X-ray light curves from realistic polar cap models: Inclined pulsar magnetospheres and multipole fields

Thermal X-ray emission from rotation-powered pulsars is believed to originate from localized 'hotspots' on the stellar surface occurring where large-scale currents from the magnetosphere return to heat the atmosphere. Light-curve modelling has primarily been limited to simple models, such as circular antipodal emitting regions with constant temperature. We calculate more realistic temperature distributions within the polar caps, taking advantage of recent advances in magnetospheric theory, and we consider their effect on the predicted light curves. The emitting regions are non-circular even for a pure dipole magnetic field, and the inclusion of an aligned magnetic quadrupole moment introduces a north-south asymmetry. As the quadrupole moment is increased, one hotspot grows in size before becoming a thin ring surrounding the star. For the pure dipole case, moving to the more realistic model changes the light curves by 5-10 per cent for millisecond pulsars, helping to quantify the systematic uncertainty present in current dipolar models. Including the quadrupole gives considerable freedom in generating more complex light curves. We explore whether these simple dipole+quadrupole models can account for the qualitative features of the light curve of PSR J0437−4715.