Theoretical astrophysics and plasma physics at RPC

Abstract:

A naive extension to modified Newtonian dynamics (MOND) of the standard computation of the two-body relaxation time t2b implies that 2b is comparable to the crossing time regardless of the number W 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 t2b 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 t2b 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. Near the centre of a spherical system that is in the deep-MOND regime, we show that the fluctuating component of the gravitational force is never small compared to the mean-field force; this conclusion surprisingly even applies to systems with a density cusp that keeps the mean-field force constant to arbitrarily small radius, and suggests that a cuspy centre can never be in the deep-MOND regime. 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 ∼10 M⊙ should have spiralled to the centres of dwarf galaxies.

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.