Application of an empirically-derived polytropic index for the solar wind to a solar wind shock propagation model
Totten, Tracy Lynn
Freeman, John W., Jr.
Doctor of Philosophy
Data from the Helios 1 spacecraft have been used to determine an empirical value for the polytropic index for the free-streaming solar wind. Application of this non-adiabatic polytropic index to a two-dimensional solar wind computer model to simulate the effects of thermal heat conduction has been investigated. The current project involves the insertion of this empirically-derived polytropic index into a magnetohydrodynamic model of solar wind propagation. This computer model is used to predict the time for shocks originating at the Sun to travel to Earth. This information is important for the protection of Earth-orbiting satellites. The model is a two and one-half-dimensional numerical code that solves the magnetohydrodynamic equations using the two-step Lax-Wendroff scheme. The shock jump ratios of the plasma parameters are determined using the Rankine-Hugoniot relations. In addition, the shock model requires a representative background solar wind as an initial condition. The original background solar wind is similar to the results obtained by Parker (Astrophysical Journal, 1958) and Weber and Davis (Astrophysical Journal, 1967). Changes to this initial condition are made by applying the non-adiabatic polytropic index to a three-dimensional, steady-state, magnetohydrodynamic model of the solar wind. The adjustments to the steady-state model produce a background solar wind that compares well to Helios 1 data. This new background solar wind is used as the initial condition for the 2D shock model. The shock model is also adjusted to include the effects of heat conduction. Comparison of model results with observational data indicate that these changes produce average transit times that are only 45 minutes late. Before the changes to the 2D shock model and its initial solar wind condition were made, the average prediction time was two hours late. Adjusting the shock model to include the effects of heat conduction but using the original background solar wind produces an average transit time that is less than one hour early. A few specific events are discussed in greater detail.