Measurement of Vorticity in Interstellar Turbulence

Vorticity is a crucial aspect of turbulence in all fluids. Vortices may be considered as a “basis” for excitations in a turbulent fluid, and they play a crucial role in formation of the turbulent cascade via the process of vortex stretching. Measurement of vorticity in the turbulence of the interstellar medium is extremely important, but would seem to be impossible. Specification of vorticity requires knowledge of the spatial dependence of all three velocity components in all three spatial coordinates, which is unavailable in astronomical observations. Nonetheless, Raymond et al (ApJ 894,108,2020) present a compelling case for vorticity in the post-shock flow in the Cygnus Loop supernova remnant. To judge the credibility of astronomical spectroscopic retrievals of vorticity, I consider the idealized case of a model vortex, calculate the emission spectrum for various lines of sight through the vortex, and “retrieve” an estimate of the vorticity which can be compared with the true value. The analysis gives an accurate value in this idealized case, which encourages further observational efforts to measure vorticity. However, a (probably unphysical) potential flow field can be constructed which also yields an observational signature indicating the presence of vorticity. The retrieval of vorticity in a fluid from astronomical spectroscopic measurements is rendered vastly more difficult in the realistic case of a fully turbulent fluid with multiple vortices along the line of sight. Further insight into this interesting topic could be obtained by using archived results from high performance numerical calculations of turbulent fluids.