GH2005 Gas Dynamics in Clusters Craig Sarazin Dept. of Astronomy University of Virginia Cluster Merger Simulation A85 Chandra (X-ray)

Clusters of Galaxies ~4 Mpc diameter ~1015 M total mass Largest gravitationally bound systems in Universe 100’s of bright galaxies, 1000’s of faint galaxies ~4 Mpc diameter ~1015 M total mass

Intracluster Gas Majority of observable cluster mass (majority of baryons) is hot gas Temperature T ~ 108 K ~ 10 keV Electron number density ne ~ 10-3 cm-3 Mainly H, He, but with heavy elements (O, Fe, ..) Mainly emits X-rays LX ~ 1045 erg/s, most luminous extended X-ray sources in Universe Age ~ 2-10 Gyr

Physical State of Intracluster Gas: Local Thermal State Mainly ionized, but not completely State of free particles (kinetic equilibrium)? bound vs. free electrons (ionization equilibrium)? bound electrons (excitation)? free continuum bound levels

Kinetic Equilibrium Free electrons, protons, other ions Coulomb collisions → thermodynamic equil.

Kinetic Equilibrium Coulomb collision time scales t(e,e) ~ 105 yr t(p,p) ~ 4 x 106 yr t(p,e) ~ 2 x 108 yr all < age (>109 yr) Kinetic equilibrium, Maxwellian at T Equipartition Te=Tp (except possibly at shocks)

Ionization Equilibrium Collisional ionization e- + X+i → e- + e- + X+i+1 Radiative, dielectronic recombination e- + X+i+1 → X+i + photon(s) (not e- + e- + X+i+1 → e- + X+i ) Not thermodynamic equilibrium (Saha)! Collisional ionization equilibrium independent of density ne depends only on temperature T (except perhaps in shocks)

Ionization Equilibrium Iron XXV = Fe+24 (helium-like iron)

Excitation Equilibrium bound levels Collisional excitation Radiative de-excitation (line emission) No collisional de-excitation (density too low) No local density diagnostics in spectrum e photon

X-ray Emission Processes Continuum emission Thermal bremsstrahlung, ~exp(-hn/kT) Bound-free (recombination) Two Photon Line Emission (line emission) Ln ∝ en (T, abund) (ne2 V) In ∝ en (T, abund) (ne2 l)

X-ray Spectrum

The Intracluster Medium as a Fluid Mean-free-path λe ~ 20 kpc < 1% of diameter → fluid (except possibly in outer regions, near galaxies, or at shocks and cold fronts)

The Intracluster Medium as a Fluid (cont.) Specify local: Density (r or ne) Pressure P Internal energy or temperature T Velocity v Ideal gas P = n k T (except for nonthermal components; cosmic rays, magnetic fields)

Transport Properties Due to finite mean free path thermal conduction viscosity diffusion and settling of heavy elements

Heat Conduction Spitzer heat conductivity Strongly dependent on temperature Q ∝ T7/2

Heat Conduction (cont.) 600 kpc 10 Gyr

Heat Conduction (cont.) If unsuppressed, heat conduction very important in centers of clusters, or where there are large temperature gradients cooling cores cold fronts near galaxies with gas

Magnetic Fields in Clusters B ~ mG → PB « Pgas in general in clusters Electron, ions gyrate around magnetic field lines rg ≈ 108 cm « scales of interest Act like effective mean free path, make ICM more of a fluid Suppress transport properties ⊥ B Could greatly reduce thermal conduction, but depends on topology of B fields B e

Heating and Cooling of ICM What determines temperature T? Why is ICM so hot? What are heating processes? gravitational heating nongravitational heating (SNe, AGNs) What are cooling processes?

Why is gas so hot? Clusters have huge masses, very deep gravitational potential wells Any natural way of introducing gas causes it to move rapidly and undergo fast shocks infall galaxy ejection All intracluster gas is shocked at ~2000 km/s

Cluster Mergers Clusters from hierarchically, smaller things form first, gravity pulls them together Abell 85 Chandra

Merger Shocks Main heating mechanism of intracluster gas

Simple Scaling Laws for Gravitational Heating (Kaiser 1986) Gas hydrostatic in gravitational potential kT ~ mmp GM/R Clusters formed by gravitational collapse 〈rcluster ~ 180 rcrit (zform) Most clusters formed recently, zform ~ now Baryon fraction is cosmological value, most baryons in gas R ∝ ( M / rcrit0 )1/3 ∝ M1/3 T ∝M2/3 LX ∝T2

