The Physics of Collisionless Accretion Flows. Eliot Quataert (UC Berkeley)

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1 The Physics of Collisionless Accretion Flows Eliot Quataert (UC Berkeley)

2 Accretion Disks: Physical Picture Simple Consequences of Mass, Momentum, & Energy Conservation Matter Inspirals on Approximately Circular Orbits V r << V orb t inflow >> t orb t inflow ~ time to redistribute angular momentum ~ viscous diffusion time t orb = 2π/Ω; Ω = (GM/r 3 ) 1/2 (Keplerian orbits; like planets in solar system) Disk Structure Depends on Fate of Released Gravitational Energy t cool ~ time to radiate away thermal energy of plasma Thin Disks: t cool << t inflow (gas collapses to a pancake) Thick Disks: t cool >> t inflow (gas remains a puffed up torus)

3 Geometric Configurations thin disk: energy radiated away (relevant to star & planet formation, galaxies, and luminous BHs/NSs) thick disk (torus; ~ spherical): energy stored as heat (relevant to lower luminosity BHs/NSs)

4 Thick Disks: Radiatively Inefficient At low densities (accretion rates), cooling is inefficient Grav. energy thermal energy; not radiated kt ~ GMm p /R: T p ~ K > T e ~ K near BH Collisionless plasma: e-p collision time >> inflow time relevant to most accreting BHs & NSs, most of the time

5 The (In)Applicability of MHD M Black Hole Observed Plasma (R ~ cm ~ 10 5 R horizon ) T ~ few kev n ~ 100 cm -3 mfp ~ cm ~ 0.1 R e-p thermalization time ~ 1000 yrs >> inflow time ~ R/c s ~ 100 yrs electron conduction time ~ 10 yrs << inflow time ~ R/c s ~ 100 yrs Hot Plasma Gravitationally Captured By BH Accretion Disk

6 The (In)Applicability of MHD M Black Hole Estimated Conditions Near the BH T p ~ K T e ~ K n ~ 10 6 cm -3 B ~ 30 G proton mfp ~ cm >>> R horizon ~ cm need to understand accretion of a magnetized collisionless plasma Hot Plasma Gravitationally Captured By BH Accretion Disk

7 Angular Momentum Transport by MHD Turbulence (Balbus & Hawley 1991) MRI: A differentially rotating plasma with a weak field (β >> 1) & dω 2 /dr < 0 is linearly unstable in MHD magnetic tension transports ang. momentum, allowing plasma to accrete nonlinear saturation does not modify dω/dr, source of free energy (instead drives inflow of plasma bec. of Maxwell stress B r B ϕ ) John Hawley

8 Major Science Questions Origin of the Low Luminosity of many accreting BHs Macrophysics: Global Disk Dynamics in Kinetic Theory e.g., how adequate is MHD, influence of heat conduction, Microphysics: Physics of Plasma Heating MHD turbulence, reconnection, weak shocks, electrons produce the radiation we observe Analogy: Solar Wind macroscopically collisionless thermally driven outflow w/ T p & T e determined by kinetic microphysics Observed Flux Time (min)

9 The MRI in a Collisionless Plasma significant growth at long wavelengths where tension is negligible angular momentum transport via anisotropic pressure (viscosity!) in addition to magnetic stresses $ F " # B zb " ' & % B 2 ) *p +*p, ( ( ) Quataert, Dorland, Hammett 2002; also Sharma et al. 2003; Balbus 2004

10 Buoyancy Instabilities ( convection ) in Low Collisionality Plasmas (Balbus 2000; Parrish & Stone 2005, 2007; Quataert 2008; Sharma & Quataert 2008) Convection (Buoyancy) may be Dynamically Impt in Hot, Thick Disks Schwarzschild Criterion for Instability in Hydro & MHD (β >> 1): ds/dr < 0 T > T ambient ρ < ρ ambient B gravity temperature t conduction < t buoyancy " T # 0 (temp constant along field lines) Magnetothermal Instabilty if dt/dr < 0

11 Nonlinear Evolution Simulated Using Kinetic-MHD Large-scale Dynamics of collisionless plasmas: expand Vlasov equation retaining slow timescale & large lengthscale assumptions of MHD (e.g., Kulsrud 1983) Particles efficiently transport heat and momentum along field-lines

12 Evolution of the Pressure Tensor adiabatic invariance of µ ~ mv 2 /B ~ T /B q = 0 CGL or Double Adiabatic Theory q " nv th k # T Closure Models for Heat Flux (temp gradients wiped out on ~ a crossing time)

13 Pressure Anisotropy µ "T # /B = constant $ T # > T as B % T T unstable to small-scale (~ Larmor radius) modes that act to isotropize the pressure tensor (velocity space anisotropy) e.g., mirror, firehose, ion cyclotron, whistler instabilities fluctuations w/ freqs ~ Ω cyc violate µ invariance & pitch-angle scatter provide effective collisions & set mean free path of particles in the disk impt in other macroscopically collisionless astro plasmas (solar wind, clusters, ) Use subgrid scattering model in accretion disk simulations "p # "t "p "t =... $ %(p #, p,&)[ p # $ p ] =... $ %(p #, p,&)[ p $ p # ]

14 Velocity Space Instabilities in the Solar Wind

15 Local Simulations of the MRI in a Collisionless Plasma magnetic energy volume-averaged pressure anisotropy Sharma et al Net Anisotropic Stress (i.e, viscosity) ~ Maxwell Stress

16 Viscous Heating in a Collisionless Plasma Heating ~ Shear*Stress Collisional Plasma Coulomb collisions determine Δp q + ~ m 1/2 T 5/2 Primarily Ion Heating Collisionless Plasma Microinstabilities regulate Δp Significant Electron Heating q + ~ T 1/2

17 Plasma Heating T i /T e in kinetic MHD sims Astrophysical Implications efficiency = L / M c 2 Sharma et al T i /T e ~ 10 at late times First Principles Prediction of Radiation Produced by Accreting Plasma

18 References Linear Kinetic MRI Calculations (a subset) Quataert, Dorland, & Hammett, 2002, ApJ, 577, 524 Balbus, 2004, ApJ, 616, 857 Krolik & Zweibel, 2006, ApJ, 644, 651 (finite Larmor radius effects) Nonlinear Simulations of Kinetic MRI (shearing box) Sharma et al., 2006, ApJ, 637, 952 Sharma et al., 2007, ApJ, 667, 714 Buoyancy instabilities ( convection ) in low collisionality plasmas Balbus, 2000, ApJ, 534, 420 (linear theory) Parrish & Stone, 2007, 664, 135 (local nonlinear simulations) Quataert, 2008, ApJ, in press (astro-ph/ ) (linear theory)

19 Summary Accretion Disk Dynamics Det. by Angular Momentum & Energy Transport Angular momentum transport via MHD turbulence initiated by the MRI Thick Disks: Gravitational Potential Energy Stored as Heat T ~ GeV; macroscopically collisionless; relevant to low-luminosity BHs/NSs Crucial role of pressure anisotropy and pitch angle scattering by small-scale kinetic instabilities ( collisions ) Ang. Momentum Transport: Anisotropic stress ~ Maxwell Stress Energetics: Significant electron heating by Anisotropic Stress