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 taking account of axion nonlinear self-interaction effects, the decay constant fa must be smaller
than the GUT scale in the mass range 1.1 × 10−12 eV < μ < 2.5 × 10−12 eV. The possibility of observing GWs from invisible isolated BHs is briefly discussed.
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