---
author:
- 'C.M. Persson , M. De Luca, B. Mookerjea, A.O.H. Olofsson, J.H. Black, M. Gerin, E. Herbst, T.A. Bell, A. Coutens B. Godard, J.R. Goicoechea, G.E. Hassel, P. Hily-Blant, K.M. Menten, H.S.P. Müller, J.C. Pearson, S. Yu'
- 
bibliography:
- 'references.bib'
date: 'Received Dec 20, 2011 / Accepted May 30, 2012'
subtitle: 'II. Analysis of [*Herschel*]{}[^1]/HIFI observations towards W49N and G10.6$-$0.4 (W31C)'
title: Nitrogen hydrides in interstellar gas
---

[As a part of the *Herschel* key programme PRISMAS, we have used the *Herschel*-HIFI instrument to observe interstellar nitrogen hydrides along the sight-lines towards eight high-mass star-forming regions in order to elucidate the production pathways leading to nitrogen-bearing species in diffuse gas. Here, we report observations towards W49N of the NH , , and , , and , transitions, and unsuccessful searches for NH$^+$. All detections show absorption by foreground material over a wide range of velocities, as well as absorption associated directly with the hot-core source itself. As in the previously published observations towards G10.6$-$0.4, the NH, NH$_2$ and NH$_3$ spectra towards W49N show strikingly similar and non-saturated absorption features. We decompose the absorption of the foreground material towards W49N into different velocity components in order to investigate whether the relative abundances vary among the velocity components, and, in addition, we re-analyse the absorption lines towards G10.6$-$0.4 in the same manner. Abundances, with respect to molecular hydrogen, in each velocity component are estimated using CH, which is found to correlate with H$_2$ in the solar neighbourhood diffuse gas. The analysis points to a co-existence of the nitrogen hydrides in diffuse or translucent interstellar gas with a high molecular fraction. Towards both sources, we find that NH is always at least as abundant as both and , in sharp contrast to previous results for dark clouds. We find relatively constant and ratios with mean values of 3.2 and 1.9 towards W49N, and 5.4 and 2.2 towards G10.6$-$0.4, respectively. The mean abundance of o-NH$_3$ is $\sim$2$\times$10$^{-9}$ towards both sources. The nitrogen hydrides also show linear correlations with CN and HNC towards both sources, and looser correlations with CH. The upper limits on the NH$^+$ abundance indicate column densities of $N$(NH), which is in contrast to the behaviour of the abundances of CH$^+$ and OH$^+$ relative to the values determined for the corresponding neutrals CH and OH. Surprisingly low values of the ammonia ortho-to-para ratio are found in both sources, , in the strongest absorption components. This result cannot be explained by current models as we had expected to find a value of unity or higher. ]{}

Introduction
============

Nitrogen is among the six most abundant elements in the universe and, despite its fundamental role in the chemistry of molecules connected with life, the chemical network of nitrogen in the interstellar medium is still poorly understood due to severe difficulties to observe key molecules from the ground. Today about 55 molecules containing nitrogen have been discovered in interstellar space and a few more in circumstellar envelopes[^2]. The major reservoir of nitrogen is believed to be in the form of atomic N and molecular N$_2$. The latter is extremely difficult to observe since it has no permanent dipole moment [@2001ApJ...548..836S]. In dense molecular clouds N$_2$H$^+$ is instead often used as a tracer of N$_2$, which remained undetected until @2004Natur.429..636K reported far-ultraviolet observations towards HD124314. The total abundance of nitrogen therefore still relies, to a high degree, on chemical modelling and observations of nitrogen-bearing species other than N$_2$.

In order to constrain the nitrogen formation pathways, observations of *nitrogen hydrides* are crucial since they are at the root of the nitrogen chemical network, appearing in its first steps in chains of reactions that lead to other more complex species. The abundances of these species are thus key diagnostics for the nitrogen chemistry. The nitrogen hydrides are, however, also problematic to observe since their ground state rotational transitions lie at sub-mm wavelengths and are thus very difficult, or impossible, to reach from the ground. Key species, such as imidogen (NH) and amidogen (NH$_2$), have therefore previously not been widely observed, and there is still no detection of the NH$^+$ radical.

Although very few observations exist of NH and NH$_2$ in interstellar space, they are well known in comets [e.g. @1941ApJ....94..320S; @1998Icar..136..268M; @1993ApJ...404..348F], and have been observed in stellar photospheres [e.g. @1969PASP...81..657S; @1989hra1.book.....F] via their electronic, vibration-rotation, and high rotational transitions. The first detection of interstellar NH was made by @1991ApJ...376L..49M by optical absorption spectroscopy. Subsequent observations by @1997MNRAS.291L..53C and @2009MNRAS.400..392W have yielded several lines of sight in diffuse and translucent gas where column densities of NH, CH, CN, and H$_2$ have been directly measured. The average value of the column density ratio in these diffuse and translucent sight-lines is $N$(NH)/$N$(H$_2$)=3$\times$10$^{-9}$.

Interstellar NH$_2$ was first detected by @1993ApJ...416L..83V in absorption towards SgrB2 in three fine-structure components of the para-symmetry form of NH$_2$, the transition, with partially resolved hyperfine structure at frequencies 461 to 469 GHz. The Infrared Space Observatory (ISO) was later used to observe unresolved absorption lines of both ortho and para symmetry forms of NH$_2$, as well as NH, towards this source through the use of the long-wavelength spectrometer [@2000ApJ...534L.199C; @2004ApJ...600..214G; @2007MNRAS.377.1122P].

In contrast to NH and NH$_2$, ammonia (NH$_3$) has been extensively observed for more than 40 years and was in fact the first polyatomic molecule to be identified in interstellar space [@1968PhRvL..21.1701C] by means of its $J\!=\!K$ inversion transitions at cm wavelengths ($K$ is the quantum number of the projection of total angular momentum $J$ on the molecule’s symmetry axis). The ammonia molecule has, however, two symmetries, like NH$_2$, which arise due to the possible orientations of the hydrogen spins and behave like two distinct species: (all H spins parallel, $K$=3$n$ where $n$ is an integer $\geq 0$) and (not all H spins parallel, $K\neq3n$). Important information about the ammonia formation pathways could be inferred from observations of both symmetries. Unfortunately, only the para form has relatively low-excitation transitions accessible from ground since the $K$=0 ladder of energy levels has no inversion splitting and the $J_K\!=\!3_3$ inversion transitions’ lower energy level is 122K above ground. Ortho inversion lines ($K$=3$n$, $n \ge 1$) can thus only be observed in relatively warm molecular gas. Only a few ammonia observations of the cold diffuse interstellar gas exist, using para inversion lines which leaves the ammonia formation mechanism poorly constrained in diffuse gas. The (0,0) ammonia ground state, with ortho symmetry, can only be studied by rotational transitions. Observations of the fundamental rotational transition of at 572 GHz, which has similar upper state energy as the inversion lines, but several orders of magnitudes higher critical densities, thus requires space telescopes. The Kuiper Airborne Observatory [@1983ApJ...271L..27K] performed the first observations of the transition using heterodyne receivers, and later on the Odin satellite continued such observations in a number of environments, for instance in photo-dissociation and star-forming regions , circumstellar envelopes [@2006ApJ...637..791H], diffuse clouds in absorption towards SgrB2 , and in comets .

[lrccrrrllcc]{} Species & Frequency & Transition & Band & $T_\mathrm{sys}$ & & &\
&&& && G10.6 & W49N & G10.6 & W49N & G10.6 & W49N\
& (GHz) && & (K) & (s)& (s)& (K) & (K) &\

NH & 946.476 & $N_J\!=\!1_0\leftarrow0_1$ & 3b & 416& 234 & 116& 2.5 &3.4 & 0.021 & 0.027\
&974.478 &$N_J\!=\!1_2\leftarrow0_1$ & 4a & 338 &186 & 103 &2.6& 3.9 & 0.018 & 0.018\
o-NH$_2$ & 952.578 & $N_{K_a,K_c} J = 1_{1,1} 3/2 \gets 0_{0,0} 1/2$ & 3b& 230 &92 &68& 2.6 & 3.6 &0.018 & 0.017\
o-NH$_3$ & 572.498& $J_K$=1$_0 \leftarrow 0_0$ & 1b & 87 & 1024 &94& 0.61 & 0.93 & 0.013 & 0.025\
& 1214.859 & $J_{K}$=2$_{0} \leftarrow 1_{0}$ & 5a & 1024 & 293 & 196 & 3.4 & 5.2 & 0.032 & 0.025\
p-NH$_3$ & 1215.246 &$J_{K}$= 2$_{1}  \leftarrow 1_{1}$ &5a & 1024 &293& 196& 3.4 & 5.2 &0.032 & 0.025\
NH$^{+}$ & 1012.540& $^2\Pi_{1/2}$ $N$=1$\leftarrow$1 $J$=3/2$\leftarrow$1/2 & 4a & 327 &171& 91& 3.0 & 4.4 &0.013& 0.013\
\[Table: transitions\]

With the launch of the *Herschel* Space Observatory [@Pilbratt2010] in May 2009, unique opportunities to perform observations of transitions between 157 and 625$\mu$m (0.48–1.9THz) became feasible with the Heterodyne Instrument for the Far-Infrared [HIFI; @Graauw2010] owing to its very high sensitivity and spectral resolution. This allowed, for the first time, searches for spectrally resolved, rotational transitions involving the ground states of NH$^+$, NH, NH$_2$, and NH$_3$ with the same instrument. Several observations have already been reported. For instance, using *Herschel*-HIFI, found very high column densities of NH and ND in the cold envelope of the class0 protostar IRAS16293-2422 (2$\times$10$^{14}$cm$^{-2}$ and $\sim$1.3$\times$10$^{14}$cm$^{-2}$, respectively). found NH:NH$_2$:NH$_3$ abundance ratios of $\sim$5:1:300 towards the same source.

The PRISMAS[^3] key programme (PRobing InterStellar Molecules with Absorption line Studies) is targeting absorption lines in the line-of-sight towards eight bright sub-millimetre-wave continuum sources using *Herschel*-HIFI: G10.6$-$0.4 (W31C), W49N, W51, G34.3+0.1, DR21(OH), SgrA (+ 50 km s$^{-1}$ cloud), G005.9-0.4 (W28A) and W33A. High-resolution absorption line spectroscopy is generally a very sensitive and model-independent method for measuring column densities of interstellar molecules, and a powerful tool to probe the diffuse interstellar gas clouds with no or little excitation.

The first results and analysis of absorption lines of nitrogen hydrides along the sight-line towards the massive star-forming region G10.6$-$0.4 (W31C) have already been presented in . Similar abundances with respect to the total amount of hydrogen $N_\mathrm{H}$=2$N(\mathrm{H_2}$)+$N(\mathrm{H}$), were found for all three species: approximately $6\times 10^{-9}$, $3\times 10^{-9}$, and $3\times 10^{-9}$ for NH, NH$_2$, and NH$_3$, respectively. They were estimated across the whole line-of-sight and using the high temperature ortho-to-para limits of three and one for NH$_2$ and NH$_3$, respectively. NH$^+$ was not detected at a 1$\sigma$ rms level of 74mK with a resolution of 1.1 MHz. The abundance patterns that we see in diffuse molecular gas are thus clearly very different from those in IRAS16293-2422 and Sgr B2, where NH:NH$_2$:NH$_3\sim$1:10:100 and the fractional abundance of NH is a few times 10$^{-9}$. The Sgr B2 results may, however, not be representative of cold dark clouds since this source is very complex and atypical.

The unexpectedly high NH abundance has been difficult to explain with chemical models and both the NH and NH$_2$ production by purely gas-phase processes is inhibited by a lack of a sufficient source of N$^+$. The models fail to simultaneously predict the absolute and relative abundances of the nitrogen hydrides. Typical steady state *dark cloud* models ($n$=1$\times$10$^{3}$–5$\times$10$^{4}$ cm$^{-3}$, $T$=10–40 K, $A_\mathrm{V}\gtrsim10$), predict an NH$_2$ abundance of , an NH abundance 10 times lower, and an NH$_2$/NH$_3$ ratio of for a wide range of assumptions , but these are not directly applicable to diffuse molecular gas. Examples of chemical models for diffuse cloud conditions are found in Fig. A.1 and A.2 in paper I. These models were also unable to explain the observed abundances and ratios. Processes on dust grains have previously been proposed as a way to increase the NH production [@1991ApJ...376L..49M; @1993MNRAS.260..420W]. Such models, however, often predict up to 1000 times more NH$_3$ than NH$_2$ [@1993MNRAS.263..589H paper I]. The importance of grain surface chemistry in diffuse clouds is also not clear since water ice mantles have not been detected in diffuse gas, and strong (UV) radiation fields counteract molecular formation on grains. Grain surface production of NH is therefore still debated, and would, if true, change our understanding of surface chemistry in diffuse gas. On the other hand, if grains indeed were unimportant in diffuse gas nitrogen chemistry it would imply that either key gas-phase reactions must have been overlooked, or that the uncertainty of some reaction rates could make a difference. Both additional high-quality observations and chemical modelling are needed to solve this problem.

