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First predicted by the Russian scientists Sunayaev and Zel’dovich in 1969.

First predicted by the Russian scientists Sunayaev and Zel’dovich in 1969. Galaxy Clusters have hot gas that produce electrons by bremsstahlung (T gas ~10-100 Kelvin ). CMB photons are cold (T CMB ~ 2.7 Kelvin ).

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First predicted by the Russian scientists Sunayaev and Zel’dovich in 1969.

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  1. First predicted by the Russian scientistsSunayaev and Zel’dovichin 1969. Galaxy Clusters havehot gasthat produce electrons by bremsstahlung (Tgas~10-100 Kelvin). CMBphotons are cold (TCMB~ 2.7 Kelvin). Inverse Compton scattering occurs betweenCMB photonsand thehot electronsof clustrer atmosphere. Energy will be transferred from the hot electrons to the low energy CMB photons changing the shape of their intensity vs. frequency plot : • measuremnts made at low frequencies will have a lower intensity, since photons which originally had these energies were scattered to higher energies. This distorts the spectrum by ~0.1%. Giuseppina Coppola

  2. SZ effect distorsion of the CMB signal • Note the decrement on the low frequency side, and the increment at higher frequencies. • The amplitude of the distorsion is proportional to Te, although shape is indipendent of Te. The relativistic equation has a slightly more complicated shape. Giuseppina Coppola

  3. Overview • CMB • Radiation basic • Scattering by electron population • Kompaneets approximation • SZ and galaxy cluster • Struments Giuseppina Coppola

  4. The Cosmic Microwave Background Radiation The CMBR is thedominant electromagnetic radiationfield in the Universe. Principal Properties • Isotropy • Trad~ 2.7K • Specific intensity of the radiation: • Peak brightness: at • Photon density: • Energy density: Giuseppina Coppola

  5. Thermal history of the Universe and CMBR The origins of the CMBR lie in an early hot phase of the expansion of the Universe. Very high z: matter and radiation were in good thermal contact because of the abundance of free electrons. z of recombination: most electrons have become bound to ions. z of decoupling: the interaction lenght of photons and electrons exceeds the scale of the Universe. z ~1000-1500: the Universe was becoming neutral, matter-dominated and transaprent to radiation. Most of the photons that are now in the CMBR were scatterated by electrons for the last time. After recombination…… • Potential fluctuations grow to form Large Scale Structure • overdensities collapse to form galaxies and galaxy cluster; • underdensities expand into voids. Giuseppina Coppola

  6. real space volume • Distribution function photon frequency • Specific intensity momentum space volume • Number density of photons in the Universe • Energy density of the radiation field I. Radiation basics Giuseppina Coppola

  7. II. Radiation basics In the presence of absorption, emission and scattering processes, and in a flat spacetime, Iνobeys atransport equation: emissivity scattering coefficient absorption coefficient scattering redistribution function Specific intensity may be changed by: • redistributing photons to different directions and frequencies (e.g. scattering); • absorbing or emitting radiation (e.g. thermal bremsstrahlung); • making photon distribution function anisotropic (Doppler effect); Giuseppina Coppola

  8. I. Single photon-electron scattering Compton scattering formula For classical Thomson cross-section formula The probability of a scattering with angle θ: ve= βc and μ = cosθ Redistribution function: Giuseppina Coppola

  9. II. Single photon-electron scattering The scattered photon frequency: Introducing thelogarithmic frequency shift: s=log(νʺ/ ν ), the probability that asingle scattering of the photon causes a frequency shift s from an electron with speed βc is: Giuseppina Coppola

  10. I. Photon Scattering by electron population Averaging over the electron β distribution If every photon is scattered once, then the resulting spectrum is given by: Probability that a scattering occurs from ν0 to ν Since Giuseppina Coppola

  11. II. Photon Scattering by electron population Optical depth The probability of N scatterings: Probability that a photon penetrates the electron cloud The full redistribution function is given by Raphaeli formula: In most situations the electron scattering medium is optically thin, then and Giuseppina Coppola

  12. I. The Kompaneets approximation In the non-relativistic limit the scattering process may be described by the Kompaneets equation, which describes the change in the occupation number, by a diffusion process. For small xe, we have: Canonical form of the diffusion equation Solution Giuseppina Coppola

  13. II. The Kompaneets approximation Giuseppina Coppola

  14. III. The Kompaneets approximation At low y and for an incident photon spectrum of the form of CMBR, we can use the Approximation: Kompaneets vs. Raphaeli formula • The spectrum of the effect is given by a simple analytical function; • the location of the spectral maxima, minima and zeros are indipendent of Te in the Kompaneets approximation; • the amplitude of the intensity change depends only on y. Giuseppina Coppola

  15. Useful to determine the intrinsic three-dimensional shape of the cluster; • Useful to extract information on thermal structure in the intracluster gas; • Useful to measure the projected mass of gas in the cluster on the line of sight if the temperature structure of the cluster is simple; • Useful to detect clusters; • Useful to test the cosmology. Giuseppina Coppola

  16. The Sunayaev-Zel’dovich effect from clusters of galaxies If a cluster atmosphere contains gas with electron concentration ne(r), then the scattering optical depth, Comptonization parameter and X-ray surface brightness are: There is no unique inversion of bx(E) to ne (r) and Te (r) Giuseppina Coppola

  17. I. Parameterized model for gas cluster They use a parameterized model for the properties of the scattering gas in the cluster and they fit the values of these parameters to the X-ray data. • Isothermal beta-model: Te is constant and ne follows the spherical distribution Giuseppina Coppola

  18. II. Parameterized model for gas cluster Hughes et al. (1998), on the basis of observations of the Coma cluster, indroduced a useful variation on beta-model Useful to describe the decrease of gas temperature at large radius Giuseppina Coppola

  19. X-ray emission mapped by ROSAT PSPC z=0.5455; DA=760 h-1 Mpc Structural parameters by isothermal beta-model β = 0.73 ∓ 0.02 Θc = 0.69 ∓ 0.04 arcmin rc = (150 ∓ 10) h-1 kpc b0 = 0.047 ∓ 0.002 counts s-1 arcmin-2 ΔT0c≈ -0.82 h-1 mK at low frequency These values are consistent with the results obtained using X-ray spectrum Giuseppina Coppola

  20. III. Parameterized model for gas cluster • Ellipsoidal model: M encodes the orientation and relative sizes of semi-major axes of the cluster. β = 0.751 ∓ 0.025 Θc = 0.763 ∓ 0.045 arcmin SZ model X-ray surface brightness model ΔT0c≈ -0.84 h-1 mK Giuseppina Coppola

  21. Mass of the gas For an isothermal model, the surface mass density in gas is: Mean mass of gas per electron If the electron temperature of the gas is constant: This quantity can be compared with mas estimates produced by lensing studies. Giuseppina Coppola

  22. Sz effect in cosmological terms Method: comparison of SZ effectpredictedfrom the model with themeasuredeffect by X-ray data. • Measuring the CMB decrement from a cluster • Mesuring X-ray emission from a cluster • Measuring the size of a cluster Since the predicted effect is proportional to h-1/2 via the dependence on DA, this comparison measures the value of H0 and other cosmological parameters Giuseppina Coppola

  23. R Te n Measuring the CMB decrement from a cluster • Consider simplest model of cluster • Spherical with radius R • Constant gas number density n • Constant temperature Te • SZ effect decrement ΔT • Directly related to density • Directly related to the cluster path length • Directly related to the temperature of the gas, Te Temperature Decrement ΔT = -Trad 2y or ΔT ≈ Trad 2Rn Giuseppina Coppola

  24. R Te n Measuring X-ray emission from a cluster • Model of cluster • Sphere of radius R • Central number density of electron gas, n • Temperature of the gas, Te • X-ray surface brightness bX • Directly related to square of density • Directly related to the cluster path length • Temperature of the gas, Te X-ray brightness bX≈2Rn2 Giuseppina Coppola

  25. Measuring Size and Distance of the cluster • Combined observations of bX and ΔT measure the path length along the line of sight • Use the radius of the cluster and the angular size to make an estimate at the cluster distance. Remember, we assumed that cluster was spherical ΔT/Trad = 2Rn bX ≈ 2Rn2 R = (ΔT/Trad)2 /2bX DA≈ R/θ R DA θ • H0 is obtained from the measured z of the cluster and the value of DA under some assumption about q0. Giuseppina Coppola

  26. Result of SZ Distance Measurements • Comments • SZ effect distances are direct (rather than relative); • SZ effect distances possible ar very large lookback times; • can see the theoretical angular diameter distance relation; SZ distance vs. z But…. • selection effect, which caues the value of H0 to be biased low • the value of H0 depends by cluster model • unknown intrinsic shape of cluster atmospheres • uncertainties in the parameters of the model Giuseppina Coppola H0 = 63 ∓ 3 km/s/Mpc for ΩM=0.3 and ΩΛ=0.7

  27. Cluster Detectability Angular position on the sky The total flux from the cluster that is requested: Any SZE clusters survey has some fixed angular resolution, which will not allow to spatially resolve low mass cluster. Therefore a background yb parameter will be present. If the gas temperature profile is isothermal, the integrated flux SZE cay be related to the cluster temperature weighted mass divided by DA2: If the temperature profile is isothermal only in the inner regions (Cardone, Piedipalumbo, Tortora (2005)) Giuseppina Coppola

  28. Interferometers used to measure the SZ effect • Cosmic Background Imager (CBI) • Located at the ALMA cite in Chajantor, Chile. These 13 antennae operate at 26-36 GHz • Degree Angular Scale Interferometer (DASI) • A sister project to CBI, located at South Pole. These interferometers are suited to measure nearby clusters Giuseppina Coppola

  29. X-ray telescopes used to measure the SZ effect • ROSAT • X-ray satellite in operation between 1990 and 1999. Mainly, its data has been used in conjunction with the radio observations to make estimates of H0 and Ωb. Uncertainties of the X-ray intensity are ~ 10%. • Chandra X-ray Observatory • Provides X-ray observations of the clusters to make etimates of the gas temperature. Chandra currently has the best resolution of all X-ray observatories. • XMM-Newton • ESA’s X-ray telescope. Has 3 European Photon Imaging Cameras (EPIC) Giuseppina Coppola

  30. All-sky project used to measure SZ effect • Microwave Anisotropy Probe • Measures temperature fluctuations in the CMB. • Planck satellite • ESA project designed to image the entire sky at CMB wavelengths. Its wide frequency coverage will be used to measure the SZ decrement and increment to the CMB photons. Giuseppina Coppola

  31. Systematic Uncertainties in current SZ effect measurements • SZ effect calibration (∓8%) • X-ray calibration (∓10%) • galactic absorption column density (∓5%) • unresoved point sources still contaminate measurement of the temperature decrement (∓16%) • Clusters that are prolate or oblate along the line of sight will be affected. Reese et al. 2001 Giuseppina Coppola

  32. References • Birkinshaw astro-ph/9808050 • Bernstein & Dodelson Physical Review, 41, 2 1990 • Cardone et al. A&A 429, 49-64 (2005) • Carlstrom et al. astro-ph/9905255 Giuseppina Coppola

  33. CL 0016+16 H0 = 68 km s-1 Mpc-1 if the cluster is modeled with a sphere isothermal Giuseppina Coppola

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