Probing the string axiverse by gravitational waves from Cygnus X-1

In the axiverse scenario, a massive scalar field (string axion) forms a cloud around a rotating black hole (BH) by superradiant instability and emits continuous gravitational waves (GWs). We examine constraints on the string axion parameters that can be obtained from GW observations. If no signal is detected in a targeted search for GWs from Cygnus X-1 in the LIGO data, the decay constant $f_a$ must be smaller than the GUT scale in the mass range $1.1\times {10}^{-12}\mathrm{e}\mathrm{V}<\mu <2.5\times {10}^{-12}\mathrm{e}\mathrm{V}$. Constraints from invisible isolated BHs are also discussed.