than the intrinsic ones.

For LIGO/Virgo, the relevant BBHs are normally in the first case because the signal is typically less than a second but each LIGO/Virgo observing run lasts several weeks to several months. This is why the previous studies found that the gas effect could be discerned in the LIGO/Virgo waveforms (see §\[sec:intro\]). For LISA, however, the majority of the in-band BBHs belong to the latter case because a BBH could dwell in the band for as long as millions of years but the canonical mission duration of LISA is only $4-5$ years. During such a short observing time, $\Gamma$ is almost constant so that discerning the gas effect is more difficult. An overestimation of the mass and distance becomes more likely.

Hydrodynamics versus GW radiation {#sec:compare}
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To evaluate the efficiency of the hydrodynamical drag, we compare the GW radiation timescale, defined as $\tau_{\rm
gw}:=|a/\dot{a}_{\rm gw}|$, and the hydrodynamical timescale, defined as $\tau_{\rm gas}:=|a/\dot{a}_{\rm gas}|$. Following these definitions, the acceleration factor $\Gamma$ equals $\tau_{\rm gw}/\tau_{\rm gas}$. Because the most sensitive band of LISA is around $3$ mHz, the corresponding BBHs have a typical semi-major axis of $$a=\left(\frac{Gm_{12}}{\pi^2 f^2}\right)^{1/3}\simeq0.0021
\left(\frac{m_{12}}{20~M_\odot}\right)^{1/3}
\left(\frac{f}{3\,{\rm mHz}}\right)^{-2/3}\,{\rm AU}.$$ According to Equation (\[eq:adotgw\]), without 