Prospects for measuring neutron-star masses and radii with X-ray pulse profile modeling

Modeling the amplitudes and shapes of the X-ray pulsations observed from hot, rotating neutron stars provides a direct method for measuring neutron-star properties. This technique constitutes an important part of the science case for the forthcoming NICER and proposed LOFT X-ray missions. In this paper, we determine the number of distinct observables that can be derived from pulse profile modeling and show that using only bolometric pulse profiles is insufficient for breaking the degeneracy between inferred neutron-star radius and mass. However, we also show that for moderately spinning (300-800 Hz) neutron stars, analysis of pulse profiles in two different energy bands provides additional constraints that allow a unique determination of the neutron-star properties. Using the fractional amplitudes of the fundamental and the second harmonic of the pulse profile in addition to the amplitude and phase difference of the spectral color oscillations, we quantify the signal-to-noise ratio necessary to achieve a specified measurement precision for neutron star radius. We find that accumulating 10⁶ counts in a pulse profile is sufficient to achieve a ≲ 5% uncertainty in the neutron star radius, which is the level of accuracy required to determine the equation of state of neutron-star matter. Finally, we formally derive the background limits that can be tolerated in the measurements of the various pulsation amplitudes as a function of the system parameters.