part ii simulations of shocks in clusters of galaxies alma users workshop 8 february, 2010 sándor...
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PART II Simulations of Shocks
inClusters of Galaxies
ALMA Users Workshop8 February, 2010
Sándor M. Molnár, Patrick KochInstitute of Astronomy and Astrophysics,
Academia Sinica, Taipei, Taiwan
Collaborators for FLASH Simulations:
Nathan Hearn (Univ. of Chicago)Joachim Stadel (Univ. of Zurich)
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
I. Shocks in Clusters of Galaxies:
Observations
Coma Cluster of Galaxies (z=0.025, 2x1015 M⦿); optical image (Kitt Peak National Observatory).
Coma Cluster of Galaxies: X-ray image (XMM-Newton).
The bullet cluster: 1E0657-56: Mach ~ 3;Markevitch & vikhlinin (2007); Clowe et al. (2006).
The bullet cluster: Bradac et al. (2006)
II. Shocks in Clusters of Galaxies:
FLASH 3D Simulations
Shocks in Clusters of Galaxies
Rankine-Hugoniot jump conditions
ρ2 / ρ1 = (γ+1) M12 / ((γ-1) M1
2 +2) P2 / P1 = 1 + 2 γ (M1
2 -1)/ (γ+1) T2 / T1 = (1+γ (2 M1
2 -1))(2+(γ-1) M12)/((γ+1)2 M1
2) M1 = ( 2 r / (γ + 1 – r (γ-1) )-1
Compression: r = ρ2 / ρ1
FLASH Simulations of clusters of galaxies
total mass: 1014 M⦿ - 1015 M⦿ dark matter
NFW from Navarro at el. (1997): ρ
gas ~ ( r/r
s )-1 (1 + r/r
s)-2 R < R
cut
σr from Lokas & Gamon (2001)
ICG model
density: β model: ρ ~ (1 + r2/r2core
)-3β/2 R < Rcut
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)
FLASH 3D simulations: line of sight collision
FLASH Simulations of clusters of galaxies
Simulations for high resolution SZ-X-ray observations:
RXJ1347
High-resolution multi-wavelength observations of RXJ1347(Mason et al. 2010; submitted to ApJ.)
FLASH 3D simu- lations for RXJ1347(Molnar et al. 2010; in prep.)
III. Applications to ALMA
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.
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
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)
THE END