Cooling of dense gas by H₂O line emission and an assessment of its effects in chondrule-forming shocks

We consider gas at densities appropriate to protoplanetary disks and calculate its ability to cool due to line radiation emitted by H₂O molecules within the gas. Our work follows that of Neufeld & Kaufman, expanding on their work in several key aspects, including use of a much-expanded line database, an improved escape probability formulism, and the inclusion of dust grains, which can absorb line photons. Although the escape probabilities formally depend on a complicated combination of optical depth in the lines and in the dust grains, we show that the cooling rate including dust is well approximated by the dust-free cooling rate multiplied by a simple function of the dust optical depth. We apply the resultant cooling rate of a dust-gas mixture to the case of a solar nebula shock pertinent to the formation of chondrules, millimeter-sized melt droplets found in meteorites. Our aim is to assess whether line cooling can be neglected in chondrule-forming shocks or if it must be included. We find that for typical parameters, H₂O line cooling shuts off a few minutes past the shock front; line photons that might otherwise escape the shocked region and cool the gas will be absorbed by dust grains. During the first minute or so past the shock, however, line photons will cool the gas at rates 10⁴ K hr^-1, dropping the temperature of the gas (and most likely the chondrules within the gas) by several hundred K. Inclusion of H₂O line cooling therefore must be included in models of chondrule formation by nebular shocks.