The effects of disc warping on the inclination of planetary orbits
Protoplanets with core masses below the critical mass fill in their Roche lobe
Monthly Notices of the Royal Astronomical Society 418:3 (2011) 1928-1934
Abstract:We study the evolution of a protoplanet of a few earth masses embedded in a protoplanetary disc. If we assume that the atmosphere of the protoplanet, i.e. the volume of gas in hydrostatic equilibrium bound to the core, has a surface radius smaller than the Roche lobe radius, we show that it expands as it accretes both planetesimals and gas at a fixed rate from the nebula until it fills in the Roche lobe. The evolution occurs on a time-scale shorter than the formation or migration time-scales. Therefore, we conclude that protoplanets of a few earth masses have an atmosphere that extends to the Roche lobe surface, where it joins on to the nebula. This is true even when the Bondi radius is smaller than the Roche lobe radius. This is in contrast to the commonly used models in which the static atmosphere extends up to the Bondi radius and is surrounded by a cold accretion flow. As a result, any calculation of the tidal torque exerted by the disc on to the protoplanet should exclude the material present in the Roche lobe, since it is bound to the protoplanet. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.
Disk dynamics and planet migration
EAS Publications Series 41 (2010) 209-218
Abstract:We review models of protoplanetary disks. In the earlier stages of evolution, disks are subject to gravitational instabilities that redistribute mass and angular momentum on short timescales. Later on, when the mass of the disk is below ten percent or so of that of the central star, accretion occurs through the magnetorotational instability. The parts of the disks that are not ionized enough to couple to the magnetic field may not accrete or accrete inefficiently. We also review theories of planet migration. Tidal interaction between a disk and an embedded planet leads to angular momentum exchange between the planetary orbital motion and the disk rotation. This results in low mass planets migrating with respect to the gas in the disk, while massive planets open up a gap in the vicinity of their orbit and migrate in as the disk is accreted. © EAS, EDP Sciences, 2010.
On the dynamics of multiple systems of hot super-Earths and Neptunes: Tidal circularization, resonance and the HD 40307 system
Monthly Notices of the Royal Astronomical Society 405:1 (2010) 573-592
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.
Eccentricity pumping of a planet on an inclined orbit by a disc
Monthly Notices of the Royal Astronomical Society 404:1 (2010) 409-414