On the Measurement of Vorticity in Astrophysical Fluids

TL;DR

This paper investigates how spectroscopic measurements can estimate vorticity in astrophysical fluids, revealing that such methods may produce misleading results, as non-vortical flows can appear vortical.

Contribution

It demonstrates that spectroscopic pseudovorticity can match true vorticity in vortical flows but also falsely indicates vorticity in irrotational flows, questioning the robustness of such measurements.

Findings

Pseudovorticity aligns with true vorticity in vortical flows.

Pseudovorticity appears nonzero even in irrotational flows.

Spectroscopic methods may not reliably distinguish vorticity presence.

Abstract

Vorticity is central to the nature of, and dynamical processes in turbulence, including turbulence in astrophysical fluids. The results of \cite{Raymond20a,Raymond20b} on vorticity in the post-shock fluid of the Cygnus Loop supernova remnant are therefore of great interest. We consider the degree to which spectroscopic measurements of an optically-thin line, the most common type of astronomical velocimetry, can yield unambiguous measurements of the vorticity in a fluid. We consider an ideal case of observations in the plane of a flow which may or may not contain vorticity. In one case, the flow possesses vorticity in a direction perpendicular to the plane of observations. In the other case, the flow is irrotational (zero vorticity) by construction. The observationally-deduced vorticity (referred to as the {\em pseudovorticity}) is inferred from spatial differences in the line-of-sight component of velocity, and assumptions of symmetry. My principal result is that in the case of the vortical flow, the pseudovorticity is a reasonable match for the true vorticity. However, and importantly, the pseudovorticity in the case of the irrotational flow field is also nonzero, and comparable in magnitude to that for a vortical flow. The conclusion of this paper is that while astronomical spectroscopic observations may yield a good estimate of the vorticity in a remote fluid, the robustness of such an inference cannot be insured.