Tidal Evolution of Close-in Extra-Solar Planets

TL;DR

This study models the coupled tidal evolution of eccentricity and semi-major axis in close-in exoplanets, revealing that tides significantly shaped their current orbits and that initial conditions differ from present observations.

Contribution

It introduces integrated coupled tidal evolution equations considering both planetary and stellar tides, providing improved estimates of tidal dissipation parameters and initial orbital configurations.

Findings

Most close-in planets had larger initial semi-major axes.

Tidal dissipation parameters are around 10^5.5 for stars and 10^6.5 for planets.

Current small semi-major axes result from gradual tidal evolution over planetary lifetimes.

Abstract

The distribution of eccentricities e of extra-solar planets with semi-major axes a > 0.2 AU is very uniform, and values for e are relatively large, averaging 0.3 and broadly distributed up to near 1. For a < 0.2 AU, eccentricities are much smaller (most e < 0.2), a characteristic widely attributed to damping by tides after the planets formed and the protoplanetary gas disk dissipated. Most previous estimates of the tidal damping considered the tides raised on the planets, but ignored the tides raised on the stars. Most also assumed specific values for the planets' poorly constrained tidal dissipation parameter Qp. Perhaps most important, in many studies, the strongly coupled evolution between e and a was ignored. We have now integrated the coupled tidal evolution equations for e and a over the estimated age of each planet, and confirmed that the distribution of initial e values of close-in planets matches that of the general population for reasonable Q values, with the best fits for stellar and planetary Q being ~10^5.5 and ~10^6.5, respectively. The accompanying evolution of a values shows most close-in planets had significantly larger a at the start of tidal migration. The earlier gas disk migration did not bring all planets to their current orbits. The current small values of a were only reached gradually due to tides over the lifetimes of the planets. These results may have important implications for planet formation models, atmospheric models of "hot Jupiters", and the success of transit surveys.