A 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 photospheric radius expansion bursts covering a large range of luminosities. Because at that phase the blackbody apparent radius depends only on the spectral hardening factor (color-correction), we suggest to fit the theoretical dependences of the color-correction versus flux in Eddington units to the observed variations of the inverse square root of the apparent blackbody radius with the flux. We show that spectral variations observed during a long photospheric radius expansion burst from 4U 1724-307 are entirely consistent with the theoretical expectations for the passively cooling neutron star atmospheres. Our method allows us to determine both the Eddington flux (which is found to be smaller than the touchdown flux by 15%) 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 14 km for masses below 2.2M_sun, independently of the chemical composition. These results suggest that the matter inside neutron stars is characterized by a stiff equation of state. We finally show that the apparent blackbody emitting area in the cooling tails of the short bursts from 4U 1724-307 is two times smaller than that for the long burst and their evolution does not follow the theory. This makes their usage for determination of the neutron star parameters questionable and casts serious doubts on the results of previous works that used for the analysis similar bursts from other sources. [abridged]