Cosmology from Galaxy Cluster Peculiar Velocities.

1. Cosmology from Galaxy Cluster Peculiar Velocities. Suman Bhattacharya. Arthur Kosowsky Department of Physics and Astronomy. University of Pittsburgh. Outstanding Questions in Cosmology. Imperial College. March 07.

2. Outline • Sunyaev-Zel’dovich effect. • What’s wrong with peculiar velocities from Galaxy surveys? • Theoretical outline: Different velocity statistics. • Results: Constraints on parameters.

3. Thermal Sunyaev-Zel’dovich Effect: • CMB photons passing through galaxy clusters undergo collisions with electrons present within clusters causing a change in the spectrum (Thermal SZ effect). • proportional to optical depth and gas temperature. Credit: Carlstrom et al 2002

4. Kinetic SZ effect: • This is due to scattering of photons off gas with bulk motion. • Being Doppler shift, (approx.) spectrum of kSZ is still blackbody unlike tSZ. • This effect is proportional to radial peculiar velocity and optical depth. • Typically kSZ ( ~ 10 µK ) << tSZ (~ 100 µK) in clusters of galaxies. . Credit: Carlstrom et al 2002

5. Upcoming SZ measurements • ACT (150 sq deg). (Kosowsky 2003; Fowler et al 2005). • SPT (4000 sq deg). (Ruhl et al. 2004) • designed to scan the microwave sky with very high sensitivity and arc minute resolution. • ACT would have the nominal sensitivity (2-10 μK) to measure kSZ. ACT Telescope

6. Q. Why are kSZ velocity surveys more reliable than redshift based surveys? • Redshift based velocity surveys: need to estimate distance. • Biases introduced in calibrating the distances. • Error increases with z. Typically ~15-20 % of the distance. • Velocity as a cosmology probe limited to near redshift z~0.024(Bridle et al 2001). • Moreover galaxy velocity surveys probe into nonlinear scale which is difficult to model.

7. On the other hand kSZ… • Use clusters of galaxies as tracers of cosmic velocity field. • kSZ effect directly measures velocities with respect to the cosmic rest frame. • These velocities respond only to larger scales which are mostly linear. • Measured velocity is independent of redshift

8. Velocity Statistics: • Probability distribution of radial velocities-> number of clusters at each velocity bin at each redshift range. • Plot shows normalized count in each velocity bin at z=0.1. • Use semi analytic halo model->2 halo term. (Sheth 2000, Hamana 2003, Cooray & Sheth 2002)

9. Mean streaming velocity: average relative velocity of all clusters at a fixed separation along the line joining them. V12(r) = < (V1 - V2 ) . r > • Plots shows mean streaming velocity at redshift =0.3 as a function of separation. • Use semi analytic halo model->2-halo term. (Sheth et al 2001, Cooray & Sheth 2002).

10. Halo model for PDF(v) and mean streaming velocity V12(r) :

11. Ωm(DM +b) = 0.29 - 0.34. n = 0.93 – 0.96. σ8 = 0.68 – 0.79. h = 0.7-0.76. w = 0.9 – 1.15 Matter density (CDM +Baryons). power spectrum index. Amplitude of fluctuations Hubble parameter Dark Energy equation of state. Cosmological Parameter space spanned by velocity statistics. Current constraints from WMAP3 Spergel et al 2006

12. PDF: Mean Streaming velocity: Bhattacharya & Kosowsky 2007, ApJL accepted. Note: Priors are computed from MCMC chains obtained http://lambda.gsfc.nasa.gov/ Results: Parameter constraints from two different velocity statistics for a SPT like survey. (5000 sq deg sky area and mass limit Mmin=1014 Msun )

13. Conclusion: • Constraints on σ8 from f(v) itself is 5.8%. A joint constraint from f(v)+ V12(r) gives 2.9% accuracy. Adding priors (WMAP 3rd year (Spergel et al 2006)+ SNLS 1st year, (Astier et al 2006), this reduces to 0.7% and 0.5% respectively. • Constraints on w from f(v) are 11.4 % and 14.0% for velocity error of 100 km/s and 300 km/s respectively. Adding priors the constraints decreases to around 4.0%. • Constraints on Ωmfrom V12(r) are 9.4% and 16% for the two velocity errors. Adding priors these decreases to 3.0%.

14. Plot shows parameter degeneracy for velocity (red), WMAP3+SNLS1 (Green), velocity + priors ( blue)

15. Forecast for ACT(400 sq deg and Mmin =1014 Msun ) • Marginalised over ns(1.5%; WMAP3) and h (8% HST Key project, Freedman et al 2000). • PDF: Mean streaming velocity: Bhattacharya & Kosowsky in prep.

16. Conclusion: • σ8 can be constrained to 4.5-6.5% accuracy with velocity only and 1.3-1.0% accuracy adding priors (WMAP 3rd year +SNLS 1st year). • Ωmcan be obtained with 7.5-9.0% accuracy (velocity only) and 2.0-6.0% accuracy (+priors). • w can be obtained with 23-35% accuracy (velocity) and 4.7-5.0% accuracy (+ priors).

17. Plot shows velocity statistics is robust against error in mass measurement. • Mmin =1014 Msun (red) & 1.2X1014 Msun (blue). • 20 % bias in measurement of minimum mass results ~3 % change for the case of mean streaming velocity and ~1% for PDF.

18. Comparing with number density of clusters… Bhattacharya & Kosowsky in prep. (Francis, Bean & Kosowsky 2005). • Plot (right) of Ωm vs σ8 shows a 20 % bias in mass estimate leads to shift in parameter estimation by more than 4- σ. Corresponding shift (left) in the case of velocity is insignificant.

19. Effect of velocity errors on parameter constraints for the case of PDF • Ωm • h • w • σ8 • ns

20. Summary: • A future wide area SPT like velocity survey will provide competitive probe to various cosmological parameters independent of any other observations. • ACT (400 sq deg) data + WMAP3+SNLS1 will provide 5-6 times improvement on current constraints of σ8 and Ωm . The constraint on w will be improved by 2-3% over existing accuracy. • Velocity statistics is robust to error in minimum mass measurement. This is an advantage over number density. • Will need to worry about other systematic error like point sources, relativistic tSZ, lensing, primary CMB…..