ALMA Lensing Cluster Survey: A spectral stacking analysis of [CII] in
  lensed $z\sim6$ galaxies
  The properties of galaxies at redshift $z>6$ hold the key to our
understanding of the early stages of galaxy evolution and can potentially
identify the sources of the ultraviolet radiation that give rise to the epoch
of reionisation. The far-infrared cooling line of [CII] at 158$\mu$m is known
to be bright and correlate with the star formation rate (SFR) of low-redshift
galaxies, and hence is also suggested to be an important tracer of star
formation and interstellar medium properties for very high-redshift galaxies.
With the aim to study the interstellar medium properties of gravitationally
lensed galaxies at $z>6$, we search for [CII] and thermal dust emission in a
sample of 52 $z\sim6$ galaxies observed by the ALMA Lensing Cluster Survey
(ALCS). We perform our analysis using \textsc{LineStacker}, stacking both [CII]
and continuum emission. The target sample is selected from multiple catalogues,
and the sample galaxies have spectroscopic redshift or low-uncertainty
photometric redshifts ($\sigma_z < 0.02$) in nine galaxy clusters. Source
properties of the target galaxies are either extracted from the literature or
computed using spectral energy distribution (SED) fitting. Both
weighted-average and median stacking are used, on both the full sample and
three sub-samples. Our analyses find no detection of either [CII] or continuum.
An upper limit on $L_{\rm [CII]}$ is derived, implying that [CII] remains
marginally consistent for low-SFR $z>6$ galaxies but likely is under-luminous
compared to the local $L_{\rm [CII]}$-SFR relationship. We discuss potential
biases and possible physical effects that may be the cause of the
non-detection. Further, the upper limit on the dust continuum implies that less
than half of the star formation is obscured.
