Dynamics of Circumstellar Disks

We present a series of 2-dimensional hydrodynamic simulations of massivedisks around protostars. We simulate the same physical problem using both a`Piecewise Parabolic Method' (PPM) code and a `Smoothed Particle Hydrodynamic'(SPH) code, and analyze their differences. The disks studied here range in massfrom $0.05 M_*$ to $1.0 M_*$ and in initial minimum Toomre $Q$ value from 1.1to 3.0. For this problem, the strengths of the codes overlap only in a limitedfashion, but similarities exist in their predictions, including spiral armpattern speeds and morphological features. Our results represent limiting cases(i.e. systems evolved isothermally) rather than true physical systems. Disksbecome active from the inner regions outward. From the earliest times, theirevolution is a strongly dynamic process rather than a smooth progression towardeventual nonlinear behavior. We calculate approximate growth rates for thespiral patterns; the one-armed ($m=1$) spiral arm is not the fastest growingpattern of most disks. In our SPH simulations, disks with initial minimum$Q=1.5$ or lower break up into proto-binary or proto-planetary clumps. However,these simulations cannot follow the physics important for the flow and must beterminated before the system has completely evolved. At their termination, PPMsimulations with similar initial conditions show uneven mass distributionswithin spiral arms, suggesting that clumping behavior might result if they werecarried further. Concern that the point-like nature of SPH exaggeratesclumping, that our representation of the gravitational potential in PPM is toocoarse, and that our physics assumptions are too simple, suggest caution ininterpretation of the clumping in both the disk and torus simulations.