Simulations of the magnetospheres of accreting millisecond pulsars

Accreting pulsars power relativistic jets and display a complex spin phenomenology. These behaviours may be closely related to the large-scale configuration of the star's magnetic field, shaped by its interaction with the surrounding accretion disc. Here, we present the first relativistic simulations of the interaction of a pulsar magnetosphere with an accretion flow. Our axisymmetric simulations treat the magnetospheric, or coronal, regions using a resistive extension of force-free electrodynamics. The magnetic field is also evolved inside the disc, which is a defined volume with a specified velocity field and conductivity profile, found using an α-disc model. We study a range of disc αparameters, thicknesses, magnetic Prandtl numbers and inner truncation radii. We find that a large fraction of the magnetic flux in the pulsar's closed zone is opened by the intrusion of the disc, leading to an enhancement of the power extracted by the pulsar wind and the spin-down torque applied to the pulsar. In our simulations, most of the spin-down contribution to the stellar torque acts on open field lines. The efficiency of field-line opening is high in the simulations' long-term quasi-steady states, which implies that a millisecond pulsar's electromagnetic wind could be strong enough to power the observed neutron-star radio jets, and may significantly affect the pulsar's spin evolution.