Observational Cosmology

Transcription

1 (C. Porciani / K. Basu) Lecture 7 Cosmology with galaxy clusters (Mass function, clusters surveys) Course website:

2 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

3 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

4 What are galaxy clusters? Galaxy clusters are the most massive, collapsed structures in the universe. They contain galaxies, hot, ionized gas ( 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 Effect Light from galaxies Gravitational lensing 4

5 Galaxy clusters in simulations 700 Mpc comoving cube Galaxy clusters: rare peaks in the density field 5

6 Space density of clusters Clusters are rare objects. For standard ΛCDM cosmology (Ωm=0.3, ΩΛ=0.7, h=0.7, σ8=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

7 Growth of structures Ωm=0.3, ΩΛ=0.7 Normalized w.r.t. local cluster density Ωm=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

8 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 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 8

9 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

10 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) 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) 10

11 Mass budget in clusters White et al. (1993) 11

12 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

13 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 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 ~ erg/s, most luminous extended X-ray sources in Universe Causes the Sunyaev-Zel dovich effect (SZE) by inverse Compton scattering the background CMB photons 13

14 X-ray emission from clusters Thermal Bremsstahlung 14

15 X-ray spectra free-free recombination 2-photon 15

16 X-ray observatories XMM-Newton Chandra Wolter type III mirror assembly (Hans Wolter, 1952) 16

17 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

18 The Sunyaev-Zel dovich (SZ) effect 1-2% of the CMB photons traversing galaxy clusters are inverse Compton scattered to higher energy 18

19 Properties of the SZ effect 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

20 SZ spectrum Thermal SZE frequency dependence: kinematic SZE: 20

21 Simple models of the ICM A consistently good empirical fit! For cool core cluster a much better fit is double β-model 21

22 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 = DA dζ) 22

23 Solving for ne Integrating over density distribution gives total gas mass: 23

24 Solving for da Reese et al

25 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, 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! Mantz, Allen et al. Next lecture!! 25