binaries and, in this way, produce a fake chirp signal. If this factor is not accounted for in the LISA data analysis, one may overestimate the masses, as we have shown in one example of our preliminary study [@chen19gas Paper I].

Here we present our full analysis of the problem and discuss the detectability of such “fake” massive BBHs in the LISA band. The paper is organized as follows. In §\[sec:theory\] we explain how mass is measured from a chirp signal and why it is affected by gas friction. Then in §\[sec:compare\] we show that in realistic astrophysical scenarios gas friction indeed can overcome GW radiation and dominate the orbital evolution of a inspiraling BBH. We compute the gas-dominated chirp signals in §\[sec:signal\] and show that they resemble the chirp signals from more massive BBHs in vacuum environments. In §\[sec:MF\], we employ the “matched-filtering” technique to quantify the similarity between the chirp signals in the cases with and without gas. Finally, in §\[sec:Dis\] we discuss the detectability of the fake massive BBHs in the LISA band.

Chirp signal and the effect of gas {#sec:theory}
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We focus on the early inspiral phase because the majority of the LISA BBHs are 