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The bright [CI] 1-0 and [CI] 2-1 lines of atomic carbon are becoming more andmore 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 ofPlanck's Dusty GEMS, the brightest gravitationally lensed galaxies on theextragalactic 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 observationsto constrain the gas excitation mechanism, excitation temperatures, opticaldepths, atomic carbon and molecular gas masses, and carbon abundances. Ratiosof L_CI/L_ FIR are similar to those found in the local Universe, and suggestthat the total cooling budget through atomic carbon has not strongly changed inthe last 12 Gyr. Both lines are optically thin and trace 1 - 6 x 10^7 M_sun ofatomic carbon. Carbon abundance ratios with H_2, X_CI, are between 2.5 and 4 x10^-5, for a "ULIRG" CO-to-H_2 conversion factor of alpha_CO=0.8 M_sun/ [K kms^-1 pc^2]. Ratios of molecular gas masses derived from [CI] 1-0 and CO agreewithin the measurement uncertainties for five galaxies, and to better than afactor of 2 for another two with [CI] 1-0 measurements, after taking COexcitation carefully into account. This does not support the idea that intense,high-redshift starburst galaxies host large quantities of "CO-dark" gas. Theseresults also support the common assumptions underlying most molecular gas massestimates made for massive, dusty, high-redshift starburst galaxies, althoughthe good agreement between the masses obtained with both tracers cannot betaken as an independent confirmation of either alpha_CO or X_CI.

Planck's Dusty GEMS. VII. Atomic carbon and molecular gas in dusty starburst galaxies at z=2 to 4