In this paper, we present new observations and analyses of absorption lines in the line-of-sight towards the high-mass star-forming region W49N, and, we also re-analyse the absorption towards G10.6$-$0.4 in more detail. W49N is one of the most luminous high-mass star-forming regions in the Galaxy ($\sim$10$^7$L$_\odot$) with a core that contains more than a dozen ultra-compact regions [@1984ApJ...283..632D; @1990ApJ...351..189D; @2000ApJ...540..308D]. It is located on the far side of the Galaxy at a distance of 11.4kpc with Galactic coordinates $l$=43.17$^\circ$ and $b$=0.012$^\circ$, in one of the most massive giant molecular clouds ($\sim$10$^6$M$_\odot$) in the Milky Way. The source velocity is about +8kms$^{-1}$ and the foreground gas along the line-of-sight is detected at , revealing gas at two locations in the near and far side of the Sagittarius spiral arm around 40 and 60kms$^{-1}$ [@1985ApJ...297..751D]. The ultra-compact region G10.6$-$0.4 in the star-forming W31 complex is an extremely luminous sub-millimetre and infrared continuum source. The source is located within the so-called 30kms$^{-1}$ arm at a kinematic distance of 4.8kpc [@2003ApJ...587..701F]. The gas associated directly with G10.6$-$0.4 is detected at a systemic source velocity of , determined from OH maser emission observations, while the foreground gas is detected at .

Section \[observations\] summarises the observations and data reduction, and the results from our *Herschel* observations are found in Sect. \[section: results\]. The hyperfine structure (hfs) components of the nitrogen hydrides are discussed in Sect. 4. In Sect. \[Section: Analysis of abundances in different velocity components\] we use three different methods to decompose the absorption lines along the sight-lines towards both sources in different velocity components, and estimate column densities, $N$, and relative abundances, $X$, in each component. We also compare the column densities of the nitrogen hydrides, both with each other to investigate possible correlations, and with other species tracing regions with both low and high molecular fractions. Section \[OPR ammonia\] presents our estimates of the ortho-to-para ratio (OPR) of NH$_3$. We end this paper with a summary and outlook in Sect. \[section summary\]. Note that the analysis of the *background* source emissions and absorptions is left for a future paper.

Observations and data reduction {#observations}
===============================

All the reported observations are a part of the more extended PRISMAS programme towards G10.6$-$0.4 and W49N. The nitrogen observations, which took place between March 2 and April 18, 2010, are summarised in Table \[Table: transitions\]. All *Herschel* identification numbers (OBSID’s) are found in Table \[Table: obsid\] (on-line material). Note that NH was observed together with CH$_2$ at 946 GHz, and ortho-NH$_3$ was observed together with para-NH$_3$ (the absorptions from the source are 97 km s$^{-1}$ apart). Before the launch of *Herschel*, no observations of these NH$_3$ transitions, nor the NH$^+$ transition, had been performed. We do not, however, analyse the transition in this paper since this line shows absorption only at the background source velocities.

We used the dual beam switch mode and the wide band spectrometer (WBS) with a bandwidth of 4$\times$1 GHz and an effective spectral resolution of 1.1 MHz. The corresponding velocity resolution is about 0.3 kms$^{-1}$ at the highest frequencies and 0.6 km s$^{-1}$ at 572 GHz. In addition, simultaneous observations were performed using the high resolution spectrometer (HRS) with an effective spectral resolution of 0.25MHz and a bandwidth of 240–340 MHz except for the 1214 and 1215 GHz lines which had an effective resolution of 0.5 MHz and a bandwidth of 780 MHz in order to cover both lines in the same band. Note that the channel separation of the observations is 0.5 MHz in the WBS and 0.12 MHz in the HRS (0.24 MHz for the 1215 GHz line). Each line was observed with three different frequency settings of the local oscillator (LO) corresponding to a change of approximately 15 km s$^{-1}$ to determine the sideband origin of the lines. During all observations two orthogonal polarisations were used.

The pointings were centred at $\alpha$=19$^\mathrm{h}$10$^\mathrm{m}$13$\fs$2, $\delta$=09$^\circ$06$\arcmin$12$\arcsec$ ($J$2000) for W49N, and $\alpha$=18$^\mathrm{h}$10$^\mathrm{m}$28$\fs$7, $\delta$=$-$19$^\circ$55$\arcmin$5$\arcsec$ ($J$2000) for G10.6$-$0.4. The recommended values for half-power beam width of the telescope are $44\farcs 2$, $22\farcs 1$, and $18\farcs 9$ at 480, 960 and 1120 GHz, respectively. The reference beams were located within 3 on either side of the source. The total calibration uncertainties are $\lesssim$9% for band 1 and $\lesssim$13% for band 5, including the sideband gain ratio uncertainty which is 3–4% for band 1b (ortho-NH$_3$), and 4–6% for band 5a (para-NH$_3$). All errors are added in quadrature. Detailed information about the HIFI calibration including beam efficiency, mixer sideband ratio, pointing, etc., can be found on the Herschel internet site[^4]. The in-flight performance is described by . Since we are interested in absorption lines and their relative strength compared to the continuum in this paper, the forward efficiency of 96% and the main beam-efficiency of 64–76% (between 1120 and 480 GHz) do not affect our results and we have therefore used a $T_\mathrm{A}^*$ intensity scale throughout this paper.

The data were processed using the standard *Herschel* Interactive Processing Environment [HIPE,[^5] @2010ASPC..434..139O], version 5.1, up to level 2 which provides fully calibrated spectra. The data quality is excellent with very low intensity ripples in most cases, typically below a few percent of the double sideband continuum. For NH$^+$ in both sources and both polarisations, and at 572 GHz in the vertical polarisation towards G10.6$-$0.4, we corrected the data from ripples using the tool in HIPE (in paper I we only used one polarisation for these two transitions). The FITS files were then exported to the spectral line software package [xs]{}[^6] which was used in the subsequent data reduction.

The two polarisations are generally in agreement to better than 10%. The three LO-tunings are also in very good agreements without contamination from the image sideband with one exception in W49N around the at 572 GHz line (see Sect. \[subsubsection: SO2 in NH3\]). In all other spectra we averaged the three LO-tunings and both polarisations.

For the above line identification work we used the Cologne Database for Molecular Spectroscopy[^7] [CDMS, @2005JMoSt.742..215M], the Jet Propulsion Laboratory catalogue [^8] [JPL, @1998JQSRT..60..883P], and Frank Lovas’ Spectral Line Atlas of Interstellar Molecules[^9] (SLAIM). Laboratory measurements of NH transitions have been performed by e.g. and @2004JMoSp.225..189F, and measurements of o-NH$_2$ by e.g. @1999JMoSp.195..177M. A review on ammonia is found in , and an investigation of the hyperfine structure components of ortho-NH$_3$ at 572 GHz was recently performed by . NH$^+$ measurements have been made by @1986CPL...132..213V and @2009JChPh.131c4311H.

![*Nitrogen hydrides towards W49N*: Double sideband WBS spectra of NH, ortho-NH$_2$, ortho- and para-NH$_3$, and NH$^+$ over the LSR velocity range -50 to 85 km s$^{-1}$. Quantum numbers are found in Table \[Table: transitions\]. Note that we only analyse the absorption in the velocity range 30–75 km s$^{-1}$ in this paper and leave the source absorption and emission for a future paper.[]{data-label="Fig: DSB W49N hydrides"}](18686Fg01.eps)

Observational results {#section: results}
=====================

Figures \[Fig: DSB W49N hydrides\] and \[Fig: W31C All original hydrides\] (on-line material) show the averaged double sideband WBS spectra of the transitions listed in Table \[Table: transitions\] towards W49N and G10.6$-$0.4, respectively (special treatment of o-NH$_3$ 1$_0$–0$_0$ in W49N is found in Sect. \[subsubsection: SO2 in NH3\]). All detected species show very similar absorption patterns over a wide range of velocities, although W49N has fewer absorbing velocity components in the line-of-sight. No detections of NH$^+$ have been found in any of the two sources.

The resulting noise and single sideband (SSB) continuum levels, for each transition, are found in Table \[Table: transitions\]. Note that since HIFI uses double side band (DSB) receivers, the observed continuum has to be divided by two to obtain the SSB continuum. The sideband gain ratio is assumed to be unity throughout this paper. This has proven to be a good assumption based on PRISMAS observations of saturated absorption lines like HF that establish the true zero levels .

Background source emission
--------------------------

Even though we only analyse the absorption lines in the foreground clouds in this paper we still have to take the source emission into account in the analysis. Several spectra show broad emission features from the background sources which extend far into the velocity range pertaining to the line-of-sight clouds.

Ammonia in particular shows strong emission at the background source velocities with self-absorption around +13 and 0kms$^{-1}$ for W49N and G10.6$-$0.4, respectively. A large part of the NH 974 GHz emission at the source velocities in both sources is most likely not from NH, but from HCN at 974.487 GHz, only 9MHz above the NH line corresponding to 2.5 km s$^{-1}$. The PRISMAS observations of these sources have detected three additional HCN emission lines: at 532GHz, at 620 GHz, and at 886 GHz which strengthens our identification. In addition, we detect no NH emission in the 946 GHz transition which is a further confirmation that the emission is due to another species. HCN in foreground gas is unlikely to produce measurable absorption in the $J=11 - 10$ transition because the excitation energy of the lower state, $E_{10}/k$=234 K, is much too high to be populated at the density and temperature of diffuse or translucent gas.

In the analysis performed in Sect. \[Section: Analysis of abundances in different velocity components\] using three different methods, we have removed the broad emission lines that overlap with the absorption in the line-of-sight by means of Gaussian fits.

### Emission line contamination {#subsubsection: SO2 in NH3}

In W49N, close to the o-NH$_3$ line at 572 GHz, an emission line from the lower sideband, identified as the SO$_2$ line, moves across the ammonia absorption lines in the different LO-tunings. Thus for the o-NH$_3$ 572 GHz transition in W49N we were only able to use the A and C LO-settings in Table \[Table: obsid\], which also had to be cut to remove the parts contaminated by the SO$_2$ line.

The o-NH$_2$ absorption towards W49N is contaminated by a an emission line in the same sideband from the source. We identify the emission line as a blend of three unresolved hfs components of NO $^2\Pi_{1/2}\;J=9.5^f\to 8.5^f$, $F=10.5-9.5$, $9.5-8.5$, and $8.5-9.5$, at 952.464201 GHz. The NO emission line is removed from the o-NH$_2$ absorption (described in Sect. \[NO removal of NH2\], on-line material), and in all following figures in this paper we show o-NH$_2$ in W49N with removed NO emission. The NO identification is strengthened by the PRISMAS observations of three additional NO lines towards W49N shown in Fig. \[Fig: W49N NO\] (on-line material). No emission of NO is found towards G10.6$-$0.4.

### The $^{15}$NH$_3$ isotopologue: only in G10.6$-$0.4

Since our observations also covered the frequency of at 572.113 GHz, we have checked the averaged spectra for emission and/or absorption features of this isotopologue. In Figs. \[Fig: W31C NH3 and 15NH3\] and \[Fig: W31C NH3 and 15NH3 normalised\] (on-line material) we show a 5$\sigma$ emission feature in G10.6$-$0.4 with an amplitude of 40 mK and a line-width of about 4 km s$^{-1}$, which we identify as giving a source velocity of $\sim -$4 km s$^{-1}$. Checking the possibility of absorption lines of o-$^{15}$NH$_3$ in the line-of-sight towards G10.6$-$0.4, we note that there seems to be an absorption feature corresponding to the strongest velocity components of at $\sim$27–32 km s$^{-1}$. This feature is, however, probably not a real detection since it would otherwise imply that This is about 20 times lower than the $^{14}$N/$^{15}$N ratio in the local ISM which is about $\sim$450 , or 441$\pm$5 in the Solar nebula [@2011Sci...332.1533M]. Odin observations of absorption towards Sgr B2 show $^{14}$NH$_3$/$^{15}$NH$_3 > 600$ . Lower ratios have been found, for instance, in low mass cores, 334$\pm$50 [@2010ApJ...710L..49L], and on Earth, $\sim$270. @2011IAUS..280P..76A find values of using CN and HNC in ten dense molecular clouds located at various galactic distances from the Galactic Centre, but this is still several times higher than inferred from a possible o-$^{15}$NH$_3$ absorption. The $^{14}$N/$^{15}$N ratio is also difficult to determine and the results using cyanides may differ from the ratio inferred from other species such as N$_2$H$^+$, and may not reflect the true $^{14}$N/$^{15}$N abundance ratio. More observations are needed to lower the noise in order to obtain a real detection of and to determine the true $^{14}$N/$^{15}$N ratio towards G10.6$-$0.4.

In W49N, no o-$^{15}$NH$_3$ detection is made due to blending SO$_2$ lines from the upper sideband which are both stronger and broader than in G10.6$-$0.4. In addition, the o-$^{14}$NH$_3$ emission is more than two times weaker than in G10.6$-$0.4, and the spectrum has a three times higher noise level which does not allow a detection of o-$^{15}$NH$_3$ emission from the source.

Hyperfine structure components {#section: hfs}
==============================

Both NH and NH$_2$ have numerous hyperfine structure (hfs) components which require a high resolution spectrometer, such as HIFI, to be spectrally resolved. The on-line Tables \[Table: NH hfs transitions\]–\[Table: NH2 hfs transitions\] list the hfs components of the NH 974 and 946 GHz, and the 953 GHz transitions which have 21, 9, and 30 hfs components, respectively. The observed NH 974 GHz and o-NH$_2$ transitions in the +39 km s$^{-1}$ velocity component towards W49N are shown in Figs. \[Fig: NH hfs lines in 39 kms in W49N\] and \[Fig: NH2 hfs lines in 39 kms in W49N\] together with models of respective transition, including hfs components, using Gaussian opacity profiles and a line width of 1 km s$^{-1}$. Here, the intensities have been normalised to the continuum in single sideband as $T_\mathrm{A}$/$T_\mathrm{C}$-1 assuming a sideband gain ratio of unity where $T_\mathrm{A}$ is the observed intensity and $T_\mathrm{C}$ is the SSB continuum as measured in line-free regions in the spectra. The large number of hfs components, in addition to many different, overlapping, velocity components in the line-of-sight, complicates the analysis substantially. In particular, the o-NH$_2$ hfs components in the line-of-sight absorption overlap with the source emission/absorption, thus requiring a source model in the analysis.

