Magnetothermal condensation modes including the effects of charged dust particles

We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of the cooling rate and the modified dust-cyclotron frequency. If the cooling rate is less than the modified dust-cyclotron frequency, then the growth rate of the condensation modes does not modify due to the existence of the charged dust particles. But, when the cooling rate is greater than (or comparable to) the modified dust-cyclotron frequency, the growth rate of unstable modes increases because of the dust particles. Also, the wavenumber of the perturbations corresponding to the maximum growth rate shifts to the smaller values (larger wavelengths) as the cooling rate becomes larger than the modified dust-cyclotron frequency. We show that the growth rate of the condensation modes increases with the electrical charge of the dust particles.     

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height.
We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.     

Perturbative analysis of two-temperature radiative shocks with multiple cooling processes

The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate because of a global thermal instability. The oscillatory behaviour depends on the functional forms of the cooling processes, the energy exchanges of electrons and ions in the shock-heated matter, and the boundary conditions. We analyse the stability of a shock with unequal electron and ion temperatures, where the cooling consists of thermal bremsstrahlung radiation which promotes instability, plus a competing process which tends to stabilize the shock. The effect of transverse perturbations is considered also. As an illustration, we study the special case in which the stabilizing cooling process is of order 3/20 in density and 5/2 in temperature, which is an approximation for the effects of cyclotron cooling in magnetic cataclysmic variables. We vary the efficiency of the second cooling process, the strength of the electron–ion exchange and the ratio of electron and ion pressures at the shock, to examine particular effects on the stability properties and frequencies of oscillation modes.     

Kelvin–Helmholtz instability in a weakly ionized layer

We study the linear theory of Kelvin–Helmholtz instability in a layer of ions and neutrals with finite thickness. In the short wavelength limit the thickness of the layer has a negligible effect on the growing modes. However, perturbations with wavelength comparable to layer’s thickness are significantly affected by the thickness of the layer. We show that the thickness of the layer has a stabilizing effect on the two dominant growing modes. Transition between the modes not only depends on the magnetic strength, but also on the thickness of the layer.     

Evolution of cold shock-bounded slabs

The stability and evolution of cold, shock-bounded slabs is studied using numerical hydrodynamic simulations. We confirm the analysis of Vishniac (1994) [ApJ, 428, 186], who showed that such slabs are unstable if they are perturbed by a displacement larger than their width. The growth rate of this nonlinear thin shell instability (NTSI) is found to increase with decreasing wavelength, in qualitative agreement with Vishniac's analysis. The NTSI saturates when the bending angle becomes large and the growth in the width of the slab pinches off the perturbation. After saturation, the slab remains greatly extended with an average density much less than the original slab density, supported primarily by supersonic turbulence within the slab. Linear perturbations are also found to be unstable in that they can lead to turbulent flow within the slab, although this response to linear perturbations is distinct from, and much less violent than the NTSI.Richard McCray     

Instability of spherical accretion — I. Shock-free Bondi accretion

We examine the spatial stability of spherical adiabatic Bondi accretion on to a point gravitating mass against external perturbations. Both transonic critical and subsonic subcritical accretion are shown to be stable against purely radial acoustic, vortex or entropy perturbations. In the case of non-radial perturbations the amplitude of the perturbations grows without limit with smaller radii. Instability manifests itself only if the size of the accreting body is much less than the Bondi radius so that the inflow is highly supersonic or highly subsonic at the surface of the accretor in the case of critical or subcritical accretion respectively. These asymptotics hold and consequently the instability may develop for adiabatic index of accreting gas γ < 5/3. We suggest that this instability may lead to an essential thermalization of accreting flow thus, particularly, solving the problem of otherwise inefficient energy release in spherical accretion on to a black hole.     

Gravitational Instability in the Dust Layer of a Protoplanetary Disk with Interaction between the Layer and the Surrounding Gas

