A double dipole geometry for PSR~J0740+6620

Abstract: Millisecond pulsars are known to show complex radio pulse profiles and polarisation position angle evolution with rotational phase. Small scale surface magnetic fields and multipolar components are believed to be responsible for this complexity due to the radiation mechanisms occurring close to the stellar surface but within the relatively small light-cylinder compared to the stellar radius. In this work, we use the latest NICER phase aligned thermal X-ray pulse profile of PSR~J0740+6620 combined with radio and $\gamma$-ray pulse profiles and radio polarisation to deduce the best magnetic field configuration that can simultaneously reproduce the light-curves in these respective bands. We assume a polar cap model for the radio emission and use the rotating vector model for the associated polarisation, a striped wind model for the $\gamma$-ray light-curves and rely on the NICER collaboration results for the hot spot geometry. We demonstrate that an almost centred dipole can account for the hot spot location with a magnetic obliquity of $\alpha \approx 51 \deg$ and a line of sight inclination angle of $\zeta \approx 82 \deg$. However, with this geometry, the hot spot areas are three times too large. We found a better solution consisting of two dipoles located just below the surface in approximately antipodal positions. Our double dipole model is able to reproduce all the salient radio and $\gamma$-ray characteristics of PSR~J0740+6620 including radio polarisation data. A double dipole solution is more flexible than an off-centred dipole because of two independent magnetic axes and could hint at a magnetic field mostly concentrated within the crust and not in the core.