Mathematics – Probability
Scientific paper
Jan 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phdt........81s&link_type=abstract
Thesis (PH.D.)--THE UNIVERSITY OF ROCHESTER, 1990.Source: Dissertation Abstracts International, Volume: 51-03, Section: B, page:
Mathematics
Probability
8
Scientific paper
We have calculated a new hydrogen equation of state (EOS) for low mass stars, substellar objects (brown dwarfs), and giant planets. The resulting tables of thermodynamic quantities cover the ranges 2.1 <=q log T (K) <=q 7.06 and - 6 <=q log rho (g/cm^3) <=q 3.75. All thermodynamic variables are derived from a Helmholtz free energy model for a mixture of atoms (H), molecules (H_2), protons, and electrons. This free energy is obtained by combining separate models for: (1) the dense atomic and molecular fluid and (2) the fully ionized plasma. In our free energy model for the atomic and molecular mixture, we use realistic potentials for the non-ideal interactions between particles. These are computed using a modified fluid perturbation theory which reproduces the results of Monte Carlo simulations to within 3%. The effect of these interactions on the internal levels of bound species is treated with a recently developed occupation probability formalism. The resulting EOS is in excellent agreement with high-pressure laboratory measurements. In the fully ionized regime, the non-ideal effects of the polarizable, strongly coupled plasma are evaluated in the framework of the semi-analytical hypernetted chain theory. The response of the strongly correlated electron gas, including exchange and correlation effects, is calculated for any degree of degeneracy in the linear response approximation. The resulting thermodynamics agree with Monte Carlo simulations to better than 1%. In the high-temperature, low-density domain, electrons and protons form a weakly coupled classical plasma. In this regime, we use the so-called Two Component Plasma model. The neutral and ionized models are combined, and the interaction between charged and neutral species is described, with a screened polarization potential. The combined model provides a description of both temperature - and pressure-ionization. In particular, our free energy model predicts a first-order "plasma phase transition" (PPT) between a neutral, insulating phase and a partially ionized, conducting phase in the regime of pressure ionization. We give both the coexistence curve and the critical point (Tc = 15300 K, P c = 0.614 Mbar, and rhoc = 0.347 g/cm ^3) for the PPT. Tables of thermodynamic quantities from our EOS are available upon request.
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