2002ApJ...567.1077S

We present an analytical theory of thermonuclear X-ray burst atmosphere structure. Newtonian gravity and diffusion approximation are assumed. Hydrodynamic and thermodynamic profiles are obtained as a numerical solution of the Cauchy problem for the first-order ordinary differential equation. We further elaborate a combined approach to the radiative transfer problem that yields the spectrum of the expansion stage of X-ray bursts in an analytical form in which Comptonization and free-free absorption-emission processes are accounted for and τ∼r^–2 opacity dependence is assumed. A relaxation method on an energy opacity grid is used to simulate a radiative diffusion process in order to match the analytical form of the spectrum, which contains the free parameter, to the energy axis. Numerical and analytical results show high similarity. All spectra consist of a power-law soft component and a diluted blackbody hard tail. We derive simple approximation formulae usable for mass-radius determination by observational spectra fitting.