ALMA Deep Field in SSA22: Reconstructed [CII] Luminosity Function at z = 6

The ADF22 line survey reported detections of two high-$z$ line-emitting source candidates above 6-$\sigma$, both of which were shown to be spurious after follow-up observations. We investigate the detectability of far-infrared emitters in ALMA deep fields using mock observations by injecting artificial line-emitting sources into the visibility planes. We also discuss our investigation, conducted together with the ALMA operations team, of a possible technical problem in the original observations. Finally, we devise a method to estimate the [CII] luminosity function (LF) at $z \sim 6$, including a full analysis of signal contamination and sample completeness. The comparison of pixel distributions between the real and mock datacubes does not show significant differences, confirming that the effect of non-Gaussian noise is negligible for the ADF22 datacube. Using 100 blank mock-mosaic datasets, we show 0.43 $\pm$ 0.67 false detections per datacube with the previous source-finding method. We argue that the underestimation of the contamination rate in the previous work is caused by the smaller number of datacubes, using only 4 real ADF22 datacubes. We compare the results of clump-finding between the time division mode and frequency division mode correlator datacubes and confirm that the velocity widths of the clumps in the TDM case are up to 3 times wider than in the FDM case. The LF estimation using our model shows that a correction for the number count is required, up to one order of magnitude, in the luminosity range of $\geq 5 \times 10^8 L_\odot$. Our reconstruction method for the line LF can be applied to future blind line surveys.