The ALPINE-ALMA [C II] survey: the luminosity function of serendipitous
  [C II] line emitters at $z\sim 5$
  We present the first [CII] 158 $\mu$m luminosity function (LF) at $z\sim 5$
from a sample of serendipitous lines detected in the ALMA Large Program to
INvestigate [CII] at Early times (ALPINE). A search performed over the 118
ALPINE pointings revealed several serendipitous lines. Based on their fidelity,
we selected 14 lines for the final catalog. According to the redshift of their
counterparts, we identified 8 out of 14 detections as [CII] lines at $z\sim 5$,
and two as CO transitions at lower redshifts. The remaining 4 lines have an
elusive identification in the available catalogs and we considered them as
[CII] candidates. We used the 8 confirmed [CII] and the 4 [CII] candidates to
build one of the first [CII] LFs at $z\sim 5$. We found that 11 out of these 12
sources have a redshift very similar to that of the ALPINE target in the same
pointing, suggesting the presence of overdensities around the targets.
Therefore, we split the sample in two (a "clustered" and "field" sub-sample)
according to their redshift separation and built two separate LFs. Our
estimates suggest that there could be an evolution of the [CII] LF between $z
\sim 5$ and $z \sim 0$. By converting the [CII] luminosity to star formation
rate we evaluated the cosmic star formation rate density (SFRD) at $z\sim 5$.
The clustered sample results in a SFRD $\sim 10$ times higher than previous
measurements from UV-selected galaxies. On the other hand, from the field
sample (likely representing the average galaxy population) we derived a SFRD
$\sim 1.6$ higher compared to current estimates from UV surveys but compatible
within the errors. Because of the large uncertainties, observations of larger
samples are necessary to better constrain the SFRD at $z\sim 5$. This study
represents one of the first efforts aimed at characterizing the demography of
[CII] emitters at $z\sim 5$ using a mm-selection of galaxies.
