# GNOMES II: Analysis of the Galactic diffuse molecular ISM in all four ground
state hydroxyl transitions using Amoeba

Anita Petzler  School of Mathematical and Physical Sciences and Research
Centre in Astronomy, Astrophysics & Astrophotonics, Macquarie University,
Sydney, 2109, Australia  [ J. R. Dawson  School of Mathematical and Physical
Sciences and Research Centre in Astronomy, Astrophysics & Astrophotonics,
Macquarie University, Sydney, 2109, Australia  Hiep Nguyen  Research School of
Astronomy and Astrophysics, The Australian National University, Canberra, ACT
2611, Australia  Carl Heiles  Department of Astronomy, University of
California, Berkeley, 601 Campbell Hall 3411, Berkeley, CA, 94720-3411, USA
M. Wardle  School of Mathematical and Physical Sciences and Research Centre in
Astronomy, Astrophysics & Astrophotonics, Macquarie University, Sydney, 2109,
Australia  M.-Y. Lee  Korea Astronomy & Space Science Institute, 776 Daedeok-
daero, Yuseong-gu, Daejeon 34055, Republic of Korea  Claire E. Murray
Department of Physics & Astronomy, Johns Hopkins University, 3400 N. Charles
Street, Baltimore, MD 21218, USA, NSF Astronomy & Astrophysics Postdoctoral
Fellow  K. L. Thompson  Davidson College, Davidson, NC, 28115, USA  Snežana
Stanimirović  Department of Astronomy, University of Wisconsin, Madison, WI
53706, USA

###### Abstract

We present observations of the four ${}^{2}\Pi_{3/2}\,J=3/2$ ground-rotational
state transitions of the hydroxyl molecule (OH) along 107 lines of sight both
in and out of the Galactic plane: 92 sets of observations from the Arecibo
telescope and 15 sets of observations from the Australia Telescope Compact
Array (ATCA). Our Arecibo observations included off-source pointings, allowing
us to measure excitation temperature ($T_{\rm ex}$) and optical depth, while
our ATCA observations give optical depth only. We perform Gaussian
decomposition using the Automated Molecular Excitation Bayesian line-fitting
Algorithm ‘Amoeba’ Petzler2021a (83) fitting all four transitions
simultaneously with shared centroid velocity and width. We identify 109
features across 38 sightlines (including 58 detections along 27 sightlines
with excitation temperature measurements). While the main lines at 1665 and
1667 MHz tend to have similar excitation temperatures (median $|\Delta T_{\rm
ex}({\rm main})|=0.6\,$K, 84% show $|\Delta T_{\rm ex}({\rm main})|<2\,$K),
large differences in the 1612 and 1720 MHz satellite line excitation
temperatures show that the gas is generally not in LTE. For a selection of
sightlines we compare our OH features to associated (on-sky and in velocity)
Hi cold gas components (CNM) identified by Nguyen2019 (74) and find no strong
correlations. We speculate that this may indicate an effective decoupling of
the molecular gas from the CNM once it accumulates.

###### keywords:

galaxies: ISM, ISM: molecules, radio lines: ISM

Australia Telescope National Facility, CSIRO Space & Astronomy, PO Box 76,
Epping, NSW 1710, Australia Anita<EMAIL_ADDRESS>Australia
Telescope National Facility, CSIRO Space & Astronomy, PO Box 76, Epping, NSW
1710, Australia University of Science and Technology, 217 Gajeong-ro, Yuseong-
gu, Daejeon 34113, Republic of Korea

##  1 Introduction

Molecular hydrogen (H2) does not have readily observable transitions in the
low densities and temperatures typical in the interstellar medium (ISM). Its
presence must therefore be inferred from measurements of other ‘tracer’
species. The most commonly used tracer of molecular hydrogen in the study of
the interstellar medium is carbon monoxide (CO), through observations of its
lower rotational transitions. The abundance of H2 can then be inferred from
the integrated intensity of CO via the so-called ‘X-factor’ Bolatto2013 (8).
However, it has become increasingly apparent that this method fails to
predictably trace significant amounts of molecular gas in more diffuse
environments (Blitz1990, 6, 87, 46, 84, 79, 58, 62, e.g.). The primary reason
for this limitation is the unreliable relationship between the integrated
intensity of CO and the H2 abundance in low extinction or low number density
environments. CO can be photodissociated in low extinction environments by
external UV radiation Tielens1985a (94, 93, 97, 103, 41, 42) even when
hydrogen exists primarily as H2because of its higher self-shielding threshold
compared to that of H2. In the local ISM the extinction threshold for H2 to
form is $A_{V}\geq 0.14$ mag, but CO requires $A_{V}\geq 0.8$ mag Wolfire2010
(103), so CO is typically photo-dissociated by external UV radiation
Tielens1985a (94, 97, 103, 41, 42). On the other hand, in low number density
molecular environments (Busch2019, 10, e.g. $n_{\rm H}\lesssim 10^{-2}\,{\rm
cm}^{-3}$ as found by) that do contain CO, the CO may not be sufficiently
excited to be detectable due to its relatively high critical density.

This has motivated a resurgence of interest in hydroxyl (OH) as an alternative
tracer of diffuse H2 (Dawson2014, 23, 1, 36, 11, 22, e.g.). OH has been
demonstrated to trace ‘CO-dark’ H2 in diffuse clouds Barriault2010 (2, 18, 1),
in the envelopes of GMCs Wannier1993 (99), in absorption sightlines scattered
across the sky Li2015 (63, 62), and recently in a thick molecular disk of
ultra-diffuse molecular gas in the outer Galaxy Busch2021 (11). Though there
may be a weak relationship between the OH/H2 abundance ratio $X_{\rm OH}$ and
visual extinction $A_{V}$, $X_{\rm OH}$ appears relatively constant ($\approx
10^{-7}$) in a wide range of environments (Nguyen2018, 75, i.e. with
$A_{V}=0.1-2.7$ and $n_{\rm H_{2}}>50\,{\rm cm}^{-3}$) including the CO-dark
gas Black1977 (5, 99, 101).

