Astrometry and Precise Radial Velocities Yield a Complete Orbital Solution for the Nearby Eccentric Brown Dwarf LHS 1610 b

The LHS 1610 system consists of a nearby ($d=9.7$ pc) M5 dwarf hosting a candidate brown dwarf companion in a $10.6$ day, eccentric ($e \sim 0.37$) orbit. We confirm this brown dwarf designation and estimate its mass ($ 49.5_{-3.5}^{+4.3}$ $M_{\text{Jup}} $) and inclination ($ 114.5^\circ$ $_{-10.0}^{+7.4}$) by combining discovery radial velocities (RVs) from TRES and new RVs from the Habitable-zone Planet Finder with the available Gaia astrometric two-body solution. We highlight a discrepancy between the measurement of the eccentricity from the Gaia two-body solution ($e=0.52 \pm 0.03$) and the RV-only solution ($e=0.3702\pm0.0003$). We discuss possible reasons for this discrepancy, which can be further probed when the Gaia astrometric time series becomes available as part of Gaia DR4. As a nearby mid-M star hosting a massive short-period companion with a well-characterized orbit, LHS 1610 b is a promising target to look for evidence of sub-Alfvénic interactions and/or auroral emission at optical and radio wavelengths. LHS 1610 has a flare rate ($0.28\pm 0.07$ flares/day) on the higher-end for its rotation period ($84 \pm 8$ days), similar to other mid-M dwarf systems such as Proxima Cen and YZ Ceti that have recent radio detections compatible with star-planet interactions. While available TESS photometry is insufficient to determine an orbital phase-dependence of the flares, our complete orbital characterization of this system makes it attractive to probe star-companion interactions with additional photometric and radio observations.