Neutron star stiff equation of state derived from cooling phases of the X-ray burster 4U 1724-307

Abstract

Thermal emission during X-ray bursts is a powerful tool to determine neutron star masses and radii, if the Eddington flux and the apparent radius in the cooling tail can be measured accurately, and distances to the sources are known. We propose here an improved method of determining the basic stellar parameters using the data from the cooling phase of long, photospheric radius expansion bursts covering a large range of luminosities. For this purpose, we computed a large set of atmosphere models for burst luminosities varying by two orders of magnitude and for various chemical compositions and surface gravities. We show that the variation of the inverse square root of the apparent blackbody radius with the flux, observed during the photospheric radius expansion burst from 4U 1724-307 located in globular cluster Terzan 2, is entirely consistent with the theoretical expectations of the color-correction factor evolution. Our method allows us to determine both the Eddington flux and the ratio of the stellar apparent radius to the distance much more reliably. We then find a lower limit on the neutron star radius of 13 km, independently of the chemical composition. These results suggest that the matter inside neutron stars is characterized by a stiff equation of state. We also find evidences in favor of hydrogen rich accreting matter and obtain an upper limit to the distance of 7 kpc. Our approach improves the old way of distances determination to X-ray bursters using Eddington fluxes.