Modelling frequency-dependent tidal deformability for environmental black-hole mergers

Motivated by events in which black holes can lose their environment due to tidal interactions in a binary system, we develop a waveform model in which the tidal deformability interpolates between a finite value (dressed black hole) at relatively low frequency and a zero value (naked black hole) at high frequency. We then apply this model to the example case of a black hole dressed with an ultralight scalar field and investigate the detectability of the tidal Love number with the Einstein Telescope. We show that the parameters of the tidal deformability model could be measured with high accuracy, providing a useful tool to understand dynamical environmental effects taking place during the inspiral of a binary system.