2017ApJ...835..110M

We observed the [C II] line in 15 lensed galaxies at redshifts 1 < z < 3 using HIFI on the Herschel Space Observatory and detected 14/15 galaxies at 3σ or better. High magnifications enable even modestly luminous galaxies to be detected in [C II] with Herschel. The [C II] luminosity in this sample ranges from 8 x 10⁷ L_☉ to 3.7 x 10⁹ L_☉ (after correcting for magnification), confirming that [C II] is a strong tracer of the ISM at high redshifts. The ratio of the [C II] line to the total far-infrared (FIR) luminosity serves as a measure of the ratio of gas to dust cooling and thus the efficiency of the grain photoelectric heating process. It varies between 3.3% and 0.09%. We compare the [C II]/FIR ratio to that of galaxies at z = 0 and at high redshifts and find that they follow similar trends. The [C II]/FIR ratio is lower for galaxies with higher dust temperatures. This is best explained if increased UV intensity leads to higher FIR luminosity and dust temperatures, but gas heating does not rise due to lower photoelectric heating efficiency. The [C II]/FIR ratio shows weaker correlation with FIR luminosity. At low redshifts highly luminous galaxies tend to have warm dust, so the effects of dust temperature and luminosity are degenerate. Luminous galaxies at high redshifts show a range of dust temperatures, showing that [C II]/FIR correlates most strongly with dust temperature. The [C II] to mid-IR ratio for the HELLO sample is similar to the values seen for low-redshift galaxies, indicating that small grains and PAHs dominate the heating in the neutral ISM, although some of the high [CII]/FIR ratios may be due to turbulent heating.