Effects Of Magnetic Fields, Viscosity, And Nonaxisymmetry On Gravitational Instability In Protoplanetary Disks

It is believed that normal stars produce their energy by nuclear fusion. Apart from nuclear energy, there is one another possible source of energy in the astrophysical universe. Matter around a star ,which is attracted by it, spirals in until to the ground .In the process, the matter lose gravitational potential energy, which is transformed into other forms such as heat and sound and radiated away. And at the same time, the angular momentum is transported outward. It is called the process accretion, in which disc like accretion is thought to be most important. It is proved qualitatively that no non-rigid, infinitesimally thin, plane sheet of gravitating matter--not even a perfectly uniform, infinite sheet—could long endure near its original state in the presence of the slightest disturbances if it lacked all stabilizing influences. And the critical wavelengths of axisymmetric disturbances are calculated. Then Toomre Q instability criterion is introduced, which is very important to the present research work in this paper. After that I summarize WKB waves, some results of the simulations and some developments in gravitational instabilities of accretion discs in the contexts of active galactic nuclei (AGN), cataclysmic variable stars (CV), and young stellar objects (YSO). At last, I introduce briefly the interaction between magnetohydrodynamic(MHD) turbulence and gravitational instabilities.Gravitational instability (GI) is widely considered to be important as providing an angular momentum transport mechanism in protoplanetary disks. It is an important physical process during the formation and evolution of the solar system. If a protoplanetary disk is unstable enough, it will fragment into several parts and/ or lead to the formation of binary stars (Bonnell 1994; Bonnell & Bate 1994). Otherwise GI will transport mass inward and angular momentum outward, then the mass of the object in the center of the disk will become larger and larger until it becomes a star(Larson 1984). GI also is a major mechanism of forming planetesimals and giant planets. Goldreich & Ward (1973) described the process in which GI dominates the formation of planetesimals. Boss (1998) suggested that GI in giant gaseous protoplanets is a more e±cient mechanism to form giant planets than core accretion. Safronov (1960) and Toomre (1964) derived the local stability criterion in gaseous disks and stellar disks respectively. However, there are several other factors, besides gaseous pressure and differential rotation, such as magnetic fields and viscosity, which can affect GI in protostellar disks.In this paper, I follow the method of Shu (1992), who applies gas dynamics and adopts WKBJ approximation (Lin & Shu 1964), to calculate the local GI criterion in protostellar disks with magnetic fields (section 4.1) and enormous viscosity (section 4.2) respectively, and find that both magnetic fields and viscosity help to stabilize the disks against self-gravity. And in section 4.3 I investigate the effect of linear nonaxisymmetric disturbances on local GI criterion of nonmagnetized disks in a different but relatively simple way from that of Goldreich &Lynden-Bell (1965) and get a equivalent result, i.e., the criterion is identical to that in the axisymmetric situation. In section 4.4, I discuss the reasonableness of our assumptions and figure out what left to be resolved.