Constraining protoplanetary discs with exoplanetary dynamics: Kepler-419 as an example

Abstract

We investigate the origins of Kepler-419, a peculiar system hosting two nearly coplanar and highly eccentric gas giants with apsidal orientations liberating around anti-alignment, and use this system to place constraints on the properties of their birth protoplanetary disc. We follow the proposal by Petrovich, Wu, & Ali-Dib that these planets have been placed on these orbits as a natural result of the precessional effects of a dissipating massive disc and extend it by using direct N-body simulations and models for the evolution of the gas discs, including photoevaporation. Based on a parameter space exploration, we find that in order to reproduce the system the initial disc mass had to be at least 95 M-Jup and dissipate on a time-scale of at least 104 yr. This mass is consistent with the upper end of the observed disc masses distribution, and the dissipation time-scale is consistent with photoevaporation models. We study the properties of such discs using simplified 1D thin-disc models and show that they are gravitationally stable, indicating that the two planets must have formed via core accretion and thus prone to disc migration. We hence finally investigate the sensitivity of this mechanism to the outer planet's semimajor axis, and find that the nearby 7:1, 8:1, and 9:1 mean-motion resonances can completely quench this mechanism, while even higher order resonances can also significantly affect the system. Assuming the two planets avoid these high-order resonances and close encounters, the dynamics seems to be rather insensitive to planet c semimajor axis, and thus orbital migration driven by the disc.