Most OH molecules in the diffuse ISM are expected to be found in the
${}^{2}\Pi_{3/2}\,J=3/2$ ground state (see Fig. 1) which is split into 4
levels via lambda doubling and hyperfine splitting. There are four allowed
transitions between these levels: the ‘main’ lines at 1665.402 and 1667.359
MHz, and the ‘satellite’ lines at 1612.231 and 1720.530 MHz (Destombes1977,
25, e.g.).

Figure 1: Energy level diagram of the ${}^{2}\Pi_{3/2},~{}J=3/2$ ground state
of hydroxyl. The ground state is split into four levels due to
$\Lambda$-doubling and hyperfine splitting, with 4 allowed transitions between
these levels: the ‘main’ lines at 1665.402 and 1667.359 MHZ, and the
‘satellite’ lines at 1612.231 and 1720.530 MHz. Figure from Petzler2020 (82).

###  1.1 Local thermodynamic equilibrium (LTE)

OH excitation is complex. Significant departures from local thermodynamic
equilibrium (LTE) are almost ubiquitous in the ISM, leading to anomalous
excitation in all four of the ground state transitions Turner1979 (95, 19, 23,
62, 82). The majority of this anomalous excitation is seen in the satellite
lines and is due to asymmetries in the infrared (IR) de-excitation cascade
pathways into the ground-rotational state from excited rotational states
Elitzur1976 (35, 34, 31, 49). All cascades into the ground-rotational state
will pass through either the first-excited ${}^{2}\Pi_{3/2}\,J=5/2$ rotational
state or the second-excited ${}^{2}\Pi_{1/2}\,J=1/2$ rotational state
Elitzur1992 (33), and these and the ground-rotational state are shown in Fig.
2. Radiative transitions between these states are subject to selection rules
based on the parity and total angular momentum quantum number $F$ of the upper
and lower levels: parity must change and $|\Delta F|$ = 1, 0. These allowed
transitions are indicated in Fig. 2 by the blue and red arrows. The number of
possible pathways into each level then introduces a natural asymmetry for
intra-ladder (blue) or cross-ladder (red) cascades Elitzur1976 (35). Selective
excitation into the first-excited ${}^{2}\Pi_{3/2}\,J=5/2$ rotational state,
for instance, will tend to cascade back into the ground state into its $F=2$
levels more often than its $F=1$ levels, while the opposite is true for
cascades from the second-excited rotational level Elitzur1976etal (34). In
most cases these cascade mechanisms will be responsible for the majority of
the divergence from equal populations seen in the levels of the ground-
rotational state Elitzur1992 (33). This implies that the ground-rotational
state transitions between levels with different $F$ quantum numbers (i.e. the
satellite lines) will often have excitation temperatures that differ widely
from one another and from those of the main lines. In contrast, the main lines
– which involve transitions between levels with the same $F$ quantum numbers –
will tend to have excitation temperatures similar to one another and to the
kinetic temperature.

Figure 2: Schematic of the three lowest rotational states of OH, indicating
their $\Lambda$ and hyperfine splitting. Excitations above the
${}^{2}\Pi_{3/2},~{}J=3/2$ ground state will cascade back down to it via the
${}^{2}\Pi_{3/2},~{}J=5/2$ state, or the ${}^{2}\Pi_{1/2},~{}J=1/2$ state.
Allowable transitions are those where parity is changed and $|\Delta F|$ = 1,
0; shown in blue at left and red on the schematic. The energy scale is given
at left in kelvin, and the wavelengths of the IR transitions are shown at
centre in $\mu$m. The splittings of the $\Lambda$ and hyperfine levels are
greatly exaggerated for clarity. Figure from Petzler2020 (82).

However, the main lines are not fully immune from this anomalous excitation as
noted observationally as early as the 1970s (NguyenQRieu1976, 76, 19, 20,
e.g.). The mechanism by which the main lines may diverge from LTE is an
extension of the mechanism that leads to anomalies in the satellite lines: an
additional imbalance in cascade pathways is introduced by an imbalance in the
excitations into the upper and lower halves of the lambda-doublets. Briefly,
this is caused by two key factors: transitions into the upper half of the
lambda-doublet in the ground-rotational state originate from the upper half of
the lambda-doublet in either the first- or second-excited rotational states
(and vice-versa), and the energy difference between arms of these lambda-
doublets increase moving up the rotational ladder. These factors imply that an
imbalance can be introduced between pathways into the upper and lower level of
the ground-rotational state lambda-doublet by a radiation field that diverges
significantly from a Planck distribution (Elitzur1978, 31, i.e. from hot dust)
or by collisional excitations from particles whose motions diverge
significantly from a Maxwellian distribution (Elitzur1979, 32, i.e. from
particle flows). In general, since the main lines tend to be seen in their LTE
ratio more often than the satellite lines, we may therefore conclude that the
conditions required to create this imbalance in cascade pathways is less
common in the ISM than those responsible for the satellite-line anomalies.

This, coupled with the fact that for practical reasons many researchers
observe only the stronger main lines of OH (Li2018, 62, 75, 36, e.g.), has led
researchers in the field of diffuse OH studies to describe the excitation of
the OH via the idea of so-called ‘main-line LTE’ – where the main lines have
excitation consistent with LTE – as evidenced most often by the ratio of their
optical depths ($\tau_{\rm peak}(1667)/\tau_{\rm peak}(1665)=1.8$ in LTE) or
brightness temperatures ($T_{\rm b}(1667)/T_{\rm b}(1667)=1.8$ in the
optically thin limit and $=1$ in the optically thin limit in LTE). Many works
(Li2018, 62, 88, 109, 30, 37, e.g.) then report the degree to which the main
lines do or do not obey this relationship.

