On the Analytical Models of Protoplanetary Formation in Extrasolar Systems

In this work, we consider a statistical theory for a cosmogonical body formation (so-called spheroidal body) to develop the analytical models of protoplanetary formation in extrasolar systems. Within the framework of this theory, the models and evolution equations of the statistical mechanics have been proposed, while the well-known problem of gravitational condensation of infinite distributed cosmic substances has been solved. This paper derives the general equation of distribution of the specific angular momentum of forming protoplanets since the specific angular momentums (for particles or planetesimals) are averaged during a conglomeration process (under a planetary embryo formation). As a result, a new law for planetary distances (which generalizes Schmidt’s law) is derived theoretically. This paper develops also an alternative thermal emission of particles model of the formation of protoplanets in extrasolar systems. Within the framework of this model, the equation for the thermal distribution function of the specific angular momentums of particles moving in elliptical orbits in the gravitational field is derived. According to this thermal escape model, only 0.8% of the total number of particles in the solar system composing the protoplanetary cloud has angular momentum 15.6 times higher than the angular momentum of the remaining 99% of particles. This conclusion agrees completely with the known fact of a nonuniform distribution of the angular momentums in our solar system noted by ter Haar. As pointed out here, the exponential laws of planetary distances occur in some extrasolar systems.