Spectra of the Expansion Stage of X-Ray Bursts

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 which yields the spectrum of the expansion stage of X-ray bursts in analytical form where Comptonization and free-free absorption-emission processes are accounted for and tau ~ r^{-2} opacity dependence is assumed. Relaxation method on an energy opacity grid is used to simulate radiative diffusion process in order to match analytical form of spectrum, which contains free parameter, to energy axis. Numerical and analytical results show high similarity. All spectra consist of a power-law soft component and diluted black-body hard tail. We derive simple approximation formulae usable for mass-radius determination by observational spectra fitting.