ethraid: A Simple Method for Characterizing Long-period Companions Using Doppler, Astrometric, and Imaging Constraints

Abstract

We present ethraid , an open-source Python package designed to measure the mass ( m _c ) and separation ( a ) of a bound companion from measurements covering a fraction of the orbital period. ethraid constrains m _c and a by jointly modeling radial velocity, astrometric, and/or direct imaging data in a Bayesian framework. Partial orbit data sets, especially those with highly limited phase coverage, are represented well by a few method-specific summary statistics. By modeling these statistics rather than the original data, ethraid optimizes computational efficiency with minimal reduction in accuracy. ethraid uses importance sampling to efficiently explore the often broad posteriors that arise from partial orbits. The core computations of ethraid are implemented in Cython for speed. We validate ethraid 's performance by using it to constrain the masses and separations of the planetary companions to HD 117207 and TOI-1694. We designed ethraid to be both fast and simple, as well as to give broad, “quick look” constraints on companion parameters using minimal data. ethraid is pip installable and available on Zenodo and GitHub.

Keywords

• Exoplanets
• Bayesian statistics
• Brown dwarfs
• Radial velocity
• Astrometry
• Gaia