PART II Simulations of Shocks in Clusters of

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PART II Simulations of Shocks in Clusters of Galaxies ALMA Users Workshop 8 February,

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

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

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:

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

I. Shocks in Clusters of Galaxies: Observations

I. Shocks in Clusters of Galaxies: Observations

Coma Cluster of Galaxies (z=0. 025, 2 x 1015 M⦿); optical image (Kitt Peak

Coma Cluster of Galaxies (z=0. 025, 2 x 1015 M⦿); optical image (Kitt Peak National Observatory).

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

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

The bullet cluster: 1 E 0657 -56: Mach ~ 3; Markevitch & vikhlinin (2007);

The bullet cluster: 1 E 0657 -56: Mach ~ 3; Markevitch & vikhlinin (2007); Clowe et al. (2006).

The bullet cluster: Bradac et al. (2006)

The bullet cluster: Bradac et al. (2006)

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

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

 Shocks in Clusters of Galaxies Rankine-Hugoniot jump conditions ρ2 / ρ1 = (γ+1)

Shocks in Clusters of Galaxies Rankine-Hugoniot jump conditions ρ2 / ρ1 = (γ+1) M 12 / ((γ-1) M 1 2 +2) P 2 / P 1 = 1 + 2 γ (M 12 -1)/ (γ+1) T 2 / T 1 = (1+γ (2 M 12 -1))(2+(γ-1) M 12)/((γ+1)2 M 12) M 1 = ( 2 r / (γ + 1 – r (γ-1) )-1 Compression: r = ρ2 / ρ1

 FLASH Simulations of clusters of galaxies total mass: 1014 M⦿ - 1015 M⦿

FLASH Simulations of clusters of galaxies total mass: 1014 M⦿ - 1015 M⦿ dark matter NFW from Navarro at el. (1997): ρgas ~ ( r/rs )-1 (1 + r/rs)-2 R < Rcut σr from Lokas & Gamon (2001) ICG model density: β model: ρ ~ (1 + r 2/r 2 core)-3β/2 R < Rcut temperature: from hydrostatic equilibrium previous simulations: GADGET 2 (SPH): Springel & Farrar (2007); GASOLINE (SPH): Mastropietro & Burkert (2008); FLASH 2 D: Milosavljevic et al. (2007) FLASH 3 D: Zu. Hone et al. (2009 a, b)

FLASH 3 D simulations: line of sight collision

FLASH 3 D simulations: line of sight collision

 FLASH Simulations of clusters of galaxies Simulations for high resolution SZ-X-ray observations: RXJ

FLASH Simulations of clusters of galaxies Simulations for high resolution SZ-X-ray observations: RXJ 1347

High-resolution multi-wavelength observations of RXJ 1347 (Mason et al. 2010; submitted to Ap. J.

High-resolution multi-wavelength observations of RXJ 1347 (Mason et al. 2010; submitted to Ap. J. )

FLASH 3 D simulations for RXJ 1347 (Molnar et al. 2010; in prep. )

FLASH 3 D simulations for RXJ 1347 (Molnar et al. 2010; in prep. )

III. Applications to ALMA

III. Applications to ALMA

 Why arc second resolution? – – To understand the physics of the cluster

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

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 3 D simulations

IV. Summary • Arc minute scale: Clusters of galaxies for cosmology – – •

IV. Summary • Arc minute scale: Clusters of galaxies for cosmology – – • numbers counts scaling relations (e. g. , AMi. BA) 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 Xray (ALMA)

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