Gravitational Instabilities in a Protoplanetary Disk
Abstract
Motivated by current observational evidence for circumstellar disks associated with young stellar objects and premain sequence stars, we investigate the gravitational instability of a thin, Keplerian protoplanetary disk without a magnetic field (ch 2) and including magnetic field effects (ch 3). The disk is a two fluid system, consisting of gas and dust (ch 2), or a three fluid system, consisting of neutral gas, ionized gas, and neutral dust (ch 3), coupled by gravity and friction. The growth rates and the eigenfunctions are calculated numerically using nonaxisymmetric linear perturbation methods. In both cases. we find that for the usual values of input parameters (e.g. mass of disk) the disk is unstable to nonaxisymmetric perturbations for some range of azimuthal wavenumber m in addition to m = 1. The growth rate has a well defined maximum in m and the number of radial nodes. The inclusion of magnetic fields generally reduces the growth rates for each m, and the values of m where the maximum instability occurs. We also study the effect of different boundary conditions (reflecting and transmitting) on the growth rates. The boundary conditions affect the instability only for small m modes. We also present the effect of various properties of dust on the instability and the change of the growth rate due to the change of parameters. In particular, the effect of the ionization abundance on the growth rates is examined for disks including a magnetic field. The inclusion of dust usually enhances the instability, although dust is a small component in mass and the gravitational potential is usually dominated by the gas component. Our study is also concentrated on the stability of the m = 1 mode (ch 4). We find that different physical mechanisms affect the m = 1 instability for high disk mass and for low disk mass. For high disk mass. the growth rates are mainly determined by the sling amplification which is associated with the indirect potential. For low disk mass, the swing amplification and the coupling between the swing and sling mechanisms are important in driving the instability. The sensitivity of the swing amplification to Toomre's stability parameter Q is somewhat reduced by the decreasing distance between the corotation and the outer disk edge as the disk mass decreases.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT.........1N
 Keywords:

 CIRCUMSTELLAR DISK;
 Physics: Astronomy and Astrophysics;
 Gravitational Fields;
 Magnetic Effects;
 Stellar Envelopes;
 Boundary Conditions;
 Dust;
 Ionization;
 Ionized Gases;
 Magnetic Fields;
 Mass;
 Neutral Gases;
 PreMain Sequence Stars;
 Protoplanets;
 Stability;
 Astrophysics