Theoretical astrophysics and plasma physics at RPC

Abstract:

We study the local stability of stratified, differentially rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity, and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch that describes a magnetized version of multi-diffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive, and heat diffusion. Therefore, in both double-diffusive limits, solid-body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive situation is more complex, and its stability criteria are not easily stated. Numerical analysis of our general dispersion relation confirms our analytic double-diffusive criteria but also shows that an unstable double-diffusive situation can be significantly stabilized by the addition of a third, ostensibly weaker, diffusion process. We describe a numerical application to the Sun's upper radiative zone and establish that it would be subject to unstable multidiffusive modes if moderate or strong radial gradients of angular velocity were present.

Abstract:

A naive extension to MOND of the standard computation of the two-body relaxation time Tb implies that Tb is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of Tb is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case we find that in the deep-MOND regime Tbb scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in groups and clusters of galaxies, two body relaxation should have substantially modified the density profiles of galaxy groups, while objects with masses in excess of ~10M_sun should have spiralled to the centres of dwarf galaxies.(Abridged)

Abstract:

Evidence is summarized which suggests that when a protogalaxy collapses, a fraction f of its gas fails to heat to the virial temperature, where f is large for haloes less massive than the value M* associated with L* galaxies. Stars and galaxies form only from the cool gas fraction. Hot gas is ejected from low-mass systems as in conventional semi-analytic models of galaxy formation. In high-mass systems it is retained but does not cool and form stars. Instead it builds up as a largely inert atmosphere, in which cooling is inhibited by an episodically active galactic nucleus. Cold gas frequently falls into galactic haloes. In the absence of a dense atmosphere of virial-temperature gas it builds up on nearly circular orbits and can be observed in the 21-cm line of H I. When there is a sufficiently dense hot atmosphere, cold infalling gas tends to be ablated and absorbed by the hot atmosphere before it can form stars. The picture nicely explains away the surfeit of high-luminosity galaxies that has recently plagued semi-analytic models of galaxy formation, replacing them by systems of moderate luminosity from old stars and large X-ray luminosities from hot gas.