the physics of collisionless accretion...
TRANSCRIPT
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