![*NH hfs components*: Normalised WBS spectrum towards W49N. Also shown are Gaussian fits with a line width of 1 km s$^{-1}$ of the NH 974 GHz hfs components in the +39 km s$^{-1}$ velocity component.[]{data-label="Fig: NH hfs lines in 39 kms in W49N"}](18686Fg03.eps)

![*Ortho-NH$_2$ hfs components*: Normalised WBS spectrum towards W49N. Also shown are Gaussian fits with a line width of 1 km s$^{-1}$ of the o-NH$_2$ 953 GHz hfs components in the +39 km s$^{-1}$ velocity component.[]{data-label="Fig: NH2 hfs lines in 39 kms in W49N"}](18686Fg04.eps)

The much simpler hyperfine structure of the ortho- and para-NH$_3$ ground state rotational transitions has never been resolved in space before *Herschel*. The Odin satellite was able to observe the 572 GHz ammonia transition, but the velocity resolution of about 0.5 km s$^{-1}$ was not enough to spectrally resolve the hfs components even though the asymmetric line shapes hinted the hfs components . Figure \[Fig: NH3 hfs lines\] shows an example of our observations of the 572 GHz o-NH$_3$ transition in the +39 km s$^{-1}$ absorption velocity component towards W49N with the HRS and a velocity resolution of 0.13 km s$^{-1}$. Three hfs components are seen at 38.4, 39.4 and 40.0 km s$^{-1}$ although the line width of 1.0 km s$^{-1}$ prevents a detailed check of the relative intensities. In the Gaussian fit we therefore use 0.2, 1 and 0.6 as relative intensities, with corresponding relative offsets at -1.05, 0.0, and 0.52 km s$^{-1}$ found by (Table \[Table: NH3 hfs components\], on-line material). The positions and relative intensities of the hfs components and the fitted opacity profiles are also shown in Fig. \[Fig: NH3 hfs lines\]. The six hfs components in the para-NH$_3$ line at 1215 GHz are even more closely spaced and not resolved (Table \[Table: NH3 1215 hfs components\]).

The WBS ammonia observations do not spectrally resolve the NH$_3$ hfs components ($\Delta v$=0.6 km s$^{-1}$ at 572 GHz and $\Delta v$=0.3 km s$^{-1}$ at 1215 GHz), but we still take the hfs components into account in the following NH$_3$ modelling since they produce a slightly asymmetric line shape and a systematic line broadening.\
\

Analysis: Velocity decomposition, column densities, and abundances {#Section: Analysis of abundances in different velocity components}
==================================================================

In paper I we estimated the abundances towards G10.6$-$0.4 simply by evaluating the integrated opacity of each line over the velocity range . This approach gave a first estimate of the average abundance in the full line-of-sight, but did not take into account possible abundance variations in the different velocity components. In addition, no source model was included, and thus the blend of the NH and o-NH$_2$ hfs components from the foreground absorptions with the source absorption was neglected.

In this paper we use three different approaches to decompose the absorption into separate velocity components, and to obtain column densities and abundances in each component. Each method has its own strengths and weaknesses, and differences in the results can be considered an estimate of the errors of the methods. If all three methods point to the same result, it will be considered as robust. We note, however, that the uncertainties of the data are higher towards W49N than for G10.6$-$0.4, since we have removed a SO$_2$ line from the upper sideband in the ortho-NH$_3$ absorption, and an NO line in the o-NH$_2$ absorption.

In this work we also only estimate $N$ and $X$ for the ortho-symmetries of NH$_2$ and NH$_3$ since our own measurements of the ammonia OPR in Sect. \[OPR ammonia\] do not point to the high temperature limit, but instead suggest an OPR *lower* than unity, which cannot be straightforwardly explained. If this unexpected low ammonia OPR is true, then the processes that affect the ammonia OPR perhaps also could affect the OPR of NH$_2$ in diffuse clouds about which we have no information. And since we want to compare relative abundances, we choose to focus on the ortho-symmetries since both are observed in NH$_2$ and NH$_3$, and also since the observations have higher S/N than the .

To obtain integrated opacities of each transition, in each velocity component, the first method uses Gaussian fitting (Sect. \[henriks method\]), while the second one uses the observed spectra of ortho-NH$_3$ and CH as templates for other species (Sect. \[massimos method\]). Both methods calculate the opacity as . The derived integrated opacities are then used to estimate column densities by means of the non-LTE (Local Thermodynamic Equilibrium) [RADEX]{} code (Sect. \[Section: RADEX\]). As a third method, we have used XCLASS (Sect. \[Bhaswatis method\]) which, in contrast to [RADEX]{}, assumes fixed excitation temperatures, to obtain column densities in each velocity component .

In order to be able to use our results as comparisons with chemical models, we need to derive the abundance of the species with respect to the total amount of gas. The difficulty is to obtain reliable estimates of $N$(H) and/or $N$(H$_2$). In paper I, we compared the nitrogen hydrides column densities to the total amount of hydrogen in the line-of-sight, $N_\mathrm{H}$=$N$(H)+2$N$(H$_2$). This can not be done in the present work since the neutral hydrogen absorption shows too broad and overlapping absorption components over much larger velocity ranges as compared to the nitrogen hydrides. In order to estimate the amount of molecular hydrogen in each (narrow) velocity component, we therefore consider the comparison with CH as an abundance determination. This can be made using the CH/H$_2$ correlation (CH/H$_2$=3.5$\times$10$^{-8}$) observed by @2008ApJ...687.1075S in the solar neighbourhood diffuse medium. This correlation is assumed to be valid in regions which are dominated by ultraviolet radiation where $N$(CH)$\lesssim$2$\times$10$^{14}$ cm$^{-2}$. In this way we can use our own PRISMAS observations of CH and measure abundance ratios obtained with the same instrument.

The physical properties of the bulk of the absorbing gas in our sight-lines are , according to the definitions of , a mixture of diffuse ($N_\mathrm{H}\!\!\lesssim\!\!500$ cm$^{-3}$ and and translucent gas ( and a shielding ). And since the comparison later in this section of the nitrogen hydrides with other species tracing both high and low density gas, points to an existence in the denser parts of the gas, molecular hydrogen is most likely the dominant form of hydrogen in these components.

Assuming that the nitrogen hydrides co-exist with HF and H$_2$O in the line-of-sight material we use the fact that the saturated absorptions of the latter two species reach the zero level, for a sideband ratio of unity, to support our assumption that the foreground absorbing material completely covers the continuum within the beam. Comparison spectra of o-NH$_3$ and o-H$_2$O are shown in Figs. \[Fig: W49N comparison species\]–\[Fig: W31C comparison species\], and with HF, ortho- and para-H$_2$O in Figs. \[fig: comparison of W31C-W49N NH, NH2 vs 572, 572 and 1215, CH\]–\[fig: comparison of W31C-W49N 572 vs CH, water, h2o+\] (on-line material).

[lrccl ]{} Species $x$ & Transition & $T_\mathrm{ex}$ & $N(x)$($\int  \tau d v$=1.0 km s$^{-1}$)\
& (GHz)& (K) & (cm$^{-2}$)\

NH & 946.476& 3.9 & 3.65$\times$10$^{13}$ & $a$\
& 974.478&4.0 & 7.47$\times$10$^{12}$ &$a$\
o-NH$_2$ & 952.578& 3.9& 3.62$\times$10$^{12}$ &$b$\
o-NH$_3$ & 572.498 & 2.8 & 3.92$\times$10$^{12}$ & ${b}$\
p-NH$_3$ & 1215.245 &4.9 & 1.65$\times$10$^{13}$ & ${b}$\
NH$^+$ & 1012.524& 4.2 & 6.48$\times$10$^{12}$ &\
CH & 532.724&2.9 & 2.28$\times$10$^{13}$ &$b$\
HNC & 90.664 &2.8 & 1.80$\times$10$^{12}$ &${b}$\
CN & 113.169 &2.8 & 1.90$\times$10$^{13}$ &${b}$\
\[Table: columns opacity one\]

[RADEX]{} {#Section: RADEX}
---------

Observations of absorption lines can provide accurate determinations of molecular column densities if the observed transitions trace all of the populated states. In the case of NH$_3$ we observe two transitions of the ortho (A-symmetry) form, arising in the $J_K=0_0$ and $1_0$ states, and one transition of the para (E-symmetry) form arising in the lower $1_1$ rotation-inversion level. Although the upper $1_1$ inversion level is less metastable than the lower one, it may still be significantly populated. The metastable $2_2$ para levels and $3_3$ ortho levels may also have significant populations in diffuse molecular clouds at low density, , owing to infrared pumping and formation. Because we are directly sensitive to three lower states and lack direct information about the excitation temperatures of the observed transitions, we use the non-equilibrium [[RADEX]{}]{} code to relate the total column density of ammonia to the observed integrated optical depths. The models provide integrated opacities of both observed and unobserved excited levels and quantify possible effects of stimulated emission, chemistry, and electron collisions. Results for one reference model are summarised in Table \[Table: columns opacity one\], where conversion factors for all nitrogen hydrides and comparison species are listed in terms of the total column density $N(x)$ of molecule $x$ that is needed to achieve an integrated optical depth $\int \tau dv = 1.0$ km s$^{-1}$ in the specified transition. In this model we treat ortho- and para-symmetries separately. The integrated optical depth is a sum over all hyperfine structure in the transition.

We have assumed diffuse molecular cloud conditions with a kinetic temperature of 30 K and a density of molecular hydrogen , which corresponds to . The resulting conversion factors for the rotational ground state transitions are not very sensitive to density, temperature or electron collisions. The critical densities of the fundamental rotational transitions of NH, NH$_2$, and NH$_3$ are high, $n_\mathrm{crit} \! \sim$10$^8$cm$^{-3}$. This means the upper energy levels of these transitions must be excited almost entirely radiatively at the low densities in diffuse gas. We find, however, that electron collisions can be responsible for excitation temperatures of $\sim\!4$ K in the cm-wave inversion transitions rather than $\lesssim\!3$ K that would be found in conventional excitation analyses at low densities, $n({\rm H}_2)\lesssim 10^3$ cm$^{-3}$. Where collision rates are unknown, we have made guesses scaled in proportion to radiative line strengths. The background radiation field includes both the 2.725 K cosmic microwave background and a model of the Galactic infrared radiation in the solar neighborhood. The resulting excitation temperatures of the observed sub-millimetre transitions are typically , which are small enough compared to $h\nu/k$ that no correction for emission is required. Note that the lower state of the 572 GHz transition contains $95\%$ of the ortho molecules while the lower state of the 1215.2 GHz transition occupies only $43\%$ of the para molecule.

Method I: Multi-Gaussian fit of the nitrogen hydrides simultaneously {#henriks method}
--------------------------------------------------------------------

We have modelled the observed spectra of NH, , and using Gaussian optical depth profiles. These were generated for each hfs component of each species in separate velocity intervals, and were made to fit the observations under the condition that the LSR velocity and width in each velocity component must be the same for all molecules. This can be made assuming that all species co-exist in the same velocity ranges and therefore show absorption at the same velocities. This assumption is supported by the striking similarities of the strongest NH, and absorptions, despite the complicated hyperfine structure patterns of NH and , shown in normalised comparison spectra in Fig. \[fig: comparison of W31C-W49N NH, NH2 vs 572, 572 and 1215, CH\] (on-line material). We note that a good fit therefore is a good indicator if this assumption is valid.

The observed line profiles are thus modelled by Gaussian components of both the hfs components and all velocity components according to $$\frac{T_\mathrm{A}}{T_\mathrm{C}} = \exp\,\biggl[-\sum_{i=1}^{N_{v}}   \sum_{j=1}^{N_\mathrm{hfs}}  
\tau_\mathrm{hfs}(j) \, \tau_0(i) \,  \exp[-4 \ln(2)\,\biggl[\frac{v-v_\mathrm{0}(i)-v_\mathrm{hfs}(j)}
{\Delta v}
\biggr]^2 \biggr]\ ,$$ where $N_v$ is the number of the modelled velocity components (same for all species), $N_\mathrm{hfs}$ is the number of hfs components (which differs between species), $\tau_\mathrm{hfs}$ is the theoretical relative line strength of each hfs component, $\tau_0$ is the opacity of the strongest hfs component in each velocity component, $v_\mathrm{0}$ is the LSR velocity of each velocity component, $v_\mathrm{hfs}$ is the relative velocity offset of the hfs components with respect to the strongest, and $\Delta v$ is the FWHM (full width of half maximum). We assume that for the hfs components of NH and o-NH$_2$, since the many overlapping velocity components prevent a check of the relative intensities of these components.

We have used both ortho- and para-NH$_{3}$, which are not significantly complicated by hfs splitting, to determine the minimum number of velocity components needed, and also to set-up reasonable initial guesses for the line properties necessary for the fitting procedure to converge at all. The fitting was done for each velocity component at a time in a loop until all fits had converged. The fits are most likely not unique. Provided that the fits are good and that we use the same velocity parameters for all species, this is, however, not considered important as we do not ascribe any physical meaning to the Gaussian components.

