http://arxiv.org/abs/1409.5525
Techniques to model the interior of planets are varied. We introduce a new approach to a century old assumption which enhances not only planetary interior calculations but also solar models and high pressure material physics. Our methodology uses the polytrope assumption which was used to model main sequence and white dwarf stars by Eddington. A polytrope is a simple structural assumption between a material’s pressure and volume, $PV^n = C$, where $C$ is a constant and $n$ is the polytrope index. We derive that the polytropic index is the derivative of the bulk modulus with respect to pressure. We then augment the theory by including a variable polytrope index which produces a high quality universal equation of state, within the confines of the Lane-Emden differential equation, making it a robust tool with the potential for excellent predictive power. Unlike most previous equations of state, which have pressure as the dependent variable, the theoretical foundation of our equation of state is the same elastic observable which we found equivalent to the polytrope index. We calculate the density-pressure of six common materials up to $10^{18}$ Pa, mass-radius relationships for the same materials, and produce plausible density-radius models for Mars, Jupiter, and Uranus. An examination of the diversity exhibited by universal equations of state follows, specifically how they functionally negotiate the pressure derivative of the bulk modulus. We analyze the potential of our model using planet Earth, our best static laboratory, ascertaining the ability of our model to include temperature. We end by constraining the material surface observables for the inner core, outer core, and mantle of planet Earth.
S. Weppner, J. McKelvey, K. Thielen, et. al.
Mon, 22 Sep 14
36/47
Comments: 29 pages, 7 figures, 6 tables. To be submitted