The Orbital Eccentricities of Directly Imaged Companions Using Observable-based Priors: Implications for Population-level Distributions

Abstract

The eccentricity of a substellar companion is an important tracer of its formation history. Directly imaged companions often present poorly constrained eccentricities. A recently developed prior framework for orbit fitting called “observable-based priors” has the advantage of improving biases in derived orbit parameters for objects with minimal phase coverage, which is the case for the majority of directly imaged companions. We use observable-based priors to fit the orbits of 21 exoplanets and brown dwarfs in an effort to obtain the eccentricity distributions with minimized biases. We present the objects’ individual posteriors compared to their previously derived distributions, showing in many cases a shift toward lower eccentricities. We analyze the companions’ eccentricity distribution at a population level, and compare this to the distributions obtained with the traditional uniform priors. We fit a Beta distribution to our posteriors using observable-based priors, obtaining shape parameters α = ${1.09}_{-0.22}^{+0.30}$ and β = ${1.42}_{-0.25}^{+0.33}$ . This represents an approximately flat distribution of eccentricities. The derived α and β parameters are consistent with the values obtained using uniform priors, though uniform priors lead to a tail at high eccentricities. We find that separating the population into high- and low-mass companions yields different distributions depending on the classification of intermediate-mass objects. We also determine via simulation that the minimal orbit coverage needed to give meaningful posteriors under the assumptions made for directly imaged planets is ≈15% of the inferred period of the orbit.

Keywords

• Exoplanet formation
• Brown dwarfs
• Orbit determination
• Orbital elements
• Extrasolar gaseous giant planets
• Bayesian statistics