Evolutionary processes in the protoplanetary accretion disk

The aim of this paper is to show that the global structure of our planetary system could be the result of diffusive ring-shaped acoustic waves, excited at the inner boundary layer of the slowly rotating protosun and propagating to the outer parts of the protoplanetary accretion disk. We show that for low-mass disks with a relatively high Toomreʹs stability number Q secular instability effects are very slow and can be neglected in a first approximation. Therefore a gravitational collapse, or, for time scales considered here, a global gravo-viscous instability can be excluded. In the framework of a WKB-analysis one can derive for the spacing ratio Λ = rn+1rn of two consecutive acoustic wave crests at the moment of maximum compression the formula Λ ≈ exp[4π(csvK)], where cs is the sound speed in the disk and vK is the local orbital speed of the disk material. We believe that the orbital spacings of the planets today reflects a definite frozen-in stage of the propagation process of these primordial acoustic waves in the protoplanetary disk. It is very likely, that in the non-linear regime the waves become shock waves and could serve as a trigger mechanism for transient high-energy processes in the dust-gas disk as well as for the very complex building processes of the planets. The theory could be relevant for the formation of the terrestrial rocky planets as well as for the cores of the giant gaseous ones.