A coplanar circumbinary protoplanetary disk in the TWA 3 triple M dwarf system

We present sensitive ALMA observations of TWA~3, a nearby, young ($\sim$10 Myr) hierarchical system composed of three pre-main sequence M3--M4.5 stars. For the first time, we detected ${}^{12}$CO and ${}^{13}$CO $J$=2-1 emission from the circumbinary protoplanetary disk around TWA~3A. We jointly fit the protoplanetary disk velocity field, stellar astrometric positions, and stellar radial velocities to infer the architecture of the system. The Aa and Ab stars ($0.29\pm0.01\,M_\odot$ and $0.24\pm0.01\,M_\odot$, respectively) comprising the tight ($P=35$ days) eccentric ($e=0.63\pm0.01$) spectroscopic binary are coplanar with their circumbinary disk (misalignment $< 6^{\circ}$ with 68% confidence), similar to other short-period binary systems. From models of the spectral energy distribution, we found the inner radius of the circumbinary disk ($r_\mathrm{inner} = 0.50 - 0.75$ au) to be consistent with theoretical predictions of dynamical truncation $r_\mathrm{cav}/a_\mathrm{inner} \approx 3$. The outer orbit of the tertiary star B ($0.40\pm0.28\,M_\odot$, $a\sim65 \pm 18$ au, $e=0.3\pm0.2$) is not as well constrained as the inner orbit, however, orbits coplanar with the A system are still preferred (misalignment $ < 20^{\circ}$). To better understand the influence of the B orbit on the TWA 3A circumbinary disk, we performed SPH simulations of the system and found that the outer edge of the gas disk ($r_\mathrm{outer}=8.5\pm0.2$ au) is most consistent with truncation from a coplanar, circular or moderately eccentric orbit, supporting the preference from the joint orbital fit.