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Description
In the phenomenon of black hole superradiance a rotating black hole loses its angular momentum to a growing cloud of particles. It has been successfully used to place limits on ultralight particles, such as axions and dark photons, with masses $\mu\sim 10^{-20}-10^{-18}$ eV and $\mu\sim 10^{-12}-10^{-11}$ eV. However, measurements of black hole spins are statistical in nature and have large uncertainties. On the other hand, it has been shown that superradiance occurs also in neutron stars due to an instability in the magnetosphere. A proper treatment has however been lacking, and no bounds analogous to those of black holes have been placed yet. In our work we calculate, for the first time, the superradiance rate and use it to place new bounds on axions of masses $\mu\sim 10^{-12}-10^{-11}$ eV. This is done by requiring that the superradiance-induced spindown not be faster than that observed by pulsar timing arrays. We compare bounds obtained from several millisecond pulsars, including the newly found supermassive pulsar PSR J0952–0607. Finally, we suggest the possibility of other signals from superradiant axion clouds around neutron stars.