The results from Method I are peak opacities, line widths and centre velocities for each velocity component and species. The integrated opacity in each velocity component was assumed to be well represented by $\int\tau \,\mathrm{d}  v  = 1.06 \,\Delta v \, \tau_\mathrm{peak}$. The non-detections of NH$^+$ are used to put upper limits on its integrated opacities (3$\sigma$). We then used the conversion factors in Table \[Table: columns opacity one\] to calculate the column densities tabulated in Table \[Table: Method I resulting ratios and columns\]. Typical errors in the G10.6$-$0.4 resulting column densities for NH, o-NH$_2$ and o-NH$_3$ are between 7 and 15%. In the $v_\mathrm{LSR}$=45 km s$^{-1}$ component, the errors are 22% for all three species, and 23% in the $v_\mathrm{LSR}$=39 km s$^{-1}$ component for NH. The errors in W49N varies between 8 to 11% for all three species, except in the 33 km s$^{-1}$ component where the uncertainties are 37, 26 and 31% for NH, o-NH$_2$ and o-NH$_ 3$, respectively. The errors include calibration uncertainties (see Sect. \[OPR ammonia\]) as well as uncertainties from the fitting procedure.

In addition to the nitrogen hydrides, we also modelled the PRISMAS CH 532 GHz transition, and the CN 113 GHz and HNC 91 GHz transitions observed with the IRAM 30 m antenna [@2010Godard]. These species were not included in the fitting procedure described above. Instead we have used the resulting velocity parameters from the fits of the nitrogen hydrides ($v_\mathrm{LSR}$ and line widths) since we want to investigate possible correlations and make abundance determinations only in the same parts of velocity space as the nitrogen hydrides. The resulting CH column densities are found in Table \[Table: Method I resulting ratios and columns\], and the CN and HNC column densities in the on-line Table \[Table: Method I, III CN and HNC columns\].

Figures \[Fig: W49N N-hydrides normalised\] and \[Fig: W31C N-hydrides normalised\] show the fits and residuals of the nitrogen hydrides together with CH. The resulting fits are well reproducing the observations for all species except for CH suggesting that CH exist in a more widely spread gas than the nitrogen hydrides.

The CH column densities are then used together with the relation \[CH\]/\[H$_2$\]=3.5$\times$10$^{-8}$ [@2008ApJ...687.1075S] to estimate the abundances listed in Table \[Table: Method I resulting ratios and columns\].

[lc ccc ccc c llll ]{}\
$v_\mathrm{LSR}$ & $\Delta v$ & $N$(NH) & $N$(oNH$_2$) & $N$(oNH$_3$) &$N$(NH$^+$) &$N$(CH) & ${{\rm NH}\over{{\rm oNH}_3}}$ &${{\rm oNH}_2\over{{\rm oNH}_3}}$ & $X$(NH) & $X$(oNH$_2$) & $X$(oNH$_3$) & $X$(NH$^+$)\
(kms$^{-1}$) &(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$)\

33.3 & 2.1 & 1.5e12 & 2.1e12 & 4.6e11 &$\lesssim$3.3e11 &1.6e13& 3.3 & 4.6 & 3.3e-9& 4.6e-9 & 1.0e-9 & $\lesssim$7.2e-10\
39.5 & 1.1 & 1.0e13 & 7.3e12 & 4.3e12 &$\lesssim$2.4e11 &2.3e13& 2.3 & 1.7 & 1.5e-8& 1.1e-8 & 6.5e-9 & $\lesssim$3.7e-10\
59.2 & 2.9 & 9.2e12 & 4.1e12 & 2.1e12 &$\lesssim$7.5e11 &6.0e13& 4.4 & 2.0 & 5.4e-9& 2.4e-9 & 1.2e-9 & $\lesssim$4.4e-10\
62.7 & 2.3 & 8.0e12 & 3.9e12 & 2.2e12 &$\lesssim$6.3e11 &5.1e13& 3.6 & 1.8 & 5.5e-9& 2.7e-9 & 1.5e-9 & $\lesssim$4.3e-10\
Total: &…&2.9e13 & 1.7e13 & 9.1e12 &$\lesssim$2.0e12& 1.5e14& 3.2 & 1.9 & 6.7e-9 & 4.1e-9 & 2.1e-9 & $\lesssim$4.6e-10\
Mean: &…&7.2e12& 4.4e12 & 2.3e12 &$\lesssim$4.9e11& 3.8e13& 3.2 & 1.9 & 6.7e-9 & 4.1e-9 & 2.1e-9 & $\lesssim$4.6e-10\
Median: &…&8.6e12& 4.0e12 & 2.2e12 &$\lesssim$4.8e11& 3.7e13& 4.0 & 1.9 & 8.1e-9 & 3.8e-9 & 2.0e-9 & $\lesssim$4.5e-10\
\
$v_\mathrm{LSR}$ & $\Delta v$ & $N$(NH) & $N$(oNH$_2$) & $N$(oNH$_3$) &$N$(NH$^+$) &$N$(CH) & ${{\rm NH}\over{{\rm oNH}_3}}$ &${{\rm oNH}_2\over{{\rm oNH}_3}}$ & $X$(NH) & $X$(oNH$_2$) & $X$(oNH$_3$) & $X$(NH$^+$)\
(kms$^{-1}$) &(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$)\
16.2 & 1.7 & 2.0e13 & 9.6e12 & 4.2e12 &$\lesssim$4.7e11 & 5.8e13 & 4.8 & 2.3 & 1.2e-8 & 5.8e-9 & 2.5e-9 & $\lesssim$2.8e-10\
18.8 & 1.5 & 6.1e12 & 3.1e12 & 8.7e11 &$\lesssim$4.1e11 &2.6e13 & 7.0 & 3.6 & 8.2e-9 & 4.2e-9 & 1.2e-9 & $\lesssim$5.5e-10\
22.1 & 4.4 & 1.6e13 & 6.9e12 & 1.8e12 & $\lesssim$1.2e12 &7.7e13 & 8.9 & 3.8 & 7.3e-9 & 3.1e-9 & 8.2e-10 & $\lesssim$5.5e-10\
22.8 & 1.0 & 1.0e13 & 3.6e12 & 1.5e12 & $\lesssim$2.7e11 & 7.1e12 & 6.7 & 2.4 & 4.9e-8 & 1.8e-8 & 7.4e-9 & $\lesssim$1.3e-9\
24.8 & 3.1 & 6.2e12 & 4.3e12 & 1.4e12 &$\lesssim$8.4e11 & 3.7e13 & 4.4 & 3.1 & 5.9e-9 & 4.1e-9 & 1.3e-9 & $\lesssim$8.0e-10\
27.8 & 1.9 & 2.7e13 & 1.2e13 & 7.3e12 &$\lesssim$5.0e11 & 7.4e13 & 3.7 & 1.6 & 1.3e-8& 5.7e-9 & 3.5e-9 & $\lesssim$2.4e-10\
29.9 & 1.7 &2.9e13 & 1.3e13 & 7.9e12 & $\lesssim$4.6e11 &5.6e13 & 3.7 & 1.6 & 1.8e-8 & 8.1e-9 & 4.9e-9 & $\lesssim$2.9e-10\
32.1 & 1.5 &9.0e12 & 3.5e12 & 1.3e12 & $\lesssim$4.1e11 &3.5e13 & 6.9 & 2.7 & 9.0e-9 & 3.5e-9 & 1.3e-9 & $\lesssim$4.1e-10\
36.1 & 4.0 & 2.0e13 & 6.5e12 & 3.2e12 & $\lesssim$1.1e12 &7.8e13 & 6.3 & 2.0 & 9.0e-9 & 2.9e-9 & 1.4e-9 & $\lesssim$4.9e-10\
39.0 & 1.2 & 1.1e13 & 3.0e12 & 4.7e11 & $\lesssim$3.1e11 & 3.3e13 & 23 & 6.4 & 1.2e-8 & 3.2e-9 & 5.0e-10 & $\lesssim$3.3e-10\
40.9 & 1.7 &3.0e13 & 1.1e13 & 4.1e12 & $\lesssim$4.7e11 &5.4e13 & 7.3 & 2.7 & 1.9e-8 & 7.1e-9 & 2.7e-9 & $\lesssim$3.0e-10\
45.0 & 1.4 & 3.0e12 & 1.1e12 & 5.9e11 &$\lesssim$3.6e11 & 1.1e13 & 5.1 & 1.9 & 9.6e-9 & 3.5e-9 & 1.9e-9 & $\lesssim$1.1e-9\
Total: & …&1.9e14 & 7.8e13 & 3.5e13 &$\lesssim$6.8e12 & 5.5e14 & 5.4 & 2.2 & 1.2e-8 & 5.0e-9 & 2.2e-9 & $\lesssim$4.4e-10\
Mean: &…&1.6e13& 6.5e12 & 2.9e12 &$\lesssim$5.7e11 &4.6e13 & 5.4 & 2.2 & 1.2e-8 & 5.0e-9 & 2.2e-9 & $\lesssim$4.4e-10\
Median: &…&1.4e13& 5.4e12 & 1.7e12 &$\lesssim$4.7e11 &4.6e13 & 8.2 & 3.3 & 1.0e-8 & 4.2e-9 & 1.3e-9 & $\lesssim$3.6e-10\
\[Table: Method I resulting ratios and columns\]

Method II: ortho-NH$_3$ and CH as templates for other species {#massimos method}
-------------------------------------------------------------

This method directly compares the opacity line profile of the non-saturated o-NH$_3$ line at 572 GHz with the line profiles of NH and o-NH$_2$, convolved with respective hyperfine structure. This assumes that all species co-exist in the same velocity ranges, and that the opacity ratios depend only on their column density ratios, which may vary from one velocity component to another. No opacity profile is assumed for a given absorbing cloud so, unlike what is done by methods I and III, we do not attempt to decompose the velocity structure of the template line into a number of Gaussian curves. We perform, instead, simple cuts of the template profile into large velocity bins.

The hfs of the o-NH$_3$ line is not resolved in the WBS data and introduces only a small broadening of the lines that is dealt with by smoothing the NH and o-NH$_2$ spectra. Before comparing the opacity profiles, we mask out those portions of the spectra where a simple scaling between template and target is not expected, such as the velocity range associated to the background sources, and remove the emission line wing by Gaussian fitting. We note that the removal of the line wing introduces very large uncertainties towards W49N around 33 km s$^{-1}$ where a weak absorption component is visible. This method therefore disregards the results in this velocity component.

The velocity bins into which the o-NH$_3$ opacity profile is split are chosen to be significantly larger than the original resolution, but narrow enough to separate the most prominent velocity features (typically a few km s$^{-1}$, see Table \[Table: Model II ratios results\]). Each velocity bin of the o-NH$_3$ template is then convolved, channel by channel, with the NH and o-NH$_2$ hfs components. We thus obtain an intermediate opacity model of how the NH and o-NH$_2$ spectra would appear if absorption were limited to the selected velocity bin. The observed o-NH$_3$ opacity is then fitted by the IDL Least Squares Fitting routine MPFIT [@2009ASPC..411..251M] with a linear combination of the intermediate models. The output of the fits consists of the opacity ratios, between the o-NH$_3$ and the modelled NH and o-NH$_2$ spectra, in the various velocity bins.

To obtain column densities in each velocity bin, we sum the opacities of all channels of the template transition, and then apply the [RADEX]{} conversion factors from Table \[Table: columns opacity one\]. The resulting abundance ratios are finally used to obtain column densities of the other species. Typical errors (including both calibration and fitting uncertainties) are except for the velocity bin in G10.6$-$0.4 and the velocity bin in W49N which both have an uncertainty of approximately 25%.

The main advantage of this method is that a small number of free parameters is needed to obtain a reasonable fit since it uses, as much as possible, the information carried by the template spectrum. The model also avoids the problem of non-uniqueness of Gaussian decompositions of the absorption profiles and allows a straightforward comparison of column densities evaluated for exactly the same velocity intervals. On the other hand, such rigidity in the definition of the velocity bins does not allow us to reliably retrieve the column density ratios if the absorption comes from very different gas volumes resulting in significant velocity shifts of the absorption features between the two species. We note that the fit quality, estimated with $\int |\mathrm{residuals}|\times \mathrm{d} v \, / \int \tau\times \mathrm{d} v$, is a good indicator of such cases. Note also that residual baseline structures, like those produced by standing waves or by an imperfect removal of ammonia emission line wings, may introduce artificial discrepancies between the template spectra and the modelled species.

![*W49N: Fits of Method I* and the SSB normalised spectra of the nitrogen hydrides and CH. The black lines are the observations, and the coloured lines are the model fits. In the bottom the residuals are plotted on top of each other with respective colour. The three transitions used in Method I to determine the $v_\mathrm{LSR}$ and line widths of the velocity components are marked in bold.[]{data-label="Fig: W49N N-hydrides normalised"}](18686Fg06.eps)

![*G10.6$-$0.4: Fits of Method I* and the SSB normalised spectra of the nitrogen hydrides and CH. Same notation as in Fig. \[Fig: W49N N-hydrides normalised\].[]{data-label="Fig: W31C N-hydrides normalised"}](18686Fg07.eps)

In addition to the above modelling, we use the o-NH$_3$ as a template for CN and HNC [@2010Godard], and also use the deconvolved CH spectrum at 532.724 GHz as a template to model all three nitrogen hydrides, in order to obtain an estimate of the abundance with respect to molecular hydrogen.

