FPOE

Kinetic Effects on MRI Turbulencein Black Hole Accretion: 

Kinetic Effects on MRI Turbulence in Black Hole Accretion Prateek Sharma, 24th Aug.’06 FPOE

How does matter fall in?: 

Accretion disks star & planet formation Energetic sources, XRBs, AGN gravitational energy radiation Consider matter falling from r1 to r2<r1 Decrease in gravitational energy radiation Luminosity (energy per time) M(dm/dt) How does matter accrete? Stable Keplerian orbit, W~R-3/2 molecular viscosity (friction between layers) insufficient turbulent “viscosity” What sustains nonlinear motions? MRI [Balbus & Hawley’91] Ionized, magnetized disk, MRI How does matter fall in? r1 r2

Spring picture of the MRI: 

Keplerian rotation Magnetic fields like a rubber-band Spring picture of the MRI Inner fluid element loses angular momentum to outer one Stable Keplerian unstable MRI nonlinear motions & turbulence Spring slow down mi, loses rotational support, falls in, spring stretches further. Run-away! Stabilized if B very strong—stable Alfven oscillations mo mi

Standard model: 

Standard model Gravitational energy radiated cold, thin disk Dense collisional disk MHD valid MRI, turbulence, and transport Good for luminous objects: quasars & binaries Are all disks thin & luminous? No. low luminosity accretion flows, energy retained as heat; hot, dilute, collisionless, thick disk.

Thesis results: 

Thesis results Motivation is to understand physics of low-luminosity thick disks Transition from kinetic to collisional MRI Kinetic Braginskii MHD as n  Presence of damped modes Local nonlinear shearing box sims. of collisionless MRI Pressure anisotropy natural as B changes, m invariance Intermittent pitch angle scattering due to mirror/IC Scattering imposes an MHD like behavior Anisotropic stress~Maxwell stress Monotonic anisotropic diffusion Simple test problems to illustrate Limited differencing of transverse gradient

Radiatively inefficient accretion flows (RIAFs): 

Radiatively inefficient accretion flows (RIAFs) Low luminosity grav. energy retained as heat, not radiated hot, dilute, collisionless, thick disk Radiative efficiency, , Accretion on BH/NS more efficient than fusion! ambient density But << observed luminosity, Why? accreted , or

Sgr A*, a RIAF: 

Sgr A*, a RIAF Sphere of influence of SMBH barely resolved

RIAFs in galactic centers: 

RIAFs also common in nearby galaxies Self-similar models for density profiles for -ADAF/Bondi, p=0, -CDAF/ADIOS, p=0-1, RIAFs in galactic centers n r

RIAF parameters: Sgr A*: 

Plasma is collisionless for Plasma is magnetized with RIAF parameters: Sgr A* Realistic plasma model MHD not enough

Plasma description of RIAFs: 

Plasma description of RIAFs Vlasov eq. for & DKE Moments of the DKE: Kinetic MHD eqs. PDF in a 5-D phase space

Closure approx. for heat fluxes: 

Closure approx. for heat fluxes Next order moment Closure problem Adiabatic invariance = const. q=0, CGL approx., free streaming particles Closure Models for heat flux (temp. gradients wiped out on ~ a crossing time) multi-pole approx. to plasma Z function, recovers Landau damping Use k║=kL=const. for sims.

Braginskii (intermediate collisionality) limit, n > k║vth: 

Braginskii (intermediate collisionality) limit, n > k║vth Kinetic MHD more general, transitions smoothly from collisionless, to Braginskii, to MHD as n increases

Linear analysis of collisionless MRI: 

Also occurs in collisionless regime Collisionless (pressure anisotropy) effects enhanced at larger b Fastest mode ~ twice faster than MHD Fastest growth at much larger scales Similar nonlinear saturation though Linear analysis of collisionless MRI W : Keplerian rotation frequency

Kinetic Braginskii MHD : 

Terms in KMHD eq. of motion Transitions as n increased for : Kinetic to Braginskii Braginskii to MHD Kinetic Braginskii MHD

Slide15: 

MHD modes in plasma w. Keplerian rotation MRI, the destabilized slow mode Damped modes can preferentially heat resonant particles Parallel eq. of motion: dv║/dt = -m║B + e E║/m Barnes Landau damping damping (TTMP) electrons ions

Nonlinear Shearing box sims.: 

Nonlinear Shearing box sims. Local shearing-box sims. analogous to flux tube sims. in fusion; shearing periodic BCs

KMHD code (based on ZEUS): 

KMHD code (based on ZEUS) Anisotropic pressure unlike MHD Thermal conduction along field lines, local Landau fluid closure instead of more accurate non-local expressions

