The polytropic index for the solar wind at Earth's bow shock

Abstract

Analysis of spacecraft shock‐crossing data on the magnetosheath thickness to determine the polytropic index γ of the solar wind is shown to overestimate the value for γ when the gasdynamic (GD) equations are used for the shock jump. This is done by comparing GD estimates for γ extrapolated from observed data points to values obtained when more appropriate MHD equations are used. As a result of this bias a shock‐crossing data analysis carried out recently using the GD equations appears to have obtained a value for γ that is over 0.5 too large. This is in part associated with the breakdown of GD with respect to nonzero angle between the bow‐shock normal and the magnetic field for finite Alfven Mach numbers. The magnetosonic phenomenological model (sonic Mach number replaced with the magnetosonic Mach number in the GD equations), which was also recently used to determine γ, is found to reduce this bias by 70–90%. This analysis also strongly suggests that the phenomenological model inadequately treats variations in the angle between the bow‐shock normal and the magnetic field, which may also produce systematic errors in the experimental determination of γ using this model.