JOYS$+$: A JWST/MIRI survey of the evolution of H$_2$ winds and jets from low-mass protostars
Protostellar outflows display wide-angle winds and collimated jets, the magnetocentrifugal launching of which enables accretion onto the protostar. The majority of the outflow mass is likely ejected or entrained molecular H$_2$, which can now be studied in unprecedented detail with JWST. Using JWST MIRI/MRS observations towards 13 single and 20 multiple Class 0 and I protostars, we investigate the nature and evolution of the H$_2$ wind and jet morphology, mass outflow rate, and velocity and temperature structure. We construct line flux and velocity maps of the H$_2$ S(1) and S(7) lines as well as the sub-mm CO traced by ALMA. Low-$J$ ($J\le4$) H$_2$ transitions trace extended wide-angle, low-velocity (0-20 km s$^{-1}$) winds within the contours of the low-velocity ($< 30$ km s$^{-1}$) sub-mm CO emission, while high-$J$ ($J >5$) transitions are associated with shocks and knots. In Class 0 sources with a known high-velocity ($> 30$ km s$^{-1}$) molecular CO or SiO jet, higher H$_2$ velocities are found along the jet axis. The opening angle of the wind traced by the H$_2$ S(1) line broadens from $\sim20^\circ$ to $\sim90^\circ$ through the Class 0 to Class I stage. Near the base of each blue-shifted outflow lobe, we extract representative spectra, where rotation diagram fitting of the H$_2$ lines is combined with the outflow width and H$_2$ line velocity to measure the mass-loss rates. The rotation diagrams show a warm $\sim 600$ K, component with two orders of magnitude more mass than the hot, 1500-3000 K component. The H$_2$ outflow mass-loss rates decline by two orders of magnitude from the Class 0 to Class II stage and are correlated with bolometric luminosity. The declining warm H$_2$ mass loss rates and increasing opening angles from the Class 0 to I stages, and the absence of H$_2$ jets in the Class I sources, are consistent with the predictions of MHD disk wind models.