Energy optimization in extrasolar planetary systems: the transition from peasinapod to runaway growth
Abstract
Motivated by the trends found in the observed sample of extrasolar planets, this paper determines tidal equilibrium states for forming planetary systems  subject to conservation of angular momentum, constant total mass, and fixed orbital spacing. In the low mass limit, valid for superEarthclass planets with masses of order m_{p} ∼ 10 M_{⊕}, previous work showed that energy optimization leads to nearly equal mass planets, with circular orbits confined to a plane. The present treatment generalizes previous results by including the selfgravity of the planetary bodies. For systems with a sufficiently large total mass $m_{\scriptstyle \rm T}$ in planets, the optimized energy state switches over from the case of nearly equal mass planets to a configuration where one planet contains most of the material. This transition occurs for a critical mass threshold of approximately $m_{\scriptstyle \rm T}\gtrsim m_{\scriptstyle \rm C}\sim 40\,{\rm M_\oplus}$ (where the value depends on the semimajor axes of the planetary orbits, the stellar mass, and other system properties). These considerations of energy optimization apply over a wide range of mass scales, from binary stars to planetary systems to the collection of moons orbiting the giant planets in our Solar system.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 April 2020
 DOI:
 10.1093/mnras/staa624
 arXiv:
 arXiv:2002.10661
 Bibcode:
 2020MNRAS.493.5520A
 Keywords:

 planets and satellites: dynamical evolution and stability;
 planetary systems;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 16 pages, 5 figures, accepted for publication in MNRAS