Theoretical astrophysics and plasma physics at RPC

Abstract:

The only way to map the Galaxy's gravitational potential $\Phi({\bf x})$ and the distribution of matter that produces it is by modelling the dynamics of stars and gas. Observations of the kinematics of gas provide key information about gradients of $\Phi$ within the plane, but little information about the structure of $\Phi$ out of the plane. Traditional Galaxy models {\em assume}, for each of the Galaxy's components, arbitrary flattenings, which together with the components' relative masses yield the model's equipotentials. However, the Galaxy's isopotential surfaces should be {\em determined\/} directly from the motions of stars that move far from the plane. Moreover, from the kinematics of samples of such stars that have well defined selection criteria, one should be able not only to map $\Phi$ at all positions, but to determine the distribution function $f_i({\bf x},{\bf v})$ of each stellar population $i$ studied. These distribution functions will contain a wealth of information relevant to the formation and evolution of the Galaxy. An approach to fitting a wide class of dynamical models to the very heterogeneous body of available data is described and illustrated.

Abstract:

We study the stability of an accretion disc with an embedded toroidal magnetic field to general perturbations. Disc models are considered in which the equilibrium variables depend on both the radial and vertical coordinates. We consider the full global problem in which the disc may be in the form of a narrow annulus, or occupy a significant radial extent. Perturbations with azimuthal mode number m in the range zero up to the ratio of the radius to disc scmithickness are considered. Discs containing a purely toroidal magnetic field are always found to be unstable. We find spectra of unstable modes using local techniques. In the absence of dissipation, these modes may occupy arbitrarily small scales in the radial and vertical directions. One class of modes is driven primarily by buoyancy, while the other is driven by shear independently of the equilibrium stratification. The first type of instability predominates if the field is large, while the second type predominates if the field is weak and the underlying medium is strongly stable to convection. We also investigate stability by solving the initial value problem for perturbations numerically. We find, for our disc models, that local instabilities predominate over any possible global instability. Their behaviour is in good accord with the local analysis. The associated growth rates become just less than the orbital frequency when the ratio of magnetic energy density to pressure reaches about 10 per cent. Instabilities of the kinds discussed here may provide a mechanism for limiting the growth of toroidal fields in dynamo models of accretion discs.