Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt........28l&link_type=abstract
PhD Dissertation, California Univ. Santa Cruz, CA United States
Astronomy and Astrophysics
Astronomy
9
Protostars, Stellar Evolution, Star Formation, Accretion Disks, Astronomical Models, Two Dimensional Models, Viscosity, Hydrodynamics, Mathematical Models
Scientific paper
This thesis begins with a series of 2-D, multi-gridded hydrodynamical simulations of the collapse of axisymmetric, rotating 1 M(solar mass) protostellar clouds, which form resolved, hydrostatic disks. We examine how the disk is affected by the inclusion of turbulent viscosity by comparing viscous simulations with an inviscid model. In the second chapter, unstable spiral wave modes in thin self gravitating protostellar disks are studied. The growth and characteristics of modes in the linear regime are examined by a method which casts the hydrodynamic equations in the form of a single integro-differential equation for the response of the surface density distribution to the growing mode. Several previously discovered disk instabilities are analyzed, along with co-rotation resonance instabilities within an idealized disk inspired by the collapse models of the first chapter. The results of the linear calculations are confirmed with full hydrodynamic calculations which push the models well into the non-linear regime. In the third chapter, effects arising from non-axisymmetric gravitational instabilities in a model protostellar disk are followed with a 3-D SPH code. It is found that the disk is prone to a series of spiral instabilities with primary azimuthal mode number m = 1 and m = 2. The torques induced by these non-axisymmetric structures elicit material transport of angular momentum and mass through the disk, readjusting the surface density profile toward more stable configurations. It is determined that an evolving disk which maintains a minimum Toomre Q value of approximately 1.4 is likely to have a total evolutionary span of several times 105 years, comparable to, but somewhat shorter than the evolutionary timescale resulting from viscous turbulence alone. The evolution resulting from nonaxisymmetric instabilities is compared with solutions of a one-dimensional viscous diffusion equation applied to the initial surface density and temperature profile. It is found that an effective a value of .03 provides a good fit to the results of the simulation. The effective alpha depends on the minimum Q in the disk at the time the instability is activated.
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