Observational Cosmology (C. Porciani / K. Basu) Lecture 7 - - PowerPoint PPT Presentation

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Course website: http://www.astro.uni-bonn.de/~kbasu/astro845.html

Lecture 7 Cosmology with galaxy clusters (Mass function, clusters surveys)

Observational Cosmology

(C. Porciani / K. Basu)

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Outline of the two lecture

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Galaxy clusters as tools for cosmology The physics and astrophysics of galaxy cluster cosmology Observation and mass modeling of clusters The X-ray and Sunyaev-Zel’dovich observables Optical and radio observation of galaxy clusters Current and future cluster surveys

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Cosmology with galaxy clusters

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• Growth of cosmic structure from cluster number counts

(use of halo mass function)

• Measuring distances using clusters as standard candles

(joint X-ray/SZE)

• Using the gas mass fraction in clusters to measure the

cosmic baryon density

• Measuring the large-scale velocity fields in the universe

from kinematic SZE

• Constraints from galaxy cluster power spectrum

Galaxy clusters are the most massive, collapsed structures in the

• universe. They contain galaxies, hot, ionized gas (107-8 K) and dark

matter. In typical structure formation scenarios, low mass clusters emerge in significant numbers at z~2-3. Clusters are good probes, because they are massive − an “easy” to detect through their:

• X-ray emission
• Sunyaev-Zel’dovich Efgect
• Light from galaxies
• Gravitational lensing

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

What are galaxy clusters?

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Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Galaxy clusters in simulations

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700 Mpc comoving cube Galaxy clusters: rare peaks in the density field

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Space density of clusters

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Clusters are rare objects. For standard ΛCDM cosmology (Ωm=0.3, ΩΛ=0.7, h=0.7, σ8=0.9), the space density of >1014 M☉ halos is 7 x 10-5 Mpc-3. Galaxy clusters represent the end result of the density fluctuations involving comoving scales of ~10-20 Mpc. This marks the transition between two distinct dynamical states: On scales above ~10 Mpc, evolution of the universe is driven by

• gravity. This regime can be analyzed by analytical methods, or more

accurately, with computer N-body simulations. At scales below ~1 Mpc, the physics of baryons start to play an important role, and complicates the process.

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Growth of structures

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Borgani & Guzzo, Nature, 2001

Example showing the role of galaxy clusters in tracing the cosmic evolution, in particular dark matter and dark energy contents. Ωm=0.3, ΩΛ=0.7 Ωm=1.0 Normalized w.r.t. local cluster density

# of clusters per unit area and z:

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

The Halo Mass Function

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• Consider the cosmic density field filtered on mass scale M
• Assume that density perturbations have collapsed by the time their

linearly evolved overdensity exceeds some critical value δc

• Number density of collapsed objects with mass M is then

proportional to an integral over a Gaussian distribution This is the famous Press-Schechter mass function

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Correction to PS approach

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Despite its very simple formalism, Press-Schechter formula has served remarkably well as a guide to constrain cosmological parameters from the mass distribution of galaxy clusters. Only with the advent of large N-body simulations, significant deviations of the PS description from the exact numerical description is noticed.

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Cluster cosmology & astrophysics

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Bayes’ theorem makes clear that identifying the most likely cosmology is dependent on knowing how likely the observations are within that cosmological model: P(C | R) ~ P(R | C) Pprior(C) For galaxy clusters, nonlinear dynamics and astropysical uncertainties (e.g. uncertain baryonic physics) complicate the computation of the observable likelihood P(R | C) . The question of computing the likelihood can be split into two parts:

• How many clusters of mass M exist in this cosmology at redshift z?
• What is the likelihood that a cluster of mass M at redshift z will

have temperature Tx (or some other observable)

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Mass budget in clusters

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White et al. (1993)

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Selection of clusters

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Cleanest selection techniques for clusters are those that couple properties of the high-density “virial” regions

• Clusters light up in X-ray or SZE only when they collapse (i.e. form

the dark matter halos counted in N-body simulations)

• Galaxy counting and shear selection is problematic because it is

challenging to separate massive clusters from surrounding large scale structures

• Shear couples to mass whether inside or outside the clusters
• Red galaxies exist in clusters and surrounding large-scale

structures

• Convergent velocity fields around massive clusters make

redshift a blunt too to determine cluster membership

• Majority of observable cluster mass (majority of baryons) is hot gas
• Temperature T ~ 108 K ~ 10 keV (heated by gravitational potential)
• Electron number density ne ~ 10-3 cm-3
• Mainly H, He, but with heavy elements (O, Fe, ..)
• Mainly emits X-rays (but also radio and gamma rays)
• LX ~ 1045 erg/s, most luminous extended X-ray sources in Universe
• Causes the Sunyaev-Zel’dovich efgect (SZE) by inverse Compton

scattering the background CMB photons

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Intra-Cluster Medium (ICM)

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Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray emission from clusters

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Thermal Bremsstahlung

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray spectra

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free-free recombination 2-photon

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray observatories

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XMM-Newton Chandra Wolter type III mirror assembly (Hans Wolter, 1952)

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray cluster samples

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The X-ray flux limit establishes a simple criterion for sample completeness and searching volume, thereby giving a reasonably accurate idea for the number of objects per unit volume.

1-2% of the CMB photons traversing galaxy clusters are inverse Compton scattered to higher energy

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

The Sunyaev-Zel’dovich (SZ) efgect

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Thermal SZE is a small (<1 mK) distortion in the CMB caused by inverse Compton scattering of the CMB photons Total cluster flux density is independent of redshift!

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Properties of the SZ efgect

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Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

SZ spectrum

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Thermal SZE frequency dependence: kinematic SZE:

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Simple models of the ICM

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A consistently good empirical fit! For cool core cluster a much better fit is double β-model

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray and SZ in β-model

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The most convenient feature of isothermal β-model is that X-ray surface brightness and SZE decrement takes simple analytical forms Try writing these two expressions in full details by solving these two integrals: (integration is along the line of sight dl = DA dζ)

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Solving for ne

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Integrating over density distribution gives total gas mass:

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Solving for dA

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Reese et al. 2002

Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Gas mass fraction

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Since galaxy clusters collapse from a scale of ~10 Mpc, they are expected to contain a fair sample of the baryonic content of the universe (mass segregation is not believed to occur at such large scales). The gas mass fraction, fgas, is therefore a reasonable estimate of the baryonic mass fraction of the cluster. It should also be reasonable approximation to the universal baryon mass fraction, fB = ΩB / Ωm In reality, fgas ≤ fB always!

Next lecture !!

Mantz, Allen et al.