It is often – though not always – the case (as these works clearly show) that
the main-line optical depths or brightness temperatures have a ratio
consistent with LTE within the observational uncertainties, and their
excitation temperatures are often very similar. However, if the satellite
lines are also observed, it is then quite clear that they do not exhibit the
same ‘LTE-like’ behaviour (Ebisawa2015, 29, 30, 108, 82, 23, 88, 98, 39,
e.g.). The nature of this divergence from LTE (i.e. the relationship between
satellite-line excitation temperatures or the presence of population
inversions) can then provide additional valuable information about the
conditions of the gas that may otherwise not be apparent if only the main
lines were considered Petzler2020 (82). In this work we examine all four
ground-rotational transitions and explore the relationships between their
optical depth ratios and differences in their excitation temperatures.

###  1.2 Observing OH

The observed continuum-subtracted line brightness temperature $T_{\rm b}$ of
an extended, homogeneous, isothermal ISM cloud towards a compact background
continuum source of brightness temperature $T_{\rm c}$ and a diffuse continuum
background of brightness temperature $T_{\rm bg}$ is related to the optical
depth $\tau_{\nu}$ and excitation temperature $T_{\rm ex}$ of the transition
via the solution to the radiative transfer equation:

$T_{\rm b}=(T_{\rm ex}-T_{\rm c}-T_{\rm bg})(1-e^{-\tau_{\nu}}).$ (1)

We are interested in $\tau_{\nu}$ and $T_{\rm ex}$ because they allow us to
characterise the excitation of the ground-rotational state. Excitation
temperature is a re-parameterisation of the populations in the upper and lower
levels of the transition, and can be described in terms of the column
densities in the upper ($N_{u}$) and lower ($N_{l}$) levels as:

$\frac{N_{u}}{N_{l}}=\frac{g_{u}}{g_{l}}\exp{\bigg{[}\frac{-h\nu_{0}}{k_{\rm
B}T_{\rm ex}}\bigg{]}},$ (2)

where $g_{u}$ and $g_{l}$ are the degeneracies of the upper and lower levels
of the transitions (determined by $g=2F+1$, see Fig. 1), and $\nu_{0}$ is the
rest frequency of the transition. Optical depth is defined by:

$\tau_{\nu}=\frac{c^{2}}{8\pi\nu^{2}_{0}}\frac{g_{u}}{g_{l}}\,N_{l}\,A_{ul}\bigg{(}1-\exp{\bigg{[}\frac{-h\nu_{0}}{k_{\mathrm{B}}T_{\mathrm{ex}}}\bigg{]}}\bigg{)}\,\phi(\nu),$
(3)

where $A_{ul}$ is the Einstein-A coefficient and $\phi(\nu)$ is the line
profile. If both optical depth and excitation temperature can be determined
for a given transition, we may then calculate the column densities in both the
upper and lower levels of that transition. Since the four ground-rotational
transitions share four levels, a minimum of two transitions are needed to
fully characterise the excitation of the ground-rotational state. This
excitation is a function of the local environment of the gas which may be
parameterised through use of (or reference to) non-LTE molecular excitation
modelling (Xu2016, 108, 30, 82, e.g.).

Unfortunately, Eq. 1 is insufficient to solve for both $\tau_{\nu}$ and
$T_{\rm ex}$ uniquely, but several strategies exist to break this degeneracy.
One such method is to make additional observations just off the compact
background continuum source. These observations should not include any of the
compact background continuum emission, but still point towards the same
extended OH gas with the same $\tau_{\nu}$ and $T_{\rm ex}$, and include the
same diffuse background $T_{\rm bg}$. In this case the average continuum-
subtracted brightness temperature of these ‘off-source’ positions will be
described by:

$T_{\rm b}^{\rm off}=(T_{\rm ex}-T_{\rm bg})(1-e^{-\tau_{\nu}}).$ (4)

Following Heiles2003 (51), we refer to this averaged off-source spectrum as
the ‘expected brightness temperature’ $T_{\rm exp}$ as it represents the
spectrum we would expect to observe if we could turn off the compact
background continuum source $T_{\rm c}$. We can then combine Eqs. 1 and 4 to
obtain the optical depth spectrum:

$\tau_{\nu}=-\ln\Bigg{(}\frac{T_{\rm b}-T_{\rm exp}}{T_{\rm c}}+1\Bigg{)}.$
(5)

As we will describe further in the Observations section, we have observations
of this type (which we refer to as ‘on-off’ observations) from the Arecibo
radio telescope toward 92 compact extragalactic continuum sources. These data
include 8 spectra per sightline: one optical depth and one expected brightness
temperature for each of the four ground-rotational transitions of OH.

The degeneracy between optical depth and excitation temperature can also be
broken by observing bright compact background continuum sources with an
interferometer – and thus rendering the $T_{\rm ex}$ and $T_{\rm bg}$ terms in
Eq. 1 insignificant. The reason for this is twofold: first, the emission from
the extended OH in the intervening cloud and the diffuse background continuum
are assumed to be smooth on the sky and large compared to the interference
fringes of the interferometer, so that the flux detected from both will be
negligible. Additionally, if $T_{\rm c}\gg|T_{\rm ex}|$ (which is likely to be
the case if a bright compact background continuum source is targeted) then the
$T_{\rm c}$ term will dominate Eq. 1, and the observed brightness temperature
will be well-described by $T_{\rm b}=T_{\rm c}(e^{-\tau_{\nu}}-1)$, even if
some flux from the extended cloud is detected. We have observations of this
type from the Australia Telescope Compact Array (ATCA) towards 15 bright
compact continuum sources in the Galactic plane. These data only include 4
spectra per sightline; since the observing strategy rendered the $T_{\rm ex}$
and $T_{\rm bg}$ terms in Eq. 1 insignificant we are unable to construct an
expected brightness temperature spectrum, and only have optical depth spectra
for each transition.

