Firehose and Mirror Instabilities in a Collisionless Shearing Plasma

Kunz, Matthew W.; Schekochihin, Alexander A.; Stone, James M.

Hybrid-kinetic numerical simulations of firehose and mirror instabilities in a collisionless plasma are performed in which pressure anisotropy is driven as the magnetic field is changed by a persistent linear shear S. For a decreasing field, it is found that mostly oblique firehose fluctuations grow at ion Larmor scales and saturate with energies ∝S^1/2; the pressure anisotropy is pinned at the stability threshold by particle scattering off microscale fluctuations. In contrast, nonlinear mirror fluctuations are large compared to the ion Larmor scale and grow secularly in time; marginality is maintained by an increasing population of resonant particles trapped in magnetic mirrors. After one shear time, saturated order-unity magnetic mirrors are formed and particles scatter off their sharp edges. Both instabilities drive sub-ion-Larmor-scale fluctuations, which appear to be kinetic-Alfvén-wave turbulence. Our results impact theories of momentum and heat transport in astrophysical and space plasmas, in which the stretching of a magnetic field by shear is a generic process.

Radiation Magnetohydrodynamic Simulations of the Formation of Hot Accretion Disk Coronae

Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.

A new mechanism to form a magnetic pressure supported, high temperature corona above the photosphere of an accretion disk is explored using three dimensional radiation magnetohydrodynamic (MHD) simulations. The thermal properties of the disk are calculated self-consistently by balancing radiative cooling through the surfaces of the disk with heating due to dissipation of turbulence driven by magneto-rotational instability (MRI). As has been noted in previous work, we find the dissipation rate per unit mass increases dramatically with height above the mid-plane, in stark contrast to the α-disk model which assumes this quantity is a constant. Thus, we find that in simulations with a low surface density (and therefore a shallow photosphere), the fraction of energy dissipated above the photosphere is significant (about 3.4% in our lowest surface density model), and this fraction increases as surface density decreases. When a significant fraction of the accretion energy is dissipated in the optically thin photosphere, the gas temperature increases substantially and a high temperature, magnetic pressure supported corona is formed. The volume-averaged temperature in the disk corona is more than 10 times larger than at the disk mid-plane. Moreover, gas temperature in the corona is strongly anti-correlated with gas density, which implies the corona formed by MRI turbulence is patchy. This mechanism to form an accretion disk corona may help explain the observed relation between the spectral index and luminosity from active galactic nucleus (AGNs), and the soft X-ray excess from some AGNs. It may also be relevant to spectral state changes in X-ray binaries.

An Algorithm for Radiation Magnetohydrodynamics Based on Solving the Time-dependent Transfer Equation

Jiang, Yan-Fei; Stone, James M.; Davis, Shane W.

We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics in the regime that light-crossing time is only marginally shorter than dynamical timescales. The transfer equation is solved in the mixed frame, including velocity-dependent source terms accurate to O(v/c). An operator split approach is used to compute the specific intensity along discrete rays, with upwind monotonic interpolation used along each ray to update the transport terms, and implicit methods used to compute the scattering and absorption source terms. Conservative differencing is used for the transport terms, which ensures the specific intensity (as well as energy and momentum) are conserved along each ray to round-off error. The use of implicit methods for the source terms ensures the method is stable even if the source terms are very stiff. To couple the solution of the transfer equation to the MHD algorithms in the ATHENA code, we perform direct quadrature of the specific intensity over angles to compute the energy and momentum source terms. We present the results of a variety of tests of the method, such as calculating the structure of a non-LTE atmosphere, an advective diffusion test, linear wave convergence tests, and the well-known shadow test. We use new semi-analytic solutions for radiation modified shocks to demonstrate the ability of our algorithm to capture the effects of an anisotropic radiation field accurately. Since the method uses explicit differencing of the spatial operators, it shows excellent weak scaling on parallel computers.

Particle-in-cell Simulations of Continuously Driven Mirror and Ion Cyclotron Instabilities in High Beta Astrophysical and Heliospheric Plasmas

Riquelme, Mario A.; Quataert, Eliot; Verscharen, Daniel

We use particle-in-cell simulations to study the nonlinear evolution of ion velocity space instabilities in an idealized problem in which a background velocity shear continuously amplifies the magnetic field. We simulate the astrophysically relevant regime where the shear timescale is long compared to the ion cyclotron period, and the plasma beta is β ~ 1-100. The background field amplification in our calculation is meant to mimic processes such as turbulent fluctuations or MHD-scale instabilities. The field amplification continuously drives a pressure anisotropy with p > p _∥ and the plasma becomes unstable to the mirror and ion cyclotron instabilities. In all cases, the nonlinear state is dominated by the mirror instability, not the ion cyclotron instability, and the plasma pressure anisotropy saturates near the threshold for the linear mirror instability. The magnetic field fluctuations initially undergo exponential growth but saturate in a secular phase in which the fluctuations grow on the same timescale as the background magnetic field (with δB ~ 0.3 langBrang in the secular phase). At early times, the ion magnetic moment is well-conserved but once the fluctuation amplitudes exceed δB ~ 0.1 langBrang, the magnetic moment is no longer conserved but instead changes on a timescale comparable to that of the mean magnetic field. We discuss the implications of our results for low-collisionality astrophysical plasmas, including the near-Earth solar wind and low-luminosity accretion disks around black holes.

Acceleration of Relativistic Electrons by Magnetohydrodynamic Turbulence: Implications for Non-thermal Emission from Black Hole Accretion Disks

Lynn, Jacob W.; Quataert, Eliot; Chandran, Benjamin D. G.; Parrish, Ian J.

We use analytic estimates and numerical simulations of test particles interacting with magnetohydrodynamic (MHD) turbulence to show that subsonic MHD turbulence produces efficient second-order Fermi acceleration of relativistic particles. This acceleration is not well described by standard quasi-linear theory but is a consequence of resonance broadening of wave-particle interactions in MHD turbulence. We provide momentum diffusion coefficients that can be used for astrophysical and heliospheric applications and discuss the implications of our results for accretion flows onto black holes. In particular, we show that particle acceleration by subsonic turbulence in radiatively inefficient accretion flows can produce a non-thermal tail in the electron distribution function that is likely important for modeling and interpreting the emission from low-luminosity systems such as Sgr A* and M87.

Linear Vlasov Theory in the Shearing Sheet Approximation with Application to the Magneto-rotational Instability

Heinemann, Tobias; Quataert, Eliot

We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low-frequency guiding center (or “kinetic MHD”) approximation, Hall magnetohydrodynamics (MHD), and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.