Constrains of the axion-like particle from black hole spin superradiance

The mass of the axion-like particles could be constrained by the observed black hole spin distribution. In this work, we update the previous calculations using the recently improved superradiance formula, which is much more accurate. The effect of the merger time scale is also carefully investigated with Bayesian analysis. After integration of the merger time ${\tau }_{\mathrm{M}}$, we find two favoured mass ranges $7.94\times {10}^{-13}\text{ eV}\le \mu \le 8.71\times {10}^{-13}\text{ eV}$ and $1.44\times {10}^{-12}\text{ eV}\le \mu \le 1.74\times {10}^{-12}\text{ eV}$ . These two favored ranges do not depend on the prior distribution of the ${\tau }_{\mathrm{M}}$. We also find the strength of evidence for the range $-12.80\le {\log }_{10}(\mu \mathrm{/}\text{eV})\le -12.34$, which is excluded in the analysis with fixed ${\tau }_{\text{M}}$, could increase by several orders of magnitude with ${\tau }_{\mathrm{M}}$ averaged.