The Influence Of Different Models For Angular Momentum Transport Due To Gravitational Instabilities On The Structure Of Protoptanetary Disks

The formation and early evolution of circumstellar disks is determined by thenature of the collapse flow that forms stars out of molecular cloud cores. As thecollapse proceeds, a pressure supported star forms at the center of the inward flow anda circumstellar disk forms around it from the infalling material with higher specificangular momentum. During this early formative stage, a protostar thus consists of acentral star/disk system which is deeply embedded within an infalling envelope ofdust and gas.Relatively massive disks are likely to be gravitationally unstable. The efficientangular momentum transport within the disks to the outer region, which is induced bythe gravitational torques, is very similar to angular momentum transport mechanismdriven by viscous torque. So Lin&Pringle (1987,1990) gave a prescription for thegravitational torque in terms of the effective viscosity. Viscosity due to gravitationalinstability works well in simulating the formation and evolution of the protoplanetarydisks, though it is not a real viscosity.The viscosity due to gravitational instability plays a great role in the formation ofstar. The study has gone further and further. Astrophysicists have given variousmodels of the effective viscosity due to gravitational instability, which are based ondifferent principles. Our goal is to put these models together in one simulation,compare and analyze the results of the simulation. It is of great importance in theastrophysical studies.In this article, we show the research background in the first chapter. Then we listthe principles, expressions, applications and consequences of different models of the effective viscosity due to gravitational instabilities in details according to the timeorder in the second chapter. In the third chapter we select four typical models of theeffective viscosity due to gravitational instabilities to discuss the influence of differentmodels of viscosity on the structure of the protoplanetary disks. We put the fourtypical models of the effective viscosity in one simulation of stellar formation andevolution with the same initial state. Then we compare and analyze the results indetails. At last, we give the conclusions and expectations for our work in the fourthchapter.Based on numerical results of the four typical models of effective viscosityinduced by gravitational instabilities, we plot graphs of irradiative descriptions of theToomer(1964) instability parameter Q, the viscosity and the surface density. Then wecompare and analyze the graphs. We compare the differences of the structures of thedisks in different times through the formation and evolution for all the models. Wefind the relations between these parameters, analyze the differences between the fourmodels for one parameter and give the explanations. We find that the influences ofthree of the four models (Kratter models，Lin&Pringle models and Zhu models) onthe structures of disks are similar. The three curves of irradiative surface densitydescriptions almost overlapped. When the disks are gravitationally unstable, viscosityefficiency is constant (=0.02) in the model of Jin&Li. Its results are different fromthe others. The curves of the surface density descriptions and the viscosity efficiencydescriptions of these four models overlapped gradually until the middle and the latephases of the disk evolution.Therefore, we get the conclusions below. When the expression of effectiveviscosity induced by gravitational instability is a local function, the curves of surfacedensity and viscosity irradiative descriptions are smooth and continuous. The curvesof the surface density descriptions for different viscous models overlapped in diskformation and evolution. Of course, the influences of these viscous models on thestructures of the protoplanetary disks are similar. As for the model of a constantviscosity for the global gravitationally unstable disks, there are obvious breaks in thecurves of viscosities in the gravitational stable phases. So the curves of the surface density descriptions are not smooth. In the simulations of the formation and evolutionof the protoplanetary disks, these results can be very useful in the studies of effectiveviscosities induced by gravitational instability.