N$_2$H$^+$ and N$^{15}$NH$^+$ towards the prestellar core 16293E in
  L1689N
  Understanding the processes that could lead to enrichment of molecules in
$^{15}$N atoms is of particular interest in order to shed light on the
relatively large variations observed in the $^{14}$N/$^{15}$N ratio in various
solar system environments. Currently, the sample of molecular clouds where
$^{14}$N/$^{15}$N ratios have been measured is small and has to be enlarged in
order to allow statistically significant studies. In particular, the N$_2$H$^+$
molecule currently shows the largest spread of $^{14}$N/$^{15}$N ratios in
high-mass star forming regions. However, the $^{14}$N/$^{15}$N ratio in
N$_2$H$^+$ was obtained in only two low-mass star forming regions (L1544 and
B1b). The current work extends this sample to a third dark cloud. We targeted
the 16293E prestellar core, where the N$^{15}$NH$^+$ $J$=1-0 line was detected.
Using a model previously developed for the physical structure of the source, we
solved the molecular excitation with a non-local radiative transfer code. For
that purpose, we computed specific collisional rate coefficients for the
N$^{15}$NH$^+$-H$_2$ collisional system. As a first step of the analysis, the
N$_2$H$^+$ abundance profile was constrained by reproducing the N$_2$H$^+$
$J$=1-0 and 3-2 maps. A scaling factor was then applied to this profile to
match the N$^{15}$NH$^+$ $J$=1-0 spectrum. We derive a column density ratio
N$_2$H$^+$ / N$^{15}$NH$^+$ = $330^{+170}_{-100}$. The current estimate
$\sim$330 agrees with the value typical of the elemental isotopic ratio in the
local ISM. It is however lower than in some other cores, where values as high
as 1300 have been reported.