The individual features in these OH spectra will be broadened by mostly
Gaussian processes (Leung1976, 61, 64, turbulent or thermal broadening, e.g.).
Other sources of broadening that are not Gaussian also contribute to the line
profile (i.e. natural and collisional broadening – both Lorentzian in shape)
but are assumed to have negligible contribution to the feature shape. A single
telescope pointing will tend to detect several blended Gaussian-shaped
features arising from the same transition at different line-of-sight
velocities. In our analysis these Gaussian-shaped profiles are interpreted as
individual isothermal clouds along the line of sight: each cloud may then be
expected to result in a feature with the same centroid velocity and full width
at half-maximum (FWHM) in all the observed spectra (8 in the case of on-off
observations, 4 if only optical depth spectra are obtained).

This work represents an unprecedented analysis of OH in the diffuse ISM due
primarily to the Gaussian decomposition method used. The observed spectra were
decomposed into individual Gaussian components using
Amoeba111https://github.com/AnitaPetzler/AMOEBA Petzler2021a (83): an
automated Bayesian line-fitting algorithm in Python. Amoeba’s key advantage
over other Gaussian decomposition methods is that it is able to simultaneously
fit optical depth and expected brightness temperature spectra in all four
ground-rotational transitions. Each Gaussian feature is parameterised by its
centroid velocity, FWHM, $\log$ column density of the lowest ground-rotational
state level ($\log N_{1}$), and inverse excitation temperatures of the 1612,
1665 and 1667 MHz transitions. These parameters are then sufficient to fully
characterise the associated peak optical depths and expected brightness
temperatures in all four transitions. Alternatively, in the case of our ATCA
data, Amoeba can take a set of 4 optical depth velocity spectra, and each
Gaussian component is then parameterised by its centroid velocity, FWHM and
peak optical depths in each of the four ground-rotational state transitions.
Further details about our usage of Amoeba are given in the Method
practicalities and limitations section.

###  1.3 OH and Hi cold neutral medium

In this work we will compare our OH data with published measurements of the
atomic Hi gas. In pressure equilibrium, most of the Hi is expected to reside
in two distinct thermal phases Field1969 (38, 69, 104, 105): the warm neutral
medium (WNM) at temperatures of several thousand kelvin, and the cold neutral
medium (CNM) at temperatures at or below $\sim 100\,$K for typical pressure
ranges found in the Galaxy (Dickey1978, 27, 52, 57, 73, 74, 72, e.g.). It is
generally accepted that, in cool regions of the ISM (like the CNM) molecular
hydrogen forms primarily on dust grains McCrea1960 (68, 44, 54), and can
accumulate once it is sufficiently shielded from dissociating UV. This is not
a uni-directional process, as matter can cycle back and forth from one stable
phase to another Ostriker2010 (78), and the phases (WNM, CNM and H2) are
generally mixed Goldsmith2009 (43). Therefore, one might expect the properties
of the molecular gas (as traced here by OH) to maintain some relationship to
the CNM gas from which it presumably formed.

72 of the 92 Arecibo sightlines with on-off observations examined in this work
were simultaneously observed in Hi. Nguyen2019 (74) identified 327 individual
CNM components along these sightlines (seen in absorption and emission, see
Nguyen2019 (74) for further details), and characterised their individual
centroid velocities, FWHMs, peak optical depths, spin temperatures and column
densities. As we describe in the Analysis section, we identify a total of 43
OH features along 20 of these sightlines, and we match these in velocity to
their closest CNM feature. Some CNM features are matched with several OH
features, for a total of 43 OH components matched with 26 CNM components that
we then discuss.

##  2 Observations

This work utilises two distinct sets of OH observations. The first is a
collection of observations toward 92 compact background continuum sources
obtained through the GNOMES (Galactic Neutral Opacity and Molecular Excitation
Survey) collaboration taken by the Arecibo telescope. The second set are
observations towards 15 bright, compact continuum sources in the region of the
Southern Parkes Large Area Survey in Hydroxyl (Dawson2014, 23, SPLASH,) made
with the Australia Telescope Compact Array (ATCA). The locations of all
sightlines examined in this work are shown in Fig. 3.

Figure 3: Positions of sightlines examined in this work from the Australia
Telescope Compact Array (ATCA), and from the projects a2600, a2769 and a3301
from the Arecibo telescope. Sightlines with detections are indicated by filled
circles, non-detections are indicated by crosses. Sightlines excluded from
analysis are indicated by triangles. The grey-scale image is CO emission
Dame2001 (21) and is included for illustrative purposes only.

###  2.1 Arecibo observations

Our observations from the Arecibo telescope obtained through the GNOMES
collaboration are comprised of data from three projects: a2600 Thompson2019
(92), a2769 Nguyen2019 (74) and a3301. This data set consists of on-off
spectra of the four OH ground-rotational transitions toward 92 sightlines in
the Arecibo sky. These sightlines are listed in Table 1 along with their
sensitivities in optical depth and expected brightness temperature (quantified
by the rms noise of the individual spectra) for each transition. As can be
seen in Fig. 3 the majority of these sightlines were out of the Galactic
Plane. The angular resolution of the Arecibo telescope at the frequency of the
OH ground-rotational transitions is $\sim 3^{\prime}.5$.