The resulting column densities and relative abundances in different velocity bins are given in Table \[Table: Model II ratios results\], except for the CN and HNC results which are found in on-line Table \[Table: Method II CN and HNC columns\].

The model fits compared to the normalised spectra in both sources are shown in Figs. \[Fig: W49N method I NH and NH2 from NH3\]–\[Fig: W31C method I NH, NH2, NH3 from CH\] (on-line material). The fit qualities of the comparisons between the o-NH$_3$, NH and o-NH$_2$ are excellent, except in the narrow and deep +39 km s$^{-1}$ component towards W49N which was very difficult to model. The modelling of the nitrogen hydrides using CH as a template show on the other hand rather low fit qualities, suggesting that the assumption that the nitrogen hydrides and CH only come from the same gas is less justified, also supported by Method I.

Method III: XCLASS {#Bhaswatis method}
------------------

Finally, we have generated synthetic spectra separately for NH, o-NH$_2$, o-NH$_3$, CH, CN, and HNC using the software XCLASS[^10] [created by P. Schilke, and described by @2005ApJS..156..127C and references therein] by considering for each species all hfs components and velocity components and the assumption of a fixed excitation temperature. The synthetic spectra generated with XCLASS were fitted to the observed spectra using MAGIX, an iterating engine that allows automatic minimization to constrain model parameters. XCLASS accesses the CDMS and JPL molecular databases, and models each molecule with the following free parameters: source size, temperature, column density, line width and velocity offset relative to the systemic velocity of the source, and derives the column density corresponding to the different velocity components detected in absorption and emission in the observed spectra. The source size refers to the relative size of the absorbing cloud vs. the continuum source, which is assumed to be fully covered within the beam. We have assumed a Gaussian profile for each hfs component, and an excitation temperature of 4 K. Since Method III explicitly assumes a fixed excitation temperature for the estimate of column densities, it is significantly different from methods I and II.

Figures \[Fig: w49n guass fits n-hydrides method III\] and \[Fig: w31c guass fits n-hydrides method III\], in the on-line material, show the model fits together with the observed SSB normalised spectra. Resulting column densities and abundance ratios of the nitrogen hydrides and CH are found in the on-line Table \[Table: Method III resulting ratios and columns\], and the CN and HNC column densities in on-line Table \[Table: Method I, III CN and HNC columns\].

Comparison of results {#Subsection: comparison of results}
---------------------

The results from all three methods agree very well, especially considering that the velocity bins used are not the same.

The total $N$(CH) from all methods are lower than found by , which is expected since we only use parts of the CH absorptions. Comparisons of CH in different velocity bins give much more similar results in both sources. Since we use CH as a tracer of H$_2$, we also compare our estimate of $N$(H$_2$) with towards W49N: for the +39 km s$^{-1}$ component they suggest and they also quote which gives using a standard conversion factor of 10$^{-6}$. They also suggest column densities towards W49N between and from $^{13}$CO observations. All these suggestions for $N$(H$_2$) are several times higher than inferred from our CH observations. This is, however, not surprising because the $^{13}$CO conversion factor is rather uncertain at such low column densities. @2004ApJ...605..247P also obtain higher $N$(H$_2$) than we do towards W49N. The total amount of $N$(H$_2$) in the sight-lines towards our sources, can also be compared with estimates from the K-band extinction : and 7.5$\times$10$^{21}$ cm$^{-2}$ towards W49N and G10.6$-$0.4, respectively.

The resulting NH mean abundances of all three methods in all velocity components are 5.5$\times$10$^{-9}$ and 1.1$\times$10$^{-8}$ in W49N and G10.6$-$0.4, respectively. This can be compared to the average $N$(NH)/$N$(H$_2$) value of 3$\times$10$^{-9}$ in diffuse and translucent sight-lines found by @2009MNRAS.400..392W. The mean values of o-NH$_2$ are 3.1$\times$10$^{-9}$ and 4.5$\times$10$^{-9}$ in W49N and G10.6$-$0.4, respectively, and 1.5$\times$10$^{-9}$ and 1.9$\times$10$^{-9}$ for o-NH$_3$.

Our upper limits on the NH$^+$ abundances, relative to molecular hydrogen, are similar in both sources with mean value $N$(NH$^+$)/$N$(H$_2$) $\lesssim$4$\times$10$^{-10}$. This is orders of magnitudes lower than previous findings from ultraviolet observations towards $\rho$Oph , but still much higher than the predictions from the chemical models presented in Paper I: approximately 10$^{-13}$–10$^{-14}$. The upper limits of the NH$^+$ abundance compared to NH are $\lesssim$2–14% in the different velocity components (except in the uncertain velocity feature around +33 km s$^{-1}$ in W49N), with a mean ratio of $\lesssim$6%. This is in contrast to the behaviour of CH$^+$ and marginally with that of OH$^+$ with respect to the corresponding neutrals. The CH$^+$ radical reaches comparable column densities to those of CH [e.g. @1995ApJS...99..107C], and $N$(OH$^+$) is a factor 30 below $N$(OH) in the visible data [@2010ApJ...719L..20K].

Since our different approaches to deconvolve the velocity components for the observed species agree well, we estimate that the uncertainties in our derived absolute column densities are $\lesssim$20–50%. The column densities for CH have larger uncertainties, but we estimate that the absolute $N$(CH) results are correct within a factor of approximately two. Furthermore, the scatter in the CH to H$_2$ relationship is estimated by @2008ApJ...687.1075S to a factor of 1.6. In summary, we believe that the abundance determinations from CH are correct within a factor of a few. The abundance ratios of the nitrogen hydrides, relative to each other, are on the other hand more accurately determined.

The results of all three methods confirm our conclusion of the analysis of G10.6$-$0.4 in paper I that NH is more abundant than NH$_2$ and NH$_3$ by a factor of approximately , assuming the high temperature ortho-to-para limits of three and one, respectively. Note that the mean abundances of are similar towards both sources, $\sim$2$\times$10$^{-9}$, in contrast to , and, in particular NH, which have higher mean abundances towards G10.6$-$0.4 than towards W49N.

Comparison and correlations of species {#Comparison and correlations of species}
--------------------------------------

Figures \[Fig: W49N comparison species\] and \[Fig: W31C comparison species\] show and five SSB normalised comparison spectra, and in the on-line material Figs. \[fig: comparison of W31C-W49N NH, NH2 vs 572, 572 and 1215, CH\]– \[fig: comparison of W31C-W49N 572 vs CH, water, h2o+\] we show additional comparisons of the nitrogen hydrides with the deconvolved CH absorption, the H 21 cm line, H$_2$O$^+$, OH$^+$, HNC, CN, ortho- and para-H$_2$O, HF, and HCO$^+$.

The CH spectra show absorption over a much wider range of velocities in both sources than the nitrogen hydrides. Ammonia largely follows the CH absorptions, but there are also large differences in some parts of the spectra where there is no or very little absorption of NH$_3$, while CH shows a much broader and stronger absorption, for instance at , and towards W49N. Ammonia seems to trace CH slightly better towards G10.6$-$0.4 than W49N. This comparison suggests that CH exists in both relatively low and high density gas, while the nitrogen hydrides only exist in the parts of the interstellar gas with a relatively high density.

These differences are even more pronounced when comparing with neutral hydrogen as observed by the VLA $\lambda$21 cm absorption by @2003ApJ...587..701F, which shows absorption over a very wide range of velocities with a resolution of 2.5 km s$^{-1}$. The much more extended velocity space coverage of the HI absorption is expected since not all foreground clouds have molecular gas.

The ammonia absorption also follow similar trends as HCO$^+$ $J$=1$\leftarrow$0 [@2010Godard], and H$_ 2$O, which is known to trace clouds of high molecular fraction . HCO$^+$ and H$_ 2$O seem to have a rather constant abundance ratio in these sight-lines, in contrast to their abundances with respect to ammonia. The comparison of ammonia to H$_ 2$O$^+$ and OH$^+$, which mostly reside in lower density gas containing considerable amounts of atomic hydrogen , shows no similarities.

When we compare ammonia with CN and HNC we find very similar absorption patterns. The CN single hyperfine component and the HNC $J$=1$\leftarrow$0 line were observed with the IRAM 30 m antenna [@2010Godard]. Note, that HNC has three hfs components that, however, lie very close in velocities (0.2 and 0.5 km s$^{-1}$), which mostly leads to a broadening of the absorption features. These species mainly reside in denser gas than CH, and both are closely connected to the NH and NH$_2$ chemistry .

### Column density correlations

In order to quantitatively examine abundance correlations of the nitrogen hydrides, CH, HNC and CN, we show column density plots in Figs. \[fig: column density plots 1\]–\[fig: column density plots 2\]. We have here plotted the results from Method I. The parameters of the linear least square fits to the data are found in the figures in addition to the correlation coefficient $R$. In the on-line material we also show column density plots with all three methods (Figs. \[Fig: column density plots 1\]–\[Fig: column density plots 4\]).

Column density plots of the nitrogen hydrides are shown on the left hand side in Fig. \[fig: column density plots 1\]. We note that the scatter is larger for $N$(NH) vs. than compared to vs. which show a rather tight correlation. This may indicate that NH does not entirely exist in the same gas as and . There is also a possibility that the NH and o-NH$_3$ correlation may only be valid for $N$()$\lesssim$5$\times$10$^{12}$ cm$^{-2}$. The $N$(NH) towards G10.6$-$0.4 appear to increase up to a maximum of $\sim$3$\times$10$^{13}$ cm$^{-2}$. Also $N$() show a slight tendency of this behaviour towards G10.6$-$0.4 with a maximum of $\sim$1.2$\times$10$^{13}$ cm$^{-2}$. This possible “chemical saturation” corresponds to a few $\mathrm{A}_{V}$ (estimated from our CH measurements and . This may be explained by a more efficient ammonia production at higher column densities, or that NH, and , are somehow consumed in the ammonia formation.

On the right hand side in Fig. \[fig: column density plots 1\] we show column density plots of the nitrogen hydrides vs. CH. The spread of the data points reflects the difficulty of finding a velocity structure common to hydrides and CH.

In Fig. \[fig: column density plots 2\] we show column density plots of the nitrogen hydrides vs. CN on the left and vs. HNC on the right. All three nitrogen hydrides show linear correlations with both CN and HNC. In dark cloud chemistry, CN and HNC are closely related to NH and NH$_2$ through the reactions of , , and [@1990MNRAS.246..183N]. Also @2009MNRAS.400..392W found a slightly better correlation between NH and CN than compared to CH, and no correlations with species such as CH$^+$.

Ortho-to-para ratio of NH$_3$ {#OPR ammonia}
=============================

There are two ways to produce molecules in interstellar space: in the gas-phase or on grain surfaces. If ammonia is formed in the gas-phase, by highly exoergic processes, the ammonia ortho-to-para ratio has been expected to be very close to the statistical equilibrium value of 1.0 (the spin statistical value is 4–2 for ortho-para, but the number of para states is on the other hand almost a factor of two larger). If ammonia is formed at temperatures lower than 40 K on cold dust grains, and then desorbed when the grains are heated above 100 K, the OPR may differ from unity since the lowest ortho level is 22 K below the lowest para level. If no conversion processes between the two symmetries exist, the OPR of ammonia is expected to increase *above* unity at low formation temperatures.

Prior to Herschel, ortho-to-para ratios have been derived from measurements of inversion transitions, the $(1,1)$ and $(2,2)$ transitions involving para states, and the $(3,3)$ and $(6,6)$ transitions probing highly excited, metastable ortho states. For example, @1999ApJ...525L.105U have found OPR=1.3–1.7 in the L 1157 outflow from the observation of six inversion lines $(J,K)=(1,1)$ to $(6,6)$. Similarly, @2009PASJ...61.1023N have inferred an even higher value of OPR=1.5–3.5 in the central molecular zone of the Galaxy.

Using *Herschel*-HIFI observations of the fundamental rotational transitions of both ortho- and para-ammonia, it is for the first time possible to estimate the ammonia OPR in cold and diffuse interstellar gas of low excitation. Our results do, however, point to the surprising result of an OPR *lower* than unity.

This is shown in Figs. \[Fig: W49N OPR NH3\] and \[Fig: W31C OPR NH3\] where the upper panels show the normalised 1$_0$–0$_0$ ortho-NH$_3$ and 2$_1$–1$_1$ para-NH$_3$ spectra, and the lower panels show the corresponding optical depth ratios for absorptions larger than 3$\sigma$ as a function of LSR velocity towards both sources (channel widths are 0.26 km s$^{-1}$). An ortho-to-para optical depth ratio of 4.2 corresponds to a column density ratio of unity using the [RADEX]{} conversion factors in Table \[Table: columns opacity one\]. The resulting column density ratios are given by the right hand y-axis in both figures. The para line has lower S/N than the ortho line in both sources and several velocity components are weak. Still, most column density ratios are found to be below unity within the uncertainties.

