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

We investigate closely the flux profile during the burst expansion stage observed from 4U 1820-30 with the Rossi X- Ray Timing Explorer on 1997 May 2. We are able to uncover the behavior of a photospheric radius and to simulate the evolution of the neutron star (NS) accretion disk system. We argue that although the bolometric luminosity is always the Eddington value L_Edd, the photon flux at the bottom of the expanded envelope can decrease during the expansion stage. In fact, at the initial moment of explosion when the bottom burning temperature is ~2×10^9 K, the bottom flux Lbot is a few times the Eddington limit, because the electron cross section is a few times less than the Thomson cross section at such 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. 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 NS atmosphere during the burst decay stage to infer the NS mass-radius relation.