The aim of project a2600 (PI Thompson) was to use Zeeman splitting of the OH
ground-rotational state transitions to measure magnetic field strengths in the
envelopes of molecular clouds. The targets for this project were compact
extragalactic continuum sources chosen from the National Radio Astronomy
Observatory Very Large Array Sky Survey (Condon1998, 17, NVSS) with brightness
$S_{\nu}\gtrsim 0.5\,$Jy behind molecular clouds identified from CO emission
maps Dame2001 (21). This project targeted regions of the inner and outer
Galaxy, and includes sightlines passing through molecular clouds with low-mass
star formation (e.g. Taurus) and high-mass star formation (e.g. Mon OB1)
mostly near the Galactic plane. Observations were made both on- and off-
source, allowing optical depth and expected brightness temperature spectra to
be produced following the method of Heiles2003 (51). The 16 off-source
pointings were arranged as illustrated in Fig. 4. This pattern of off-source
pointings was also used in the other projects outlined in this section. We
have observations towards 12 sightlines from this project.

Figure 4: Offsets (in degrees) of off-source pointings (blue circles) in RA
and Dec in terms of the telescope half-power beam width (HPBW) relative to the
on-source pointing (black cross). The 16 off-source pointings are placed at
distances of 1 and $\sqrt{2}$ times the HPBW in the four cardinal directions
and in directions rotated 45∘ from these as shown.

The aim of project a2769 (PI Stanimirović) was to explore the relationships
between WNM, CNM and molecular gas in the Taurus and Gemini regions. Their
observations also included on-off measurements, and targeted compact
extragalactic continuum sources in the Taurus, California, Rosette, Mon OB1
and NGC 2264 giant molecular clouds. Their continuum sources were also
selected from the NVSS catalog and have typical flux densities of
$S_{\nu}\gtrsim 0.6\,$Jy at 1.4 GHz. Our data include observations towards 73
sightlines from this project.

The aim of project a3301 (PI Petzler) was to follow up lines of sight observed
in previous projects included in the GNOMES collaboration that showed
‘anomalous excitation’: this generally involved interesting patterns of
emission and absorption across the available transitions. Most of these were
chosen because not all four transitions had been observed in the original
project. These sightlines will therefore be biased towards anomalous
excitation, but due to poor data quality in some of the 1720 MHz spectra, only
6 of the 16 sightlines observed in that project were included in this work.

###  2.2 ATCA observations

Our ATCA data (taken under project code C2976) include sightlines towards 15
bright compact continuum sources selected from the 843 MHz Molongo Galactic
Plane Survey catalogue (Murphy2007, 71, MGPS,), the Southern Galactic Plane
Survey (Haverkorn2006, 50, SGPS,) and the NVSS 1.4 GHz continuum images. All
sources were cross-checked against the recombination line measurements of
Caswell1987 (15) in order to discriminate between Hii regions and other source
types, and were also examined for evidence of Hi absorption in SGPS datacubes
in order to confirm near- or far-side Galactic distances where relevant.
Bright, compact sources (unresolved or with sufficient unresolved structure at
a beam size of $\sim 30^{\prime\prime}$) were chosen, located between
$332^{\circ}<l<8^{\circ}$, $|b|<2.1^{\circ}$ to match the region mapped in the
Southern Parkes Large Area Survey of Hydroxyl (Dawson2022, 22, SPLASH).
Sources with a spectral flux density $\sim 1$ Jy at 1.6 GHz were preferred,
which would result in brightness temperatures of $\sim 500$ K when observed
with our array configuration (ATCA 1.5D, excluding antenna 6). Distant sources
were considered preferable as they probe a larger number of absorbing
components along the line of sight. However, the number of extragalactic and
far-side Galactic sources with sufficient flux density and compact structure
was small. Therefore the target criteria were expanded to include nearside Hii
regions with evidence for bright and compact substructure and intervening Hi
absorption.

The CFB 1M-0.5k mode on the ATCA Compact Array Broadband Backend (CABB) was
used to simultaneously observe all four ground state OH lines in zoom bands
centred on the line rest frequencies (a single zoom band was used for the main
lines, centred at 1666 MHz). This provided a raw channel width of 0.09 km s-1.
The 1.5D array resulted in a synthesised beam size of $\sim 30^{\prime\prime}$
at 1.6 GHz. The total observing time for all 15 sources was 50 hours.

The raw visibility data from the ATCA (excluding antenna 6) was reduced using
the miriad222http://www.atnf.csiro.au/computing/software/miriad package
Sault1995 (89). The main-line observations at 1666 MHz contained more radio
frequency interference (RFI) than the satellite-line observations. Flagging
this RFI resulted in systematically larger synthesised beams for the main-line
observations, and hence lower continuum brightness temperatures in the main
lines (see Table 2). This would not affect the peak optical depths measured in
our analysis as they are derived from a ratio of $T_{\rm b}$ and $T_{\rm c}$
which are equally affected by this increase in synthesised beam. The
visibilities were inverted using a Brigg’s visibility weighting robustness
parameter of 1 Briggs1995 (9), corresponding to roughly natural weighting. The
velocity spectrum at the location of the brightest continuum pixel was
selected for further analysis. A linear baseline was fit to these velocity
spectra to determine the background continuum brightness temperature
$T_{\mathrm{c}}$, which was subtracted to produce line brightness temperature
($T_{\mathrm{b}}$) spectra. These were then converted to optical depth
($\tau_{\nu}$) spectra, assuming that $T_{\rm b}=T_{\rm
c}(e^{-\tau_{\nu}}-1)$. The rms noise levels of the optical depth spectra
ranged from 0.006 to 0.023, and are outlined in Table 2.

