Heat Transport and Buoyancy Instabilities in Astrophysical Plasmas. Eliot Quataert (UC Berkeley)

Transcription

1 Heat Transport and Buoyancy Instabilities in Astrophysical Plasmas Eliot Quataert (UC Berkeley) Galaxy Cluster Hydra A w/ Chandra Surface of the Sun ~ 1 Million light-years

2 Overview Microscopic Energy Transport in Astrophysical Plasmas electron conduction vs. photons Hydrodynamic Convection linear instability nonlinear saturation & heat transport by induced turbulence brief application to the sun (& other stars and gaseous planets) Convection induced by Anisotropic Thermal Conduction new linear instabilities -- the MTI & HBI -- & nonlinear saturation application to plasma in clusters of galaxies

3 Microscopic Energy Transport Photons dominate in non-degenerate dense plasmas w/ l photon<< system size e.g., stars Thermal conduction dominates in degenerate plasmas: white dwarfs and neutron stars conduction typically ~ isotropic for WDs, but ~ anisotropic for NS surfaces dilute, hot non-degenerate plasmas e.g., the solar corona & solar wind, clusters of galaxies, accretion flows onto black holes le >>> ρe conduction highly anisotropic

4 Hydrodynamic Convection Schwarzschild criterion for convection: ds/dz < 0 Motions slow (<< cs) & adiabatic: pressure equil & s ~ const solar interior: tsound ~ hr << tbuoyancy ~ month << tphoton ~ 10 4 yr low s background fluid gravity high s convectively unstable

5

6

7

8 Heat Flux by Convection ( Mixing Length Theory )

9 Convective Flow: Diverging Upflows, Turbulent Downflows Bob Stein Velocity arrows, temperature fluctuation image (red hot, blue cool)

10 N2

11

12

13 Surface Manifestations of Convection sunspot convection

14 Solar Granulation ~ 90 min long; ~ 0.1 Rsun on a side

15 How does Anisotropic Thermal Conduction in Magnetized Plasmas change the properties of convective (i.e., buoyancy) instabilities and the resulting transport of heat?

16 The Magnetothermal Instability (MTI) Balbus 2000, 2001; Parrish & Stone 2005, 2007; Quataert 2008; Sharma, Quataert, & Stone 2008 cold g hot thermal conduction time << dynamical time weak B-field (Bx) no dynamical effect; only channels heat flow (note: no initial heat flux) convectively unstable (dt/dz < 0) growth time ~ dyn. time

17 The MTI magnetic field lines cold g hot 2D simulation courtesy of Ian Parrish

18 The Heat Flux-Driven Buoyancy Instability (HBI) Quataert 2008; Parrish & Quataert 2008 hot converging & diverging heat flux conductive heating & cooling of the plasma cold g, Qz heat flux weak B for dt/dz > 0 upwardly displaced fluid is heated & rises convectively unstable

19 The HBI hot magnetic field lines cold g, Qz bg heat flux Parrish & Quataert 2008

20 Buoyancy Instabilities in Magnetized Plasmas MTI (dt/dz < 0) HBI (dt/dz > 0) Parrish & Stone 2005 Parrish & Quataert 2008 a weakly magnetized plasma w/ anisotropic heat transport is always buoyantly unstable, independent of dt/dz! Instabilities suppressed by 1. strong B (β < 1; e.g., solar corona) or 2. isotropic heat transport >> anisotropic heat transport (e.g., solar interior)

21 Nonlinear Saturation: The HBI hot cold g, Qz bg heat flux 2D simulation by Ian Parrish

22 Nonlinear Saturation: HBI Magnetic Energy Angle wrt Horizontal Field lines become largely horizontal time (dynamical time) Parrish & Quataert 2008 turbulent convection w/ time (dynamical time) Local 3D Simulations initial weak B (β >>1)

23 Nonlinear Saturation: HBI Heat Flux (relative to initial value) heat flux strongly suppressed Qf ~ 0.01 Qi remains conductive, not convective (very different from hydro convection) Saturation can be qualitatively understood using linear theory when B is ~ horizontal, heat flux that drives the instability is minimized & growth is strongly suppressed For B ~ Bx time (dynamical time) Local 3D Simulations initial weak B (β >>1) instability saturates by rearranging the B-field

