X-ray burst ignition location on the surface of accreting X-ray pulsars: can bursts preferentially ignite at the hotspot?

Hotspots on the surface of accreting neutron stars have been directly observed via pulsations in the lightcurves of X-ray pulsars. They are thought to occur due to magnetic channelling of the accreted fuel to the neutron star magnetic poles. Some X-ray pulsars exhibit burst oscillations during Type I thermonuclear X-ray bursts which are thought to be caused by asymmetries in the burning. In rapidly rotating neutron stars, it has been shown that the lower gravity at the equator can lead to preferential ignition of X-ray bursts at this location. These models, however, do not include the effect of accretion hotspots at the the neutron star surface. There are two accreting neutron star sources in which burst oscillations have been observed to track exactly the neutron star spin period. We analyse whether this could be due to the X-ray bursts igniting at the magnetic pole of the neutron star, because of heating in the accreted layers under the hotspot causing ignition conditions to be reached earlier. We investigate heat transport in the accreted layers using a 2D model and study the prevalence of heating down to the ignition depth of X-ray bursts for different hotspot temperatures and sizes. We perform calculations for accretion at the pole and at the equator, and infer that ignition could occur away from the equator at the magnetic pole for hotspots with temperature THS & 1× 108 K. However, current observations have not identified such high temperatures in AXPs.