A physical model for [CII] line emission from galaxies
  A tight relation between the [CII]158$\mu$m line luminosity and star
formation rate is measured in local galaxies. At high redshift ($z>5$), though,
a much larger scatter is observed, with a considerable (15-20\%) fraction of
the outliers being [CII]-deficient. Moreover, the [CII] surface brightness
($\Sigma_{\rm CII}$) of these sources is systematically lower than expected
from the local relation. To clarify the origin of such [CII]-deficiency we have
developed an analytical model that fits local [CII] data, and has been
validated against radiative transfer simulations performed with CLOUDY. The
model predicts an overall increase of $\Sigma_{\rm CII}$ with the surface star
formation rate ($\Sigma_*$). However, for $\Sigma_* > 1 M_\odot~{\rm
yr}^{-1}~{\rm kpc}^{-2}$, $\Sigma_{\rm CII}$ saturates. We conclude that
underluminous [CII] systems can result from a combination of three factors: (a)
large upward deviations from the Kennicutt-Schmidt relation ($\kappa_s \gg 1$),
parameterized by the "burstiness" parameter $\kappa_s$; (b) low metallicity;
(c) low gas density, at least for the most extreme sources (e.g. CR7).
Observations of [CII] emission alone cannot break the degeneracy among the
above three parameters; this requires additional information coming from other
emission lines (e.g. [OIII]88$\mu$m, CIII]1909A, CO lines). Simple formulae are
given to interpret available data for low and high-$z$ galaxies.
