We have studied the nonlinear evolution of a magnetized disk of isothermal gas, which is sustained by its self-gravity. Our objective is to investigate how the Jeans, Parker, and convective instabilities compete with each other in structuring/de-structuring large scale condensations in such disk. The Poisson equation for the self-gravity has been solved with a fourth-order accurate Fourier method along with the Green function, and the MHD part has been handled by an isothermal TVD code. When large wavelength perturbations are applied, the combined action of the Jeans and Parker instabilities suppresses the development of the convection and forms a dense core of prolate shape in the mid-plane. Peripheral structures around it are filamentary. The low density filaments connect the dense core to the diffuse upper region. On the other hand, when small wavelength perturbations are applied, the disk develops into an equilibrium state which is reminiscent of the Mouschovias's 2-D non-linear equilibrium of the classical Parker instability under an externally given gravity.

We present the whole basis of numerical method and useful formulae for general relativistic magnetohydrodynamic simulations in Kerr space-time.

We observed the thermal transitions of SiO (J=I-0, 2-1) and 29SiO (J=l-O) toward the Sgr A molecular clouds. The distribution and the velocity structure of SiO are very similar to previous results for 'quiet' interstellar molecules. We think· that the SiO has been well mixed with other molecules such as H2 which may indicate that the formation of Sgr A molecular clouds was affected by the activities, such as shock waves or energetic photons, from the Galactic center in large scales. The total column density of SiO is about 4.1×1014cm−2 and the fractional abundance SiO/H2 appears to be about 10 times larger than those of other clouds in the central region of our galaxy. The derived values are thought to be lower limits since the optical depths of the observed SiO lines are not very thin. The formation of SiO has been known to be critically related to shocks, and our results provide informative data on the environment of our Galactic center.