Modelling line emission of deuterated H_3^+ from prestellar cores

Context: The depletion of heavy elements in cold cores of interstellar molecular clouds can lead to a situation where deuterated forms of H_3^+ are the most useful spectroscopic probes of the physical conditions. Aims: The aim is to predict the observability of the rotational lines of H_2D^+ and D_2H^+ from prestellar cores. Methods: Recently derived rate coefficients for the H_3^+ + H_2 isotopic system were applied to the "complete depletion" reaction scheme to calculate abundance profiles in hydrostatic core models. The ground-state lines of H_2D^+(o) (372 GHz) and D_2H^+(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 H_2. 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 D_3^+ abundance at the cost of other isotopologues. Furthermore, the present model predicts a lower H_2D^+ (o/p) ratio, and a slightly higher D_2H^+ (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 H_2D^+(o) and D_2H^+(p). The previously detected H_2D^+ and D_2H^+ lines towards the core I16293E, and the H_2D^+ line observed towards Oph D can be reproduced using the present excitation model and the physical models suggested in the original papers.