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.

Automated summary

The Mach number is a crucial parameter for collisionless shocks, and understanding shock physics requires knowledge of the spatial scales within the shock transition layer. Standard methods for determining the Mach number and spatial scales typically require measuring the magnetic field as well as particle density, velocity, and temperature. However, particle measurements are often unavailable or not properly adjusted to the plasma conditions. This study demonstrates that theoretical arguments can be used to overcome these observational limitations and determine the Mach number and spatial scales of low-Mach number shocks using only magnetic field data.