![[*W*49N.]{} *(Upper)* WBS spectra of ortho-NH$_3$ and para-NH$_3$ normalised to SSB continuum. *(Lower)* The optical depth ratios are shown for absorptions larger than 3$\sigma$ as a function of LSR velocity. The column density ratios (OPR), estimated with [RADEX]{}, are given by the right hand y-axis. The horisontal dashed line marks an ortho-to-para optical depth ratio of 4.2 corresponding to a column density ratio of unity. []{data-label="Fig: W49N OPR NH3"}](18686Fg22.eps)

![[*G*10.6$-$0.4 (W31C).]{} Notation as in Fig. \[Fig: W49N OPR NH3\]. []{data-label="Fig: W31C OPR NH3"}](18686Fg23.eps)

We have also used Method I and II to estimate the OPR. Method I gives and in the strongest velocity components towards W49N (+39 km s$^{-1}$ component) and G10.6$-$0.4 (+16, 28, 30 and 41 km s$^{-1}$ components), respectively. The results from Method II gives similar results towards G10.6$-$0.4: in the velocity bins , , and ; but lower results towards W49N in $v_\mathrm{LSR}$=36–42 km s$^{-1}$, 0.4$\pm$0.2.

The errors are dominated by the noise and the uncertainty in the sideband gain ratio. We have used the errors in sideband gain ratios stated on the *Herschel* internet site (4% for ortho and 6% for para). There is also an additional error arising from the rather large sideband separation of 12 GHz which means that the assumption of equal continuum temperature is not fully valid. This effect mimics a sideband gain ratio different from unity and is also taken into account (4 and 2% for ortho and para, respectively, estimated by $T_\mathrm{C,L}/T_\mathrm{C,U} = (\nu_\mathrm{L}/\nu_\mathrm{U})^\beta$ with $\beta = 2$). The errors from the noise is estimated by $\delta \tau$=$\exp(\tau) \times \delta I /I_0$, and the errors from the sideband gain ratio and differences in the continuum in the sidebands are estimated by $\delta \tau = \epsilon - ln(1 + \epsilon \exp(\tau))$ where $\epsilon$ is both errors added in quadrature. The derivation of this formula assumes that the depth of the absorption line is correct, which means that $T_\mathrm{C}$(SSB)–$T_\mathrm{A}$ is conserved but the continuum level is not. The noise and calibration errors are finally added in quadrature. The error estimates for Method I and II add respective uncertainties from the methods to the calibration errors.

Some previous measurements of ammonia have resulted in an OPR lower than unity, although not in diffuse gas. In Orion KL @1988AA...201..285H obtained OPR(NH$_3$)=0.5 from inversion emission lines, and @1985AA...146..134H found OPR($^{15}$NH$_3$)=0.7. The latter low value was suggested to be caused by an excitation effect: a possible over-abundance of the unobserved $K$=0 state. This explanation cannot be applied in our case, since we actually observe the $K$=0 ortho state. modelled several NH$_3$ inversion transitions in the frame of C-shock models towards the warm and dense SgrB2 envelope and their best OPR of ammonia was $\sim$0.5, also lower than the statistical value of unity. , however, observed 21 high excitation ortho- and para-ammonia lines, both metastable and non-metastable levels, towards SgrB2 using ISO, and derived an ammonia OPR of unity.

There are to our knowledge no previous estimate of the OPR(NH$_3$) in *diffuse* gas, and it may very well be very different from the OPR in dense gas. We can, however, compare our strong absorption of the para-NH$_3$ line to the observations by who observed the two lowest inversion lines of para-NH$_3$ towards W49N. Their estimate of is 2.5$\times 10^{12}$ cm$^{-2}$ which is less than half our value, $\sim$6$\times 10^{12}$ cm$^{-2}$. If this column density is correct, it would imply an OPR higher than unity in this velocity component in W49N. In our excitation model, however, the integrated optical depth observed by in the $1_1$ inversion line at $+39$ km s$^{-1}$ implies a in good agreement with our value, since we obtain a higher excitation temperature than the 2.7 K used by for the $1_1$ inversion transition.

We have no clear explanation yet of our surprising result and we can only speculate about its origin. Either there are to us unknown instrumental effects, or that our assumption that the line-of-sight gas completely covers the background continuum within the beam is not correct, or there must exist some physical or chemical processes that affect the OPR in diffuse gas. In general, the fact that interstellar clouds are weak plasmas allows for conversion processes at low temperatures that would not be present in a purely neutral gas. What OPR these processes lead to must be determined by careful modelling. In diffuse molecular clouds of relatively low density, $n({\rm H}_2) \lesssim 10^3$, but relatively high ionisation fraction, $n(e)/n({\rm H}_2)\ga10^{-4}$, the rate of destruction of NH$_3$ by reactions with C$^+$, H$^+$, and H$_3^+$, can be as high as $10^{-9}$ s$^{-1}$ at kinetic temperatures $T\!\sim\!30$ K. The latter two ions can also interchange ortho and para states directly by proton substitution, perhaps at a comparable rate. These rates of destruction and interchange can approach the rates of radiative and collisional excitation out of the metastable levels, which means that the excitation and chemistry of NH$_3$ should be treated together in a self-consistent fashion. Under these conditions, NH$_3$ is a non-equilibrium system and a “spin temperature” derived from an ortho-to-para ratio is not expected to be meaningful.

The NH$_4^+$ molecule could also affect the ammonia OPR in a similar manner. The fastest gas-phase reaction sequence of ammonia is $$\mathrm{N^+}   \rightarrow^\mathrm{H_2}  \mathrm{NH^+}  \rightarrow^\mathrm{H_2} \mathrm{NH_2^+}  \rightarrow^\mathrm{H_2} \mathrm{NH_3^+} \rightarrow^\mathrm{H_2} \mathrm{NH_4^+}  \rightarrow^\mathrm{e^-}  \mathrm{NH_3}, \, \mathrm{NH_2},$$ where N$^+$ is formed by cosmic ray ionisation, or by reactions of He$^+$ with N$_2$ or CN which are formed by neutral-neutral reactions. Whether or not ammonia is produced on grains or in the gas, its destruction in the gas by protonating ions such as H$_3^+$ also leads to NH$_4^+$, which can have a variety of nuclear spin states depending on the overall nuclear spin of H$_3^+$. The ammonia OPR could then simply reflect the spin states of NH$_4^+$.

In addition, some laboratory evidence exists that dissociative recombination reactions have different rate coefficients depending upon the nuclear spin configuration of the molecular ion.

Observations of the ortho-to-para ratio of NH$_3$ could thus provide a valuable insight into the competing processes of formation and destruction, radiative and collisional excitation, and reactive interchange processes.

Summary {#section summary}
=======

Our spectrally resolved rotational transitions of NH, o-NH$_2$, ortho- and para-NH$_3$ along the sight-lines towards the high-mass star-forming regions W49N and G10.6$-$0.4 show remarkable similarities of line profiles and abundances. We find similar abundances of all three species and a co-existence in diffuse or translucent interstellar gas with a high molecular fraction. The mean abundance of abundance is towards both sources. The mean ratios of all three methods of the nitrogen hydrides in all velocity components, are , and and 2.0, towards G10.6$-$0.4 and W49N, respectively. This is in sharp contrast to previous observations of the nitrogen hydrides in dark clouds where the ammonia abundances are found to be $\sim$100 times higher than $X$(NH), and $\sim$10–300 times higher than $X$(NH$_2$). NH and are found to be linearly correlated with at least for $N$()$\lesssim$5$\times$10$^{12}$ cm$^{-2}$ which corresponds to a few $A_\mathrm{V}$. Upper limits of $N$(NH$^+$) in both sources indicate a $N$(NH$^+$)/$N$(NH) ratio of $\lesssim$2–14%, with a mean of $\lesssim$6%.

Linear correlations are also found for all three nitrogen hydrides with respect to CH, CN and HNC, although CH displays a more loose correlation than the latter two species. The nitrogen hydrides also largely follow the absorption pattern in Doppler velocity space of HCO$^+$ and water, a species also known to trace regions of a high molecular fraction.

We have obtained a surprisingly low ortho-to-para ratio of ammonia, , in the strongest velocity components, which is below the high-temperature limit of unity. No clear explanation has been found. More observations are needed of both the rotational transitions and the inversion lines with ground-based facilities, to be able to make firm conclusions about the ammonia OPR in diffuse gas.

We will continue to investigate the absorption lines in the sight-lines towards the other six PRISMAS sources. This will allow an analysis of the nitrogen chemistry at various galactic distances from the Galactic Centre. We will also use new Open Time 1 (OT1) *Herschel*-HIFI data of higher excitation lines to analyse the hot core sources which will be compared and contrasted with the diffuse interstellar gas. The ortho-to-para ratio of NH$_3$ will also be further investigated both in the sources and in the diffuse gas, in addition to the OPR of NH$_2$, for which new OT1 data in four of the PRISMAS sources will be analysed and compared to the ammonia OPR.

The *Herschel* spacecraft was designed, built, tested, and launched under a contract to ESA managed by the Herschel/Planck Project team by an industrial consortium under the overall responsibility of the prime contractor Thales Alenia Space (Cannes), and including Astrium (Friedrichshafen) responsible for the payload module and for system testing at spacecraft level, Thales Alenia Space (Turin) responsible for the service module, and Astrium (Toulouse) responsible for the telescope, with in excess of a hundred subcontractors. HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada and the United States under the leadership of SRON Netherlands Institute for Space Research, Groningen, The Netherlands and with major contributions from Germany, France and the US. Consortium members are: Canada: CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS; Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri- INAF; Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astronómico Nacional (IGN), Centro de Astrobiología (CSIC-INTA). Sweden: Chalmers University of Technology - MC2, RSS & GARD; Onsala Space Observatory; Swedish National Space Board, Stockholm University - Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA: Caltech, JPL, NHSC. CP and JHB acknowledge generous support from the Swedish National Space Board. MdL and MG acknowledge funding by CNES and by the ANR SCHISM project (ANR-09-BLAN-0231-01). T.A.B, B.G. and J.R.G. thank the Spanish MICINN for funding support through grants AYA2009-07304 and CSD2009-00038. H.S.P.M. is very grateful to the Bundesministerium für Bildung und Forschung (BMBF) for financial support aimed at maintaining the Cologne Database for Molecular Spectroscopy, CDMS. This support has been administered by the Deutsches Zentrum für Luft- und Raumfahrt (DLR). We also thank the referee Harvey Liszt whose constructive comments led to a significant improvement of the paper.

Herschel observations
=====================

[llrccccc ]{} Source & Species & Frequency & Band & LO-setting$^a$ & Date & OBSID\

& & (GHz)\

W49N & NH$^b$ & 946.476 & 3b & A &2010-04-13 & 1342194700\
& & & & B & & 1342194701\
& & & & C & & 1342194702\

& NH & 974.478 & 4a & A &2010-04-18 & 1342195004\
& & & & B & & 1342195005\
& & & & C & & 1342195006\

& o-NH$_2$ & 952.578 & 3b & A &2010-04-13 & 1342194706\
& & & & B & & 1342194707\
& & & & C & & 1342194708\

& o-NH$_3$ & 572.498 & 1b & A & 2010-04-11 & 1342194517\
& & & & B & & 1342194518\
& & & & C & & 1342194519\

& p-NH$_3^c$ & 1215.246 & 5a & A &2010-04-18 & 1342195067\
& & & & B & & 1342195068\
& & & & C & & 1342195069\

& NH$^+$ & 1012.540 & 4a & A & 2010-04-18 & 1342194998\
& & & & B & & 1342194999\
& & & & C & & 1342195000\
G10.6-0.4 & NH$^b$ & 946.476 & 3b & A &2010-03-18 & 1342192316\
& & & & B & & 1342192317\
& & & & C & & 1342192318\

& NH & 974.478 & 4a & A &2010-03-03 & 1342191620\
& & & & B & & 1342191621\
& & & & C & & 1342191622\

& o-NH$_2$ & 952.578 & 3b & A &2010-03-18 & 1342192319\
& & & & B & & 1342192320\
& & & & C & & 1342192321\

& o-NH$_3$ & 572.498 & 1b & A &2010-03-02 & 1342191578\
& & & & B & & 1342191579\
& & & & C & & 1342191580\

& p-NH$_3^c$ & 1215.246 & 5a & A &2010-03-05 & 1342191697\
& & & & B & & 1342191698\
& & & & C & & 1342191699\

& NH$^+$ & 1012.540 & 4a & A & 2010-03-03 & 1342191623\
& & & & B & & 1342191624\
& & & & C & & 1342191625\
\[Table: obsid\]

Emission line contamination of o-NH$_2$ towards W49N {#NO removal of NH2}
====================================================

The o-NH$_2$ absorption towards W49N is contaminated by an emission line in the same sideband from the source, a more complicated situation than an emission line from the other sideband. In Fig. \[Fig:W49N NH2 and NO\] an emission line is clearly visible around 47kms$^{-1}$ in the o-NH$_2$ spectrum. Here, the intensities have been normalised to the continuum in single sideband as $T_\mathrm{A}$/$T_\mathrm{C}$-1 assuming a sideband gain ratio of unity where $T_\mathrm{A}$ is the observed intensity and $T_\mathrm{C}$ is the SSB continuum as measured in line-free regions in the spectra. We identify the emission line as a blend of three unresolved hfs components of NO $^2\Pi_{1/2}\;J=9.5^f\to 8.5^f$, $F=10.5-9.5$, $9.5-8.5$, and $8.5-9.5$, at 952.464201 GHz [weighted mean frequency, cf. @1999JMoSp.196....5V]. The emission line appearing near 142kms$^{-1}$ in this figure is consequently identified as the hfs blend in the lower half of the same spin-rotation doublet of NO $^2\Pi_{1/2}\;J=9.5^e\to 8.5^e$ at an average rest frequency of 952.145441 GHz. The PRISMAS observations have also found three additional NO lines in W49N shown in Fig. \[Fig: W49N NO\], each one consisting of unresolved hfs components, while no emission of NO is found in G10.6$-$0.4.