We consider gravitational instability of the dust layer in the midplane of a protoplanetary disk with turbulence and shear stresses between the gas in the disk and that in the dust layer. We solve a linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation. We take into account the gas drag of solid particles (dust aggregates), turbulent diffusion and the velocity dispersion of particles, and the perturbation of the azimuthal velocity of gas in the layer upon the transfer of angular momentum from solid particles to it and from this gas to the surrounding gas in the disk. We obtain and solve the dispersion equation for the layer with the ratio of surface densities of the dust phase and gas being well above unity. The following parameters of gravitational instability in the dust layer are calculated: the critical surface density of solid matter and the Stokes number of particles corresponding to the onset of instability, the wavelength range in which instability occurs, and the rate of its growth as a function of the perturbation wavelength in the circumsolar disk at radial distances of 1 and 10 AU. We show that at 10 AU, the maximum instability growth rate increases due to the transfer of angular momentum of gas in the layer to gas outside it, a new maximum emerges at a longer wavelength, a long-wavelength instability “tail” forms, and the critical surface density initiating instability decreases relative to that determined without the transfer of angular momentum to gas outside the layer. None of these effects are observed at 1 AU, since instability in this region probably develops faster than the transfer of angular momentum to the surrounding gаs of a protoplanetary disk occurs.     

Do high-velocity clouds form by thermal instability?

We examine the proposal that the H  i 'high-velocity' clouds (HVCs) surrounding the Milky Way and other disc galaxies form by condensation of the hot galactic corona via thermal instability. Under the assumption that the galactic corona is well represented by a non-rotating, stratified atmosphere, we find that for this formation mechanism to work the corona must have an almost perfectly flat entropy profile. In all other cases, the growth of thermal perturbations is suppressed by a combination of buoyancy and thermal conduction. Even if the entropy profile were nearly flat, cold clouds with sizes smaller than  10 kpc  could form in the corona of the Milky Way only at radii larger than  100 kpc  , in contradiction with the determined distances of the largest HVC complexes. Clouds with sizes of a few kpc can form in the inner halo only in low-mass systems. We conclude that unless even slow rotation qualitatively changes the dynamics of a corona, thermal instability is unlikely to be a viable mechanism for formation of cold clouds around disc galaxies.     

High-order 2MASS galaxy correlation functions: probing the Gaussianity of the primordial density field

We study Parker instability (PI) operating in a non-adiabatic, gravitationally stratified, interstellar medium. We discuss models with two kinds of heating mechanisms. The first one results from photoionization models. The other, relying on supplemental sources, has been postulated by Reynolds, Haffner & Tufte. The cooling rate, corresponding to radiative losses, is an approximation to the one given by Dalgarno & McCray. An unperturbed state of the system represents a magnetohydrostatic and thermal equilibrium. We perform linear stability analysis by solving the boundary value problem. We find that the maximum growth rate of PI rises for increasing magnitudes of non-adiabatic effects. In the pure photoionization model, the maximum growth rate of the general non-adiabatic case coincides with the isothermal limit. Adding other sources of heat leads to a maximum growth rate that is larger than the one corresponding to the isothermal limit. We find that the influence of the supplemental heating on PI also leads to a decrease in temperature in magnetic valleys. Finally, we conclude that the initial gas cooling due to the action of PI may promote a subsequent onset of thermal instability in magnetic valleys and formation of giant molecular clouds.     

On the influence of cooling and heating processes on the Parker instability – II. Numerical simulations

We investigate the Parker instability (PI) influenced by thermal processes in a non-adiabatic, gravitationally stratified interstellar medium and discuss a model including the photoionization heating together with the supplemental heating mechanisms postulated by Reynolds, Haffner and Tufte. A cooling rate due to radiative losses is described by an approximation to the realistic cooling function of Dalgarno and McCray for ionized interstellar gas. An unperturbed initial state of the system simultaneously represents both a magnetohydrostatic and thermal equilibrium, and is thermally stable. We perform a set of 3D numerical magnetohydrodynamic simulations using the zeusmp code. We find that PI developing in the presence of non-adiabatic effects promotes a transition of gas in magnetic valleys to a thermally unstable regime. We find that the region of initially enhanced density due to PI starts to condense more as the result of thermal instability action. The density in this region rises above the classical isothermal limit of two times the equilibrium value at the mid-plane. The maximum density in an evolved system reaches 10–40 times the equilibrium value at the mid-plane, and the structures so formed attain oval shapes. These results lead to the conclusion that PI, operating in the presence of realistic cooling and heating processes, can trigger the formation of dense clouds, which may give rise to giant molecular complexes.     

Oscillatory instability of radiative shocks with multiple cooling processes

The stand-off shock formed in the accretion flow on to a stationary wall, such as the surface of a white dwarf, may be thermally unstable, depending on the cooling processes which dominate the post-shock flow. Some processes lead to instability, while others tend to stabilize the shock. We consider competition between the destabilizing influence of thermal bremsstrahlung cooling, and a stabilizing process which is a power law in density and temperature. Cyclotron cooling and processes which are of order 1, 3/2 and 2 in density are considered. The relative efficiency and power-law indices of the second mechanism are varied, and particular effects on the stability properties and frequencies of oscillation modes are examined.     

