The effect of interstellar medium on LVK's black holes

Gravitational radiation alone is not efficient in hardening the orbit of a wide binary black hole (BBH). By employing a toy model for the interstellar medium (ISM) surrounding BBHs, here we discuss the effect of this baryonic medium on BBH dynamics. Depending on the BBH's mass, we show that a binary surrounded by an isotropic cold neutral medium (i.e. an asymptotic temperature $T_{\infty } \approx 100$ K) with a time-averaged particle density of $\langle n_\mathrm{ H} \rangle = \mathcal {O}(1)$ cm$^{-3}$ can play a significant role in hardening the binary orbit over a $\mathcal {O}(10^9)$ yr time-scale. Additionally, this causes the black hole's mass to grow at a rate ${\propto} m^2$. We thus discuss the impact of the ISM on the LIGO-Virgo-KAGRA (LVK) observables and quantify the properties of the ISM under which the latter could act as an additional important pathway for driving a subset of LVK's BBH mergers.