T - UCLA Physics & Astronomy

19
The Physics of Collisionless Accretion Flows Eliot Quataert (UC Berkeley)

Transcript of T - UCLA Physics & Astronomy

The Physics of CollisionlessAccretion Flows

Eliot Quataert(UC Berkeley)

Accretion Disks: Physical Picture

• Simple Consequences of Mass, Momentum, & Energy Conservation

• Matter Inspirals on Approximately Circular Orbits

– Vr << Vorb tinflow >> torb

– tinflow ~ time to redistribute angular momentum ~ viscous diffusion time– torb = 2π/Ω; Ω = (GM/r3)1/2 (Keplerian orbits; like planets in solar system)

• Disk Structure Depends on Fate of Released Gravitational Energy

– tcool ~ time to radiate away thermal energy of plasma

– Thin Disks: tcool << tinflow (gas collapses to a pancake)– Thick Disks: tcool >> tinflow (gas remains a puffed up torus)

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)

Thick Disks: Radiatively Inefficient

• At low densities (accretion rates), cooling is inefficient

• Grav. energy ⇒ thermal energy; not radiatednot radiated

• kT ~ GMmp/R: Tp ~ 1011-12 K > Te ~ 1010-11 K near BH

• Collisionless plasmaCollisionless plasma: e-p collision time >> inflow time• relevant to most accreting BHs & NSs, most of the time

Observed Plasma(R ~ 1017 cm ~ 105 Rhorizon)

T ~ few keV n ~ 100 cm-3

mfp ~ 1016 cm ~ 0.1 R

e-p thermalization time ~ 1000 yrs >>

inflow time ~ R/cs ~ 100 yrs

electron conduction time ~ 10 yrs <<

inflow time ~ R/cs ~ 100 yrs

The (In)Applicability of MHD

Hot Plasma Gravitationally CapturedBy BH ⇒ Accretion Disk

3.6 106 M

BlackHole

Estimated ConditionsNear the BH

Tp ~ 1012 KTe ~ 1011 Kn ~ 106 cm-3

B ~ 30 G

proton mfp ~ 1022 cm >>> Rhorizon ~ 1012 cm

need to understandaccretion of a magnetized

collisionless plasma

The (In)Applicability of MHD

Hot Plasma Gravitationally CapturedBy BH ⇒ Accretion Disk

3.6 106 M

BlackHole

Angular Momentum Transport by MHD Turbulence(Balbus & Hawley 1991)

• MRI: A differentially rotating plasma witha weak field (β >> 1) & dΩ2/dR < 0is linearly unstable in MHD

• magnetic tension transports ang.momentum, allowing plasma to accrete

• nonlinear saturation does not modifydΩ/dr, source of free energy (instead drives inflow of plasma bec. of Maxwell stress BrBϕ)

John Haw

ley

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/ Tp & Te determined by kinetic microphysics

Obs

erve

d Fl

ux

Time (min)

The MRI in a Collisionless Plasma

Quataert, Dorland, Hammett 2002; also Sharma et al. 2003; Balbus 2004

significant growth at longwavelengths where tension is negligible

angular momentum transportvia anisotropic pressure (viscosity!)

in addition to magnetic stresses

!

F" #BzB"

B2

$

% &

'

( ) *p|| +*p,( )

gravity temperature

• Convection (Buoyancy) may be Dynamically Impt in Hot, Thick Disks

• Schwarzschild Criterion for Instability in Hydro & MHD (β >> 1): ds/dr < 0

B

!

"||T # 0tconduction < tbuoyancy ⇒ (temp constant along field lines)

T > Tambientρ < ρambient

Buoyancy Instabilities (“convection”) inLow Collisionality Plasmas

(Balbus 2000; Parrish & Stone 2005, 2007; Quataert 2008; Sharma & Quataert 2008)

“Magnetothermal Instabilty” if dT/dr < 0

Nonlinear Evolution SimulatedUsing Kinetic-MHD

• Large-scale Dynamics of collisionless plasmas: expand Vlasov equationretaining “slow timescale” & “large lengthscale” assumptions of MHD(e.g., Kulsrud 1983)

• Particles efficiently transport heat and momentum along field-lines

Evolution of the Pressure Tensor

!

q "nvth

| k|||#||T

adiabatic invarianceof µ ~ mv2

⊥/B ~ T⊥/B

Closure Models for Heat Flux (temp gradients

wiped out on ~ a crossing time)

q = 0 CGL or Double Adiabatic Theory

Pressure Anisotropy

• 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 ~ Ωcyc 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#, p||,&) p# $ p||[ ]

"p||

"t= ... $ % (p#, p||,&) p|| $ p#[ ]

!

µ"T# /B = constant $ T# > T|| as B %

Velocity Space Instabilities in the Solar Wind

Local Simulations of the MRI in aCollisionless Plasma

Sharma et al. 2006

volume-averaged pressure anisotropymagnetic energy

Net Anisotropic Stress (i.e, viscosity)

~ Maxwell Stress

‘Viscous’ Heating in a Collisionless Plasma

• Heating ~ Shear*Stress

• Collisional Plasma

– Coulomb collisions determine Δp ⇒ q+ ~ m1/2T5/2

– Primarily Ion Heating

• Collisionless Plasma– Microinstabilities regulate Δp– Significant Electron Heating

q+ ~ T1/2

Plasma HeatingTi/Te in kinetic MHD sims

Ti/Te ~ 10 at late times

Astrophysical Implications

First Principles Prediction of Radiation Produced by Accreting Plasma

!

efficiency = L / ˙ M c2

Sharma et al. 2007

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/0710.5521) (linear theory)

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