Minimum magnetic-equilibrium spin period 2026-10-20
With magnetic spin equilibrium at the magnetospheric truncation radius, at fixed mass. Inserting the surface accretion Eddington rate changes the radius power to . The relation assumes the boundary remains outside the star; very weak fields instead encounter surface-accretion and mass-shedding limits.
Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 321 1 d Solution Created 2026-10-03 Updated 2026-10-05
The magnetic torque transfers angular momentum from the faster rotator to the slower one. When , the neutron star supplies angular momentum to the inner accretion disk and possible propeller flow, so it tends to spin down. When the inner accretion disk rotates faster than the star, the magnetic connection and accreted angular momentum tend to spin it up.
For slowly varying mass accretion rate and magnetic dipole moment, these tendencies favour a magnetic spin equilibrium with the corotation radius near the magnetospheric truncation radius:The precise balance depends on accreted and ejected angular momentum and on the extent of magnetic coupling across the accretion disk; corotation is a scaling estimate, not an exact zero-torque theorem.