We investigate the effects of ambipolar diffusion and the Hall effect on the stability of weakly-ionized, magnetized planar shear flows. Employing a local approach similar to the shearing-sheet approximation, we solve for the evolution of linear perturbations in both streamwise-symmetric and non-streamwise-symmetric geometries using WKB techniques and/or numerical methods. We find that instability arises from the combination of shear and non-ideal magnetohydrodynamic processes, and is a result of the ability of these processes to influence the free energy path between the perturbations and the shear. They turn what would be simple linear-in-time growth due to current and vortex stretching from shear into exponentially-growing instabilities. Our results aid in understanding previous work on the behaviour of weakly-ionized accretion discs. In particular, the recent finding that the Hall effect and ambipolar diffusion destabilize both positive and negative angular velocity gradients acquires a natural explanation in the more general context of this paper. We construct a simple toy model for these instabilities based upon transformation operators (shears, rotations, and projections) that captures both their qualitative and, in certain cases, exact quantitative behaviour.
We construct partially ionized hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with surface fields B=10^12-5 \times 10^14 G and effective temperatures T_eff \sim a few \times 10^5-10^6 K. These models are based on the latest equation of state and opacity results for magnetized, partially ionized hydrogen plasmas that take into account various magnetic and dense medium effects. The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars. For the models with B=10^12-10^13 G, the spectral features due to neutral atoms lie…
Observations of protostellar disks indicate the presence of the magnetic field of thermal (or superthermal) strength. In such a strong magnetic field, many MHD instabilities responsible for turbulent transport of the angular momentum are suppressed. We consider the shear-driven instability that can occur in protostellar disks even if the field is superthermal. This instability is caused by the combined influence of shear and compressibility in a magnetized gas and can be an efficient mechanism to generate turbulence in disks. The typical growth time is of the order of several rotation periods.
We construct hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with surface fields B=10^12-5x10^14 G and effective temperatures T_eff a few x 10^5-10^6 K by solving the full radiative transfer equations for both polarization modes in the magnetized hydrogen plasma. The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars. We study the effects of vacuum polarization and bound atoms on the atmosphere structure and spectra. For the lower magnetic field models (B 10^12 G), the spectral features due to neutral atoms lie at…
We present results of three-dimensional (3D) simulations of the magnetohydrodynamic Kelvin-Helmholtz instability in a stratified shear layer. The magnetic field is taken to be uniform and parallel to the shear flow. We describe the evolution of the fluid flow and the magnetic field for a range of initial conditions. In particular, we investigate how the mixing rate of the fluid depends on the Richardson number and the magnetic field strength. It was found that the magnetic field can enhance as well as suppress mixing. Moreover, we have performed two-dimensional (2D) simulations and discuss som…
We construct hydrogen atmosphere models for strongly magnetized neutron stars in thermodynamic equilibrium, taking into account partial ionization. The presence of bound states affects the equation of state, absorption coefficients, and polarizability tensor of a strongly magnetized plasma. Therefore the partial ionization influences the polarization vectors and opacities of normal electromagnetic waves, and thus the spectra of outgoing radiation. Here we review a model suitable for the most typical neutron-star atmospheres and focus on the problems that remain to be solved for its extension t…
The effect of magnetic shear and shear flow on local gravitationally induced instabilities is investigated. A simple model is constructed allowing for an arbitrary entropy gradient and a shear plasma flow in the Boussinesq approximation. A transformation to shearing magnetic coordinates achieves a model with plasma flow along the magnetic field lines where the coordinate lines are coincident with the field lines. The solution for the normal modes of the system depends on two parameters: the Alfven Mach number of the plasma flow and the entropy gradient. The behavior of the unstable normal mode…
