for $T_{\ensuremath{\mathrm{ex}}}$ and $\Delta\varv$ had to be used and the corresponding parameters were kept fixed in the least-squares fit. The single-sideband continuum temperature $T_{\ensuremath{\mathrm{C}}}$, inserted in the radiative transfer equality of Eq. , has been estimated using the linear formula given by @hily2010nitrogen, $T_{\ensuremath{\mathrm{C}}}/{\ensuremath{\mathrm{[K]}}} =1.10\,\nu - 0.42$, with $\nu$ expressed in THz.

The spectroscopic data for , , and have been taken from the most recent laboratory studies [@martin2014nh2; @bizzocchi2020nhd; @melosso2017terahertz], and the $Q_{\ensuremath{\mathrm{rot}}}$ values used in Eq.  have been computed at any given temperature by cubic interpolation on a grid of finely spaced entries spanning the 2.7–19K interval. These were obtained by direct summation on all rotational levels through the `SPCAT` spectral tool [@pickett1991], with the $ortho$ and $para$ species of the symmetric isotopologues and treated separately. A brief explanation of the energy levels structure of and is given in Appendix \[app:levels\], while the complete list of HFS components used for the analysis of each transition is reported in Appendix \[app:list\]. The partition function values of both species computed at temperatures between 2.725 and 300K are given in Appendix \[app:partit\].

Results
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The line parameters obtained from the analysis of the observed transitions of , , and are collected 