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In the presence of massive bosonic degrees of freedom, rotationalsuperradiance can trigger an instability that spins down black holes. Thisleads to peculiar gravitational-wave signatures and distribution in thespin-mass plane, which in turn can impose stringent constraints on ultralightfields. Here, we demonstrate that there is an analogous spindown effect forconducting stars. We show that rotating stars amplify low frequencyelectromagnetic waves, and that this effect is largest when the time scale forconduction within the star is of the order of a light crossing time. This hasinteresting consequences for dark photons, as massive dark photons would causestars to spin down due to superradiant instabilities. The time scale of thespindown depends on the mass of the dark photon, and on the rotation rate,compactness, and conductivity of the star. Existing measurements of thespindown rate of pulsars place direct constraints on models of dark sectors.Our analysis suggests that dark photons of mass $m_V \sim 10^{-12}$ eV areexcluded by pulsar-timing observations. These constraints also excludesuperradiant instabilities triggered by dark photons as an explanation for thespin limit of observed pulsars.

Superradiance in rotating stars and pulsar-timing constraints on dark photons