Statistical Study of Magnetic Overshoots at Collisionless Shocks

Abstract

We use data from the Magnetospheric Multiscale, Solar Orbiter, and Cassini spacecraft to statistically study magnetic overshoots at Earth's bow shock, interplanetary shocks, and Saturn's bow shock. The size of the magnetic overshoot exhibits a clear positive correlation with the Alfvénic Mach number and its dependence on the upstream plasma beta is investigated. We present updated empirical relationships from which the Alfvénic Mach number can be estimated using only magnetic field data via measurement of the magnetic overshoot. The magnetic overshoot and Alfvén Mach numbers are compared with a 2D hybrid simulation and previous observations at Saturn's bow shock. The comparison with Saturn displays a slight offset between the data sets. The reason for this offset is discussed and might arise from the different methods of obtaining the Mach numbers. Finally, we explore the possibility of estimating the cross-shock potential with a theoretical expression using each shock's calculated magnetic overshoot, Mach number, and plasma beta.