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AY202a Galaxies & Dynamics Lecture 18: Galaxy Clusters & Cosmology

AY202a Galaxies & Dynamics Lecture 18: Galaxy Clusters & Cosmology. X-ray Scaling Laws. Note small range in T!. Temperature versus X-ray Luminosity. Mushotzky & Scharf ‘97. Compilation of Diego & Partridge ‘09.

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AY202a Galaxies & Dynamics Lecture 18: Galaxy Clusters & Cosmology

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  1. AY202a Galaxies & DynamicsLecture 18:Galaxy Clusters& Cosmology

  2. X-ray Scaling Laws Note small range in T! Temperature versus X-ray Luminosity Mushotzky & Scharf ‘97

  3. Compilation of Diego & Partridge ‘09

  4. Strong correlation between x-ray gas temperature and galaxy velocity dispersion

  5. p = rvirial/rcore X-ray Luminosity vs Size Diego & Partridge ‘09

  6. Chemistry Cluster gas element abundances from x-ray spectra (Mushotzky)

  7. Evolution, or lack thereof, of [Fe/H]

  8. Cooling Flows Gas cooling time tcool = u/εff  8.5x1010 yr x ( )-1 ( ) ½ Long except at cluster centers where densities are high ne T 10-3cm-3 108 K Fabian Perseus red= 0.5-1 kev green = 1-2 kev blue = 2-7 kev

  9. 2 L μm 5 k T Typical cooling timescale for cluster centers < 109 yr where does the material go? Mass deposition rate calculated as dM/dt = where L is bolometric L Problem is that there is little evidence except in a very few cases (e.g. Perseus) for recent star formation. Solutions? AGN Heating? Thermal Conduction? Thermal Mixing? Cosmic ray heating? Absorption?

  10. Clusters & Cosmology Ωmatter (Zwicky  ) from <M/L> and total luminosity density. Hubble Constant from Sunyaev-Zeldovich effect (more on that later) The Baryon Problem Tracing Dark Matter Cluster Abundances vs Redshift & Cosmological Parameters

  11. 2MASS Galaxy Groups δρ/ρ = 12 δρ/ρ = 80 ------------------------------------------------------- σP (km/s) 197 183 RPV (Mpc) 1.71 0.97 log MV/LK 1.70 1.53 Log MP/LK 1.90 1.67 ΩM,V 0.14+/-0.02 0.10+/-0.02 ΩM,P 0.23+/-0.03 0.13+/-0.02 -------------------------------------------------------- V=Virial Estimator P = Projected Mass

  12. Gravitational Lensing Mass reconstruction Distance Measurement Einstein radius θE = 28.8”( )2( ) O L S v Dds 1000 km/s Ds Dds Ds

  13. Lensing Mass Profile for A2218

  14. Sunyaev-Zeldovich Effect In 1970 Sunyaev & Zeldovich realized that the CMB spectrum would be affected by passage through a hot gas via Inverse Compton scattering.

  15. CMB Exaggerated spectral distortion due to the SZ effect. Scattered through an atmosphere with Compton parameter y = 0.1 and τβ = 0.05 (Birkinshaw) Distorted CMB

  16. Narrower frequency range from Carlstrom (2002)

  17. We calculate the Thermal SZ effect (SZ from thermalized electron distribution) from an electron gas with density distribution ne(r): Scattering optical depth τe =  ne(r)T dl (dl along l.o.s.) Comptonization parameter y =  ne(r)T dl X-ray spectral surface brightness along l.o.s. BX(E) =  (ne(r))2Λ(E,Te) dl k Te(r) me c 2 1 4  (1+z)3 Where Λ is the spectral emissivity of the gas at energy E

  18. 8  e2 3 me c2 and again the Thomson cross-section is T = ()2 In the Rayleigh-Jeans region, we generally have for the change in brightness = -2y For distance determinations, assume a round cluster with effective diameter L then  ne L T and the x-ray intensity IX L ne2 and the x-ray angular diameter θ = L/dA Δ Iυ Iυ Δ Iυ Iυ

  19. Which gives dA = ~  ( )2 where χis the comoving distanceand k is the curvature density 1 - Total R L ΔIυ 1 θθ Iυ IX

  20. Kinematic SZ Effect Cluster motions also can affect the CMB viewed through them. The size of the effect depends on the peculiar velocity of the cluster w.r.t. the expansion

  21. SZ measurements of A2163 from Holzapfel (1997) with SuZie (SZ Infrared experiment on Mauna Kea)

  22. A2163 again SZ Maps from J. Carlstrom’s group (BIMA/OVRO; Carlstrom, Holder & Reese 2002)

  23. SZ in WMAP data (stacked clusters) W band V band Q band (90 GHz) (60 GHz) (40 GHz) Diego & Partridge (2009)

  24. Planck (launched May 14, 2009) will do an all-sky SZ survey for galaxy clusters. Two instruments (LFI and HFI) will survey in nine frequency bands between 30 and 857 GHz

  25. Cluster Baryon “Problem” Lets compare the Baryonic cluster mass = Gas Mass + Galaxy Mass to the Dynamical Total Mass of the cluster. Mgas (<R) = 4 πo ro3  x2 (1+x2)-3/2 dx where X = R/ro, and MTot (<R) = ( + ) where both are derived from x-ray data. c.f. White & Frenk 1991, White et al. 1993 X 0 -kTR R d R dT Gmp  dr T dr

  26. by some simple trick substitutions, and remembering the Beta model: z = x2/(1 + x2) T(r) = To (r/ro)-  R/ d/dr = -3Zβ And MTot (<R) = (3Zβ + ) with  0 β  1 k T R G  mp

  27. we also find that for the typical cluster MGal,baryonic < Mgas or even << MGas In the average cluster MGas ~ 0.1 h-1.5 MTotal Simulations (White & Frenk, etc.) suggest that at least on 1 Mpc scales, Gas = CDM distributions But we also have baryon (nucleosynthesis) ~ 0.02 h-2 ~ 0.044 for h = 0.7  Total ~ 0.25  1 (!) (in 1993 this was big, bad news for SCDM, but do go a long way towards solving the baryon problem)

  28. The Bullet Cluster

  29. Cosmological Parameters from Cluster Mass Functions

  30. Constraints from the evolution of the mass function. Vikhlinin et al 2009

  31. Combined constraints from clusters plus BAO, CMB & SN Ia Chandra Cluster Cosmology project Vikhlinin et al. 2009

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