High sensitivity maps of molecular ions in L1544: I. Deuteration of N2H+
  and HCO+ and first evidence of N2D+ depletion
  Context. The deuterium fraction in low-mass prestellar cores is a good
diagnostic indicator of the initial phases of star formations, and it is also a
fundamental quantity to infer the ionisation degree in these objects.
  Aims. With the analysis of multiple transitions of $\rm N_2H^+$, $\rm
N_2D^+$, $\rm HC^{18}O^+$ and $\rm DCO^+$ we are able to determine the
molecular column density maps and the deuterium fraction in $\rm N_2H^+$ and
$\rm HCO^+$ toward the prototypical prestellar core L1544. This is the
preliminary step to derive the ionisation degree in the source.
  Methods. We use a non-local thermodynamic equilibrium (non-LTE) radiative
transfer code, combined with the molecular abundances derived from a chemical
model, to infer the excitation conditions of all the observed transitions,
which allows us to derive reliable maps of each molecule's column density. The
ratio between the column density of a deuterated species and its non-deuterated
counterpart gives the searched deuteration level.
  Results. The non-LTE analysis confirms that, for the analysed molecules,
higher-J transitions are characterised by excitation temperatures $\approx
1-2\,$K lower than the lower-J ones. The chemical model that provides the best
fit to the observational data predict the depletion of $\rm N_2H^+$ and to a
lesser extent of $\rm N_2D^+$ in the innermost region. The peak values for the
deuterium fraction that we find are $\mathrm{D/H_{N_2H^+}} =
0.26^{+0.15}_{-0.14}$ and $\mathrm{D/H_{HCO^+}} = 0.035^{+0.015}_{-0.012}$, in
good agreement with previous estimates in the source.
