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 fromthe 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 expansionstage. Applying a semi-analytical model we are able to uncover the behavior ofa photospheric radius and to simulate the evolution of neutron star(NS)-accretion disk system. The bottom flux L_{bot} is a few times theEddington limit L_{Edd} for outer layers, because the electron cross-section isa 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 theburning zone starts the surplus decreases and thus the envelope shrinks whilethe emergent photon flux stays the same $L=L_{Edd}$. At a certain moment the NSlow-hemisphere, previously screened by the disk, becomes visible to theobserver. Consequently, the flux detected by the observer increases. Indeed, weobserve to the paradoxical situation when the burning zone cools, but theapparent flux increases because of the NS-accretion disk geometry. Wedemonstrate a strong observational evidence of NS-accretion disk occultation inthe behavior of the observed bolometric flux. We estimate the anisotropy due togeometry and find that the system should have a high inclination angle.Finally, we apply an analytical model of X-ray spectral formation in theneutron star atmosphere during burst decay stage to infer the neutron star (NS)mass-radius relation.Comment: 15 pages, 3 figures, accepted to ApJ