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We present a Bayesian method to constrain the masses and radii of neutronstars (NSs) using the information encoded in the X-ray pulse profiles ofaccreting millisecond pulsars. We model the shape of the pulses using "oblateSchwarzschild" approximation, which takes into account the deformed shape ofthe star together with the special and general relativistic corrections to thephoton trajectories and angles. The spectrum of the radiation is obtained froman empirical model of Comptonization in a hot slab in which a fraction of seedblackbody photons is scattered into a power-law component. By using anaffine-invariant Markov chain Monte Carlo ensemble sampling method, we obtainposterior probability distributions for the different model parameters,especially for the mass and the radius. To test the robustness of our method,we first analyzed self-generated synthetic data with known model parameters.Similar analysis was then applied for the observations of SAX J1808.4-3658 bythe Rossi X-ray Timing Explorer (RXTE). The results show that our method canreproduce the model parameters of the synthetic data, and that accurateconstraints for the radius can be obtained using the RXTE pulse profileobservations if the mass is a priori known. For a mass in the range 1.5-1.8Msun, the radius of the NS in SAX J1808.4-3658 is constrained between 9 and 13km. If the mass is accurately known, the radius can be determined with anaccuracy of 5% (68% credibility). For example, for the mass of 1.7 Msun theequatorial radius is Req = 11.9+0.5 -0.4 km. Finally, we show that furtherimprovements can be obtained when the X-ray polarization data from the ImagingX-ray Polarimeter Explorer will become available.

Bayesian parameter constraints for neutron star masses and radii using X-ray timing observations of accretion-powered millisecond pulsars