Statistical nuclear spin ratios of deuterated ammonia in the pre-stellar core L1544

Context. The relative abundances of the nuclear spin modifications of molecules contain information on their formation mechanism. Aims. We determined the ortho/para (o/p) ratios of NH2D and NHD2 in the archetypical pre-stellar core L1544. Methods. L1544 was observed in the two lowest rotational lines of ortho- and para-NH2D using the Atacama Pathfinder EXperiment (APEX) and the IRAM 30 m telescopes. The ground-state lines of ortho- and para-NHD2 were observed with APEX. The distributions of chemical abundances in the core were predicted using a gas-grain chemistry model with two different scenarios concerning proton transfer reactions in the gas. One of the scenarios, the so-called full scrambling (FS), allows protons and deuterons to be completely mixed in the intermediate reaction complex before dissociation, whereas the other describes these reactions as proton or deuteron hops (PH). We also tested assumed abundance profiles independent of the chemistry models. Radiative transfer calculations were used to simulate the observed NH2D and NHD2 lines from the predicted and assumed abundance profiles. Results. Our modelling efforts suggest that the ground-state lines of NH2D and NHD2 at the wavelength λ = 0.9 mm that are observable with the same beam and in the same spectrometer band are the most reliable probes of the o/p ratios. Simulations using the PH reaction scheme show systematically better agreement with the observations than simulations with the FS model. Simulations using a broken power law abundance profile as a function of the gas density, which seems to agree with previous observations and models, give spin ratios that are close to the predictions of the PH scenario: o/p-NH2D = 2.85 ± 0.05, o/p-NHD2 = 2.10 ± 0.06 (1 σ). Conclusions. The o/p ratios predicted by the PH scenario in the gas phase correspond to the nuclear spin statistical weights, that is, o/p-NH2D = 3, o/p-NHD2 = 2. In view of the fact that H and D atom addition reactions on grain surfaces also result in these ratios, it is reasonable to assume that the spin ratios of interstellar ammonia and its deuterated forms are in general equal to their statistical values.