Pairwise tidal equilibrium states and the architecture of extrasolar planetary systems
Abstract
Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order m_{p} ̃ 10 M_{⊕}. Motivated by the observational sample, this paper determines the tidal equilibrium states for this class of extrasolar planetary systems. We start by considering twoplanet systems with fixed orbital spacing and variable mass ratios. The basic conjecture explored in this paper is that the planet formation process will act to distribute planetary masses in order to achieve a minimum energy state. The resulting minimum energy configuration  subject to the constraint of constant angular momentum  corresponds to circular orbits confined to a plane, with nearly equal planetary masses (as observed). We then generalize the treatment to include multiple planet systems, where each adjacent pair of planets attains its (local) tidal equilibrium state. The properties of observed planetary systems are close to those expected from this pairwise equilibrium configuration. In contrast, observed systems do not reside in a global minimum energy state. Both the equilibrium states of this paper and observed multiplanet systems, with planets of nearly equal mass on regularly spaced orbits, have an effective surface density of the form σ ∝ r^{2}, much steeper than most disc models.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 2019
 DOI:
 10.1093/mnras/stz1832
 arXiv:
 arXiv:1907.00915
 Bibcode:
 2019MNRAS.488.1446A
 Keywords:

 planets and satellites: dynamical evolution and stability;
 planetary systems;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 18 pages, 5 figures, accepted to MNRAS