Planck's Dusty GEMS. VII. Atomic carbon and molecular gas in dusty
  starburst galaxies at z=2 to 4
  The bright [CI] 1-0 and [CI] 2-1 lines of atomic carbon are becoming more and
more widely employed tracers of the cold neutral gas in high-redshift galaxies.
Here we present observations of these lines in the 11 galaxies of the set of
Planck's Dusty GEMS, the brightest gravitationally lensed galaxies on the
extragalactic submillimeter sky probed by the Planck satellite. We have [CI]
1-0 measurements for seven, and [CI] 2-1 measurements for eight galaxies,
including four galaxies where both lines are measured. We use our observations
to constrain the gas excitation mechanism, excitation temperatures, optical
depths, atomic carbon and molecular gas masses, and carbon abundances. Ratios
of L_CI/L_ FIR are similar to those found in the local Universe, and suggest
that the total cooling budget through atomic carbon has not strongly changed in
the last 12 Gyr. Both lines are optically thin and trace 1 - 6 x 10^7 M_sun of
atomic carbon. Carbon abundance ratios with H_2, X_CI, are between 2.5 and 4 x
10^-5, for a "ULIRG" CO-to-H_2 conversion factor of alpha_CO=0.8 M_sun/ [K km
s^-1 pc^2]. Ratios of molecular gas masses derived from [CI] 1-0 and CO agree
within the measurement uncertainties for five galaxies, and to better than a
factor of 2 for another two with [CI] 1-0 measurements, after taking CO
excitation carefully into account. This does not support the idea that intense,
high-redshift starburst galaxies host large quantities of "CO-dark" gas. These
results also support the common assumptions underlying most molecular gas mass
estimates made for massive, dusty, high-redshift starburst galaxies, although
the good agreement between the masses obtained with both tracers cannot be
taken as an independent confirmation of either alpha_CO or X_CI.
