Galaxy Clusters and Implications for Dark Matter (Part II)

1. Galaxy Clusters and Implications for Dark Matter (Part II) Presented by Kisha Delain and Sean O’Neill 4/17/2003

2. Outline • Methods of Dark Matter Analysis • Is Hydrostatic Equilibrium a Valid Assumption? • Cluster Mass Profiles from X-rays and Lensing • Dark Matter Constraints • Conclusions

3. Methods Used to Estimate the Properties of Dark Matter in Clusters • Cluster Dynamics virial theorem  M=3<v||2>Rcl/G • Sunyaev-Zeldovich Effect Observations of CMB estimate integral of gas pressure along line of sight • X-Ray Observations brehm + thermo  M(<r) is function of T, r, and spatial gradients of , T • Gravitational Lensing GR  M(<p) = pc2/4G ( is deflection, p is impact parameter)

4. Methods Used to Estimate the Properties of Dark Matter in Clusters • Cluster Dynamics virial theorem  M=3<v||2>Rcl/G • Sunyaev-Zeldovich Effect Observations of CMB estimate integral of gas pressure along line of sight • X-Ray Observations brehm + thermo  M(<r) is function of T, r, and spatial gradients of , T • Gravitational Lensing GR  M(<p) = pc2/4G ( is deflection, p is impact parameter)

5. Hydrostatic Equilibrium? • As illustrated, the assumption of hydrostatic equilibrium must be examined before it can be used to derive mass estimates from X-ray observations. • On a case-by-case basis, high-resolution X-ray observations and/or comparison with lensing can test the assumption. • Features such as the presence of cooling flows and regular isophotes suggest that hydrostatic equilibrium may be valid.

6. Chandra Observations of EMSS 1358+6245 (Arabadjis et al, 2002)

7. Mass Profiles of EMSS 1358 asDerived from X-ray Observations (Arabadjis et al, 2002)

8. Comparison of Lensing and X-ray Results for EMSS 1358+6245 (Arabadjis et al, 2002)

9. NFW Profile • Simulations done by Navarro, Frenk, and White (1997) suggest that equilibrium CDM density profiles in clusters all have similar shape, independent of halo mass, density fluctuations, or cosmology. • Density profile:   1/[(r/rs)(1+r/rs)2] rs is scale radius

10. Chandra Observations of Abell 2029 (Lewis et al, 2000)

11. Chandra Observations of Abell 2029 (Lewis et al, 2000)

12. Possible Types of Dark Matter • As seen in lecture, baryonic DM and hot relics are insufficient to explain cluster dynamics. • Assuming some sort of cold dark matter, we can examine whether self-interacting or collisionless CDM is favored by simulations and observations.

13. Simulations of Dark Matter Clusters by Yoshida et al (2000)

14. Simulations of Dark Matter Clusters by Yoshida et al (2000) Collisionless Self-interacting

15. What Can Chandra Say About the Nature of Dark Matter? • High-resolution X-ray observations have the advantage of being able to partially probe the cores of clusters. • Central density profiles (along with external astrophysical constraints) can exclude possible DM interaction cross-sections. • When one also considers the core mass profiles of dwarf galaxies, the DM cross-sections are constrained to be velocity-dependent.

16. Summary of Data on Self-Interacting Dark Matter Cross-Sections (Arabadjis et al, 2002)

17. Dark Matter Profiles Dark matter can be constrained through a variety of methods, including lensing and X-ray studies. The DM is cold, and the observations currently favor collisionless or low interaction probability DM. Deeper Chandra X-ray observations of relaxed clusters will provide more information on typical mass profiles. Conclusions Hydrostatic Equilibrium • Sometimes valid, but not always! • Specific clusters must be examined for absence of mergers, regular spacing of isophotes, presence of cooling flows, or other signs of relaxation. • The determination of hydrostatic equilibrium allows X-ray data to supply mass profiles.