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

Abstract: We present \texttt{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. \texttt{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, \texttt{ethraid} optimizes computational efficiency with minimal reduction in accuracy. \texttt{ethraid} uses importance sampling to efficiently explore the often broad posteriors that arise from partial orbits. The core computations of \texttt{ethraid} are implemented in Cython for speed. We validate \texttt{ethraid}'s performance by using it to constrain the masses and separations of the planetary companions to HD 117207 and TOI-1694. We designed \texttt{ethraid} to be both fast and simple, and to give broad, "quick look" constraints on companion parameters using minimal data. \texttt{ethraid} is pip installable and available on Github.