We develop a simplified model for studying the long-term evolution of giant planets in protoplanetary discs. The model accounts for the eccentricity evolution of the planets and the dynamics of eccentric discs under the influences of secular planet–disc interactions and internal disc pressure, self-gravity, and viscosity. Adopting the ansatz that the disc precesses coherently with aligned apsides, the eccentricity evolution equations of the planet–disc system reduce to a set of linearized ordinary differential equations, which allows for fast computation of the evolution of planet–disc eccentricities over long time-scales. Applying our model to ‘giant planet + external disc’ systems, we are able to reproduce and explain the secular behaviours found in previously published hydrodynamical simulations. We re-examine the possibility of eccentricity excitation (due to secular resonance) of multiple planets embedded in a dispersing disc, and find that taking into account the dynamics of eccentric discs can significantly affect the evolution of the planets’ eccentricities.
We present a new mechanism of generating large planetary eccentricities. This mechanism applies to planets within the inner cavities of their companion protoplanetary disks. A massive disk with an inner truncation may become eccentric due to nonadiabatic effects associated with gas cooling and can retain its eccentricity in long-lived coherently precessing eccentric modes; as the disk disperses, the inner planet will encounter a secular resonance with the eccentric disk when the planet and the disk have the same apsidal precession rates; the eccentricity of the planet is then excited to a large value as the system goes through the resonance. In this work, we solve the eccentric modes of a model disk for a wide range of masses. We then adopt an approximate secular dynamics model to calculate the long-term evolution of the “planet + dispersing disk” system. The planet attains a large eccentricity (between 0.1 and 0.6) in our calculations even though the disk eccentricity is quite small (≲0.05). This eccentricity excitation can be understood in terms of the mode conversion (“avoided crossing” between two eigenstates) phenomenon associated with the evolution of the “planet + disk” eccentricity eigenstates.
more » « less- PAR ID:
- 10486095
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 956
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 17
- Size(s):
- Article No. 17
- Sponsoring Org:
- National Science Foundation
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