Planet-planet scattering in systems of multiple planets of unequal mass

Abstract

A large sample of planet-planet scattering events for three planet systems with different orbital separations and masses is analyzed with a multiple regression model. The dependence of the time for the onset of instability on the masses of the planets and on their initial orbital separations is modeled with a quadratic function. The same analysis is applied to the timespan of the chaotic evolution dominated by mutual close encounters. The configurations with the less massive planet on an outside orbit are stable over longer timescales. The same configuration leads to shorter chaotic evolution times before the ejection of one planet. In about 70\% of the cases the lighter planet is the one escaping from the system. If a different separation is assumed between the inner and outer planet pairs, then the dominant effect on the instability time is due to the pair with the smaller separation, as a first approximation.