GRAVITATIONAL INSTABILITIES IN A PROTOPLANETARY DISK INCLUDING THE EFFECTS OF MAGNETIC-FIELDS

We investigate the gravitational instability of a thin, Keplerian prot oplanetary disk including the effects of a largely azimuthal magnetic field. The model follows that of our previous work (Noh, Vishniac, & C ochran 1991) except for the inclusion of a magnetic field. The disk is assumed to consist of neutral and ionized gas and neutral dust which are coupled by gravity and friction. The growth rates and eigenfunctio ns are calculated numerically using nonaxisymmetric linear perturbatio n methods. The results show that the growth rate has a maximum at some intermediate azimuthal number m, but for each value of m it is reduce d relative to the unmagnetized case. The effects of the magnetic field appear more strongly on small scales. As the strength of the equilibr ium magnetic field increases the growth rates decrease, and the maximu m instability occurs at a lower value of m due to the increasing magne tic pressure. The response of each component to the magnetic field is discussed using the behavior of the eigenfunctions in the radial direc tion. With the inclusion of the magnetic field, the effects of the ion ization fraction and friction on the growth rates also appear to be im portant for high m modes. Increasing the ionization fraction or the fr iction suppresses instability, but only slightly changes the maximally unstable azimuthal scales. The enhanced growth rates due to a dust co mponent for which thermal pressure is negligible are somewhat reduced by the inclusion of a magnetic field. The effects of different boundar y conditions (reflecting and transmitting) on the growth rates are als o shown.