Gravitational wave searches for ultralight bosons with LIGO and LISA

Ultralight bosons can induce superradiant instabilities in spinning black holes, tapping their rotational energy to trigger the growth of a bosonic condensate. Possible observational imprints of these boson clouds include (i) direct detection of the nearly monochromatic (resolvable or stochastic) gravitational waves emitted by the condensate, and (ii) statistically significant evidence for the formation of ``holes'' at large spins in the spin versus mass plane (sometimes also referred to as ``Regge plane'') of astrophysical black holes. LIGO could observe a stochastic background of gravitational radiation in the range $m_s\in [2\times 10^{-13}, 10^{-12}]$~eV, and up to $10^4$ resolvable events in a $4$-year search if $m_s\sim 3\times 10^{-13}\,{\rm eV}$. LISA could observe a stochastic background for boson masses in the range $m_s\in [5\times 10^{-19}, 5\times 10^{-16}]$, and up to $\sim 10^3$ resolvable events in a $4$-year search if $m_s\sim 10^{-17}\,{\rm eV}$. LISA could further measure spins for massive black-hole binaries, either ruling out scalar fields in the mass range $\sim [4 \times 10^{-18}, 10^{-14}]$~eV, or measuring $m_s$ with ten percent accuracy if light scalars in the mass range $\sim [10^{-17}, 10^{-13}]$~eV exist.