Axion and the Supermassive Black Holes at high $z$

Axion dark matter (DM) is studied on the formation of supermassive black holes (SMBHs) at high red shift $z$. It is shown that the attractive self interaction of this DM may solve the tension between the high angular momentum of SMBH and its early time formation. We consider the ultra-light axion DM around $O({10}^{-21})$ eV as its origin, which may also cause nano-Hz stochastic gravitational wave background recently observed.