Visual Orbits of Wolf-Rayet Stars I: The Orbit of the dust-producing Wolf-Rayet binary WR\,137 measured with the CHARA Array

Classical Wolf-Rayet stars are the descendants of massive OB stars that have lost their hydrogen envelopes and are burning helium in their cores prior to exploding as type Ib/c supernovae. The mechanisms for losing their hydrogen envelopes are either through binary interactions or through strong stellar winds potentially coupled with episodic mass-loss. Amongst the bright classical WR stars, the binary system WR\,137 (HD\,192641; WC7d + O9e) is the subject of this paper. This binary is known to have a 13-year period and produces dust near periastron. Here we report on interferometry with the CHARA Array collected over a decade of time and providing the first visual orbit for the system. We combine these astrometric measurements with archival radial velocities to measure masses of the stars of $M_{\rm WR} = 9.5\pm3.4 M_\odot$ and $M_{\rm O} = 17.3\pm 1.9 M_\odot$ when we use the most recent \textit{Gaia} distance. These results are then compared to predicted dust distribution using these orbital elements, which match the observed imaging from \textit{JWST} as discussed recently by Lau et al. Furthermore, we compare the system to the BPASS models, finding that the WR star likely formed through stellar winds and not through binary interactions. However, the companion O star did likely accrete some material from the WR's mass-loss to provide the rotation seen today that drives its status as an Oe star.