1. PART II Simulations of Shocks in Clusters of Galaxies ALMA Users Workshop 8 February, 2010 Sándor M. Molnár, Patrick Koch Institute of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan

2. Collaborators for FLASH Simulations : Nathan Hearn (Univ. of Chicago)‏ Joachim Stadel (Univ. of Zurich)‏

3. Outline I. Shocks in Clusters of Galaxies: Observations II. Shocks in Clusters of Galaxies: FLASH 3D Simulations III. Applications to ALMA: work in progress IV. Summary

4. I. Shocks in Clusters of Galaxies: Observations

5. Coma Cluster of Galaxies (z=0.025, 2 x 10 15 M); optical image (Kitt Peak National Observatory)‏.

6. Coma Cluster of Galaxies: X-ray image (XMM-Newton).

7. The bullet cluster: 1E0657-56: Mach ~ 3; Markevitch & vikhlinin (2007)‏; Clowe et al. (2006).

8. The bullet cluster: Bradac et al. (2006)‏

9. II. Shocks in Clusters of Galaxies: FLASH 3D Simulations

10. Shocks in Clusters of Galaxies  Rankine-Hugoniot jump conditions ρ 2 / ρ 1 = (γ+1) M 1 2 / ((γ-1) M 1 2 +2)‏ P 2 / P 1 = 1 + 2 γ (M 1 2 -1)/ (γ+1) T 2 / T 1 = (1+γ (2 M 1 2 -1))(2+(γ-1) M 1 2 )/((γ+1) 2 M 1 2 )‏ M 1 = ( 2 r / (γ + 1 – r (γ-1) ) -1 Compression: r = ρ 2 / ρ 1

11. FLASH Simulations of clusters of galaxies total mass: 10 14 M - 10 15 M  dark mat‏ter NFW from Navarro at el. (1997)‏: ρ gas ~ ( r/r s ) -1 ( 1 + r/r s ) -2 R < R cut σ r‏ from Lokas & Gamon (2001)  ICG model  density: β model: ρ ~ ( 1 + r 2 /r 2 core ) -3β/2 R < R cut  temperature: from hydrostatic equilibrium  previous simulations: GADGET2 (SPH): Springel & Farrar (2007)‏; GASOLINE (SPH): Mastropietro & Burkert (2008); FLASH 2D: Milosavljevic et al. (2007)‏ FLASH 3D: ZuHone et al. (2009a, b)

12. FLASH 3D simulations: line of sight collision

13. FLASH Simulations of clusters of galaxies  Simulations for high resolution SZ-X-ray observations: RXJ1347

14. High-resolution multi-wavelength observations of RXJ1347 (Mason et al. 2010; submitted to ApJ.)

15. FLASH 3D simu- lations for RXJ1347 (Molnar et al. 2010; in prep.)

16. III. Applications to ALMA

17. Why arc second resolution? – To understand the physics of the cluster gas: The role of transport proceses Thermal viscosity Conduction Turbulence Magnetic fields – Can we model clusters well enough to do precision cosmology? Example: arc second resolution in X-ray: – Turbulent intra-cluster gas with disturbed struct. – shock physics: below the Coulomb mean free path Arc sec SZ (ALMA) – Accurate pressure distribution: same as X-ray resol.

18. Work in progress – Accretion shocks in clusters of galaxies: hard to observe but important (Molnar et al 2009) – Merger shocks in clusters of galaxies: CASA simulations based on images from FLASH 3D simulations

19. IV. Summary Arc minute scale: Clusters of galaxies for cosmology – numbers counts – scaling relations (e.g., AMiBA) Few arc second to (sub)arc second: Cluster physics – 10 arc second: shock features appear (e.g., Mustang) – 1 arc second: detailed maps comparable to X- ray (ALMA)

20. THE END