High Energy Astrophysics

1. High Energy Astrophysics Clusters of Galaxies II

2. Introduction • Clusters of Galaxies constitute the largest gravitationally collapsed structures in the universe • Clusters are composed mainly of galaxies, hot gas and dark matter • Clusters of galaxies were first detected in X-ray in the early 70s with the large sky area observations of the Uhuru X-ray satellite (Giaconni et al, 1972).

3. Introduction: First observed properties • The X-ray luminosities are of the order of 1043-45 erg/s • The X-ray emission is spatially extended • The X-ray emission did not vary in temporally in their brightness • The X-ray spectra were consistent with a thermal bremsstrahlung spectrum from hot gas • The X-ray spectra showed emission lines from Fe implying that the intracluster medium is enriched

4. Coma Cluster Briel et 01

5. Cluster X-ray Observations X-ray luminosities & luminosity function • Observe count-rates => flux => luminosity • They are extremely luminous Lx ~ 1043-45 erg/s • The luminosity function is the number of clusters per unit volume with X-ray luminosities in the range of Lx to Lx+dLx : f(Lx)dLx • The observed luminosity function is well-fit to a Schechter function • f(Lx) = A (L/L*)α exp (-L/L*)

6. Cluster X-ray Observations Spatial distribution of X-ray emission • Extended emission • The surface brightness is well fit in the majority of cases by the so-called beta model profile • Sx = Sxo [1 + (r/rc)2]-3β+1/2

7. Cluster X-ray Observations X-ray Spectra • Clusters exhibit thermal bremsstrahlung spectra from their thin, high temperature, highly ionized intracluster medium • Typical temperatures are of the order of a few keV • Typical metallicities are of the order of 1/3 solar • Spectra show α-element enhancement • In most (non-cooling flow) clusters there is negligible low energy absorption • Cooling flows

8. Hot Intracluster Medium Emission X-ray emission • The X-ray continuum emission from a hot diffuse plasma is due primarily to three processes: thermal bremsstrahlung (free-free emission), recombination (free-bound emission), and two-photon decay of metastable levels • The radiative recombination continuum emissivity is usually calculated by applying the Milne relation for detailed balance to the photoionization cross sections • The two-photon continuum comes from the metastable states of hydrogen or helium-like ions • At clusters Ts: thermal bremsstrahlung is dominant

9. Raymond & Smith 1977

10. Raymond & Smith 1977

11. Raymond & Smith 1977

12. Raymond & Smith 1977

13. Tozzi et al03

14. Hot Intracluster Medium Emission Distribution of the X-ray gas • In general, the elastic collision times for ions and electrons in the ICM are much shorter than the time scales for heating or cooling or any dynamical process, and the gas can be treated as a fluid. • The time required for a sound wave in the ICM to cross a cluster is • ts ~ 6.6 108 yr (Tg/108 K) -1/2 (D/Mpc) • Since this time is short compared to the age of the cluster ( t ~ 1010 yr), the gas will be hydrostatic and the pressure will be a smooth function of position unless the potential varies on a shorter time scale or the gas heats or cools more rapidly

15. Hot Intracluster Medium Emission Distribution of the X-ray gas • Hydrostatic equation

16. Cluster Physics Input Hydrostatic Equilibrium Poisson’s Equation Isothermal Equation of State Hydrostatic Equilibrium Spherical Symmetry Isothermal

17. Hot Intracluster Medium Emission Isothermal models • The simplest distribution of gas temperatures is isothermal • The cluster would become isothermal if thermal conduction were sufficiently rapid or if reaches approximately the same temperature when falls into the cluster and the thermal condition is unchanged • If the potential is that of the King approximation to an isothermal sphere then

18. Hot Intracluster Medium Emission Adiabatic and Polytropic distributions • If thermal conduction is slow, but the ICM is well-mixed, then the entropy per atom is constant • Adiabatic gas: P αργ • γ is the ratio of the specific heat and is 5/3 for a monoatomic ideal gas • Gas models with an arbitrary γ are referred as polytropic, with 5/3 for adiabatic and 1 for isothermal • Temperature distribution

19. Hot Intracluster Medium Emission Empirical distributions • The gas distributions in clusters can be derived directly from observations of the X-ray surface brightness of the cluster, if the shape is known and if the cluster observations are sufficiently detailed and accurate • This method also leads to a way of determining the cluster mass

20. Hot ICM Emission Observations • X-ray surface brightness

21. Mohr et al 1999

22. Hot ICM Emission Observations Observables • X-ray surface brightness • X-ray spectrum

23. Tozzi et al 2003

24. Borgani et al 2003

25. Hot ICM Emission Observations Derived properties • X-ray gas density and gas mass • X-ray temperature • Metallicity • Hydrogen column of absorbing material • Redshift • Total mass • Baryon fraction

26. Baumgartner et al 2003

27. Baumgartner et al 2003

28. Baumgartner et al 2003

29. Cooling Flows • The cooling time in the central regions of clusters can be shorter than the Hubble time tcool = kBT / (nΛ(T)) • As gas cools down, the lack of pressure support makes the gas flow in generating a cooling flow (Fabian 1984) • The luminosity emitted . dL/dT = 5/2 k M/μmp . can be used to estimate the luminosity in any spectral feature produced in the cooling flow by integrating dL over the fraction of the total emission in the feature as a function of temperature

30. Cooling Flows • the mass deposition rate can be estimated from the previous equation at the cooling radius rcool . M(r) α r

31. Fabian 1994

32. Cooling Flows Concerns • The surface brightness was not as peak as expected => a multiphase was assumed • High mass deposition rates: (100-1000 Msolar/yr) but cD galaxies were not as bright and blue as expected • Spectrum inconsistent with cooling flow => intrinsic absorption • Effect of heating neglected (central and due to thermal conduction)

33. Cooling Flows The nail in the coffin • The XMM-Newton X-ray spectra show that the gas is not cooling below 1-2 keV

34. Peterson et al 2003

35. Cooling Flows Explanations without heating • The gas may be cooling and yet appear to vanish when it reaches ~ 2keV (due to photoelectric absorption?) • The gas may become dense enough to separate from the flow and mix with hotter gas • A central radio source may transport cold gas to outside the cooling region • lack of metal mixing

36. Cooling Flows Explanations with heating • Heating from a central radio source • Conductivity of heat from the outer hot gas

37. Cluster Scaling Relations • If cluster gas properties determined only by gravitational collapse then clusters should be scaled versions of each other: • Lx α M ρgas Tx1/2 • Lx α Tx2 (1+z)3/2 • Lx α M4/3 (1+z)7/2 • S α Tx (1+z)-2 • Observationallythese relations do not hold • Lx α Tx3

38. Cluster Scaling Relations Rosati et al 2002

39. Breaking Cluster Scaling Relations: Entropy Floor • Gas heating by a non-gravitational source (Kaiser 1991; Evrard & Henry 1991): increases entropy, reduces the central density and thus the X-ray luminosity. • Stronger effect in lower mass systems

41. Borgani et al 2001

42. Breaking Cluster Scaling Relations

43. Cluster Scaling Relations Evolution

44. Ettori et al 2003

45. Ettori et al 2003

46. Ettori et al 2003

47. Cluster Abundance & Evolution Cosmological tool • The cluster abundance at a given epoch is a function of Ωm and σ8 • The evolution of the cluster abundance depends on Ωm • Theoretically, one can predict the mass function • Observationally in X-rays, one find clusters due to their surface brightness and measures their Lx • X-rays studies more widely used due to its nicer selection function

48. Tegmark et al 2003

49. Rosati et al 2002

50. Borgani et al 2001