  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 $\langle
n_H \rangle = \mathcal{O}(1)$ 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.