Aims: To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows. Method: The Rayleigh quotient in modal approaches for the linearized equations (with time-dependent wavenumber) and the amplitudes from direct shearing sheet simulations using a finite difference code are compared. Results: Both approaches agree in their predicted growth behavior. The magneto-rotational instability for axisymmetric and non-axisymmetric perturbations is shown to h…
We present numerical simulations of the growth and saturation of the Kelvin-Helmholtz instability in a compressible fluid layer with and without a weak magnetic field. In the absence of a magnetic field, the instability generates a single eddy which flattens the velocity profile, stabilizing it against further perturbations. Adding a weak magnetic field - weak in the sense that it has almost no effect on the linear instability - leads to a complex flow morphology driven by MHD forces and to enhanced broadening of the layer, due to Maxwell stresses. We corroborate earlier studies which showed t…
When the ion mean free path much exceeds the Larmor radius in a plasma, the viscous stress tensor is altered dramatically, and depends only upon quantities measured along the field lines. This regime corresponds to typical interstellar medium conditions in galaxies and protogalaxies, even if the magnetic field is extremely weak, with a negligible Lorentz force on all scales of interest. In this work, the only role of the magnetic field is to channel angular momentum transport along its lines of force. We show that differential rotation in such a gas is highly unstable, with a maximum growth ra…
The set of equations for magnetohydrodynamic (MHD) waves in a shear flow is consecutively derived. The proposed scenario involves the presence of a self-sustained turbulence and magnetic field. In the framework of Langevin--Burgers approach the influence of the turbulence is described by an additional external random force in the MHD system. Kinetic equation for the spectral density of the slow magnetosonic (Alfvenic) mode is derived in the short wavelength (WKB) approximation. The results show a pressing need for conduction of numerical Monte Carlo (MC) simulations with a random driver to tak…
Ambient interstellar material may become entrained in outflows from massive stars as a result of shear flow instabilities. We study the linear theory of the Kelvin - Helmholtz instability, the simplest example of shear flow instability, in a partially ionized medium. We model the interaction as a two fluid system (charged and neutral) in a planar geometry. Our principal result is that for much of the relevant parameter space, neutrals and ions are sufficiently decoupled that the neutrals are unstable while the ions are held in place by the magnetic field. Thus, we predict that there should be …
We investigate the dynamical condensation process in a magnetized thermally bistable medium. We perform one-dimensional two fluid numerical simulations that describe the neutral and ionized components in the interstellar medium with purely transverse magnetic fields. We find that the clouds that are formed as a consequence of the thermal instability always have a magnetic field strength on the order of a few microgauss irrespective of the initial strength. This shows good agreement with the measurements of the magnetic field strength in diffuse clouds. We show analytically that the final magne…
We construct partially ionized hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with fixed surface fields between B=10^12 and 2x10^13 G and effective temperatures logT_eff=5.5-6.8, as well as with surface B and T_eff distributions around these values. The models are based on the latest equation of state and opacity results for magnetized, partially ionized hydrogen plasmas. The atmospheres directly determine the characteristics of thermal emission from the surface of neutron stars. We also incorporate these model spectra into XSPEC, under the model name NSMAX, t…
The magnetorotational instability (MRI) of a weakly ionized, differentially rotating, magnetized plasma disk is investigated in the multi-fluid framework. The disk is threaded by a uniform vertical magnetic field and charge is carried by electrons and ions only. The inclusion of ion dynamics causes significant modification to the conductivity tensor in a weakly ionized disk. The parallel, Pedersen and Hall component of conductivity tensor become time dependent quantities resulting in the AC and DC part of the conductivity. The conductivity may change sign leading to the significant modificatio…