|  |  |  |  $T_{\rm bg}$ (K) | $\tau_{\sigma}~{}(10^{-3})$ |  $T_{{\rm exp}\,\sigma}$ (10-2 K) |
---|---|---|---|---|---|---|---
Sourcea | Projectb | $l^{\circ}$ | $b^{\circ}$ | 1612 | 1665 | 1667 | 1720 | 1612 | 1665 | 1667 | 1720 | 1612 | 1665 | 1667 | 1720 | Det.c
∗B1858+0407 | a2600 | 37.76 | -0.21 | 9 | 10 | 10 | 10 | 3 | 3 | 3 | 3 | 4 | 5 | 5 | 4 | N
∗B1853+0749 | a2600 | 40.50 | 2.54 | 7 | 7 | 7 | 7 | 3 | 2 | 2 | 4 | 5 | 4 | 4 | 6 | N
∗B190840+09 | a2600 | 43.25 | -0.18 | 8 | 9 | 9 | 9 | 1 | 1 | 1 | 1 | 5 | 6 | 5 | 5 | N
∗B1919+1357 | a2600 | 48.92 | -0.28 | 12 | 12 | 12 | 13 | 3 | 2 | 3 | 3 | 10 | 9 | 9 | 8 | N
∗B1920+1410 | a2600 | 49.21 | -0.34 | 11 | 12 | 12 | 12 | 2 | 2 | 2 | 2 | 9 | 8 | 8 | 8 | N
∗B1921+1424 | a2600 | 49.49 | -0.38 | 11 | 12 | 12 | 12 | 1 | 1 | 1 | 1 | 12 | 11 | 12 | 11 | N
∗PKS1944+251 | a2600 | 61.47 | 0.09 | 5 | 5 | 5 | 5 | 2 | 2 | 2 | 3 | 4 | 3 | 7 | 5 | N
SRC44 | a3301 | 68.83 | -3.49 | 214 | 234 | 235 | 257 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 | Y
3C417 | a2600 | 73.33 | -5.45 | 14 | 24 | 26 | 8 | 4 | 4 | 4 | 6 | 3 | 3 | 3 | 4 | Y
4C+30.04 | a3301 | 154.92 | -23.69 | 164 | 179 | 180 | 197 | 2 | 3 | 3 | 5 | 3 | 4 | 4 | 4 | N
3C092 | a2600 | 159.74 | -18.41 | 9 | 32 | 33 | 9 | 3 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | Y
4C+24.06 | a2769 | 161.92 | -26.26 | 4 | 6 | 2 | 5 | 4 | 3 | 3 | 4 | 2 | 2 | 1 | 2 | N
3C115 | a2769 | 164.76 | -10.24 | 10 | 5 | 6 | 5 | 6 | 4 | 4 | 6 | 4 | 3 | 3 | 4 | N
4C+28.11 | a2769 | 166.06 | -17.22 | 4 | 7 | 11 | 4 | 5 | 3 | 4 | 6 | 3 | 2 | 2 | 3 | Y
4C+16.09 | a2769 | 166.64 | -33.60 | 79 | 110 | 110 | 81 | 2 | 1 | 1 | 2 | 5 | 4 | 4 | 6 | N
∗SRC10 | a3301 | 170.58 | -11.66 | 3 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 4 | 5 | 5 | 6 | N
PKS0319+12 | a2769 | 170.59 | -36.24 | 18 | 24 | 29 | 19 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | Y
3C131 | a2600 | 171.44 | -7.80 | 36 | 51 | 52 | 23 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | Y
3C108 | a3301 | 171.47 | -20.70 | 166 | 182 | 182 | 199 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | Y
4C+11.15 | a2769 | 171.98 | -35.48 | 6 | 10 | 13 | 6 | 4 | 4 | 4 | 5 | 3 | 3 | 3 | 4 | Y
4C+18.11 | a2769 | 172.23 | -25.66 | 7 | 3 | 4 | 5 | 4 | 3 | 3 | 4 | 3 | 2 | 2 | 3 | N
4C+36.10 | a2769 | 172.98 | 2.44 | 5 | 6 | 11 | 4 | 5 | 3 | 4 | 5 | 3 | 2 | 2 | 3 | Y
3C090 | a2769 | 173.15 | -33.30 | 15 | 17 | 17 | 14 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | N
4C+29.16 | a2769 | 174.77 | -5.97 | 4 | 5 | 4 | 4 | 7 | 4 | 5 | 7 | 3 | 2 | 2 | 3 | N
4C+27.14 | a3301 | 175.46 | -9.96 | 171 | 187 | 188 | 205 | 2 | 5 | 5 | 5 | 2 | 4 | 4 | 5 | Y
4C+21.17 | a2769 | 175.70 | -18.36 | 6 | 7 | 8 | 10 | 3 | 2 | 2 | 3 | 3 | 2 | 2 | 3 | N
3C096 | a2769 | 176.27 | -28.26 | 6 | 8 | 9 | 5 | 3 | 2 | 2 | 3 | 2 | 2 | 2 | 2 | N
4C+17.23 | a2769 | 176.36 | -24.24 | 6 | 10 | 18 | 5 | 3 | 2 | 3 | 4 | 2 | 2 | 2 | 2 | Y
J035613+130535 | a2769 | 177.02 | -29.78 | 5 | 4 | 5 | 4 | 3 | 2 | 2 | 3 | 2 | 1 | 1 | 2 | N
