Tidal deformability of dressed black holes and tests of ultralight bosons in extended mass ranges

The deformability of a compact object under the presence tidal perturbation is encoded in Love numbers (TLNs), which vanish for isolated black holes vacuum. We show that TLNs surrounded by matter fields do not and can be used to probe environment around binary holes. In particular, we compute case hole scalar condensate vector perturbations, finding strong power-law behavior TLN terms mass field. Using this result as proxy gravitational future gravitational-wave detectors like Einstein Telescope LISA impose stringent constraints on ultralight bosons due accretion or superradiance. Interestingly, could measure dressed across range from stellar-mass ($\approx 10^2 M_\odot$) supermassive 10^7 objects, providing measurement $(10^{-17} - 10^{-13}) \, {\rm eV}$ with less than $10\%$ accuracy, thus filling gap between other superradiance-driven coming terrestrial space interferometers. Altogether, effects combined 10^{-11}) eV}$.