The theory of spectral formation during the explosion and contraction
stages of X-ray bursters, which include the effects of Comptonization
and free-free absorption and emission, is described. Analytical expres
sions are provided for color ratios, and the spectral shape is given a
s a function of input parameters, elemental abundance, neutron star ma
ss and radius, and Eddington ratio. An Eulerian calculation is used to
determine the photospheric evolution accurately during the Eddington
luminosity phase. The developed analytical theory for hydrodynamics of
the expansion takes into account the dependence of Compton scattering
opacity on electron temperature. An analytic expression is derived fr
om the sonic point position and the value of the sonic velocity. Using
this value as a boundary condition at the sonic point, the velocity,
density, and temperature profile are calculated throughout the whole p
hotosphere. It is shown that the atmosphere radiates spectra having a
low-energy power-law shape and blackbody-like hard tail. In the expans
ion stage the spectra depend strongly on the temperature of the helium
-burning zone at the neutron star surface. The X-ray photospheric radi
us increases to approximately 100 km or more, depending on the conditi
on of the nuclear burning on the surface of the neutron star in the co
urse of the expansion.