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

## TL;DR

This paper examines the Barrow-Gibbons conjecture relating magnetic moments and angular momentum of neutron stars, suggesting that high multipole fields and external torques may resolve existing tensions with observed magnetar parameters.

## Contribution

It proposes that considering higher multipole magnetic fields and external torques can reconcile the conjecture with magnetar observations.

## Key findings

- The conjecture implies a maximum magnetic dipole moment constrained by angular momentum.
- High multipole fields and external torques are necessary to explain observed magnetar spin-down rates.
- The tension between the conjecture and magnetar parameters can be alleviated by these considerations.

## Abstract

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, $c\mu/J\sqrt{G}$ 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.