Need for Nongravitational Heating Scaling laws disagree with observations, particularly for lower mass systems (groups) Gas distributions are too extended, may have cores Explanations: nongravitational heating, puffs up gas distribution inhomogeneous gas and radiative cooling removes cooler gas

Nongravitational Heating and Entropy If heating done now, need e ~2 keV per particle For preheating, or more complex history, better variable is amount of extra entropy per particle s = (3/2) k ln (P/r5/3) + s0 P = rkT/( mmp) define K ≡ kT/(ne)2/3 keV cm2 (s ∝ln K)

Specific Entropy - Advantages Lagrangian variable, moves with gas, mirrors history of each gas parcel For any reversible change to gas, remains constant ds/dt = 0, dK/dt = 0 Reversible changes: slow compression or expansion Irreversible changes include: shocks heating cooling

Nongravitational Entropy Purely gravitational heating (entropy from merger shocks) gives scaling K ∝T ∝ M2/3

Cluster and Group Entropies at 0.1 Rvir K ∝T gravity (Lloyd-Davies et al. 2000)

Nongravitational Entropy Purely gravitational heating (entropy from merger shocks) gives scaling K ∝T ∝ M2/3 Observed clusters and groups require extra entropy K ~ 125 keV cm2 Entropy increases outwards in clusters. convectively stable

Entropy vs. Radius data gravity (Ponman et al. 2003)

Heating by Supernovae Core-collapse supernovae, massive stars, during period of galaxy formation, galactic winds Type Ia supernovae, older binary stars, more continuous Supernovae also make heavy elements e ~ 1.6 ZSi (Esn/1051 ergs) keV ≲ 0.3 keV (Loewenstein 2000) Probably a bit low, but possible

Heating by AGN Need energy deposited in ICM: large scale kinetic energy (jets) and particles, not radiation from AGN Clusters → E & S0 galaxies → radio galaxies and radio QSOs Estimate total energy input from MBH today, MBH ∝ Mbulge . Assume MBH due to gaseous accretion, E = e MBH . Provides enough energy, if a significant part deposited in ICM

Universal Pre-Heating of Intergalactic Gas? Lyman a forest clouds at z ~ 2 → much of IGM relatively cool

Radiative Cooling of ICM Main cooling mechanism is radiation, mainly X-rays L = L(T,abund) ne2 ergs/cm3/s T ≳ 2 kev, L ∝ T1/2 Thermal bremsstrahlung T ≲ 2 keV, L ∝ T-0.4 X-ray lines

Radiative Cooling (cont.) Cooling time (isobaric, constant pressure) Longer than Hubble time in outer parts of clusters Short in centers of ~1/2 clusters, “cooling flows”, tcool ~ 3 x 108 yr

Pre-Cooling vs. Pre-Heating Cooling time, in terms of entropy: Shorter than Hubble time for K ≲ 130 kev cm2 If clusters start with gas with a wide range of entropies, low entropy gas cools out, leaves behind high entropy gas (Voit & Bryan 2001) Cooled gas → galaxy formation, stars

Heating of ICM - Summary Most of energy in large clusters due to gravity, mergers of clusters Smaller clusters, groups, centers of clusters → significant evidence of nongravitational heating Due to galaxy and star formation, supernovae, formation of supermassive BHs ICM/IGM records thermal history of Universe

Hydrodynamics Add viscosity, thermal conduction, … Add magnetic fields (MHD) and cosmic rays Gravitational potential f from DM, gas, galaxies

Sound Crossing Time Sound speed Sound crossing time Less than age → unless something happens (merger, AGN, …), gas should be nearly hydrostatic

Hydrostatic Equilibrium Isothermal (T = constant)

Cluster Potentials NFW (Navarro, Frenk, & White 1997) r-1 ln r NFW r-3

Cluster Potentials (cont.) Analytic King Model (approximation to isothermal sphere NFW King r-1 flat core ln r ln r r-3

Beta Model (Cavaliere & Fusco-Femiano 1976) Assume King Model DM potential Alternatively, assume galaxies follow King Model, and have isotropic, constant velocity dispersion

Beta Model (cont.)

Beta Model (cont.) Fit outer parts of clusters (Multiple beta models) ≈ 2/3 ∝ r -2 IX ∝ r -3 Beta model XMM/Newton A1413 Pratt & Arnaud

Hydrostatic Equilibrium (cont.) Adiabatic (Polytropic) Models

Cluster Temperature Profiles Rapid T rise with r at center (100 kpc, “cooling core”) T flat to 0.125 rvir Slow T decline with r at large radii g ~ 1.2 Chandra (Vikhlinin et al 2005)