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

Observational Cosmology (C. Porciani / K. Basu) Lecture 7 Cosmology with galaxy clusters (Mass function, clusters surveys) Course website: http://www.astro.uni-bonn.de/~kbasu/astro845.html Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Outline of the two lecture 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 2 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Cosmology with galaxy clusters • 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 3 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

What are galaxy clusters? Galaxy clusters are the most massive, collapsed structures in the universe. They contain galaxies, hot, ionized gas (10 7-8 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 E fg ect • Light from galaxies • Gravitational lensing 4 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Galaxy clusters in simulations 700 Mpc comoving cube Galaxy clusters: rare peaks in the density field 5 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Space density of clusters Clusters are rare objects. For standard Λ CDM cosmology ( Ω m =0.3, Ω Λ =0.7, h=0.7, σ 8 =0.9), the space density of >10 14 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. 6 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Growth of structures Ω m =0.3, Ω Λ =0.7 Normalized w.r.t. local cluster density Ω m =1.0 Borgani & Guzzo, Nature, 2001 Example showing the role of galaxy clusters in tracing the cosmic evolution, in particular dark matter and dark energy contents. 7 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

The Halo Mass Function # of clusters per unit area and z: • 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 δ c • 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 8 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Correction to PS approach 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. 9 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Cluster cosmology & astrophysics 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) P prior (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 T x (or some other observable) 10 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Mass budget in clusters White et al. (1993) 11 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Selection of clusters 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 12 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Intra-Cluster Medium (ICM) • Majority of observable cluster mass (majority of baryons) is hot gas • Temperature T ~ 10 8 K ~ 10 keV (heated by gravitational potential) • Electron number density n e ~ 10 -3 cm -3 • Mainly H, He, but with heavy elements (O, Fe, ..) • Mainly emits X-rays (but also radio and gamma rays) • L X ~ 10 45 erg/s, most luminous extended X-ray sources in Universe • Causes the Sunyaev-Zel’dovich e fg ect (SZE) by inverse Compton scattering the background CMB photons 13 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray emission from clusters Thermal Bremsstahlung 14 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray spectra free-free recombination 2-photon 15 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray observatories XMM-Newton Wolter type III mirror assembly (Hans Wolter, 1952) Chandra 16 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray cluster samples 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. 17 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

The Sunyaev-Zel’dovich (SZ) e fg ect 1-2% of the CMB photons traversing galaxy clusters are inverse Compton scattered to higher energy 18 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Properties of the SZ e fg ect 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! 19 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

SZ spectrum Thermal SZE frequency dependence: kinematic SZE: 20 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Simple models of the ICM A consistently good empirical fit! For cool core cluster a much better fit is double β -model 21 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

X-ray and SZ in β -model 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 = D A d ζ ) 22 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Solving for n e Integrating over density distribution gives total gas mass: 23 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Solving for d A Reese et al. 2002 24 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters

Gas mass fraction 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, f gas , 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, f B = Ω B / Ω m In reality, f gas ≤ f B always! Mantz, Allen et al. Next lecture !! 25 Observational Cosmology Lecture 7 (K. Basu): Cosmology with Galaxy Clusters