Polytropic Index at the Bow Shock Inferred From Density and Field Compression

Data from the Cluster spacecraft obtained during crossings of the earth's bow shock is studied to attempt to obtain a value for the polytropic index γ of the plasma in that region. Specifically, the compression ratio (average downstream density / average upstream density) and magnetic field ratio (average downstream magnetic field / average upstream magnetic field) are found for numerous instances of the shock and then used to determine the polytropic index, through the use of the MHD Rankine-Hugoniot equations. We find that in both cases, the polytropic index is consistent with a value falling in the range 5/3 < γ < 2 over a wide range of Mach numbers.