Ultralight scalar fields around spinning black holes can trigger superradiant instabilities , forming a long-lived bosonic condensate outside the horizon .
We use numerical solutions of the perturbed field equations and astrophysical models of massive and stellar-mass black hole populations to compute , for the first time , the stochastic gravitational-wave background from these sources .
In optimistic scenarios the background is observable by Advanced LIGO and LISA for field masses m _ { s } in the range \sim [ 2 \times 10 ^ { -13 } , 10 ^ { -12 } ] { eV } and \sim 5 \times [ 10 ^ { -19 } , 10 ^ { -16 } ] { eV } , respectively , and it can affect the detectability of resolvable sources .
Our estimates suggest that an analysis of the stochastic background limits from LIGO O1 might already be used to marginally exclude axions with mass \sim 10 ^ { -12.5 } { eV } .
Semicoherent searches with Advanced LIGO ( LISA ) should detect \sim 15 ~ { } ( 5 ) to 200 ~ { } ( 40 ) resolvable sources for scalar field masses 3 \times 10 ^ { -13 } ( 10 ^ { -17 } ) eV .
LISA measurements of massive BH spins could either rule out bosons in the range \sim [ 10 ^ { -18 } , 2 \times 10 ^ { -13 } ] eV , or measure m _ { s } with ten percent accuracy in the range \sim [ 10 ^ { -17 } , 10 ^ { -13 } ] eV .