Since the two NO lines seen in Fig. \[Fig:W49N NH2 and NO\] have almost equal line strength, and are also observed with the same instrument in the same band, we have used the observed 952.145 GHz transition as a template to remove the interfering NO line at 952.464 GHz from the o-NH$_2$ absorption. In order to do this we use $$\label{NO removal}
 T_\mathrm{norm} = \frac{T_\mathrm{A} - T_\mathrm{C}} {T_\mathrm{C} + T_\mathrm{NO} },$$ to calculate the normalised SSB intensity $T_\mathrm{norm}$ in K, where $T_\mathrm{C}$ is the SSB continuum, and $T_\mathrm{NO}$ is the intensity of the NO line . The model NO line, shown in Fig. \[Fig: W49N: NO model\], is then moved to the velocity of the emission line. The resulting absorption line spectrum of o-NH$_2$ towards W49N with removed NO emission is shown in green in Fig. \[Fig:W49N NH2 and NO\].

![*W49N*: Double sideband WBS spectra of four NO emission lines from the source itself. Each NO line consists of 3 hfs components, with quatum numbers $^2\Pi_{1/2}\;J=6.5^e\to 5.5^e$ (651 GHz), $J=6.5^f\to 5.5^f$ (652 GHz), $J=7.5^e\to 6.5^e$ (752 GHz), and $J=9.5^e\to 8.5^e$ (952 GHz). The emission line at $-$18kms$^{-1}$ blended with NO 651.433 GHz is SO 11$_{11}$–11$_{10}$. []{data-label="Fig: W49N NO"}](18686Fg25.eps)

Hyperfine structure components {#hyperfine-structure-components}
==============================

[cccc ]{}

Frequency & $A_{ul}$& $\Delta v $ & Rel. Intensity\
(MHz) &(s$^{-1}$)& (kms$^{-1}$) & $\frac {A_{ul}\times g_u} {A_{ul}\mathrm{(main)}\times g_u \mathrm{(main)}}$\

974315.58 & 1.78e-6 & 50.08& 0.0001\
974342.57 & 6.02e-6 & 41.78 & 0.0007\
974354.64 & 4.54e-6 & 38.07& 0.0003\
974410.56 & 8.91e-5 & 20.87& 0.006\
974411.39 & 5.13e-4 & 20.61 & 0.018\
974436.35 & 2.28e-3 & 12.93 & 0.164\
974437.54 & 1.27e-3 & 12.56 & 0.137\
974444.04 & 1.81e-3 & 10.56 & 0.130\
974450.44 & 4.80e-3 & 8.60 & 0.173\
974462.22 & 5.04e-4 & 4.97 & 0.363\
974471.00 & 5.67e-3 & 2.27 & 0.612\
974475.41 & 3.38e-3 & 0.91 & 0.243\
974478.38 & 6.94e-3 & 0 & 1.0\
974479.34 & 6.01e-3 & -0.30 & 0.649\
974531.32 & 2.59e-4 &-16.29 & 0.019\
974539.82 & 6.46e-4 &-18.90 & 0.023\
974558.07 & 9.82e-4 &-24.52& 0.035\
974564.78 & 7.67e-4 &-26.58 & 0.055\
974574.43 & 8.15e-4 &-29.55& 0.088\
974583.03 & 2.59e-4 &-32.20& 0.019\
974607.78 & 1.21e-4 &-39.81 & 0.013\
\[Table: NH hfs transitions\]

[cccc ]{}

Frequency & $A_{ul}$& $\Delta v $ & Rel. Intensity\
(MHz) &(s$^{-1}$)& (kms$^{-1}$) & $\frac {A_{ul}\times g_u} {A_{ul}\mathrm{(main)}\times g_u \mathrm{(main)}}$\

946380.79 & 2.40e-3 & 30.100375183108216 & 0.369\
946380.79 & 9.58e-4 & 30.100375183108216& 0.295\
946419.79 & 3.66e-4 & 17.746741564471662 & 0.056\
946419.98 & 8.99e-4 & 17.688682017264846 & 0.276\
946475.82 & 3.25e-3 & 0 & 1.0\
946509.24 & 1.93e-3& -10.586919289910648 &0.297\
946509.24 & 1.21e-3 &-10.586919289910648 & 0.372\
946527.48 & 1.81e-3& -16.363416629849031 & 0.278\
946527.56 & 1.84e-4& -16.389231431253044 & 0.057\
\[Table: NH 946 hfs transitions\]

[cccc ]{}

Frequency & $A_{ul}$& $\Delta v $ & Rel. Intensity\
(MHz) &(s$^{-1}$)& (kms$^{-1}$) & $\frac {A_{ul}\times g_u} {A_{ul}\mathrm{(main)}\times g_u \mathrm{(main)}}$\

952435.66 & 4.86e-6& 44.91 & 0.0002\
952446.99 & 1.33e-5 &41.34 & 0.0006\
952463.69 & 3.07e-5 & 36.09 & 0.002\
952490.73 & 3.5e-3 & 27.58 & 0.079\
952502.06 & 1.28e-3 & 24.01 & 0.029\
952503.09 & 1.79e-3 & 23.69 & 0.081\
952514.42 & 3.65e-3 & 20.12 & 0.164\
952528.90 & 2.03e-3 & 15.56 & 0.046\
952533.03 & 2.23e-4 & 14.27 & 0.010\
952540.23 & 6.53e-3 & 12.00 & 0.147\
952542.21 & 7.02e-3 & 11.37 & 0.474\
952549.73 & 2.63e-3 & 9.01 & 0.178\
952560.41 & 3.32e-3 & 5.65 & 0.149\
952562.12 & 6.42e-3 & 5.11 & 0.289\
952571.74 & 7.55e-3 & 2.08 & 0.340\
952573.46 & 3.88e-3 & 1.54 & 0.174\
952577.11 & 8.47e-3 & 0.39 & 0.570\
952578.35 & 1.11e-2 & 0 & 1.0\
952600.46 & 1.59e-3 & -6.96 & 0.072\
952615.49 & 3.58e-3 & -11.69 & 0.081\
952626.82 & 2.73e-3 & -15.25 & 0.061\
952627.84 & 2.67e-3 & -15.57 & 0.120\
952628.25 & 3.35e-3 & -15.70 & 0.226\
952639.17 & 1.40e-3 & -19.14 & 0.063\
952653.66 & 9.66e-3 & -23.70 & 0.022\
952655.64 & 7.43e-4 & -24.32 & 0.050\
952659.49 & 4.40e-4 & -25.54 & 0.020\
952664.99 & 1.58e-3 & -27.27 & 0.036\
952686.88 & 2.97e-4 & -34.16 & 0.013\
952698.21 & 7.06e-5 & -37.72 & 0.003\
\[Table: NH2 hfs transitions\]

[ccc ]{}

Frequency & $\Delta v$ & Rel. Intensity\
(MHz) & (kms$^{-1}$) &\

572.4971 & -1.0473 & 0.1999\
572.4984 & 0.0 & 1.0\
572.5002 & 0.5237 & 0.6\
\[Table: NH3 hfs components\]

[cccc ]{}

Frequency & $A_{ul}$& $\Delta v $ & Rel. Intensity\
(MHz) &(s$^{-1}$)& (kms$^{-1}$) & $\frac {A_{ul}\times g_u} {A_{ul}\mathrm{(main)}\times g_u \mathrm{(main)}}$\

1215.2443 &1.02e-2 & 0.31 & 0.536\
1215.2449 &3.39e-3 & 0.16 & 0.179\
1215.2453 &5.65e-3 & 0.06 & 0.179\
1215.2456 &1.36e-2 & 0 & 1.0\
1215.2459 &3.77e-4 & -0.09 & 0.012\
1215.2468 &7.53e-3 & -0.32 & 0.238\
\[Table: NH3 1215 hfs components\]

Method II results
=================

[ll c ccc c ccc cc ]{}

\
$v_\mathrm{LSR}$ & $N$(NH) & $N$(o-NH$_2$) & $N$(o-NH$_3$) &$N$(CH) & NH/o-NH$_3$ & o-NH$_2$/o-NH$_3$ & $X$(NH)& $X$(o-NH$_2$) & $X$(o-NH$_3$)\
(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$) &\
36.0 - 42.0 & 1.1e13 & 8.3e12 &4.1e12 & 6.3e13 &2.7 & 2.0 & 6.1e-9 & 4.6e-9 & 2.3e-9\
50.0 - 57.0 & 1.4e12&1.4e12&1.2e12 & 6.6e13 & 1.2 & 1.2 & 7.4e-10 & 7.4e-10 & 6.4e-10\
57.0 - 61.0 & 7.8e12&3.5e12 & 1.9e12 & 7.3e13 &4.1 & 1.8 &3.7e-9 & 1.7e-9 & 9.1e-10\
61.0 - 70.0 & 1.0e13&4.8e12 & 3.0e12 & 9.1e13 & 3.3 & 1.6 & 3.8e-9 & 1.8e-9 & 1.2e-9\
Total &3.0e13 &1.8e13& 1.0e13 & 2.9e14 & 3.0 & 1.8 & 3.6e-9 & 2.2e-9 & 1.2e-9\
Mean & 7.6e12 &4.5e12 & 2.6e12 & 7.3e13 & 3.0 & 1.8 & 3.6e-9 & 2.2e-9 & 1.2e-9\
Median & 9.0e12&4.2e12 & 2.5e12 & 7.0e13& 3.6 & 1.7 & 4.5e-9 & 2.1e-9 & 1.2e-9\

\
$v_\mathrm{LSR}$ & $N$(NH) & $N$(o-NH$_2$) & $N$(o-NH$_3$) &$N$(CH) & NH/o-NH$_3$ & o-NH$_2$/o-NH$_3$ & $X$(NH)& $X$(o-NH$_2$) & $X$(o-NH$_3$)\
(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$) &\
12.5 - 20.0 & 2.9e13 & 1.4e13 &5.4e12 & 1.2e14 & 5.4 & 2.6 & 8.5e-9 & 4.1e-9 & 1.6e-9\
20.0 - 25.0 & 2.7e13 &1.2e13 & 3.8e12 &9.3e13 &7.1 & 3.2 & 1.0e-8 &4.5e-9 & 1.4e-9\
25.0 - 29.0 & 3.0e13 &1.5e13 & 8.4e12 & 1.2e14 &3.6 & 1.8 & 8.8e-9 &4.4e-9 & 2.5e-9\
29.0 - 31.0 & 2.8e13 &1.2e13 & 6.9e12 & 5.4e13 &4.1 & 1.7 & 1.8e-8 &7.8e-9 & 4.5e-9\
31.0 - 35.0 & 1.4e13 &5.0e12 & 2.8e12 & 7.1e13 & 5.0 & 1.8 & 6.9e-9 &2.5e-9 & 1.4e-9\
35.0 - 39.5 & 2.6e13 & 8.2e12 & 3.0e12 & 1.1e14 & 8.7 & 2.7 & 8.3e-9 &2.6e-9 & 9.6e-10\
39.5 - 43.5 & 3.2e13 &1.1e13 & 3.9e12 & 6.3e13 &8.2 & 2.8 & 1.8e-8 &6.1e-9 & 2.2e-9\
43.5 - 50.0 & 1.8e12 &1.0e12 & 8.0e11 & 1.9e13 & 2.3 & 1.3 & 3.3e-9 & 1.8e-9 & 1.5e-9\
Total & 1.9e14 & 7.8e13 & 3.5e13 & 6.5e14 & 5.4 & 2.2& 1.0e-8 & 4.2e-9 & 1.9e-9\
Mean & 2.3e13 &9.8e12 & 4.4e12& 8.1e13 & 5.4 & 2.2 & 1.0e-8 & 4.2e-9 & 1.9e-9\
Median & 2.7e13& 1.1e13 & 3.9e12& 8.2e13 & 7.1 & 3.0 &1.2e-8 & 4.9e-9 & 1.6e-9\
\[Table: Model II ratios results\]

