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Fuzzy dark matter (FDM) consisting of ultra-light axions has been invoked toalleviate galactic-scale problems in the cold dark matter scenario. FDMfluctuations, created via the superposition of waves, can impact the motion ofa central supermassive black hole (SMBH) immersed in an FDM halo. The SMBH willundergo a random walk, induced by FDM fluctuations, that can result in itsejection from the central region. This effect is strongest in dwarf galaxies,accounting for wandering SMBHs and the low detection rate of AGN in dwarfspheroidal galaxies. In addition, a lower bound on the allowed axion masses isinferred both for Sagittarius $A^*$ and heavier SMBH; to avoid ejection fromthe galactic centres, axion masses of the order of $10^{-22}{\rm eV}$ orlighter are excluded. Stronger limits are inferred for merging galaxies. Wefind that the event rate of SMBH mergers in FDM haloes and the associated SMBHgrowth rates can be reduced by at least an order of magnitude.

Ejection of supermassive black holes and implications for merger rates in fuzzy dark matter haloes