Spectral Analysis of Non-Ideal MRI Modes: The effect of Hall diffusion

The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of the Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal MRI. Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearing box simulations and find very good agreement with the results derived from linear analysis. As the modes in consideration are also exact solutions of the non-linear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the non-linear evolution in some regions of protoplanetary disks.Comment: 16 pages, 11 figures, accepted by Ap

Orbital stability in static axisymmetric fields

We investigate the stability of test-particle equilibrium orbits in axisymmetric, but otherwise arbitrary, gravitational and electromagnetic fields. We extend previous studies of this problem to include a toroidal magnetic field. We find that, even though the toroidal magnetic field does not alter the location of the circular orbits, it enters the problem as a gyroscopic force with the potential to provide gyroscopic stability. This is in essence similar to the situation encountered in the reduced three-body problem where rotation enables stability around the local maxima of the effective potential. Nevertheless, we show that gyroscopic stabilization by a toroidal magnetic field is impossible for axisymmetric force fields in source-free regions because in this case the effective potential does not possess any local maxima. As an example of an axisymmetric force field with sources, we consider the classical problem of a rotating, aligned magnetosphere. By analyzing the dynamics of halo and equatorial particle orbits we conclude that axisymmetric toroidal fields that are antisymmetric about the equator are unable to provide gyroscopic stabilization. On the other hand, a toroidal magnetic field that does not vanish at the equator can provide gyroscopic stabilization for positively charged particles in prograde equatorial orbits.Comment: 11 pages, 3 figures, submitted to Celestial Mechanics and Dynamical Astronom

Analytical Models of Exoplanetary Atmospheres. V. Non-gray Thermal Structure with Coherent Scattering

We apply the picket fence treatment to model the effects brought about by spectral lines on the thermal structure of irradiated atmospheres. The lines may be due to purely absorption processes, purely coherent scattering processes or some combination of absorption and scattering. If the lines arise as a pure absorption process, the surface layers of the atmosphere are cooler whereas this surface cooling is completely absent if the lines are due to pure coherent isotropic scattering. The lines also lead to a warming of the deeper atmosphere. The warming of the deeper layers is, however, independent of the nature of line formation. Accounting for coherent isotropic scattering in the shortwave and longwave continuum results in anti-greenhouse cooling and greenhouse warming on an atmosphere-wide scale. The effects of coherent isotropic scattering in the line and continuum operate in tandem to determine the resulting thermal structure of the irradiated atmosphere.Comment: 8 pages, 5 figures, accepted for publication in Ap

Dust Segregation in Hall-dominated Turbulent Protoplanetary Disks

Imaging of the dust continuum emitted from disks around nearby protostars reveals diverse substructure. In recent years, theoretical efforts have been intensified to investigate how far the intrinsic dynamics of protoplanetary disks (PPDs) can lead to such features. Turbulence in the realm of non-ideal magnetohydrodynamics (MHD) is one candidate for explaining the generation of zonal flows which can lead to local dust enhancements. Adopting a radially varying cylindrical disk model, and considering combinations of vertical and azimuthal initial net flux, we perform 3D non-ideal MHD simulations aimed at studying self-organization induced by the Hall effect in turbulent PPDs. To this end, new modules have been incorporated into the NIRVANA-III and FARGO3D MHD codes. We moreover include dust grains, treated in the fluid approximation, in order to study their evolution subject to the emerging zonal flows. In the regime of a dominant Hall effect, we robustly obtain large-scale organized concentrations in the vertical magnetic field that remain stable for hundreds of orbits. For disks with vertical initial net flux alone, we confirm the presence of zonal flows and vortices that introduce regions of super-Keplerian gas flow. Including a moderately strong net-azimuthal magnetic flux can significantly alter the dynamics, partially preventing the self-organization of zonal flows. For plasma beta-parameters smaller than 50, large-scale, near-axisymmetric structures develop in the vertical magnetic flux. In all cases, we demonstrate that the emerging features are capable of accumulating dust grains for a range of Stokes numbers.Comment: 20 pages, 14 figures. Accepted for publication in The Astrophysical Journa