Ekman layer damping of r modes revisited

We investigate the damping of neutron star r modes due to the presence of a viscous boundary (Ekman) layer at the interface between the crust and the core. Our study is motivated by the possibility that the gravitational wave driven instability of the inertial r modes may become active in rapidly spinning neutron stars, for example, in low-mass X-ray binaries, and the fact that a viscous Ekman layer at the core–crust interface provides an efficient damping mechanism for these oscillations. We review various approaches to the problem and carry out an analytic calculation of the effects due to the Ekman layer for a rigid crust. Our analytic estimates support previous numerical results, and provide further insight into the intricacies of the problem. We add to previous work by discussing the effect that compressibility and composition stratification have on the boundary-layer damping. We show that, while stratification is unimportant for the r-mode problem, composition suppresses the damping rate by about a factor of 2 (depending on the detailed equation of state).     

Viscous overstability and eccentricity evolution in three-dimensional gaseous discs

We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent, and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes.     

Analytical Study of Supernova Remnant Non-Stationary Expansions

We study analytically the Rayleigh–Taylor instability in expanding supernova gas shell. The instability appears at the inner shell surface accelerated by blowing pulsar wind. The most dangerous perturbations correspond to wavelengths comparable to the shell thickness. We analyze the fragility of the supernova remnant shell in function of the initial perturbation amplitude and the shell thickness.     

The generation of ionization-shock front oscillations by a variable radiation flux

The effect of a time-varying radiation flux incident on an ionization front on the generation of ionization-shock front oscillations in the interstellar medium is analyzed analytically and numerically. We take into account both variations in the flux of ionizing radiation directly from the source that produces the ionization front and the absorption of energetic photons by the post-front plasma. Based on our calculations, we show that the time dependence of the radiation flux can be an additional factor (apart from small inhomogeneities in the interstellar medium) that contributes to the amplification of oscillations and to the kinetic energy input to the observed turbulent motions in H II regions.     

Self-regulated gravitational accretion in protostellar discs

We present a numerical model for the evolution of a protostellar disc that has formed self-consistently from the collapse of a molecular cloud core. The global evolution of the disc is followed for several million years after its formation. The capture of a wide range of spatial and temporal scales is made possible by use of the thin-disc approximation. We focus on the role of gravitational torques in transporting mass inward and angular momentum outward during different evolutionary phases of a protostellar disc with disc-to-star mass ratio of order 0.1. In the early phase, when the infall of matter from the surrounding envelope is substantial, mass is transported inward by the gravitational torques from spiral arms that are a manifestation of the envelope-induced gravitational instability in the disc. In the late phase, when the gas reservoir of the envelope is depleted, the distinct spiral structure is replaced by ongoing irregular non-axisymmetric density perturbations. The amplitude of these density perturbations decreases with time, though this process is moderated by swing amplification aided by the existence of the disc's sharp outer edge. Our global modelling of the protostellar disc reveals that there is typically a residual non-zero gravitational torque from these density perturbations, i.e. their effects do not exactly cancel out in each region. In particular, the net gravitational torque in the inner disc tends to be negative during first several million years of the evolution, while the outer disc has a net positive gravitational torque. Our global model of a self-consistently formed disc shows that it is also self-regulated in the late phase, so that it is near the Toomre stability limit, with a near-uniform Toomre parameter Q ≈ 1.5–2.0. Since the disc also has near-Keplerian rotation, and comparatively weak temperature variation, it maintains a near-power-law surface density profile proportional to r ^−3/2.