Caroline Terquem

Abstract:

In this paper, we show that the eccentricity of a planet on an inclined orbit with respect to a disc can be pumped up to high values by the gravitational potential of the disc, even when the orbit of the planet crosses the disc plane. This process is an extension of the Kozai effect. If the orbit of the planet is well inside the disc inner cavity, the process is formally identical to the classical Kozai effect. If the planet's orbit crosses the disc but most of the disc mass is beyond the orbit, the eccentricity of the planet grows when the initial angle between the orbit and the disc is larger than some critical value which may be significantly smaller than the classical value of 39{ring operator}. Both the eccentricity and the inclination angle then vary periodically with time. When the period of the oscillations of the eccentricity is smaller than the disc lifetime, the planet may be left on an eccentric orbit as the disc dissipates. © 2010 The Authors. Journal compilation. © 2010 RAS.

Abstract:

In this paper, 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. In HD 40307, we expect that three resonant angles could be involved in this way. We propose that the planets in this system 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 occur 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 ×10-3, but then we find that the evolution to the present system in a reasonable time is possible only if the masses are significantly larger than the minimum masses and the 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 ∼0.15. We remark that 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. © 2010 The Authors. Journal compilation © 2010 RAS.