that the best FF and the corresponding best-match ${\cal M}_c$ are both functions of $T_{\rm obs}$. Figure \[fig:FFsingle\] shows such a dependence on time. The model parameters are the same as in Figure \[fig:heatmap\]. During the first $1-2$ years, the FF remains close to $1$ and afterwards decreases with time. The FF deteriorates on a long timescale because the perturbation on the GW phase by the gas effect is accumulative. For the best-fit ${\cal M}_c$, it decreases with time but remains close to $37\,M_\odot$.

![Variation of the maximum FF and the best-fit chirp mass with the observational period. The real chirp mass of the BBH is $8.7\,M_\odot$.[]{data-label="fig:FFsingle"}](FFtime.pdf){width="50.00000%"}

Whether or not LISA is able to distinguish $h_1$ from $h_2$ depends on not only the FF but also the SNR, since noise also plays a role. The SNR is defined as $$\label{eq:SNR2}
{\rm SNR}^2:=\left<h|h\right>.$$ According to @lindblom08, two waveforms are distinguishable when $\left<\delta h|\delta h\right> >1$, where $\delta h:=\tilde{h}_1(f)-\tilde{h}_2(f)$. This criterion can be simplified in our problem because we are often in a situation where $h_1\simeq h_2$. In this case we have ${\rm SNR}^2\simeq\left<h_1|h_1\right>\simeq\left<h_2|h_2\right>$, and the criterion reduces to $${\rm
    FF}<1-1/(2\,{\rm SNR}^2).\label{eq:FF}$$ If we take ${\rm SNR}\simeq10$ as the threshold for LISA 