Abstract
The thermal evolution of a hot, dense medium, cooling via neutrino and photon emission, is analyzed. The medium is assumed to be a plane-parallel, semi-infinite atmosphere in hydrostatic equilibrium and initially isothermal. The thermal history of the neutrino photosphere is governed by a nonlinear diffusion equation. At late times the solution of this equation acquires a self-similar form. Since the photon opacity everywhere exceeds the neutrino opacity, the photon flux is significantly below the neutrino flux and can be treated as a small perturbation. The temperature profile, together with the neturino and photon fluxes, are obtained as functions of depth and time by a combination of numerical and analytic calculations. Key results are summarized by a convenient set of compact, closed-form similarity formulae. These are employed to examine the cooling of a young neutron star during the first approx.15 s of its lifetime, when the star is hot, optically thick to photons and neutrinos, and quasi-static out to the neutrino photosphere.
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