MHD Analysis at Planetary Bow Shocks for Differing Polytropic Indices Across the Shock Layer

Physics – Plasma Physics

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Scientific paper

MHD theory of planetary bow shocks is analyzed for the case of polytropic index variation across the shock layer, so the index γ inside the magnetosheath differs from γ 0 of the solar wind. The Rankine-Hugoniot equations are solved numerically for arbitrary γ 0 and γ. Several cases are analyzed, including the case of an adiabatic condition in the solar wind and an isothermal one in the magnetosheath. The density ratio X of the solar wind plasma to plasma just inside the bow shock varies widely from a factor of over 10 for γ at low values just above 1, down to near 1 for switch-on roots at very low Alfven Mach numbers MA close to 1. Changes in γ cause much greater changes in the shock characteristics of equivalent roots than changes in γ _0. Furthermore, these changes are particularly prominent when γ is close to 1, with the morphology of the γ =1 solutions different than for γ>1. Analysis also indicates that a conceivable value of γ > γ 0 (not observed) is inconsistent with the presence of a bow shock, leading to the conjecture that γ <=γ 0 at all planetary bow shocks at which MHD is valid.

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