The maximum dipole moments of neutron stars implied by the Barrow-Gibbons conjecture

The maximum magnetic moment to angular momentum conjecture, recently posed by Barrow & Gibbons, is in tension with the generally accepted parameters of magnetars. According to the conjecture the dimensionless Schuster-Wilson-Blacket number, $c\mu \mathrm{/}J\sqrt{G}$ where $\mu$ is the magnetic moment and $J$ is the angular momentum, should be of order unity. A resolution is to assume that not only the low-magnetic field magnetars, but all magnetars have their super-critical fields in the higher multipoles. This requires the presence of external torques other than the magnetic dipole torque, such as from fallback disks or winds, on these systems to yield the measured high spin-down rates.