Distortion of neutron stars with a toroidal magnetic field
  Models of rotating relativistic stars with a toroidal magnetic field have been computed for a sample of eight equations of state of cold dense matter. Non-rotating models admit important levels of magnetization and quadrupole distortion accompanied by a seemingly unlimited growth in size. Rotating models reach the mass-shedding limit at smaller angular velocities than in the non-magnetized case according to the larger circumferential equatorial radius induced by the magnetic field. Moreover, they can be classified as prolate-prolate, oblate-prolate, or oblate-oblate with respect to surface deformation and quadrupole distortion. Simple expressions for surface and quadrupole deformation are provided that are valid up to magnetar field strengths and rapid rotation. 
Joachim Frieben, Luciano Rezzolla
gr-qc astro-ph.SR