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

TL;DR

This paper demonstrates that black holes surrounded by matter, such as scalar condensates, have non-zero tidal Love numbers which can be used with gravitational-wave data to constrain ultralight boson masses across a wide mass range.

Contribution

It introduces the calculation of tidal Love numbers for black holes with scalar condensates and shows how future detectors can use these to measure ultralight boson masses.

Findings

Black holes with matter fields have non-zero TLNs.

Future detectors can constrain ultralight boson masses from $10^{-17}$ to $10^{-13}$ eV.

LISA can measure the tidal deformability of dressed black holes across stellar to supermassive scales.

Abstract

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