Multi-wavelength emission in resistive pulsar magnetospheres

Context. Neutron star magnetospheres are well described in the two extreme cases of a vacuum field and a plasma-filled force-free regime. However, neither of these descriptions allows for magnetic field dissipation into particle kinetic energy and thus high-energy radiation. Some physical processes must be invoked to produce observational signatures typical of pulsars. Aims. In this paper, we compute a full set of neutron star magnetosphere structures from the basic vacuum regime to the dissipation-less force-free regime by implementing a resistive prescription for the plasma. A comparison to the radiation reaction limit is also discussed. We investigated the impact of these resistive magnetospheres on the multi-wavelength emission properties based on the polar cap model for radio wavelengths, the slot gap model for X-rays, and the striped wind model for γ -rays. Methods. We performed time-dependent pseudo-spectral simulations of the full Maxwell equations including a resistive Ohm’s law. We deduced the polar cap shape and size, the Poynting flux, the magnetic field structure, and the current sheet surface, depending on magnetic obliquity χ and conductivity σ . Results. We found that the geometry of the magnetosphere close to the stellar surface is not impacted by the amount of resistivity. Polar cap rims remain very similar in shape and size. However, the Poynting flux varies significantly, as well as the magnetic field sweep-back in the vicinity of the light cylinder. This bending of field lines reflects in the γ -ray pulse profiles, changing the γ -ray peak separation Δ as well as the time lag δ between the radio pulse and γ -ray peaks. X-ray pulse profiles are also drastically affected by resistivity. Conclusions. A full set of multi-wavelength light curves can be compiled for future comparison with the third γ -ray pulsar catalogue. This systematic study will help constrain the amount of magnetic energy that flows into particle kinetic energy and is shared by radiation.