Theoretical astrophysics and plasma physics at RPC

Abstract:

The light distribution in the inner few kiloparsecs of the Milky Way is recovered non-parametrically from a dust-corrected near-infrared COBE/DIRBE surface brightness map of the inner Galaxy. The best fits to the photometry are obtained when the Sun is assumed to lie $\sim14\pm4\pc$ below the plane. The recovered density distributions clearly show an elongated three-dimensional bulge set in a highly non-axisymmetric disk. In the favoured models, the bulge has axis ratios $1{:}0.6{:}0.4$ and semi-major axis length $\sim2\kpc$. Its nearer long axis lies in the first quadrant. The bulge is surrounded by an elliptical disk that extends to $\sim2\kpc$ on the minor axis and $\sim3.5\kpc$ on the major axis. In all models there is a local density minimum $\sim2.2\kpc$ down the minor axis. The subsequent maximum $\sim3\kpc$ down the minor axis (corresponding to $l\simeq-22\deg$ and $l\simeq 17\deg$) may be associated with the Lagrange point L$_4$. From this identification and the length of the bulge-bar, we infer a pattern speed $\Omega_b\simeq 60-70\kms\kpc^{-1}$ for the bar. Experiments in which pseudo-data derived from models with spiral structure were deprojected under the assumption that the Galaxy is either eight-fold or four-fold symmetric, indicate that the highly non-axisymmetric disks recovered from the COBE data could reflect spiral structure within the Milky Way if that structure involves density contrasts greater than $\gta 3$ at NIR wavelengths. These experiments indicate that the angle $\phi_0$ between the Sun--centre line and a major axis of the bulge lies near $20\deg$.

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.

Abstract:

We present the results of non-linear, hydrodynamic simulations, in three dimensions, of the tidal perturbation of accretion discs in binary systems where the orbit is circular and not necessarily coplanar with the disc mid-plane. The accretion discs are assumed to be geometrically thin, and of low mass relative to the stellar mass so that they are governed by thermal pressure and viscosity, but not self-gravity. The parameters that we consider in our models are the ratio of the orbital distance to the disc radius, D/R, the binary mass ratio, Ms/Mp, the initial inclination angle between the orbit and disc planes, δ, and the Mach number in the outer parts of the unperturbed disc, ℳ. Since we consider non-self-gravitating discs, these calculations are relevant to protostellar binaries with separations below a few hundred au. For binary mass ratios of around unity and D/R in the range 3 to 4, we find that the global evolution of the discs is governed primarily by the value of ℳ. For relatively low Mach numbers (i.e. ℳ = 10 to 20) we find that the discs develop a mildly warped structure, are tidally truncated, and undergo a near rigid body precession at a rate which is in close agreement with analytical arguments. For higher Mach numbers (ℳ ≈ 30), the evolution is towards a considerably more warped structure, but the disc none the less maintains itself as a long-lived, coherent entity. A further increase in Mach number to ℳ = 50 leads to a dramatic disruption of the disc as a result of differential precession, since the sound speed is too low to allow efficient communication between constituent parts of the disc. Additionally, it is found that the inclination angle between the disc and the orbital angular momentum vectors evolves on a longer time-scale, which is probably the viscous evolution time-scale of the disc. The calculations are relevant to a number of observed astrophysical phenomena, including the precession of jets associated with young stars, the high spectral index of some T Tauri stars, and the light curves of X-ray binaries such as Hercules X-1 which suggest the presence of precessing accretion discs.