Sunyaev-Zel’dovich Signals in Cluster Models

1. Sunyaev-Zel’dovich Signals in Cluster Models Beth Reid David Spergel Princeton University

2. Outline • SZE surveys: Mass-Observable relation • Thermodynamics of the Intracluster Medium (ICM) • Clues from X-ray observations • Results: LSZ(M,z) in cluster models • Implications for cosmological studies and cluster physics

3. Sunyaev-Zel’dovich Effect • Spectral Distortion of the CMB with magnitude fixed by y: • LSZ integrates over the entire cluster: • LSZ is the observable!

4. Cosmology with SZE Surveys:Measuring w with Cluster Number Counts Figure 1, Mohr, astro-ph/0408484

5. Cosmology with SZE Surveys:Cluster Number Counts • SZE surveys count clusters Selection Function - depends on LSZ(M, z), and possibly gas distribution Eqn 1, Mohr, astro-ph/0408484

6. Motivation up-scattered clusters • Understand LSZ(M, z) • Explore sources of scatter -- will introduce bias down-scattered clusters Figure 1 in Lima and Hu (2005), PRD 72, 043006

7. DM halo Gas Accretion shock radius Gravitational Heating • Tgas ~ Tdark • rac ~ rvir • Scaling Relations • LX ~ T2 • T ~ M2/3 • K(r) ~ r1.1 rvir LX ~ T2.6-2.9

8. Thermodynamics of the ICM • Assume spherical symmetry • Assume hydrostatic equilibrium • ICM properties determined by • Gravitational Potential, NFW(r) • Bounding Accretion Pressure, Pac • Entropy Profile, K(r)

9. X-ray Cluster Observations • Measure n2(T), Tspec • Spherical symmetry • n(r), T(r) • Hydrostatic Equilibrium: • Agreement with NFW(r) and CDM c 30’ Perseus Cluster Churazov et al, 2003, ApJ 590 225

10. X-ray Cluster Observations 2 • Simple scalings broken: • LX ~ T2.6-2.9 • Non-gravitational processes significant • Entropy gradients observed: Figure 13b, Pratt and Arnaud, A&A 408, 1 (2003)

11. Non-gravitational processes: Heating • Supernovae, AGN -- relativistic component? • Uncertainties encoded in fICM, K(r) MS0735 (Credit: X-ray: NASA/CXC/Ohio U./ B.McNamara et al.; Radio: NRAO/VLA) Perseus (Credit: NASA/CXC/IoA/A.Fabian et al.)

12. Non-gravitational processes:Cooling • Central cooling times short, little gas below Tvir/4 • ‘Cold Cores’ require central distributed heating source (AGN?) • Uncertainties encoded in fICM, K(r) Data from Allen et al. 2001, MNRAS 328, 37; Figure 7, astro-ph/0512549 (Peterson and Fabian)

13. Cluster Models • Smooth Accretion Model (Voit et al 2003) • Phenomenological models vary • concentration C • accretion pressure Pac • entropy profile K(r) • ICM mass fraction fICM • Parameterize K(r) as double power law • Solve the equation of hydrostatic equilibrium

14. Results • Assumed fICM, Pac consistent with observations of hot clusters (Vikhlinin et al 2005)

15. models models models

16. yo and Lx,cut provide similar ‘information’ • Our models agree well with the observed LX-yo relation X-ray/SZ data assembled in McCarthy et al. 2003, ApJ 591, 526.

17. Energy Content of the ICM • Observables: LSZ, rsz • Thermal: • Potential:

18. ICM Mass Fraction • Trends observed with mass in nearby clusters in both X-ray and SZ: f2500 f500 Figure 21, Vikhlinin et al (2006), ApJ 640, 691 Afshordi, Lin, Sanderson (2005), ApJ 629, 1

19. Measuring fICM with kSZ • Simultaneous tSZ and kSZ detection can statistically constrain fICM within same radius known from CDM

20. Conclusions • LSZ ~ fICM M5/3, largely independent of feedback energy injection (SN, AGN, ?) • SZ redshift evolution determined by well-understood DM properties • fICM is the largest remaining uncertainty; can be constrained with kSZ • SZ observations can measure total energy of the bound ICM to probe cluster physics • Scatter: c - 8%; K - <10%; simulations - 10-15%