The ortho-to-para ratio of water in interstellar clouds

The nuclear-spin chemistry of interstellar water is investigated using the University of Grenoble Alpes Astrochemical Network (UGAN). This network includes reactions involving the different nuclear-spin states of the hydrides of carbon, nitrogen, oxygen and sulphur, as well as their deuterated forms. Nuclear-spin selection rules are implemented within the scrambling hypothesis for reactions involving up to seven protons. The abundances and ortho-to-para ratios (OPRs) of gas-phase water and water ions (H$_2$O$^+$ and H$_3$O$^+$) are computed under the steady-state conditions representative of a dark molecular cloud and during the early phase of gravitational collapse of a prestellar core. The model incorporates the freezing of the molecules on to grains, simple grain surface chemistry and cosmic-ray induced and direct desorption of ices. The predicted OPRs are found to deviate significantly from both thermal and statistical values and to be independent of temperature below $\sim$30~K. The OPR of H$_2$O is shown to lie between 1.5 and 2.6, depending on the spin-state of H$_2$, in good agreement with values derived in translucent clouds with relatively high extinction. In the prestellar core collapse calculations, the OPR of H$_2$O is shown to reach the statistical value of 3 in regions with severe depletion ($n_{\rm H}> 10^7$~cm$^{-3}$). We conclude that a low water OPR ($\lesssim 2.5$) is consistent with gas-phase ion-neutral chemistry and reflects a gas with OPR(H$_2)\lesssim 1$. Available OPR measurements in protoplanetary disks and comets are finally discussed.