Stability of Terrestrial Protoplanet Systems and Alignment of Orbital Elements

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Abstract
The dynamical characteristics of terrestrial protoplanet systems have been investigated. Diagrams which show the instability timescale of terrestrial protoplanet systems as a function of the protoplanet separation (we call them CWB diagrams) were analyzed and interpreted. We have produced CWB diagrams for several different initial parameters, mainly with perturbations from Jupiter and Saturn. One-peakedness of the diagrams for small random velocity cases is interpreted from the viewpoint of orbital alignment in protoplanets. The orbital alignment serves as a stabilizer of the protoplanet system by preventing particles from making close encounters. Terrestrial protoplanet systems appear to be most stable where the tidal force produced by perturbers and mutual gravitational interaction among particles balance; in such cases, orbital alignment is realized. Thus, the terrestrial protoplanet systems turn out to be another example of the so-called secular orbit-orbit resonance frequently found in planet-satellite or satellite-ring systems. Gradual breaking of the orbital alignment invokes an instability in protoplanet systems, which can lead to the collisional evolution of protoplanets into the present planets.