Chemistry and Radiative Transfer of Water in Cold, Dense Clouds
  The Herschel Space Observatory's recent detections of water vapor in the
cold, dense cloud L1544 allow a direct comparison between observations and
chemical models for oxygen species in conditions just before star formation. We
explain a chemical model for gas phase water, simplified for the limited number
of reactions or processes that are active in extreme cold ($<$ 15 K). In this
model, water is removed from the gas phase by freezing onto grains and by
photodissociation. Water is formed as ice on the surface of dust grains from O
and OH and released into the gas phase by photodesorption. The reactions are
fast enough with respect to the slow dynamical evolution of L1544 that the gas
phase water is in equilibrium for the local conditions thoughout the cloud. We
explain the paradoxical radiative transfer of the H$_2$O ($1_{10}-1_{01}$)
line. Despite discouragingly high optical depth caused by the large Einstein A
coefficient, the subcritical excitation in the cold, rarefied H$_2$ causes the
line brightness to scale linearly with column density. Thus the water line can
provide information on the chemical and dynamical processes in the darkest
region in the center of a cold, dense cloud. The inverse P-Cygni profile of the
observed water line generally indicates a contracting cloud. This profile is
reproduced with a dynamical model of slow contraction from unstable
quasi-static hydrodynamic equilibrium (an unstable Bonnor-Ebert sphere).