Chemical spots and oscillatory diffusion modes in magnetic stars

The stars of the middle main sequence often have spot‐like chemical structures at their surfaces. We consider diffusion caused by electric currents and argue that such current‐driven diffusion can form chemical inhomogeneities in a plasma. The considered mechanism can contribute to a formation of element spots in Hg‐Mn and Ap‐stars. Due to the Hall effect, diffusion in the presence of electric currents can be accompanied by the propagation of a particular type of magnetohydrodynamic modes in which only the impurity number density oscillates. Such modes exist if the magnetic pressure is much greater than the gas pressure and can be the reason for variations of the abundance peculiarities in stars. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Instability of the structure of strong oblique MHD cosmic-ray shocks

A criterion of the instability of a flow of a thermal plasma and cosmic rays in front of an oblique MHD shock wave with respect to short-wavelength magnetosonic disturbances is derived. The dependence of a cosmic-ray diffusion tensor on a plasma density and a large-scale magnetic field is taken into account. The most unstable disturbances propagate at an angle to the magnetic field if diffusion is strongly anisotropic. In some cases the most strong instability connects with the off-diagonal terms of the diffusion tensor.     

A non-adiabatic analysis for axisymmetric pulsations of magnetic stars

This paper presents the results of a non-adiabatic analysis for axisymmetric non-radial pulsations including the effect of a dipole magnetic field. Convection is assumed to be suppressed in the stellar envelope, and the diffusion approximation is used to radiative transport. As in a previous adiabatic analysis, the eigenfunctions are expanded in a series of spherical harmonics. The analysis is applied to a  1.9-M_⊙  , main-sequence model  (log  T _eff= 3.913)  . The presence of a magnetic field always stabilizes low-order acoustic modes. All the low-order modes of the model that are excited by the κ-mechanism in the He  ii ionization zone in the absence of a magnetic field are found to be stabilized if the polar strength of the dipole magnetic field is larger than about 1 kG. For high-order p modes, on the other hand, distorted dipole and quadrupole modes excited by the κ-mechanism in the H ionization zone remain overstable, even in the presence of a strong magnetic field. It is found, however, that all the distorted radial high-order modes are stabilized by the effect of the magnetic field. Thus, our non-adiabatic analysis suggests that distorted dipole modes and distorted quadrupole modes are most likely excited in rapidly oscillating Ap stars. The latitudinal amplitude dependence is found to be in reasonable agreement with the observationally determined one for HR 3831. Finally, the expected amplitude of magnetic perturbations at the surface is found to be very small.     

Instabilities in a nonstationary model of self-gravitating disks. I. Bar and ring perturbation modes

The instabilities of bar and ring mode perturbations against the background of a disk oscillating nonlinearly in its own plane are examined in a disk model which is a nonstationary generalization of the well known Bisnovatyi-Kogan-Zel'dovich model. Nonstationary analogs corresponding to a dispersion relation are found for these two oscillation modes. The results of the calculations are presented in the form of critical dependences of the initial virial ratio on the degree of rotation. A comparative analysis of the growth rates of the gravitational instability for these modes is also carried out. The bar mode instability occurs if the initial total kinetic energy of the disk is no more than 10.4% of the initial potential energy. The mechanism is associated with an instability in the radial motions which is aperiodic for small values of the rotation parameter Ω < 0.1, but is otherwise oscillatory. Calculations show that a ring structure can be formed as a result of an instability in the radial motions if the initial total energy of the model is no more than 5.2% of the initial potential energy, regardless of the value of Ω. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 487–499 (August 2008).     

The radial–azimuthal instability of a hot two-temperature accretion disc with advection

The radial–azimuthal instability of a hot two-temperature accretion disc with advection is examined in this paper. We find that the inclusion of very little advection has significant effects on two acoustic modes for a geometrically thin, cooling-dominated two-temperature disc, but has no effect on acoustic modes for a geometrically slim, cooling-dominated two-temperature disc. We also find that, when azimuthal perturbations are considered, the stability properties of the disc are different from those in the pure radial perturbation case. An increase of the azimuthal wavenumber will stabilize the acoustic modes but make the viscous and thermal modes more unstable for a geometrically thin, cooling-dominated two-temperature disc. It makes the thermal mode more unstable and the acoustic mode more stable, but only affects the instability of the viscous mode for short-wavelength perturbations for a geometrically slim, cooling-dominated two-temperature disc. For a geometrically slim, advection-dominated two-temperature disc, the increase of the azimuthal perturbation makes the I- and O-modes more stable and the thermal mode more unstable, but has no effect on the viscous mode.     

