Rotational corrections to neutron-star radius measurements from thermal spectra

We calculate the rotational broadening in the observed thermal spectra of neutron stars spinning at moderate rates in the Hartle-Thorne approximation. These calculations accurately account for the effects of the second-order Doppler boosts as well as for the oblate shapes and the quadrupole moments of the neutron stars. We find that fitting the spectra and inferring the bolometric fluxes under the assumption that a star is not rotating causes an underestimate of the inferred fluxes and, thus, radii. The correction depends on the stellar spin, mass, radius, and the observer's inclination. For a 10 km, 1.4 M_⊙ neutron star spinning at 600 Hz, the rotational correction to the flux is ∼1%-4%, while for a 15 km neutron star with the same spin period, the correction ranges from 2% for pole-on sources to 12% for edge-on sources. We calculate the inclination-averaged corrections to inferred radii as a function of the neutron-star radius and mass and provide an empirical formula for the corrections. For realistic neutron-star parameters (1.4 M_⊙, 12 km, 600 Hz), the stellar radius is on the order of 4% larger than the radius inferred under the assumption that the star is not spinning.