Spin-state chemistry of deuterated ammonia

Aims. We aim to develop a chemical model that contains a consistent description of spin-state chemistry in reactions involving chemical species with multiple deuterons. We apply the model to the specific case of deuterated ammonia, to derive values for the various spin-state ratios. Methods. We apply symmetry rules in the complete scrambling assumption to calculate branching ratio tables for reactions between chemical species that include multiple protons and/or deuterons. Reaction sets for both gas-phase and grain-surface chemistry are generated using an automated routine that forms all possible spin-state variants of any given reaction with up to six H/D atoms. Single-point and modified Bonnor-Ebert models are used to study the density and temperature dependence of ammonia and its isotopologs, and the associated spin-state ratios. Results. We find that the spin-state ratios of the ammonia isotopologs are, at late times, very different from their statistical values. The ratios are rather insensitive to variations in the density, but present strong temperature dependence. We derive high peak values ($\sim$ 0.1) for the deuterium fraction in ammonia, in agreement with previous (gas-phase) models. The deuterium fractionation is strongest at high density, corresponding to a high degree of depletion, and also presents temperature dependence. We find that in the temperature range 5 to 20 K, the deuterium fractionation peaks at $\sim$ 15 K while most of the ortho/para (and meta/para for $\rm ND_3$) ratios present a minimum at 10 K (ortho/para $\rm NH_2D$ has instead a maximum at this temperature). Conclusions. Owing to the density and temperature dependence found in the abundances and spin-state ratios of ammonia and its isotopologs, it is evident that observations of ammonia and its deuterated forms can provide important constraints on the physical structure of molecular clouds.