Photon Propagation around Compact Objects and the Inferred Properties of Thermally Emitting Neutron Stars

Anomalous X-ray pulsars, compact nonpulsing X-ray sources in supernova remnants, and X-ray bursters are three distinct types of sources for which there are viable models that attribute their X-ray spectra to thermal emission from the surface of a neutron star. Inferring the surface area of the emitting regions in such systems is crucial in assessing the viability of different models and in providing bounds on the radii of neutron stars. We show that the spectroscopically inferred areas of the emitting regions may be over- or underestimated by a factor of ≲2, because of the three-dimensional geometry of the system and general relativistic light deflection, combined with the effects of phase averaging. Such effects make the determination of neutron star radii uncertain, especially when compared to the ~5% level required for constraining the equation of state of neutron star matter. We also note that, for a given spectral shape, the inferred source luminosities and pulse fractions are anticorrelated because they depend on the same properties of the emitting regions, namely, their sizes and orientations. As a result, brighter sources have on average weaker pulsation amplitudes than fainter sources. We argue that this property can be used as a diagnostic tool in distinguishing between different spectral models. As an example, we show that the high inferred pulse fraction and brightness of the pulsar RXS J1708-40 are inconsistent with isotropic thermal emission from a neutron star surface. Finally, we discuss the implication of our results for surveys in the soft X-rays for young, cooling neutron stars in supernova remnants and show that the absence of detectable pulsations from the compact source at the center of Cas A (at a level of ≳30%) is not a strong argument against its identification with a spinning neutron star.