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Effects of Spot Size on Neutron-Star Radius Measurements from Pulse Profiles

We calculate the effects of spot size on pulse profiles of moderately rotating neutron stars. Specifically, we quantify the bias introduced in radius measurements from the common assumption that spots are infinitesimally small. We find that this assumption is reasonable for spots smaller than 10$^\circ$-18$^\circ$ and leads to errors that are $\le$10% in the radius measurement, depending on the location of the spot and the inclination of the observer. We consider the implications of our results for neutron star radius measurements with the upcoming and planned X-ray missions NICER and LOFT. We calculate the expected spot size for different classes of sources and investigate the circumstances under which the assumption of a small spot is justified.