Effects of finite resistivity on magnetorotational instabilities in a realistic accretion flow

A local perturbation analysis is performed on a realistic background accretion flow in a global magnetic field. The adopted background model is an analytic solution to the resistive MHD equations and describes magnetically-controlled advection-dominated accretion flows (ADAFs) with an accuracy to the first order in the resistive corrections. The results show that there are three independent wave modes, which may be called the Rayleigh, Balbus–Hawley and resistive modes. Within our resistive-MHD corrections to the ideal-MHD limit, a Balbus–Hawley-like criterion for the instability of axisymmetric perturbations appears as a consequence of the competition between damping due to magnetic diffusion and excitation due to shear flow. As for non-axisymmetric perturbations, the former two modes are likely to be unstable in the presence of shears because the magnetic diffusion acts as a stabilizer only to axisymmetric perturbations within our approximation.     

Interfacial instabilities driven by self-gravity: first numerical results

The evolution of the interstellar medium (ISM) is driven by a variety of phenomena, including turbulence, shearing flows, magnetic fields and the thermal properties of the gas. Among the most important forces at work is self-gravity, which ultimately drives protostellar collapse. As part of an ongoing study of instabilities in the ISM, Hunter, Whitaker & Lovelace have discovered another process driven by self-gravity: the instability of an interface of discontinuous density. Theory predicts that this self-gravity driven interfacial instability persists in the static limit and in the absence of a constant background acceleration. Disturbances to a density interface are found to grow on a time-scale of the order of the free-fall time, even when the perturbation wavelength is much less than the Jeans length. Here we present the first numerical simulations of this instability. The theoretical growth rate is confirmed and the non-linear morphology displayed. The self-gravity interfacial instability is shown to be fundamentally different from the Rayleigh–Taylor instability, although both exhibit similar morphologies under the condition of a high density contrast, such as is commonly found in the ISM. Such instabilities are a possible mechanism by which observed features, such as the pillars of gas seen near the boundaries of interstellar clouds, are formed.     

On the linear analysis of unstable radiative shocks

We study the stability properties of strong hydrodynamic shocks and their associated radiative cooling layers. We explore a range of conditions which covers both molecular and atomic gas impacting against a rigid wall. Through a linear analysis employing a cooling function of the form  Λ∝ρ^β T ^α  and a specific heat ratio of γ, we determine the overstability regime in the parameter space consisting of  α, β  and γ. In general, if α is sufficiently low, the fundamental mode leads to long-wavelength growing oscillations. For the fundamental mode, we find that values of γ corresponding to molecular hydrodynamics lead to a significantly restricted instability range for α in comparison with the shocks in a monatomic medium. The conditions for the growth of higher-order modes, however, are relatively unchanged. This predicts that certain molecular shocks are prone to displaying signatures of small-scale rapid variability. Dissociative shocks, however, can be subject to a large-scale overstability if subsequent molecule formation in the cooling layer abruptly increases the cooling rate. In contrast to the dynamical rippling overstability, the cooling overstability is suppressed for a sufficiently low specific heat ratio.     

Axisymmetry vs. nonaxisymmetry of a Taylor‐Couette flow with azimuthal magnetic fields

The instability of a supercritical Taylor‐Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm = 1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current‐induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m = 1 are excited even without rotation for large enough Hartmann numbers (“Tayler instability”). For slow rotation their growth rates scale with the Alfvén frequency of the magnetic field but for fast rotation they scale with the rotation rate of the inner cylinder. In the nonlinear regime the ratio of the energy of the magnetic m = 1 modes and the toroidal background field is very low for the non‐rotating Tayler instability but it strongly grows if differential rotation is present. For super‐Alfv´enic rotation the energies in the m = 1 modes of flow and field do not depend on the molecular viscosity, they are almost in equipartition and contain only 1.5 % of the centrifugal energy of the inner cylinder. The geometry of the excited magnetic field pattern is strictly nonaxisymmetric for slow rotation but it is of the mixed‐mode type for fast rotation – contrary to the situation which has been observed at the surface of Ap stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)