The molecular gas content of normal galaxies at z > 4 is poorly constrained because the commonly used molecular gas tracers become hard to detect at these high redshifts. We use the [C II] 158 μm luminosity, which was recently proposed as a molecular gas tracer, to estimate the molecular gas content in a large sample of main sequence star-forming galaxies at z = 4.4 - 5.9, with a median stellar mass of 109.7M·, drawn from the ALMA Large Program to INvestigate [C II] at Early times survey. The agreement between the molecular gas masses derived from [C II] luminosities, dynamical masses, and rest-frame 850 μm luminosities extrapolated from the rest-frame 158 μm continuum supports [C II] as a reliable tracer of molecular gas in our sample. We find a continuous decline of the molecular gas depletion timescale from z = 0 to z = 5.9, which reaches a mean value of (4.6 ± 0.8) × 108 yr at z ∼ 5.5, only a factor of between two and three shorter than in present-day galaxies. This suggests a mild enhancement of the star formation efficiency toward high redshifts. Our estimates also show that the previously reported rise in the molecular gas fraction flattens off above z ∼ 3.7 to achieve a mean value of 63%±3% over z = 4.4 - 5.9. This redshift evolution of the gas fraction is in line with that of the specific star formation rate. We use multi-epoch abundance-matching to follow the gas fraction evolution across cosmic time of progenitors of z = 0 Milky Way-like galaxies in ∼1013M· halos and of more massive z = 0 galaxies in ∼1014M· halos. Interestingly, the former progenitors show a monotonic increase of the gas fraction with redshift, while the latter show a steep rise from z = 0 to z ∼ 2 followed by a constant gas fraction from z ∼ 2 to z = 5.9. We discuss three possible effects, namely outflows, a pause in gas supply, and over-efficient star formation, which may jointly contribute to the gas fraction plateau of the latter massive galaxies.
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