Tracing the formation of molecular clouds via [CII], [CI] and CO
  emission
  Our understanding of how molecular clouds form in the interstellar medium
(ISM) would be greatly helped if we had a reliable observational tracer of the
gas flows responsible for forming the clouds. Fine structure emission from
singly ionised and neutral carbon ([CII], [CI]) and rotational line emission
from CO are all observed to be associated with molecular clouds. However, it
remains unclear whether any of these tracers can be used to study the inflow of
gas onto an assembling cloud, or whether they primarily trace the cloud once it
has already assembled. In this paper, we address this issue with the help of
high resolution simulations of molecular cloud formation that include a
sophisticated treatment of the chemistry and thermal physics of the ISM. Our
simulations demonstrate that both [CI] and CO emission trace gas that is
predominantly molecular, with a density n ~ 500-1000 cm$^{-3}$, much larger
than the density of the inflowing gas. [CII] traces lower density material (n ~
100 cm$^{-3}$) that is mainly atomic at early times. A large fraction of the
[CII] emission traces the same structures as the [CI] or CO emission, but some
arises in the inflowing gas. Unfortunately, this emission is very faint and
will be difficult to detect with current observational facilities, even for
clouds situated in regions with an elevated interstellar radiation field.
