Magnetically threaded thin discs in the presence of the quadrupole magnetic field

Neutron stars might have multipole magnetic fields as implied by recent observations of pulsars. The presence of the quadrupole field might have an effect on the interaction between the disc and the neutron star depending on the location of the inner radius of the disc, and the strength of the quadrupole field. For a quadrudipole stellar field, we calculate the toroidal field generated within the disc, the magnetospheric radius, and the torque exerted on to the star. Also, we deduce the effect of the rotation of the star on the magnetospheric radius which is relevant even for pure dipole magnetic fields.