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

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