Theory Helps Observations: Determination of the Shock Mach Number and Scales From Magnetic Measurements

The Mach number is one of the key parameters of collisionless shocks. Understanding shock physics requires knowledge of the spatial scales in the shock transition layer. The standard methods of determining the Mach number and the spatial scales require simultaneous measurements of the magnetic field and the particle density, velocity, and temperature. While magnetic field measurements are usually of high quality and resolution, particle measurements are often either unavailable or not properly adjusted to the plasma conditions. We show that theoretical arguments can be used to overcome the limitations of observations and determine the Mach number and spatial scales of the low-Mach number shock when only magnetic field data are available.