Method III results
==================

[lc ccc ccc ccc ]{}\
$v_\mathrm{LSR}$ & $\Delta v$ & $N$(NH) & $N$(o-NH$_2$) & $N$(o-NH$_3$) & $N$(CH) & NH/o-NH$_3$ & o-NH$_2$/o-NH$_3$ & $X$(NH)& $X$(o-NH$_2$)& $X$(o-NH$_3$)\
(kms$^{-1}$) &(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$) &\
33.5 & 1.9 & 1.1e12 & 2.2e12 & 3.6e11 & 3.2e13 & 3.1 & 6.1 & 1.2e-9 & 2.4e-9 & 3.9e-10\
39.6 & 1.1& 1.2e13 & 7.4e12 & 3.2e12 &3.3e13& 3.8 & 2.3 & 1.3e-8 & 7.8e-9 & 3.4e-9\
59.4 & 3.0 & 1.1e13 & 3.5e12 & 1.7e12 & 7.0e13 & 6.5 & 2.1 & 5.5e-9 & 1.8e-9 & 8.5e-10\
62.8 & 2.4& 9.7e12 & 3.2e12 & 1.9e12 & 5.8e13 & 5.1 & 1.7 & 5.9e-9 & 1.9e-9 & 1.1e-9\
Total: &…&3.4e13 & 1.6e13 & 7.2e12 & 1.9e14 & 4.7 & 2.3 & 6.1e-9 & 3.0e-9 & 1.3e-9\
Mean: &…& 8.5e12 & 4.1e12 & 1.8e12 & 4.8e13 & 4.7 & 2.3 & 6.1e-9 & 3.0e-9 & 1.3e-9\
Median: &…& 1.0e13 & 3.4e12 & 1.8e12 & 4.6e13 & 5.8 & 1.9 & 8.0e-9 & 2.6e-9 & 1.4e-9\
\
$v_\mathrm{LSR}$ & $\Delta v$ & $N$(NH) & $N$(o-NH$_2$) & $N$(o-NH$_3$) & $N$(CH) & NH/o-NH$_3$ & o-NH$_2$/o-NH$_3$ & $X$(NH)& $X$(o-NH$_2$)& $X$(o-NH$_3$)\
(kms$^{-1}$) &(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$) &\
tables 16.3 & 1.9 & 2.4e13 & 9.6e12 & 3.4e12 & 7.7e13 & 7.1 & 2.8 & 1.1e-8 & 4.4e-9 & 1.5e-9\
19.0 & 1.3 & 6.8e12 & 2.3e12 & 6.0e11 & 2.6e13 & 11 & 3.8 & 9.2e-9 & 3.1e-9 & 8.1e-10\
22.2 & 4.2 & 1.9e13 & 7.4e12 & 1.7e12 & 9.0e13 & 11 & 4.4 & 7.4e-9 & 2.9e-9 & 6.6e-10\
22.9 & 1.0 & 1.1e13 & 3.0e12 & 1.0e12 & 1.2e13 & 11 & 3.0 & 3.2e-8 & 8.8e-9 & 2.9e-9\
25.0 & 3.3 & 8.3e12 & 4.8e12 & 1.1e12 & 4.0e13 & 7.5 & 4.4 & 7.3e-9 & 4.2e-9 & 9.6e-10\
28.0 & 1.9 & 3.2e13 & 1.2e13 & 6.4e12 & 9.8e13 & 5.0 & 1.9 & 1.1e-8 & 4.3e-9 & 2.3e-9\
30.0 & 1.5 & 3.1e13 & 1.4e13 & 6.8e12 & 6.1e13 & 4.6 & 2.1 & 1.8e-8 & 8.0e-9 & 3.9e-9\
32.2 & 1.7 & 1.2e13 & 3.1e12 & 8.9e11 & 2.5e13 & 13 & 3.5 & 1.7e-8 & 4.3e-9 & 1.2e-9\
36.2 & 3.8 & 2.2e13 & 7.3e12 & 2.5e12 & 9.4e13 & 8.8 & 2.9 & 8.2e-9 & 2.7e-9 & 9.3e-10\
39.1 & 1.2 & 1.4e13 & 3.2e12 & 5.5e11 & 4.6e13 & 25 & 5.8 & 1.1e-8 & 2.4e-9 & 4.2e-10\
41.0 & 1.7 & 3.5e13 & 1.1e13 & 3.1e12 & 8.5e13 & 11 & 3.5 & 1.4e-8 & 4.5e-9 & 1.3e-9\
45.1 & 1.3 & 3.7e12 & 1.6e12 & 3.8e11 & 1.4e13 & 9.7 & 4.2 & 9.3e-9 & 4.0e.9 & 9.5e-10\
Total: & …&2.2e14 & 7.9e13 & 2.8e13 & 6.7e14& 7.7 & 2.8 & 1.1e-8 & 4.2e-9 & 1.5e-9\
Mean: &…&1.8e13& 6.6e12 & 2.4e12 & 5.6e13& 7.7 & 2.8 &1.1e-8 & 4.2e-9 & 1.5e-9\
Median: &…&1.7e13& 6.1e12 & 1.4e12 & 5.4e13& 12 & 4.3 & 1.1e-8 & 4.0e-9 & 9.2e-10\
\[Table: Method III resulting ratios and columns\]

Results for CN and HNC
======================

[l c | cc cc | c ccc ]{} W49N && &\
$v_\mathrm{LSR}$ & $\Delta v$ & $N$(CN) & $N$(HNC) & CN/o-NH$_3$ & HNC/o-NH$_3$ & $N$(CN) & $N$(HNC) & CN/o-NH$_3$ & HNC/o-NH$_3$\
(kms$^{-1}$) &(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & && (cm$^{-2}$) &(cm$^{-2}$)\
33.5 & 1.9 & 8.1e12 & 4.3e11 & 18 & 0.93 &7.5e12& 4.5e11 & 21 & 1.3\
39.6 & 1.1 & 6.6e13 & 2.9e12 & 15 & 0.67 &6.3e13& 2.9e12 & 20 & 0.91\
59.4 & 3.0 & 3.5e13 & 2.1e12 & 17 & 1.0 &3.3e13& 2.2e12 & 19 & 1.3\
62.8 & 2.4 & 2.8e13 & 1.5e12 & 13 & 0.68 &2.6e13& 1.7e12 & 14 & 0.89\
Total: && 1.4e14 & 6.9e12 & 15 & 0.76 &1.3e14 & 7.3e12 & 18 & 1.0\
Mean: && 3.4e13 & 1.7e12 & 15 & 0.76 &3.2e13 & 1.8e12 & 18 & 1.0\
Median: && 3.2e13 & 1.8e12& 15 & 0.84 &3.0e13 & 2.0e12 & 16 & 1.1\
G10.6$-$0.4 && &\
$v_\mathrm{LSR}$ & $\Delta v$ & $N$(CN) & $N$(HNC) & CN/o-NH$_3$ & HNC/o-NH$_3$ & $N$(CN) & $N$(HNC) & CN/o-NH$_3$ & HNC/o-NH$_3$\
(kms$^{-1}$) &(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) & && (cm$^{-2}$) &(cm$^{-2}$)\

16.3 & 1.9 & 1.0e14 & 3.6e12 & 24 & 0.86 & 9.0e13 &4.1e12 &26 & 1.2\
19.0 & 1.3 & 3.3e13 & 1.3e12 & 38 & 1.5 & 2.9e13 &1.5e12 &48 &2.5\
22.2 & 4.2 & 5.7e13 & 2.7e12 & 32 & 1.5 & 5.1e13 &3.1e12 &30 & 1.8\
22.9 & 1.0 & 6.6e13 & 2.5e12 & 44 & 1.7 & 5.8e13 &2.9e12 &58 & 2.9\
25.0 & 3.3 & 9.5e12 & …& 6.8 & …& 8.4e12 &1.7e12 &7.6 &1.5\
28.0 & 1.9 & 1.2e14 & 4.1e12 & 16 & 0.56 & 1.1e14 &4.7e12 &17 &0.73\
30.0 & 1.5 & 1.4e14 & 5.8e12 & 18 & 0.73 & 1.3e14 &6.7e12 &19 &1.0\
32.2 & 1.7 & 2.5e13 & 1.0e12 & 19 & 0.77 & 2.3e13 &1.2e12 &26 &1.3\
36.2 & 3.8 & 1.0e14 & 5.1e12 & 31 & 1.6 & 9.0e13 &5.9e12 &36 &2.4\
39.1 & 1.2 & 3.7e13 & 1.1e12 & 79 & 2.3 & 3.3e13 &1.3e12 &60 &2.4\
41.0 & 1.7 & 1.6e14 & 5.9e12 & 39 & 1.4 & 1.4e14 &6.8e12 &45 &2.2\
45.1 & 1.3 & 1.2e13 & 8.5e11 & 20 & 1.4 & 1.1e14 &9.7e12 &289 &26\
Total: & & 8.6e14& 3.4e13 & 25 & 1.0 & 8.7e14 & 5.0e13 & 31 & 1.7\
Mean: && 7.2e13 & 3.1e12 & 25 & 1.0 & 7.4e13 &3.6e12 & 53 & 2.6\
Median: && 6.2e13 & 2.7e12 & 37 & 1.5 & 7.3e13 & 4.1e12& 31 & 1.7\
\[Table: Method I, III CN and HNC columns\]

[l c ccc]{}

\
$v_\mathrm{LSR}$ & $N$(CN) & $N$(HNC) & CN/o-NH$_3$ & HNC/o-NH$_3$\
(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) &\
36.0 - 42.0 & 5.3e13 & 2.9e12 & 13 & 0.71\
50.0 - 57.0 & 4.4e12 & 5.7e11 & 3.7 & 0.48\
57.0 - 61.0 & 2.1e13 & 1.7e12 & 11 & 0.89\
61.0 - 70.0 & 2.6e13 & 2.0e12 & 8.7 & 0.67\
Total & 1.0e14 & 7.2e12 & 10 & 0.70\
Mean & 2.6e13 & 1.8e12 & 10 & 0.70\
Median & 2.4e13 & 1.9e12 & 9.6 & 0.76\

\
$v_\mathrm{LSR}$ & $N$(CN) & $N$(HNC) & CN/o-NH$_3$ & HNC/o-NH$_3$\
(kms$^{-1}$) & (cm$^{-2}$) &(cm$^{-2}$) &\

12.5 - 20.0 &1.0e14 &5.8e12 & 19 & 1.1\
20.0 - 25.0 &9.1e13 &5.2e12 & 24 & 1.4\
25.0 - 29.0 &9.6e13 &5.6e12 & 11 & 0.67\
29.0 - 31.0 &8.8e13 &4.9e12 & 13 & 0.71\
31.0 - 35.0 &4.2e13 &2.3e12 & 15 & 0.82\
35.0 - 39.5 &8.0e13 &5.3e12 & 27 & 1.8\
39.5 - 43.5 &1.4e14 &7.4e12 & 36 & 1.9\
43.5 - 50.0 &9.8e12 &1.1e12 & 12 & 1.4\
Total & 6.5e14 & 3.8e13 & 18 & 1.1\
Mean &8.1e13 & 4.7e12 & 18 & 1.1\
Median & 9.0e13 & 5.3e12 & 23 & 1.4\
\[Table: Method II CN and HNC columns\]

Figures
=======

![*W49N:* Fits of method II to NH and o-NH$_2$, and their observed spectra. Residuals are found at the bottom. Template spectrum is o-NH$_3$ at 572GHz.[]{data-label="Fig: W49N method I NH and NH2 from NH3"}](18686Fg29.eps)

![*W49N:* Fits of method II to NH, o-NH$_2$ and o-NH$_3$, and their observed spectra. Residuals are found at the bottom. Template spectrum is CH at 532GHz.[]{data-label="Fig: W49N method I NH, NH2, NH3 from CH"}](18686Fg30.eps)

![*G10.6$-$0.4 (W31C):* Fits of method II to NH and , and their observed spectra. Residuals are found at the bottom. Template spectrum is o-NH$_3$ at 572GHz.[]{data-label="Fig: W31C method I NH and NH2 from NH3"}](18686Fg31.eps)

![*G10.6$-$0.4 (W31C):* Fits of method II to NH, and o-NH$_3$, and their observed spectra. Residuals are found at the bottom. Template spectrum is CH at 532GHz.[]{data-label="Fig: W31C method I NH, NH2, NH3 from CH"}](18686Fg32.eps)

![*W49N:* Method III (XCLASS) fits to the Nitrogen hydrides and CH. []{data-label="Fig: w49n guass fits n-hydrides method III"}](18686Fg33.eps)

![*G10.6$-$0.4 (W31C):* Method III (XCLASS) fits to the Nitrogen hydrides and CH. []{data-label="Fig: w31c guass fits n-hydrides method III"}](18686Fg34.eps)

Comparison plots of different methods
=====================================

In Figs. \[Fig: column density plots 1\]–\[Fig: column density plots 4\] we plot the resulting column densities from our three different methods.

Note that since Method I and Method III use Gaussians with smaller line widths than the velocity bins of Method II towards G10.6$-$0.4, the number of velocity components is not the same in this source. The +33 km s$^{-1}$ component towards W49N is not used in Method II, which on the other hand models a velocity bin that is difficult to fit using Gaussians in Method I and III . The comparison of the nitrogen hydrides vs. CH in W49N, in two of the four velocity bins, shows the only cases in which the results do not agree reasonably well between the methods. The resulting CH column densities also show a larger spread between the methods than the other species. The reason is not fully understood, but is probably caused by the different approaches to the CH modelling. Method II uses the deconvolved CH spectra as a template for the nitrogen hydrides and is thereby trying to fit the broader CH absorption to the more narrow features of the nitrogen hydrides with moderate success. The other two methods use an opposite approach: they use the output of the fitting of the nitrogen hydrides as an input to CH to fit Gaussians only in the same parts in velocity space, and are thereby trying to fit narrow features to the broader CH absorption. The fit is good in some parts of the velocity space, and very bad in the velocity space in which CH has absorption but the nitrogen hydrides do not, which is expected.

[^1]: *Herschel* is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

[^2]: www.astrochymist.org, www.astro.uni-koeln.de/cdms/molecules

[^3]: http://astro.ens.fr/?PRISMAS

[^4]: http://herschel.esac.esa.int/Docs/HIFI/html/ch5.html

[^5]: HIPE is a joint development by the *Herschel* Science Ground Segment Consortium, consisting of ESA, the NASA *Herschel* Science Centre, and the HIFI, PACS and SPIRE consortia.

[^6]: Developed by Per Bergman at Onsala Space Observatory, Sweden; [http://www.chalmers.se/rss/oso-en/observations/data-\
    reduction-software]{}

[^7]: 

[^8]: 

[^9]: 

[^10]:
