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Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies

This workshop discusses relativistic corrections to the Sunyaev-Zeldovich effects, including thermal, kinematical, and polarization effects for galaxy clusters. Detailed analysis on the impact of relativistic corrections on high-temperature clusters and spectral intensity distortions is presented.

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Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies

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  1. Carolina Neutrino Workshop April 16-17th, 2004 1/33 Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies Satoshi NozawaJosai Junior College for Women Collaborators: N. Itoh, Y. Kohyama

  2. 2/33 Contents • Introduction(a) Clusters of Galaxies(b) Thermal SZ Effect(c) Kinematical SZ Effect (2) Relativistic Corrections to SZ Effects(a) Thermal SZ Effect(b) Kinematical SZ Effect(c) Polarization SZ Effect (3) Summary

  3. 3/33 (1) Introduction (a) Cluster of Galaxies (CG)RX J1347 (z=0.45, 5×109 light years) 0.9 Mpc Optical Image by Subaru X-ray Image by Chandra

  4. Galaxies Hot plasmas 4/33 Structure of CG

  5. CMB photons ν ν=218GHz 5/33 (b) Thermal Sunyaev-Zeldovich (SZ) Effect Distortion of the Cosmic Microwave Background (CMB)photon spectrum due to electrons in the CG.(Inverse Compton scattering) Sunyaev & Zeldovich, CommentsAstrophys. Space Phys. 4, 173 (1972)

  6. Determination of the Hubble constant with CG --- Thermal SZ effect of CG --- X-ray intensity of CG : diameter of CG along the line of sight 6/33 Thermal SZ effect determines ΔTCMB． Low frequency region --- temperature decrement High frequency region --- temperature increment

  7. With the redshift observation, the Hubble constant H0 is determined (H0=v/DA). WMAP data 7/33 Assumption: CG is spherical.

  8. 8/33 Advantages of the SZ effects: ・Total radiation intensity is redshift independent! ECMB ∝ (1+z)4 (energy density of CMB) DA ∝ (1+z)2 (angular diameter distance) Itotal ∝ ECMB/D2---z-dependences cancel out!・Determination of H0, cosmological constants, peculiar velocity field, etc. Disadvantages of the SZ effects:・Assumption of the spherical symmetry for CG・ Small signals ΔTCMB～10-3 Chandra and XMM-Newton have opened a new era for precise observation of the SZ effect.

  9. Determination of cosmological constants with SZ effect

  10. ν ν=218GHz Temperature Map for RXJ1347 9/33 150 GHz (Nobeyama, Japan) 350 GHz (Maxwell, USA) Contours: X-ray intensity observed by Chandra

  11. 10/33 Recent observations:High temperature CG Te = 10～20keV. Relativisitic corrections become significant! Typical order of magnitude

  12. 11/33 (c) Kinematical Sunyaev-Zeldovich (SZ) Effect Peculiar motion of CG (Bulk Motion of CG relative to CMB by the local gravitational field) produces ΔTCMB.Doppler Effect vz Sunyaev & Zeldovich,Mon. Not. R. Astr. Soc. 190, 413 (1980) Relativisitic corrections become significant!

  13. 12/33 Typical magnitudes of SZ effects Distortion of spectral intensity

  14. 13/33 (2) Relativistic Corrections to SZ Effects • Thermal SZ Effect • Itoh, Kohyama & Nozawa, ApJ 502, 7 (1998) Boltzman equation for the photon distribution function n(ω).

  15. 14/33 Fokker-Planck expansion

  16. 15/33

  17. 16/33

  18. 17/33 Distortion of the CMB spectrum Expansion in terms of Relativistic corrections --- Non-relativistic term

  19. 18/33 Relativistic corrections

  20. 19/33

  21. 20/33

  22. 21/33 Distortion of the spectral intensity

  23. 22/33 Summary for thermal SZ effect ・Relativistic corrections are very important for high-temperature CG Te> 10keV. ・ Relativistic corrections are significant for large X region (sub-millimeter region)For X>10, factor 4 effect! ・Fokker-Planck expansion approximation is OK for Te < 15keV.

  24. Peculiar velocity of CGrelative to CMB. 23/33 (b) Kinematical SZ Effect Nozawa, Itoh & Kohyama ApJ, 508, 17 (1998) Lorentz boosted Boltzman equation

  25. Kinematical SZ effect 24/33 Distortion of the CMB spectrum

  26. 25/33 Relativistic corrections

  27. 26/33 Distortion of the spectral intensity

  28. 27/33 Summary for kinematical SZ effect ・Relativistic corrections are very important for high-temperature CG Te> 10keV.

  29. 28/33 (c) Polarization SZ Effect Sunyaev & Zeldovich,Mon. Not. R. Astr. Soc. 190, 413 (1980) Magnitude of the polarization of CMB

  30. 29/33 Itoh, Nozawa & Kohyama ApJ, 533, 588 (2000) Polarized photons with Lorentz boosted Boltzman equation

  31. 30/33 Relativistic corrections

  32. 31/33 Distortion of the spectral intensity

  33. 32/33 Summary for Polarization SZ effect ・Relativistic corrections are very important for high-temperature CG Te> 10keV. ・Distortion of the spectral intensity is extremely small.

  34. 33/33 (3) Summary ・We have presented a relativistically covariant formalism for the thermal SZ effect. ・With the formalism one can treat kinematical SZ effect, polarization SZ effect, and multiple scattering effect in an unified manner. ・Relativistic corrections are very important for high-temperature CG Te> 10keV for all SZ effects.

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