Clusters of galaxies The ICM, mass measurements and statistical measures of clustering

1. Clusters of galaxiesThe ICM, mass measurements and statistical measures of clustering

2. Plan of this class • The intracluster medium, its origin, dynamics and general properties • Evidence of Dark Matter in clusters • Masses derived by the virial theorem, x-rays and gravitational lensing • Results from studies of gravitational lensing in clusters • Statistical measures of clustering

3. The intracluster medium

4. X-ray observations provide information on the amount, distribution, temperature and chemical composition of the Intracluster gas Clusters are among the most luminous X-ray sources in the sky. This X-ray emission comes from hot intracluster gas.

5. For comparison, • Cataclismic variables Lx = 1032 – 1038 erg/s • Milky Way, M31 Lx = 1039 erg/s • Clusters of galaxies Lx = 1043– 1045 erg/s • Only Seyferts, QSOs, and other AGN rival clusters in X-ray output • Clusters may emit nearly as much energy at X-ray wavelengths as visible L(optical) = 100 L* galaxies = 1045 erg/s

6. The Lx – σ correlation

7. What is the origin of cluster X-ray emission? • Answer: hot (107 – 108 K) low-density (10-3 cm-3) gas, mostly hydrogen and helium, that fills space between galaxies. At these high temperatures the gas is fully ionized. • Two emission mechanisms: 1) Thermal bremsstrahlung (important for T > 4 x 107 K) free electrons may be rapidly accelerated by the attractive force of atomic nuclei, resulting in photon emission because the emission is due to Coulomb collisions, X-ray luminosity is a function of gas density and temperature Lx = nelectron nion T1/2 = rho_gas2 T_gas1/2 2) Recombination of electrons with ions (important T < 4 x 107 K)

8. Dynamics of the intracluster gas The intracluster gas can be treated as: • An ideal fluid • In hydrostatic equilibrium • At a uniform temperature

14. X-ray spectra • Spectroscopy of the intracluster gas provides information on its temperature and composition • Observed spectra show exponential decrease at high-frequencies that is characteristic of bremsstrahlung. Coma Cluster Hughes et al. 93

15. Emission lines due to Fe, Ni and other heavy elements are seen. This suggests that much of the intracluster gas must have been processed through stars. • Chemical abundance of the intracluster gas can be measured from the equivalent widths of these emission lines. It is found to be about 30-40% of solar abundance • If the galaxies and gas are both in thermal equilibrium in the cluster potential well, then one expects m v(gal)2 = 3 kbTgas Tgas proportional to v(gal) 2

16. What is the origin of the intracluster gas? Two possibilities: • The intracluster gas once resided in galaxies and was later removed. - this would explain high metallicity of gas - galaxies in the cores of rich clusters are observed to be deficient in HI gas, which suggests that stripping has occurred. • The gas is primordial, originating at the time of cluster formation. - but since Mgas >> Mgal it is difficult to understand how so much material could have been stripped from galaxies

17. How much gas is there in clusters?

18. Cluster Mass estimates: X-ray gas

19. The total gas mass in clusters exceeds the total galaxy mass. Gas contributes as much as 10-20% of the total cluster mass. David, Jones and Forman 95

20. Evidence of Dark Matter (DM) in clusters

21. Dark Matter in ClustersA more accurate name for “clusters of galaxies” would be “clusters of dark matter”Observational evidence suggests that 80-90% of the mass in clusters is in an invisible form1) What evidence is there for dark matter?2) How much dark matter is there?3) What is the distribution within clusters?

22. Evidence of Dark Matter in clusters • Virial mass estimates If a cluster is in virial equilibrium then its mass can be estimated from Mvirial = R<v2>/G Observations indicate that the total cluster mass exceeds the combined masses of all galaxies by factors of 10-20. • Example: the Coma Cluster Mvirial = 1 x 1015 h-1 solar masses Ltot = 4 x 1012 h-2 solar luminosities Assuming a typical galaxy with M/L = 10 Then Mvirial/Mgalaxies = 25

23. Typical mass to light ratios • Globular clusters 1-2 M/L • Elliptical galaxies 5-10 h M/L • Groups of galaxies 100-300 h M/L • Rich clusters 300-500 h M/L

24. Mass to light ratio of Coma

25. Galaxy Dynamics Mass estimate using the Virial theorem

26. X-ray mass estimates • If the intracluster gas is in hydrostatic euilibrium in the cluster potential, then the cluster mass can be determined from

27. Gravitational lensing studies provide another independent evidence for DM in clusters

28. Gravitational Lensing – some history • 1913 – Einstein predicted that the gravitational field of massive objects can deflect light rays. • 1919 – Eddington measured the deflection of starlight by the Sun, confirming Einstein’s prediction. • 1937 – Zwicky suggested that galaxy clusters may produce observable lensing. • 1987 – First evidence of “strong” gravitational lensing by clusters was found (Lynds/Petrosian, Soucail et al.) • 1990 – “Weak” gravitational lensing by clusters was discovered (Tyson et a. 1990). • Today – Evidence of lensing has been found for several dozen clusters. New examples are being discovered all the time.

30. STRONG LENSING 1986 – Lynds & Petrossian discover the first gravitational arcs in clusters of galaxies 1987 – Soucail et al. determine the distance to the arc: twice the distance to the cluster that “contains” it.

31. Gravitational lensing: the basic ideas

33. Observer Galaxy cluster Background galaxy Strong lens Weak lens

34. “Strong” lensing occurs when Long arcs and multiple images are produced. • “Weak” lensing occurs when Small arclets and distortions are produced.

37. Strong Lensing A 1451 z = 0,199 

39. A 1451 z = 0,199 

40. Weak Gravitational Lensing Mellier 99

41. Allows the reconstruction of the surface mass density Classical techniques (dynamics of the galaxies and X-ray emission of the hot intra-cluster gas) are based of the assumption of dynamical equilibrium Why Weak Lensing ?

42. Measuring Faint Galaxy Shapes Cypriano et al. 2005

43. Mass  Light A2029 In 77% of the cases the center of light and mass distributions are consistent with each other... Light Mass

44. ...but there are exceptions A3739 Mass Light Mass  Light

45. Mass  Light A4010 Light Mass

46. Mass  Light There is a strong alignment between the BGC and the dark mater main axis

47. TX~ TSIS,SIE Comparison with X-Rays A1451 A2163 A2744

48. A2744 A2163 A1451 σv~ σSIS,SIE Comparison with the Velocity Dispertion

49. Most of the clusters appears to be relaxed (lensing  dynamical methods) Cluster with TX > 8 keV (σv >1120 km/s) shows signs of dynamical activity The dynamical state of the clusters

50. A2744 – Virial mass> Lensing > X-rays • σtotal = 1777 km/s • σA = 1121 km/s • σB = 682 km/s Girardi & Mezzetti (2001) The dynamical state of the clusters Interpretation: There are two structures along the line of sight Chandra observations confirms fusion along the line of sight (Kempner & David 2004)