24 Saturation is Quasilinear Magnetic Energy (relative to initial energy) blue & red: initial B ( B0) differing by a factor of 10 time (dynamical time) For weak fields Bf ~ B0 independent of B0 A fixed Bf/B0 is required to reorient the field (for larger B, tension suppresses the growth)

25 Nonlinear Saturation: MTI Local 3D simulations Field ~ vertical Angle wrt Horizontal Heat Flux ~ Field-free value consistent w/ linear theory; vertical fields minimize the growth rate saturation again ~ quasilinear with Parrish & Stone 2007 time (dynamical time) Bf ~ B0

26 Buoyancy Instabilities in Magnetized Plasmas MTI (dt/dz < 0) HBI (dt/dz > 0) Heat Flux in a weakly magnetized low collisionality plasma must be determined dynamically via evolution of HBI/MTI; not simply a fixed fraction of Spitzer set by, e.g., wandering field lines Parrish & Stone 2005 Parrish & Quataert 2008 Saturation: turbulent convection Field ~ vertical heat flux ~ field-free value quasilinear: Bf ~ B0 Saturation: turbulent convection Field ~ horizontal heat flux strongly suppressed (conductive flux dominates over convective) quasilinear: Bf ~ B0

27 Clusters of Galaxies largest gravitationally bound objects: Mvir ~ Msun Rvir ~ lt-yrs ~ 84% dark matter; ~ 14 % plasma; ~ 2% stars on exponential tail of the mass function: useful cosmological probe host the most massive galaxies (~ Msun) and BHs (~ Msun) x-ray (thermal plasma) ~ 0.1 Rvir optical (stars) radio (BH & relativistic plasma)

28 Hot Plasma in Clusters T/<T> cluster temperature profile Lx ~ erg s -1 n ~ cm -3 T ~ 1-15 kev Radius (Rvir) Piffaretti et al large electron mean free path: thermal conduction important

29 Cool Core Clusters in at least ~ 50% of clusters, tcool < Hubble time for r lt-yrs absent a heat source: Ṁcool ~ Msun yr -1 not observed: Ṁstar ~ 1 Msun yr -1 ; Tmin ~ 1/3 <T> a heat source must balance radiative cooling ~ spherically out to ~ lt-yrs proposed sources of heating include a central accreting BH thermal conduction from large radii... Hydra A Wise et al. 2007

30 Cluster Entropy Profiles Entropy ds/dr > 0 Radius (Rvir) Schwarzschild criterion clusters are stable Piffaretti et al. 2005

31 The MTI & HBI in Clusters average cluster temperature profile MTI r lt-yrs T/<T> HBI r lt-yrs Radius (Rvir) Piffaretti et al ~ 10 6 lt-yrs The Entire Cluster is Convectively Unstable!

32 Global Cluster Simulations 3D w/ cooling & anisotropic conduction (Athena) non-cosmological: isolated cluster core ( 10 6 lt-yrs) Angle wrt Horizontal volume averaged T(R) at several HBI B-field exacerbates angle the problem times of vs. cooling time in cluster cores by reducing conductive heating from large radii (Q 10% Spitzer) (relatively robust: occurs for a range of cluster masses, initial T(r), B-strength & geometry,...) time (Myr) Radius (kpc)

33 Effects on CR Mixing Heating by central BH is the most promising mechanism balancing cooling; but precise physical mechanism & how it couples throughout the cluster unclear CRs + B- fields + anisotropic conduction 1.7 Gyr 3.4 Gyr 5 Gyr 7 Gyr 40 kpc 40 kpc real cluster plasma: buoyantly unstable & easier to mix CRs (equator: pcr/p ~ 3% out to ~ 20 kpc) CRs + adiabatic plasma adiabatic plasma: buoyantly stable & harder to mix CRs pcr/p logarithmic scale; red/blue = high/low pcr

34 Summary