues The XMM cluster survey [XCS] Detecting clusters Cluster classification Redshift estimates High redshift cluster Mass estimate 1; Scaling relations Mass estimate 2; Weak lensing The magnification bias The future
XMM Cluster Survey [XCS]XMM Cluster Survey [XCS]
The XCS: Archival pointings Serendipitous detections
170 sq. deg. Present
500 sq. deg. Total 0.1<z<2 Currently 1847 Expect ~ 2000
The XCS: Archival pointings Serendipitous detections
170 sq. deg. Present
500 sq. deg. Total 0.1<z<2 Currently 1847 Expect ~ 2000
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allXCS
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500XCS
Detecting clustersDetecting clusters
Color key Extended sources, Green ellipses Point sources, red circles Unsure, Pink circles
Color key Extended sources, Green ellipses Point sources, red circles Unsure, Pink circles
From simulations we can recover our selection function.
Extended sources Simulated clusters
Cluster classificationCluster classification
Cluster zoo SDSS optical images Centered on X-ray
ra,dec Optical & X-ray
overlays X-ray photon density
contours 610 XCS extended
sources 7 classification types 9+ classifications
Cluster zoo SDSS optical images Centered on X-ray
ra,dec Optical & X-ray
overlays X-ray photon density
contours 610 XCS extended
sources 7 classification types 9+ classifications
Cluster classificationCluster classification
Results: Gold sample High Z False detections Cuts improve sample
Results: Gold sample High Z False detections Cuts improve sample
Soft counts % Gold Clusters
% All Clusters
>0 18 55
>200 41 77
>500 54 81
Redshift estimatesRedshift estimatesEmpirically, see LRGs inhabit the central regions of clusters. Empirically, see LRGs inhabit the central regions of clusters.
SDSS LRGs•Spec and Photo redshifts•Good Agreement
Test on ROSAT 400 sq. deg•Spectroscopic redshifts
Look along line of sight of the cluster, encounter an clump of LRGs. Assign LRG redshift to cluster
Redshift estimatesRedshift estimates
Apply the LRG redshift estimate technique to the XCS
Apply the LRG redshift estimate technique to the XCS
193 free cluster redshifts
Redshift estimates Redshift estimates Dedicated XCS photometric follow up NOAO + XCS -> NXSDedicated XCS photometric follow up NOAO + XCS -> NXS
More than 300 redshifts
136 for
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500XCS
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z = 0.27 ± 0.02
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z = 0.53 ± 0.01
High redshift clusterHigh redshift cluster The most distant spectroscopically confirmed cluster of galaxies found to date. XMM-XCS J2215.9-1738 or J2215.
The most distant spectroscopically confirmed cluster of galaxies found to date. XMM-XCS J2215.9-1738 or J2215.
• 5 pointings of a z=2.215 quasar• Cluster redshift 1.45• Temp > 6KeV
Standford et al astro-ph/0606075Hilton et al astro-ph/0708.3258
High redshift clusterHigh redshift cluster The most distant spectroscopically confirmed cluster of galaxies found to date. XMM-XCS J2215.9-1738 or J2215.
The most distant spectroscopically confirmed cluster of galaxies found to date. XMM-XCS J2215.9-1738 or J2215.
• 5 pointings of a z=2.215 quasar• Cluster redshift 1.45• Temp > 6KeV•
Standford et al astro-ph/0606075Hilton et al astro-ph/0708.3258
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σ v = 620 ±120km /s
OverviewOverview Clusters Clusters & Cosmology Cluster collapse; cosmology Cluster surveys X-ray cluster catalogues The XMM Cluster Survey [XCS] Detecting clusters Cluster classification Redshift estimates High redshift cluster Mass estimates 1; Scaling relations Mass estimate 2; Weak lensing The magnification bias The future
Clusters Clusters & Cosmology Cluster collapse; cosmology Cluster surveys X-ray cluster catalogues The XMM Cluster Survey [XCS] Detecting clusters Cluster classification Redshift estimates High redshift cluster Mass estimates 1; Scaling relations Mass estimate 2; Weak lensing The magnification bias The future
Mass estimate 1: Scaling relationsMass estimate 1: Scaling relationsCombining optical [large numbers, no masses] and X-ray [small numbers, masses] cluster catalogues to obtain a mass proxy applicable to optically selected clusters.
Combining optical [large numbers, no masses] and X-ray [small numbers, masses] cluster catalogues to obtain a mass proxy applicable to optically selected clusters.
X-ray clusters • eBCs,BCS,R400d,XCS• Reprocessed equally• [Dai et al ‘06]
Optical Clusters• Mass estimates• Constrain cosmology
Empirical Relationship
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Lopt =1035−0.35+0.35
Mass0.7−0.21+0.22
Examine properties of X-ray clusters with a counter part in SDSS
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TX → Mass
Mass estimates 2: Weak lensingMass estimates 2: Weak lensing
The Sloan has enabled the creation of two massive optical catalogues:
The Sloan has enabled the creation of two massive optical catalogues:
We can follow Scranton et al ’05, and use a weak lensing mass measurement, called magnification bias.
MaxBCG clusters [Koester et al ’07]~13.10^30.1<z<0.3 volume limitedWell determined redshiftsNumber of galaxiesLack mass estimatesMember Galaxy luminosity
DR4 Quasars [Richards et al]~3.10^50.5<z<2.255-band SDSS magnitudes
The magnification bias The magnification bias
The QSO unlensed source density:
The QSO unlensed source density:
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n0(> f ) = a0 f−α ( f )
The magnification bias The magnification bias Lensing changes the measured source density, by stretching the solid angle
Lensing changes the measured source density, by stretching the solid angle
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n →n0
μ
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μ =μ(θ,Mass,zqso,zcluster )
The magnification bias The magnification bias
Lensing magnifies the source flux
Lensing magnifies the source flux
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f →f
μ
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μ =μ(θ,Mass,zqso,zcluster )
The magnification bias The magnification bias
• The sign of the correlation• The signal strength• The sign of the correlation• The signal strength
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wCQ = α −1( )b δμ.δ(θ + φ)
The cross correlation, is a function of bias, b, the weak lensing departure from unity, ,and the line of sight integrated density contrast,
Where alpha is the gradient of the QSO distribution, multiplied by 2.5There is a change of sign of€
∝δμ
€
∝ α −1
Schnieder & Bartelmann astro-ph/9912508€
δμ
€
δ
€
α −1
The magnification bias, resultsThe magnification bias, resultsWe find [preliminary results]:We find [preliminary results]:
Expect a strong correlation Expect a weak anti-correlation
Stack similar clusters, expect the signal strength to increase with cluster mass.
The futureThe futureWeak Lensing SDSS DR6 QSO 1 million QSO’s Redo with full MaxBCG Check systematics
Weak Lensing SDSS DR6 QSO 1 million QSO’s Redo with full MaxBCG Check systematics
Mass estimatesCompare X-ray & weak lensing mass measurementsAssign MaxBCG clusters masses
CosmologyAssume LCDM constrain cosmological parametersConstrain modified gravity models [Schaefer & Koyama ‘07]