We study the evolution of magnetized clusters in a cosmological environment using magneto-hydro dynamical simulations. Large scale flows and merging of subclumps generate shear flows leading to Kelvin-Helmholtz instabilities, which, in addition to the compression of the gas where the magnetic field is frozen in, further amplify the magnetic field during the evolution of the cluster. Therefore, well-motivated initial magnetic fields of $<B^2>^{1/2}=10^{-9} {\rm G}$ reach the observed $\simμ{\rm G}$ field strengths in the cluster cores at $z=0$. These magnetized clusters can be used to study the…
We investigate the susceptibility of gaseous, magnetized galactic disks to formation of self-gravitating condensations using two-dimensional, local models. We focus on two issues: (1) determining the threshold condition for gravitational runaway, taking into account nonlinear effects, and (2) distinguishing the magneto-Jeans instability (MJI) that arises under inner-galaxy rotation curves from the modified swing amplification (MSA) that arises under outer-galaxy rotation curves. For axisymmetric density fluctuations, instability is known to require a Toomre parameter Q<1. For nonaxisymmetric f…
The linearized relativistic magnetohydrodynamic (RMHD) equations describing a uniform axially magnetized cylindrical relativistic jet spine embedded in a uniform axially magnetized relativistically moving sheath are derived. The displacement current is retained in the equations so that effects associated with Alfven wave propagation near light speed can be studied. A dispersion relation for the normal modes is obtained. Analytical solutions for the normal modes in the low and high frequency limits are found and a general stability condition is determined. A trans-Alfvenic and even a super-Alfv…
The self-sustained turbulence which develops in magnetized accretion disks is suppressed in the weakly-ionized, quiescent disks of close binary stars. Because accretion still proceeds during quiescence, another viscosity mechanism operates in these systems. An anticorrelation of the recurrence times of SU UMa dwarf novae with their mass ratio supports spiral waves or shock-waves tidally induced by the companion star as the main process responsible for accretion in the quiescent disks. Other weakly-ionized gaseous disks in systems lacking a massive companion have to rely on yet another transpor…
We study partially ionized hydrogen plasma at temperatures T = 10^{5.5}-10^{6.5} K and magnetic fields B = 10^{12}-10^{13} G, typical of photospheres of isolated neutron stars. We construct an analytic model of the plasma free energy and derive a generalized Saha equation which is used to obtain the opacities.
We present the results of a 2-D, two fluid (ions and neutrals) simulation of the ambipolar filamentation process, in which a magnetized, weakly ionized plasma is stirred by turbulence in the ambipolar frequency range. The higher turbulent velocity of the neutrals in the most ionized regions gives rise to a non-linear force driving them out of these regions, so that the initial ionization inhomogeneities are strongly amplified. This effect, the ambipolar filamentation, causes the ions and the magnetic flux to condense and separate from the neutrals, resulting in a filamentary structure.
The overshooting convective motions in the solar photosphere are frequently proposed as the source for the excitation of Alfvén waves. However, the photosphere is a) very weakly ionized, and, b) the dynamics of the plasma particles in this region is heavily influenced by the plasma-neutral collisions. The purpose of this work is to check the consequences of these two facts on the above scenario and their effects on the electromagnetic waves. It is shown that the ions and electrons in the photosphere are both un-magnetized; their collision frequency with neutrals is much larger than the gyro-fr…
A new general relativistic magnetohydrodynamics (GRMHD) code ``RAISHIN'' used to simulate jet generation by rotating and non-rotating black holes with a geometrically thin Keplarian accretion disk finds that the jet develops a spine-sheath structure in the rotating black hole case. Spine-sheath structure and strong magnetic fields significantly modify the Kelvin-Helmholtz (KH) velocity shear driven instability. The RAISHIN code has been used in its relativistic magnetohydrodynamic (RMHD) configuration to study the effects of strong magnetic fields and weakly relativistic sheath motion, c/2, on…
There has been significant recent work which examines a situation where a thin magnetic layer is `draped' over a core merging into a larger cluster; the same process also appears to be at work at a bubble rising from the cluster centre. Such a thin magnetic layer could thermally isolate the core from the cluster medium, but only if the same shear process which generates the layer does not later disrupt it. On the other hand, if the magnetized layer can stabilize against the shear instabilities, then the magnetic layer can have the additional dynamical effect of reducing the shear-driven mixing…
