Measurement of neutron star parameters: a review of methods for low-mass X-ray binaries

Measurement of at least three independent parameters, for example, mass, radius and spin frequency, of a neutron star is probably the only way to understand the nature of its supranuclear core matter. Such a measurement is extremely difficult because of various systematic uncertainties. The lack of knowledge of several system parameter values gives rise to such systematics. Low-mass X-ray binaries, which contain neutron stars, provide a number of methods to constrain the stellar parameters. Joint application of these methods has a great potential to significantly reduce the systematic uncertainties, and hence to measure three independent neutron star parameters accurately. Here we review the methods based on (1) thermonuclear X-ray bursts; (2) accretion-powered millisecond-period pulsations; (3) kilohertz quasi-periodic oscillations; (4) broad relativistic iron lines; (5) quiescent emissions; and (6) binary orbital motions.