On the dynamics of multiple systems of hot super-Earths and Neptunes: Tidal circularization, resonance and the HD 40307 system

Abstract

[Abridged] We consider the dynamics of a system of hot super-Earths or Neptunes such as HD 40307. We show that, as tidal interaction with the central star leads to small eccentricities, the planets in this system could be undergoing resonant coupling even though the period ratios depart significantly from very precise commensurability. In a three planet system, this is indicated by the fact that resonant angles librate or are associated with long term changes to the orbital elements. We propose that the planets in HD 40307 were in a strict Laplace resonance while they migrated through the disc. After entering the disc inner cavity, tidal interaction would cause the period ratios to increase from two but with the inner pair deviating less than the outer pair, counter to what occurs in HD 40307. However, the relationship between these pairs that occurs in HD 40307 might be produced if the resonance is impulsively modified by an event like a close encounter shortly after the planetary system decouples from the disc. We find this to be in principle possible for a small relative perturbation on the order of a few 1.d-3 but then we find that evolution to the present system in a reasonable time is possible only if the masses are significantly larger than the minimum masses and tidal dissipation is very effective. On the other hand we found that a system like HD 40307 with minimum masses and more realistic tidal dissipation could be produced if the eccentricity of the outermost planet was impulsively increased to about 0.15. The form of resonantly coupled tidal evolution we consider here is quite general and could be of greater significance for systems with inner planets on significantly shorter orbital periods characteristic of for example CoRoT 7 b.