3C114 | a2769 | 177.30 | -22.24 | 7 | 6 | 6 | 5 | 3 | 2 | 2 | 3 | 2 | 2 | 1 | 2 | N
4C+17.25 | a2769 | 178.11 | -21.31 | 5 | 6 | 2 | 4 | 5 | 3 | 3 | 5 | 3 | 2 | 2 | 3 | N
4C+17.26 | a2769 | 178.56 | -20.88 | 5 | 6 | 7 | 5 | 5 | 4 | 4 | 6 | 4 | 3 | 3 | 4 | N
4C+07.13 | a2769 | 178.87 | -36.27 | 10 | 10 | 5 | 7 | 4 | 3 | 3 | 4 | 3 | 2 | 2 | 3 | Y
4C+29.19 | a2769 | 179.53 | -0.59 | 3 | 4 | 3 | 4 | 5 | 4 | 4 | 6 | 3 | 2 | 2 | 3 | N
B0531+2730 | a2769 | 179.87 | -2.83 | 7 | 15 | 17 | 5 | 4 | 4 | 4 | 5 | 3 | 2 | 2 | 3 | Y
4C+23.14 | a2769 | 180.86 | -8.01 | 7 | 8 | 7 | 5 | 5 | 4 | 4 | 5 | 3 | 2 | 2 | 3 | N
4C+26.18b | a2769 | 182.36 | -0.62 | 7 | 7 | 15 | 5 | 6 | 4 | 5 | 7 | 4 | 3 | 3 | 4 | Y
4C+08.15 | a2769 | 186.21 | -26.51 | 5 | 3 | 6 | 5 | 2 | 2 | 2 | 3 | 2 | 1 | 1 | 2 | N
PKS0531+19 | a2769 | 186.76 | -7.11 | 85 | 74 | 84 | 84 | 2 | 2 | 2 | 2 | 6 | 4 | 4 | 6 | N
3C138 | a2769 | 187.41 | -11.34 | 122 | 97 | 105 | 101 | 2 | 1 | 2 | 2 | 6 | 4 | 4 | 6 | N
PKS0509+152 | a2769 | 187.41 | -13.79 | 4 | 4 | 1 | 4 | 7 | 5 | 4 | 6 | 3 | 2 | 2 | 3 | N
PKS0446+11 | a2769 | 187.43 | -20.74 | 7 | 5 | 6 | 5 | 5 | 4 | 3 | 5 | 3 | 2 | 2 | 3 | N
4C+22.12 | a2769 | 188.07 | 0.04 | 23 | 22 | 32 | 21 | 2 | 2 | 2 | 3 | 3 | 2 | 3 | 4 | Y
4C+17.33 | a2769 | 188.22 | -7.67 | 4 | 5 | 3 | 3 | 6 | 4 | 5 | 7 | 3 | 2 | 3 | 3 | N
4C+14.14 | a2769 | 189.04 | -12.85 | 4 | 4 | 3 | 3 | 4 | 3 | 4 | 5 | 3 | 2 | 2 | 2 | Y
Table 1: Summary of sightlines observed by the Arecibo telescope included in this work. aSource names are given along with the original Arecibo bproject designation and the galactic longitude and latitude. cSources with detections are indicated ‘Y’ and those without are indicated ‘N’. Source names indicated with asterisks were excluded from analysis due to contamination of off-source pointings as described in the text. The brightness temperature of the background continuum $T_{\rm bg}$ at each of the four OH ground-rotational state transitions are given along with the rms noise of the optical depth $\tau_{\sigma}$ and expected brightness temperature spectra $T_{\rm exp\,\sigma}$. |  |  |  |  $T_{\rm bg}$ (K) | $\tau_{\sigma}~{}(10^{-3})$ |  $T_{{\rm exp}\,\sigma}$ (10-2 K) |
---|---|---|---|---|---|---|---
Sourcea | Projectb | $l^{\circ}$ | $b^{\circ}$ | 1612 | 1665 | 1667 | 1720 | 1612 | 1665 | 1667 | 1720 | 1612 | 1665 | 1667 | 1720 | Det.c
4C+17.34 | a2769 | 189.21 | -6.93 | 11 | 7 | 9 | 8 | 4 | 3 | 3 | 4 | 4 | 2 | 2 | 4 | N
4C+19.18 | a2769 | 190.09 | -2.17 | 7 | 6 | 13 | 5 | 5 | 3 | 3 | 5 | 3 | 2 | 2 | 3 | Y
4C+19.19 | a2769 | 190.13 | -1.64 | 5 | 6 | 14 | 4 | 3 | 3 | 3 | 4 | 2 | 2 | 2 | 2 | Y
4C+22.16 | a2769 | 190.16 | 3.91 | 8 | 4 | 5 | 5 | 4 | 3 | 4 | 5 | 3 | 2 | 2 | 3 | N
J062019+210229 | a2769 | 190.74 | 2.94 | 9 | 6 | 10 | 5 | 4 | 2 | 3 | 4 | 3 | 2 | 2 | 3 | N
PKS0528+134 | a2600 | 191.37 | -11.01 | 22 | 43 | 60 | 24 | 3 | 2 | 2 | 2 | 4 | 3 | 3 | 3 | Y
3C166 | a2769 | 193.12 | 8.30 | 16 | 15 | 20 | 14 | 2 | 2 | 2 | 2 | 3 | 2 | 2 | 3 | N
