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