of $f$ is small during the observation period, it is detectable by LISA because LISA’s resolution is approximately $10^{-8}(1\,{\rm yr}/T_{\rm obs})(10/ {\rm
SNR})$ Hz [@seto02]. Comparing the blue solid and the red dashed lines, we see that the presence of gas increases the slop the chirp signal. The steeper line resembles the chirp signal of a more massive BBH in a vacuum with a chirp mass of $37\,M_\odot$.

![Chirp signals in the LISA observational window. The blue solid curve is computed with the gas effect and the red dashed one without. The model parameters are the same as in Fig. \[fig:long\]. The gray dashed curves show the dependence of the chirp signal on the chirp mass when there is no gas.[]{data-label="fig:short"}](shortscale.pdf){width="50.00000%"}

We have seen that with or without gas, the chirp signals in the LISA band are almost straight lines and are relatively featureless compared to those in the LIGO/Virgo band. This is the main reason that in this band a BBH in a gaseous environment could be misidentified as a more massive binary in a vacuum.

Misidentification {#sec:MF}
=================

LISA uses a technique called “matched filtering” to search for BBHs in the data stream [@Finn92; @cutler94]. In this section, 