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.
