Formation, early evolution, and gravitational stability of protoplanetary disks

The formation, viscous evolution, and gravitational stability of protoplanetary disks are investigated. The formation process is parameterized by the angular velocity of the molecular cloud core omega, while the viscous evolution is parameterized by the viscosity parameter alpha in the disk; in this study we consider a range of (0.4-6) x 10-14/s for omega and from 10-5 to 10-1 for alpha. The axisymmetric gravitational stabilities of the disks are checked using Toomre's criterion. The resulting disk surface temperature distribution, (d log Ts/d log R) approximately = -0.6 (R is the cylindrical radius), can be attributed to two heating sources: the viscous heating dominant in the inner disk region, and the accretion shock heating dominant in the outer disk region. This surface temperature distribution matches that observed in many disks around young stellar objects. During the infall stage, disks with alpha less than 10-1.5 become gravitationally unstable independent of omega. The gravitational instabilities occur at radii ranging from 5 to 40 AU. The ratio of the disk mass to the central star mass ranges from 0.2 to 0.5 at the times of instability, about 4 x 10-5 x (omega/10-14/s)-0.67 yr. Most disks with low alpha and high omega become gravitationally unstable during their formation phase.