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

2. Contents (1)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 2/33

3. (1) Introduction Optical Image by Subaru (a) Cluster of Galaxies (CG) RX J1347 (z=0.45, 5×10 9 light years) X-ray Image by Chandra 3/33 0.9 Mpc

4. Structure of CG Galaxies Hot plasmas 4/33

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

6. Low frequency region --- temperature decrement High frequency region --- temperature increment Thermal SZ effect determines ΔT CMB ． 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

7. Assumption: CG is spherical. 7/33 With the redshift observation, the Hubble constant H 0 is determined (H 0 =v/D A ). WMAP data

8. Advantages of the SZ effects: ・ Total radiation intensity is redshift independent! E CMB ∝ (1+z) 4 (energy density of CMB) D A ∝ (1+z) 2 (angular diameter distance) I total ∝ E CMB /D 2 --- z-dependences cancel out! ・ Determination of H 0, cosmological constants, peculiar velocity field, etc. Disadvantages of the SZ effects: ・ Assumption of the spherical symmetry for CG ・ Small signals ΔT CMB ～ 10 - 3 Chandra and XMM-Newton have opened a new era for precise observation of the SZ effect. 8/33

9. Determination of cosmological constants with SZ effect

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

11. 10/33 Recent observations: High temperature CG T e = 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 ΔT CMB. Doppler Effect vzvz Relativisitic corrections become significant! Sunyaev & Zeldovich, Mon. Not. R. Astr. Soc. 190, 413 (1980)

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

14. 13/33 (2) Relativistic Corrections to SZ Effects (a)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 --- Non-relativistic term Relativistic corrections

19. 18/33 Relativistic corrections

20. 19/33

21. 20/33

22. Distortion of the spectral intensity 21/33

23. ・ Relativistic corrections are very important for high-temperature CG T e > 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 T e < 15keV. Summary for thermal SZ effect 22/33

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

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

26. Relativistic corrections 25/33

27. Distortion of the spectral intensity 26/33

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

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

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

31. 30/33 Relativistic corrections

32. Distortion of the spectral intensity 31/33

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

34. (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 T e > 10keV for all SZ effects. 33/33