The MHD Rankine-Hugoniot jump conditions and the terrestrial bow shock: A statistical comparison

We have examined 204 bow shock crossings observed in the magnetic field and plasma data on ISEE-1. Using the measured upstream field and plasma data we calculated the downstream field magnitudes by using the single-fluid MHD Rankine-Hugoniot jump conditions, and compared the results with the observed downstream field magnitudes. We find that on the average, the observed downstream conditions are well approximated by the basic MHD model with a polytropic index of 5 3 provided that the angle between the upstream field and the shock normal is greater than 45°, and the Alfvén Mach number is less than about 10. For angles less than 45°, and for MA ≳ 10, the basic MHD model must be expanded to include additional physical processes to explain the observations.