Dispersion Across Twelve Decades of Frequency in the Crab Pulsar

The Crab pulsar flashes across the electromagnetic spectrum, from radio waves at hundreds of megahertz to gamma rays above 100 MeV — twelve decades of frequency from one rotating neutron star 2 kpc away. Its dispersion measure of 56.77 pc per cubic centimetre sweeps its radio pulse by 1.35 s between 0.4 and 1.4 GHz, and by 23.6 s across a 0.1 to 10 GHz span, yet after that plasma sweep is removed, its radio and gamma-ray pulse peaks align to within a few tenths of a millisecond. Charging a conservative 0.2 ms residual to any vacuum effect bounds fractional propagation differences across those twelve decades at 9.72e-16. The framework examined here predicts the alignment, because it assigns the entire frequency dependence to the plasma and none to the vacuum; six decades of pulsar timing practice, which this event summarises, support that division. Computed from published data; not a new measurement.