Signatures of resonant terrestrial planets in long-period systems

TL;DR

This paper explores how to detect low-mass planets in 2:1 resonance with larger planets by analyzing orbital period variations in long-period systems, providing analytical tools for such detection.

Contribution

It introduces simple analytical expressions for libration period and orbital period change, enabling the estimation of a companion planet's mass and eccentricity from observational data.

Findings

Detection of low-mass resonant planets is feasible through orbital period modulation analysis.

The derived expressions are valid for arbitrary eccentricities and planet masses.

System proximity to exact resonance affects the detectability of period variations.

Abstract

The majority of extrasolar planets discovered to date have significantly eccentric orbits, some if not all of which may have been produced through planetary migration. During this process, any planets interior to such an orbit would therefore have been susceptible to resonance capture, and hence may exhibit measurable orbital period variations. Here we summarize the results of our investigation into the possibility of detecting low-mass planets which have been captured into the strong 2:1 resonance. Using analytical expressions together with simulated data we showed that it is possible to identify the existence of a low-mass companion in the internal 2:1 resonance by estimating the time-dependant orbital period for piecewise sections of radial velocity data. This works as long as the amplitude of modulation of the orbital period is greater than its uncertainty, which in practice means that the system should not be too close to exact resonance. Here we provide simple expressions for the libration period and the change in the observed orbital period, these being valid for arbitrary eccentricities and planet masses. They in turn allow one to constrain the mass and eccentricity of a companion planet if the orbital period is sufficiently modulated.