Limits on surface magnetic fields of fast pulsars

The rapid rotation rate of millisecond pulsar¹ PSR1937+214 suggests that it may be close to the point of rotational instability. Rotational stability implies lower limits on the mass and moment of inertia, and an upper limit on the radius of the rotating neutron star. I show here that if fast pulsars are remnants of galactic bulge X-ray sources^2-4, the limits on the structure of rotating neutron stars, as implied by the requirement of rotational stability, can be used to set limits on the surface dipole magnetic field and the slow-down rate.