Modelling line emission of deuterated H₃+ from prestellar cores

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Context: The depletion of heavy elements in cold cores of interstellar molecular clouds can lead to a situation where deuterated forms of H₃+ are the most useful spectroscopic probes of the physical conditions. Aims: The aim is to predict the observability of the rotational lines of H₂D+ and D₂H+ from prestellar cores. Methods: Recently derived rate coefficients for the H₃+ + H₂ isotopic system were applied to the "complete depletion" reaction scheme to calculate abundance profiles in hydrostatic core models. The ground-state lines of H₂D+(o) (372 GHz) and D₂H+(p) (692 GHz) arising from these cores were simulated. The excitation of the rotational levels of these molecules was approximated by using the state-to-state coefficients for collisions with H₂. We also predicted line profiles from cores with a power-law density distribution advocated in some previous studies. Results: The new rate coefficients introduce some changes to the complete depletion model, but do not alter the general tendencies. One of the modifications with respect to the previous results is the increase of the D₃+ abundance at the cost of other isotopologues. Furthermore, the present model predicts a lower H₂D+ (o/p) ratio, and a slightly higher D₂H+ (p/o) ratio in very cold, dense cores, as compared with previous modelling results. These nuclear spin ratios affect the detectability of the submm lines of H₂D+(o) and D₂H+(p). The previously detected H₂D+ and D₂H+ lines towards the core I16293E, and the H₂D+ line observed towards Oph D can be reproduced using the present excitation model and the physical models suggested in the original papers.