Secular ring instability in the protoplanetary accretion disk

Astronomy and Astrophysics – Astronomy

Scientific paper

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Accretion Disks, Dynamic Stability, Flow Stability, Planetary Evolution, Protoplanets, Secular Variations, Solar System Evolution, Astronomical Models, Compressible Fluids, Dispersing, Stellar Mass Accretion

Scientific paper

It is shown that an accretion disk, the material of which satisfies the Navier-Stokes equations of a compressible fluid, is secularly unstable to axisymmetric density disturbances even if Toomre's parameter Q is greater than 1. The characteristic wave number and the corresponding time scale of the mode of maximum secular instability are calculated on the basis of a local theory. In the global theory, a complex linear integral equation describing the diffusion instability in the accretion disk is formulated. The radial distances of the rings to the protosun obey, in the outer range of the disk, an exponential law, provided that the vertically integrated viscosity is nearly constant throughout the disk. It is proposed that the formation process is shorter for the outer gaseous than for the inner rocky planets, because the global secular ring instability is evanescent in the inner regions of the disk.

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