Axion Superradiance in Dipole Magnetic Fields of Pulsars

We consider constraints on the axion-photon coupling by superradiance due to a plasma instability in the magnetospheres of millisecond pulsars. We compute the growth rate of a superradiant axion cloud in a dipole magnetic field, and give a semi-analytical formula for the superradiance rate for the lowest state. By requiring the associated instability time to be longer than the characteristic age of the supermassive black-widow millisecond pulsar PSR J0952-0607, we examine the pulsar-timing array constraints on axions of mass $\sim 10^{-12}\text{ eV}$. We find that competitive axion bounds from plasma instabilities are unlikely unless a new high spin pulsar is discovered.