Mass Shedding, Observed Spin and the Rotation Rate Implied by the Density Bound in Neutron Stars

The fastest neutron stars rotate hundreds of times per second, close enough to their mass-shedding limit that spin is a real structural constraint. This paper sets three rotation scales side by side: the observed spins of millisecond pulsars up to 716 Hz, the Kepler frequency of 1.650e+03 Hz for a canonical 1.4-solar-mass, 12 km star, and the rotation rate of 2.62e+23 Hz that a star compressed to the neutron-branch density bound could sustain before shedding, on a radius floor of 4.089e-10 m. The record pulsar turns at 4.338e-01 of its shedding rate, while the fractional correction the density bound makes to the shedding rate itself, at a central density of 2.8e18 kg per cubic metre, is 2.88e-40. Rotation constrains neutron star structure through ordinary gravity alone; the bound adds nothing measurable. Simulated, not measured.