A New Diagnostic of Magnetic Field Strengths in Radiatively-Cooled Shocks

We show that it is possible to measure Alfv\'enic Mach numbers, defined as the shock velocity in the flow divided by the Alfv\'en velocity, for low-velocity (V$_{shock}$ $\lesssim$ 100 km$\,$s$^{-1}$) radiative shocks. The method combines observations of bright forbidden lines with a measure of the size of the cooling zone, the latter typically obtained from spatial separation between the Balmer emission lines and the forbidden lines. Because magnetic fields become compressed as gas in the postshock region cools, even relatively weak preshock magnetic fields can be detected with this method. We derive analytical formulae that explain how the spatial separations relate to emission-line ratios, and compute a large grid of radiatively-cooled shock models to develop diagnostic diagrams that can be used to derive Alfv\'enic Mach numbers in flows. Applying the method to existing data for a bright knot in the HH 111 jet, we obtain a relatively low Alfv\'enic Mach number of $\sim$ 2, indicative of a magnetized jet that has super-magnetosonic velocity perturbations within it.