Gravitational Instabilities in Protostellar Disks

Over the past decade there has also been increasing evidence for disks around young stellar objects (YSO) and pre-main sequence (PMS) stars, by both direct observations, and inferred from IR and UV excesses and, more recently, from millimetre and submillimetre interferometry. Models based on these observations suggest disk masses and radii of the order 0.01 - 1.0 M_sun and 10-500 AU respectively, and substantial luminosity (comparable to stellar). Motivated by these observations, a great deal of work has been aimed at understanding the role of gravitational instabilities in massive disks.

The study of gravitational instabilities in protostellar disks is important in understanding both star and planetary formation. It is expected that in the very early stages of disk formation that they will be massive, continuing to accrete material from their infalling parent cloud. Disk evolution seems to be mass dependent, with disk turbulence driving viscous evolution in low mass disks, and non-axisymmetric perturbations excited by gravitational instabilities inducing torques in massive disks which can transfer angular momentum over extended regions of the disk.

Adams, Ruden & Shu (1989) explored the idea that disk accretion ultimately owes its origin to the growth of spiral gravitational instabilities. Their semi-analytic analysis of selfgravitating protostellar disks found that m=1 modes forced the central star from the system's centre of mass, thus allowing angular momentum transfer to the disk. They suggested that the instability could lead to mass accretion or possibly the formation of a binary companion. Continued semi-analytic and non-linear numerical calculations of selfgravitating disks found a wide variety of instabilities that lead to the outward transport of angular momentum in the these disks.

Motivated by these studies, we run a series of numerical experiments to investigate the effects of disk mass, temperature and density profile, and outer boundary conditions on selfgravitating protostellar disks. We find, as expected, that the strength of the resulting instability increases with increasing disk mass and decreasing temperature. We also find that less centrally condensed density profiles will become unstable at the position of peak density and redistribute matter to a more stable configuration. A reflecting outer boundary acts to enhance any disk clumping already present. And finally, if the disk temperature, or Q profile, is low, the disk can fragment into a series of clumps. We also investigate the effects of adding a protoplanetary perturber to the disk. The protoplanet opens a gap in the disk around its orbit due to tidal torques on the disk. If these gaps are void of material, accretion onto the protoplanet will cease. If, however, material can "cross the gap", the protoplanet can continue to grow into a protogiant planet as recently detected around solar-like stars, or possibly a brown dwarf. We find that increasing the ratio of the disk scale height to radius, H/R, as suggested by Atrymowicz & Lubow (1996), causes an accretion stream to cross the gap and continue to supply disk material to the protoplanet.

The final chapter of this thesis presents a two-phase SPH code which models gas and dust following Monaghan & Kocharyan (1995). The two components interact via pressure, gravity and drag forces. Simulations are presented which test the stability, accuracy, drag and gravity coupling of the code. The simulations agree well with analytic and expected results. With this code we hope to follow the non-linear evolution of dusty-gas protostellar disks in a variety of scenarios, in order to determine the dynamic effects that the addition of dust in these protostellar systems causes.