| Summary: | The observed orbits of emission-line stars may be affected by systematics owing to their broad emission lines being formed in complex and extended environments. This is problematic when orbital parameter probability distributions are estimated assuming radial-velocity data are solely comprised of Keplerian motion plus Gaussian white noise, leading to overconfident and inaccurate orbital solutions, with implications for the inferred dynamical masses and hence evolutionary models. We present a framework in which these systems can be meaningfully analysed. We synthesize benchmark data sets, each with a different and challenging noise formulation, for testing the performance of different algorithms. We make these data sets freely available with the aim of making model validation an easy and standardized practice in this field. Next, we develop an application of Gaussian processes to model the radial-velocity systematics of emission-line binaries, named marginalized GP. We benchmark this algorithm, along with current standardized algorithms, on the synthetic data sets and find our marginalized GP algorithm performs significantly better than the standard algorithms for data contaminated by systematics. Finally, we apply the marginalized GP algorithm to four prototypical emission-line binaries: Eta Carinae, GG Carinae, WR 140, and WR 133. We find systematics to be present in several of these case studies; and consequently, the predicted orbital parameter distributions, and dynamical masses, are modified from those previously determined.
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