CGL SB sims., b=400, vertical B: 

CGL SB sims., b=400, vertical B As B amplified by MRI, p┴ , as = const. Field lines become stiff, stabilizing all the resolved modes, linear anisotropic Alfven waves B.B  [1+(p┴-p║)/B2]B.B pressure anisotropy 4pΔp/B2~ few 10s Mirror, ion-cyclotron instabilities expected to at these pressure anisotropies

Microinstabilities: 

Change in B results in pressure anisotropy as m conserved Anisotropy results in instabilities: ion-cyclotron mirror Firehose For MRI turbulence B sustained p ┴ > p║ IC/mirror Even with microinstabilities m conserved unless Pressure anisotropy slightly larger than marginal allowed Microinstabilities firehose mirror

MRI simulations w. subgrid models: 

MRI simulations w. subgrid models Similar turbulent saturation, variability as in MHD Stronger channels b=400, initially vertical field Much smaller magnetic energy when pressure anisotropy not restricted Factor of ~105 Pitch angle scattering makes a qualitative difference; imposes MHD like behavior That’s why MHD so good for collisionless plasmas!

Pitch angle scattering: 

Pitch angle scattering Pitch angle scattering makes a qual. difference Mirror dominates over IC for b100 Scattering only in small fraction of box Scattering centers intermittent Effective scattering at Sc. Ctrs. But Sc. Ctrs. are rare So, m.f.p. can be large even after pitch angle scattering Volume fraction where pitch angle scattering occurs

Anisotropic (viscous) stress: 

Anisotropic stress ~ Maxwell stress, well correlated Viscous heating, collisionless damping in anisotropic stress Important for e & ion heating & hence radiation Aniso. stress  as n , transition to MHD Anisotropic (viscous) stress

Global MHD sims.: 

Usually starts with a const. ang. mom. torus surrounded by a low density corona. Density/temp. jump at bdry. Black hole at the origin Flow settles into a turbulent thick disk, dilute corona, & weak magnetized outflows Global MHD sims. Q. mfp~disk height, what is the effect of anisotropic conduction? Implementation of anisotropic diffusion non-trivial

Anisotropic thermal conduction: 

Anisotropic thermal conduction Conduction along field lines,  Parallel temp. gradient

Centered Differencing: 

Centered Differencing Asymmetric Symmetric n,cTi,j (i+1/2,j) (i+1/2,j+1/2) [Gunter et al. 2005]

Negative temp. w. asymm. method: 

Negative temp. w. asymm. method Reflective B.C. Heat flux out of temp. minimum! T<0

Negative temp. w. symm. method: 

Negative temp. w. symm. method Same temp. as before, different (i,j) labels qy=0, dT/dx non-zero only at (i-1/2,j+1/2) Only non-vanishing heat flux is

Why negative temperature?: 

Why negative temperature? For asymm. method, qxx always from higher to lower temp., but qxy can have any sign. Need to carefully interpolate qxy responsible for heat flowing in wrong direction What is the best interpolation? Arithmetic average for dT/dy?No. Centered differencing not always the best,e.g., gas dynamics Limiters for interpolating will solve it.

Limiting transverse gradient: 

Limiting transverse gradient We limit transverse temperature gradient to calculate qx L is a limiter like: minmod, van Leer, monotonized central (MC) Limiters return zero if arguments of opposite sign Only normal term remain at extrema Temperature extrema not amplified At extremum dT/dx = 0 dT/dy = 0

Perpendicular numerical diffusion: 

Perpendicular numerical diffusion MC limiter just twice more diffusive than asymm. MC is the least diffusive of Limiters (for 100 grid pts. In each dirn.) Sufft. to study qualitative effects,e.g., MTI Symmetric method least diffusive, but T<0 problem!

Thesis contributions: 

Thesis contributions Transition from kinetic to collisional MRI Kinetic Braginskii MHD as n  Presence of damped modes Local shearing box sims. Pressure anisotropy natural as B changes Intermittent pitch angle scattering due to mirror/IC Scattering imposed an MHD like behavior Anisotropic stress~Maxwell stress Monotonic anisotropic diffusion Simple test problems to illustrate Limited differencing of transverse gradient

Future Work: 

Future Work Two fluid sims., electron vs. ion heating Effect of anisotropic stress on electrons Global sims. w. anisotropic conduction Effect on Outflows, convection, role of MTI Directly solving DKE in 5-D phase space Role of intermittent pitch angle scattering On heat conduction MHD vs. free streaming, collisionless damping Pitch angle sc. common in collisionless plasmas, e.g, X-ray clusters, solar wind Thank you for your attention!