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

We characterize the LHS 1610 system, a nearby (\(d=9.7\) pc) M5 dwarf hosting a brown dwarf in a \(10.6\) day, eccentric (\(e \sim 0.37\)) orbit. A joint fit of the available Gaia two-body solution, discovery radial velocities (RVs) from TRES, and new RVs obtained with the Habitable-zone Planet Finder, yields an orbital inclination of \(117.2\pm0.9^\circ\) and a mass constraint of \(50.9\pm0.9\) M\(_J\). This gives LHS 1610 b the second most precise mass of brown dwarfs orbiting M stars within 25pc. We highlight a discrepancy between the Gaia two-body solution eccentricity (\(e=0.52 \pm 0.03\)) and that from the RVs (\(e=0.3702\pm0.0003\)), which requires the astrometric time-series release (Gaia DR4) for further diagnostics. With a flare rate of \(0.28\pm 0.07\) flares/day from TESS photometry, and a rotation period of \(84 \pm 8\) days, LHS 1610 joins other mid M stars -- including Proxima Centauri and YZ Ceti -- as nearby mid M dwarfs with flare rates on the higher end for their long rotation periods. These stars are promising candidates for searching for sub-Alfvénic star-companion interactions, raising the question whether LHS 1610 b could be driving the flares on its host star. However, the available TESS photometry is insufficient to confirm or rule out any orbital phase-dependence of the flares. We show that the LHS 1610 system, as a nearby mid M star with a large, short-period companion, is a promising target to look for evidence of star-companion interactions or aural emission from the brown dwarf at radio wavelengths.