The [C II] emission as a molecular gas mass tracer in galaxies at low
  and high redshift
  We present ALMA Band 9 observations of the [C II]158um emission for a sample
of 10 main-sequence galaxies at redshift z ~ 2, with typical stellar masses
(log M*/Msun ~ 10.0 - 10.9) and star formation rates (~ 35 - 115 Msun/yr).
Given the strong and well understood evolution of the interstellar medium from
the present to z = 2, we investigate the behaviour of the [C II] emission and
empirically identify its primary driver. We detect [C II] from six galaxies
(four secure, two tentative) and estimate ensemble averages including non
detections. The [C II]-to-infrared luminosity ratio (L[C II]/LIR) of our sample
is similar to that of local main-sequence galaxies (~ 2 x 10^-3), and ~ 10
times higher than that of starbursts. The [C II] emission has an average
spatial extent of 4 - 7 kpc, consistent with the optical size. Complementing
our sample with literature data, we find that the [C II] luminosity correlates
with galaxies' molecular gas mass, with a mean absolute deviation of 0.2 dex
and without evident systematics: the [C II]-to-H2 conversion factor (alpha_[C
II] ~ 30 Msun/Lsun) is largely independent of galaxies' depletion time,
metallicity, and redshift. [C II] seems therefore a convenient tracer to
estimate galaxies' molecular gas content regardless of their starburst or
main-sequence nature, and extending to metal-poor galaxies at low and high
redshifts. The dearth of [C II] emission reported for z > 6 - 7 galaxies might
suggest either a high star formation efficiency or a small fraction of UV light
from star formation reprocessed by dust.
