Equation of state in a strong magnetic field: Finite temperature and gradient corrections

We construct the equation of state for condensed matter in a strong magnetic field. We treat the regime for which statistical models and spherical Wigner-Seitz lattice cells are valid approximations. First, the equation of state for a free, nonrelativistic, homogeneous electron gas in a uniform magnetic field is examined as a function of temperature. This treatment is then refined by incorporating Coulomb interactions in a magnetic Thomas-Fermi model which allows for finite temperature. This model is characterized by four distinct length scales: the Bohr radius a₀, the cyclotron radius r_cyc, the thermal de Broglie wavelength λ_T, and the lattice cell radius r₀. Gradient corrections to the zero-temperature equation of state are next evaluated by constructing a magnetic Thomas-Fermi-Dirac-Weizsäcker model. These corrections have a considerable effect on the zero-pressure density for matter in strong magnetic fields. Finally, we integrate the hydrostatic equilibrium equation for the surface structure of a neutron star using our computed equations of state.