Tidal Evolution of a Secularly Interacting Planetary System

TL;DR

This paper derives formulae for how tidal dissipation affects the orbital evolution of multi-planet systems through secular interactions, illustrating the process with the CoRoT 7 system.

Contribution

It provides new analytical formulae quantifying the combined effects of semi-major axis changes and eccentricity damping in two-planet systems due to tidal dissipation.

Findings

Derived formulae for orbital evolution due to tidal effects

Application to the CoRoT 7 system example

Enhanced understanding of secular interactions in planetary systems

Abstract

In a multi-planet system, a gradual change in one planet's semi-major axis will affect the eccentricities of all the planets, as angular momentum is distributed via secular interactions. If tidal dissipation in the planet is the cause of the change in semi-major axis, it also damps that planet's eccentricity, which in turn also contributes to the evolution of all the eccentricities. Formulae quantifying the combined effects on the whole system due to semi-major axis changes, as well as eccentricity damping, are derived here for a two-planet system. The CoRoT 7 system is considered as an example.