On the nature of the flux variability during an expansion stage of a   type I X-ray burst: Constraints on Neutron Star Parameters for 4U 1820-30
  Powerful Type I X-ray burst with strong radial expansion was observed from the low mass X-ray binary 4U 1820-30 with Rossi X-ray Timing Explorer on May 2,   1997. We investigate closely the flux profile during the burst expansion stage. Applying a semi-analytical model we are able to uncover the behavior of a photospheric radius and to simulate the evolution of neutron star (NS)-accretion disk system. The bottom flux L_{bot} is a few times the Eddington limit L_{Edd} for outer layers, because the electron cross-section is a few times less than the Thomson cross-section at such a high temperatures. The surplus of energy flux with respect to the Eddington, $L_{bot}-L_{Edd}$, goes into the potential energy of the expanded envelope. As cooling of the burning zone starts the surplus decreases and thus the envelope shrinks while the emergent photon flux stays the same $L=L_{Edd}$. At a certain moment the NS low-hemisphere, previously screened by the disk, becomes visible to the observer. Consequently, the flux detected by the observer increases. Indeed, we observe to the paradoxical situation when the burning zone cools, but the apparent flux increases because of the NS-accretion disk geometry. We demonstrate a strong observational evidence of NS-accretion disk occultation in the behavior of the observed bolometric flux. We estimate the anisotropy due to geometry and find that the system should have a high inclination angle. Finally, we apply an analytical model of X-ray spectral formation in the neutron star atmosphere during burst decay stage to infer the neutron star (NS) mass-radius relation. 
Nickolai Shaposhnikov and Lev Titarchuk