Visibility {#sec:simul}
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Even with our deep integration of 10 hr, we detected only one Ly$\alpha$ emission line with a moderate rest-frame Ly$\alpha$ EW of 16 Å. To put this result in context, we computed the number of detections expected from our observations, with the aim of placing constraints on the evolution of the Ly$\alpha$ visibility with redshift.

First, we quantified the limiting sensitivity of our observations by simulating Ly$\alpha$ lines in our MOSFIRE spectra. We modeled the Ly$\alpha$ line as an asymmetric Gaussian, similar to the detected line in z7\_GSD\_3811. Then, we inserted the lines with varying line fluxes into each of the actual 1D spectra in our mask at varying positions between the MOSFIRE $Y$-band wavelength coverage (9800–11200 Å), to find the line flux as a function of wavelength that ensures an $X$-$\sigma$ detection ($X \ge 3$). The upper left panel of Figure \[fig:simul\] presents the results, showing that our deep spectroscopy reaches a median 5$\sigma$ limiting sensitivity in line flux of $\sim$5 $\times 10^{-18}$ erg s$^{-1}$ cm$^{-2}$ between sky lines. Scaling our limiting sensitivity by $\sqrt{t}$, where $t$ is the integration time, we find it consistent with the quoted limits of other MOSFIRE $Y$-band observations reported by 