The cooling phase of thermonuclear ( type-I ) X-ray bursts can be used to constrain the neutron star ( NS ) compactness by comparing the observed cooling tracks of bursts to accurate theoretical atmosphere model calculations .
By applying the so-called cooling tail method , where the information from the whole cooling track is used , we constrain the mass , radius , and distance for three different NSs in low-mass X-ray binaries 4U 1702 - 429 , 4U 1724 - 307 , and SAX J1810.8 - 260 .
Care is taken to only use the hard state bursts where it is thought that only the NS surface alone is emitting .
We then utilize a Markov chain Monte Carlo algorithm within a Bayesian framework to obtain a parameterized equation of state ( EoS ) of cold dense matter from our initial mass and radius constraints .
This allows us to set limits on various nuclear parameters and to constrain an empirical pressure-density relation for the dense matter .
Our predicted EoS results in NS radius between 10.5 - 12.8 ~ { } \mathrm { km } ( 95 \% confidence limits ) for a mass of 1.4 ~ { } \mathrm { M } _ { \sun } depending slightly on the assumed composition .
Due to systematic errors and uncertainty in the composition these results should be interpreted as lower limits for the radius .