Evidence for Decay of Turbulence by MHD Shocks in Molecular Clouds via CO Emission

We utilize observations of sub-millimeter rotational transitions of CO from a Herschel Cycle 2 open time program ("COPS", PI: J. Green) to identify previously predicted turbulent dissipation by magnetohydrodynamic (MHD) shocks in molecular clouds. We find evidence of the shocks expected for dissipation of MHD turbulence in material not associated with any protostar. Two models fit about equally well: model 1 has a density of 10$^{3}$ cm$^{-3}$, a shock velocity of 3 km s$^{-1}$, and a magnetic field strength of 4 ${\mu}$G; model 2 has a density of 10$^{3.5}$ cm$^{-3}$, a shock velocity of $2$ km s$^{-1}$, and a magnetic field strength of 8 $\mu$G. Timescales for decay of turbulence in this region are comparable to crossing times. Transitions of CO up to $J$ of 8, observed close to active sites of star formation, but not within outflows, can trace turbulent dissipation of shocks stirred by formation processes. Although the transitions are difficult to detect at individual positions, our Herschel-SPIRE survey of protostars provides a grid of spatially-distributed spectra within molecular clouds. We averaged all spatial positions away from known outflows near seven protostars. We find significant agreement with predictions of models of turbulent dissipation in slightly denser (10$^{3.5}$ cm$^{-3}$) material with a stronger magnetic field (24 $\mu$G) than in the general molecular cloud.