Formation of a star and planets around it through a gravitational instability in a disk of gas and dust

The position is adopted that involve a simultaneous formation of a star and planets around it through a gravitational Jeans-type instability in a protostellar disk of gas and dust. The possibility that the disk is dynamically unstable to axisymmetric (radial) and nonaxisymmetric (spiral) gravity perturbations (e.g., those produced by a spontaneous disturbance or, in rare cases, a satellite system) with characteristic scales much larger than the vertical scale height is discussed, using a local WKB approximation. It is shown analytically that the dynamically cold thin disk is likely subject to both radial and spiral Jeans instabilities of small-amplitude perturbations and might therefore be clumpy. The mass of a typical clump in actual disks is coincident in order of magnitude with the masses of giant planets in the solar system. These gravitationally bound clumps may further collapse to become planets. In unstable, inhomogeneous disks spiral perturbations can effectively transfer angular momentum outward to the outer parts of the system, as mass flows inward to the growing star through gravitational torques. It is proposed that the spontaneous generation of Jeans-unstable modes of collective oscillations is the source of self-sustained hydrodynamic turbulence in protostellar disks; in the nonlinear regime, gravitational instabilities can produce self-gravitating turbulence with outward angular momentum transport. The turbulence is related to stochastic motions of gas elements, and allows potential energy to be converted into kinetic energy which can then be dissipated. Equations are derived to describe the turbulent heating of the disk that results from the buildup of Jeans instability. The heating and the mass redistribution bring the disk toward stability-unless some cooling mechanism is available, e.g., by radiation-against all perturbations, including the most unstable nonaxisymmetric ones. As cooling process always exists in the systems, the Jeans instability can be considered to be a long-term generating mechanism for fresh, gravitationally unstable density waves, thereby leading to recurrent short-lived ∼ 10⁴ yr arc-and-lump or spiral patterns in the protostellar (protoplanetary) disks. N-body experiments that simulate the nonlinear development of gravitational instabilities are also used to test the validities of the theory.