ethraid: A simple method for characterizing long-period companions using Doppler, astrometric, and imaging constraints

We present $\mathtt{\text{ethraid}}$, 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. $\mathtt{\text{ethraid}}$ constrains $m_c$ and $a$ by jointly modeling radial velocity (RV), astrometric, and/or direct imaging data in a Bayesian framework. Partial orbit data sets, especially those with highly limited phase coverage, are well-represented by a few method-specific summary statistics. By modeling these statistics rather than the original data, $\mathtt{\text{ethraid}}$ optimizes computational efficiency with minimal reduction in accuracy. $\mathtt{\text{ethraid}}$ uses importance sampling to efficiently explore the often broad posteriors that arise from partial orbits. The core computations of $\mathtt{\text{ethraid}}$ are implemented in Cython for speed. We validate $\mathtt{\text{ethraid}}$'s performance by using it to constrain the masses and separations of the planetary companions to HD 117207 and TOI-1694. We designed $\mathtt{\text{ethraid}}$ to be both fast and simple, and to give broad, “quick look” constraints on companion parameters using minimal data. $\mathtt{\text{ethraid}}$ is pip installable and available on Github.