The original scientific goals of my GCI proposal were to develop a 3D magnetohydrodynamics (MHD) code for massively parallel machines and apply it to a variety of problems in astrophysical fluid dynamics. I was able to get the code running on the CM-200 in the first year of support. In subsequent years I ported it to the CM-5 and the MasPar MP-2. With this code, I was able to tackle a large number of applications over the last 3 years. Following is a brief summary of all the projects that resulted in a manuscript published, accepted, or submitted to a refereed journal.
(1) Graduate student J. Xu and I used the code in "hydrodynamic mode" to compute the largest 3D simulations of the interaction of a strong shock with an interstellar cloud yet presented. In 3D, instabilities produce rapid mixing of the shocked cloud material and the postshock ambient gas. The simulations allow us to quantitatively measure this mixing rate. We also find that the initial shape of the target cloud strongly affects the subsequent evolution, by changing the effective cross sectional area of the cloud as seen by the shock. Our results will appear in October in The Astrophysical Journal.
(2) M. Edelman (CIMS) and I used the code to study the nonlinear evolution of the corrugation instability in slow magnetosonic shocks. Our numerical results confirm the growth rates predicted by a linear stability analysis. In the nonlinear regime, we find that in parallel shocks the instability results in fragmentation of the shock front into discrete fingers, while for oblique shocks the instability saturates as finite amplitude waves that propagate along the front. Our results have application to accretion shocks in strongly magnetized stars, and to shocks in the interstellar medium (ISM). They will appear in November in The Astrophysical Journal.
(3) In collaboration with M. Norman and B.I. Jun (Univ. of Illinois), the code was used to compute high-resolution simulations of the nonlinear development of the Rayleigh-Taylor instability in magnetized fluids. All lower-resolution simulations were performed on a Cray; the improved performance of the code on massively parallel machines was vital for the higher-resolution runs. The results will appear in an upcoming issue of The Astrophysical Journal.
(4) Using the code in "hydrodynamic mode" again, the first 3D evolution of an impact of a High Velocity Cloud (HVC) with a galactic disk was modeled. These calculations were motivated by HI observations of the edge-on spiral galaxy NGC4631 obtained by R. Rand (Univ. of Maryland), which show a 3 Kpc-diameter hole in the galactic disk in both position and velocity space. Since the galaxy is in an interacting system, an impactor is a likely explanation for such a large disturbance of the disk. Our calculations demonstrate that the oblique impact of a large HVC reproduces the observed morphology and kinematics of the galactic disk very well, strengthening the impact interpretation. A manuscript has been submitted to The Astronomical Journal.
(5) Using the code in "hydrodynamic mode", S. Balbus (Univ. of Virginia) and I studied the effect of 3D vertical convection in providing angular momentum transport in an accretion disk. The calculations are done in the local frame using the "shearing sheet" approximation in the horizontal plane of the disk but extend over several scale heights in the vertical direction. Thus, the computational domain represents a small column of fluid embedded in a larger disk. The calculations begin from an analytic, convectively unstable initial state. Surprisingly, we find convection results in a very small angular momentum transport rate, and moreover, the transport is predominately inward. This result was predicted by a linear analysis, but our simulations are the first to show that 3D nonlinear convection in a Keplerian disk results in inward transport. We are able to interpret the results by considering the effect of epicyclic oscillations on angular momentum transport. The results are reported in a manuscript submitted to The Astrophysical Journal.
(6) Finally, the largest science project undertaken over the course of my grant is 3D MHD studies of the nonlinear stage of the Balbus-Hawley instability in stratified accretion disks. Our simulations have shown that in 3D, the B-H instability results in MHD turbulence, which is a vigorous source of outward angular momentum transport. Thus, the B-H instability is an attractive mechanism for explaining the anomalous angular momentum transport in accretion disks. Moreover, we find that in stratified disks, magnetic buoyancy results in the production of a strongly magnetized envelope in the outer, low density regions of the disk that surround a weakly magnetized core at the center of the disk. The results are particularly important to understanding the nature of the nonlinear, saturated stage of the B-H instability and the dynamics of accretion disks in general. In all, the simulations performed as part of this single study consumed 1,000 SUs on the CM systems at NCSA. A manuscript describing the work has been submitted to The Astrophysical Journal.
"A Numerical Study of Rayleigh-Taylor Instability in Magnetic Fluids", by B.-I. Jun, M.L. Norman, & J.M. Stone, The Astrophysical Journal, 453, 332 (1995).
"The Hydrodynamics of Shock-Cloud Interactions in Three Dimensions", by J. Xu & J.M. Stone, The Astrophysical Journal, 454, 172 (1995).
"The Corrugation Instability in Slow MHD Shocks", by J.M. Stone & M. Edelman, The Astrophysical Journal, 454, 182 (1995).
"Modeling the HI Supershell in the Edge-on Galaxy NGC4631 as an Impact of a HVC", by J.M. Stone & R.J. Rand, The Astronomical Journal, 111, 190 (1996).
"Three Dimensional Magnetohydrodynamical Simulations of Vertically Stratified Accretion Disks", by J.M. Stone, J.F. Hawley, S.A. Balbus, & C.F. Gammie, The Astrophysical Journal, 463, 000 (1996).
"Angular Momentum Transport in Accretion Disks by Convection", by J.M. Stone & S.A. Balbus, The Astrophysical Journal, 464, 000 (1996).
Jianjun Xu, Ph.D. (pending), "The Kelvin-Helmholtz Instability in Cooling Jets"
Glenn Piner, M.Sc. (1995), "Gas Flow in Barred Galaxies"
Kurt Roettiger, postdoctoral associate