JWST/MIRI Detection of Molecular H$_2$ Winds from an Edge-on Class II Source HV Tau C

The evolution of protoplanetary disks is regulated by accretion onto the central star and mass loss through jets and winds. While atomic and ionized outflows are commonly observed, molecular winds in evolved Class II disks remain rarely detected. We characterize the spatial, thermal, kinematic, and dynamical properties of molecular hydrogen (H$_2$) emission from the nearly edge-on Class II disk HV Tau C and assess the impact of its molecular wind. We also constrain accretion using H I recombination lines detected in the same mid-infrared spectrum. Using JWST/MIRI-MRS data from the MINDS Cycle 1 GTO program, we analyze spatially resolved pure-rotational H$_2$ emission. Rotational and position-velocity diagrams constrain excitation and kinematics, from which we estimate wind properties. We detect extended H$_2$ emission tracing a wide-angled, biconical molecular wind extending beyond the near-infrared scattered-light disk, ALMA 887 $\mu$m dust continuum, and compact $^{12}$CO ($J=3$-$2$) gas disk. The H$_2$ rotational diagram requires warm ($\sim$600K) and hot ($\sim$2000K) components, similar to those in younger protostars. The gas shows outward motions of a few tens of km s$^{-1}$ and dynamical timescales of tens to hundreds of years. The inferred mass-loss rate is $\sim10^{-8}$ M$_\odot$ yr$^{-1}$, while accretion rates derived from H I lines are $10^{-10}$-$10^{-8}$ M$_\odot$ yr$^{-1}$. The accretion rate may be underestimated because of the edge-on geometry. Our results show that wide-angled molecular H$_2$ winds can persist into the Class II phase, with outflow rates comparable to some protostellar systems, suggesting that such winds may remain important for angular momentum removal, disk evolution, and dispersal. (Abstract modified; see the paper for the full version.)