2020ApJ...899..139M

We develop a new method to measure neutron star (NS) parameters and derive constraints on the equation of state (EoS) of dense matter by fitting the frequencies of simultaneous quasi-periodic oscillation (QPO) modes observed in the X-ray flux of accreting NSs in low-mass X-ray binaries. To this aim, we calculate the fundamental frequencies of geodesic motion around rotating NSs based on an accurate general-relativistic approximation for their external spacetime. Once the fundamental frequencies are related to the observed frequencies through a QPO model, they can be fit to the data to obtain estimates of the three parameters describing the spacetime, namely the NS mass, angular momentum and quadrupole moment. From these parameters we derive information on the NS structure and EoS. We present a proof of principle of our method applied to pairs of kHz QPO frequencies observed from three systems (4U1608-52, 4U0614+09, and 4U1728-34). We identify the kHz QPOs with the azimuthal and the periastron precession frequencies of matter orbiting the NS, and via our Bayesian inference technique we derive constraints on the neutrons stars' masses and radii. This method is applicable to other geodesic-frequency-based QPO models.