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

We investigate the origins of Kepler-419, a peculiar system hosting two nearly coplanar and highly eccentric gas giants with apsidal orientations librating around anti-alignment, and use this system to place constraints on the properties of their birth protoplanetary disk. We follow the proposal by Petrovich, Wu, & Ali-Dib (2019) that these planets have been placed on these orbits as a natural result of the precessional effects of a dissipating massive disk and extend it by using direct N-body simulations and models for the evolution of the gas disks, including photoevaporation. Based on a parameter space exploration, we find that in order to reproduce the system the initial disk mass had to be at least 95 M_Jup and dissipate on a timescale of at least 10^4 yr. This mass is consistent with the upper end of the observed disk masses distribution, and the dissipation timescale is consistent with photoevaporation models. We study the properties of such disks using simplified 1D thin disk models and show that they are gravitationally stable, indicating that the two planets must have formed via core accretion and thus prone to disk migration. We hence finally investigate the sensitivity of this mechanism to the outer planet's semi major 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/or close encounters, the dynamics seems to be rather insensitive to planet c semi major axis, and thus orbital migration driven by the disk.