|Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1992: ¥1,200,000 (Direct Cost: ¥1,200,000)
Because of recent developments in observational instruments, around a T Tauri stars a rotating disk is found and it is considered as a protoplanetary disk. The structure and evolution of such a disk have not been, however, investigated well yet. Hence the purpose of this research project is to construct the model of the protoplanetary disk and to study the stability and evolution of the disk by a linear perturbation theory and numerical simulations.
As a beginning in order to study the stability of a disk around the central star, the linear analysis of the perturbation equation has been done. As a result, I find that the stability of the disk is determined by the minimum value (Qmin) of the Toomre's Q in the disk. If the value of Qmin is less that unity, the disk is unstable and its growth rate of the perturbation is nearly equal to the rotational angular velocity. Because of such a high growth-rate, this instability is considered as one of a gravitational instability. On the other hand, if the value of Qmin is greater than unity, such a disk is also unstable. But in this case the instability is considered as one of shear instability from the shape of the eigenfunction.
After investigation of the linear stability analysis, I have done numerical simulations to study the nonlinear growth of the perturbations. From numerical computations, the disk with Qmin < 1 fragments into many pieces and they are considered as brown dwarfs because of their mass. From my investigation, the criterion of the stability of the protoplanetary disk is firstly obtained.