4C+16.15b | a2769 | 193.64 | -1.53 | 3 | 5 | 8 | 4 | 4 | 3 | 3 | 5 | 2 | 2 | 2 | 2 | Y
J063451+190940 | a2769 | 193.99 | 5.10 | 7 | 5 | 6 | 5 | 4 | 3 | 3 | 5 | 3 | 2 | 2 | 3 | N
4C+21.22 | a2769 | 194.63 | 11.26 | 3 | 3 | 2 | 3 | 6 | 5 | 5 | 7 | 2 | 2 | 2 | 3 | N
4C+09.21 | a2769 | 194.89 | -11.98 | 5 | 5 | 5 | 5 | 6 | 4 | 4 | 6 | 4 | 3 | 3 | 4 | N
4C+07.16 | a2769 | 195.51 | -15.35 | 5 | 5 | 4 | 5 | 5 | 4 | 4 | 5 | 3 | 2 | 2 | 3 | N
3C158 | a2769 | 196.64 | 0.17 | 14 | 27 | 10 | 14 | 3 | 2 | 2 | 3 | 4 | 3 | 3 | 4 | Y
J053239+073243 | a2769 | 196.84 | -13.74 | 16 | 14 | 18 | 17 | 3 | 2 | 2 | 3 | 4 | 3 | 3 | 4 | N
4C+19.26 | a2769 | 196.91 | 12.80 | 4 | 3 | 5 | 3 | 4 | 4 | 4 | 5 | 2 | 2 | 2 | 2 | N
4C+14.18 | a2600 | 196.98 | 1.10 | 20 | 45 | 47 | 22 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | Y
4C+13.32 | a2769 | 197.15 | -0.85 | 4 | 4 | 4 | 4 | 2 | 2 | 2 | 3 | 3 | 2 | 2 | 3 | Y
PKS0715+20 | a2769 | 197.52 | 14.74 | 4 | 5 | 4 | 5 | 5 | 4 | 4 | 5 | 3 | 2 | 2 | 3 | N
J061622+115553 | a2769 | 198.33 | -2.20 | 3 | 6 | 5 | 5 | 3 | 3 | 3 | 4 | 2 | 2 | 2 | 2 | N
J070001+170922 | a2769 | 198.47 | 9.58 | 9 | 11 | 8 | 8 | 3 | 2 | 2 | 3 | 3 | 2 | 2 | 3 | N
4C+14.20 | a2769 | 199.52 | 6.04 | 5 | 7 | 6 | 4 | 4 | 3 | 3 | 5 | 3 | 2 | 2 | 3 | N
4C+17.41 | a2769 | 201.13 | 16.42 | 2 | 4 | 8 | 4 | 5 | 4 | 3 | 5 | 2 | 2 | 2 | 2 | Y
∗4C+10.20 | a2769 | 201.53 | 0.51 | 4 | 4 | 4 | 4 | 4 | 3 | 3 | 4 | 5 | 4 | 4 | 5 | N
3C175.1 | a2769 | 202.29 | 11.53 | 10 | 18 | 14 | 12 | 2 | 2 | 2 | 3 | 3 | 2 | 2 | 3 | N
4C+15.20 | a2769 | 203.42 | 15.42 | 9 | 11 | 9 | 9 | 3 | 2 | 2 | 3 | 3 | 2 | 2 | 3 | N
4C+08.21 | a2769 | 203.54 | -0.27 | 6 | 5 | 8 | 5 | 4 | 2 | 3 | 4 | 3 | 2 | 2 | 3 | N
4C+14.23 | a2769 | 203.64 | 13.91 | 5 | 5 | 5 | 6 | 4 | 3 | 3 | 4 | 3 | 2 | 2 | 3 | N
3C181 | a2769 | 203.75 | 14.63 | 12 | 8 | 11 | 14 | 2 | 2 | 2 | 2 | 3 | 2 | 2 | 3 | N
4C+10.21 | a2769 | 203.85 | 5.82 | 6 | 5 | 3 | 4 | 5 | 3 | 4 | 5 | 3 | 2 | 2 | 3 | N
J061900+050630 | a2769 | 204.66 | -4.84 | 7 | 5 | 4 | 3 | 6 | 5 | 4 | 7 | 4 | 2 | 2 | 3 | N
PKS0722+12 | a2769 | 205.35 | 13.17 | 4 | 4 | 4 | 3 | 5 | 5 | 5 | 6 | 2 | 2 | 2 | 2 | N
4C+04.22 | a2769 | 205.41 | -4.43 | 8 | 7 | 14 | 4 | 5 | 3 | 3 | 5 | 3 | 2 | 2 | 3 | Y
J134217-040725 | a2769 | 205.58 | -4.14 | 4 | 4 | 4 | 4 | 5 | 3 | 4 | 5 | 3 | 2 | 2 | 3 | Y
4C+08.23 | a2769 | 205.81 | 4.91 | 3 | 2 | 3 | 4 | 6 | 4 | 4 | 6 | 3 | 2 | 2 | 3 | N
4C+04.24 | a2769 | 205.92 | -3.57 | 4 | 4 | 4 | 4 | 5 | 3 | 4 | 5 | 3 | 2 | 2 | 3 | Y
4C+01.17 | a2769 | 206.08 | -9.37 | 3 | 2 | 2 | 3 | 6 | 5 | 5 | 7 | 2 | 2 | 2 | 3 | N
4C+12.30 | a2769 | 206.09 | 13.67 | 6 | 9 | 3 | 4 | 6 | 4 | 4 | 6 | 4 | 3 | 2 | 4 | N
J065917+081331 | a2769 | 206.48 | 5.48 | 8 | 6 | 4 | 5 | 5 | 4 | 4 | 5 | 3 | 2 | 2 | 3 | N
4C+09.27 | a2769 | 206.72 | 8.44 | 8 | 5 | 6 | 5 | 4 | 2 | 3 | 4 | 2 | 2 | 2 | 2 | N
3C167 | a2769 | 207.31 | 1.15 | 9 | 7 | 8 | 7 | 5 | 4 | 3 | 5 | 4 | 3 | 3 | 4 | N
4C+10.22 | a2769 | 207.31 | 12.37 | 9 | 7 | 10 | 7 | 4 | 3 | 3 | 4 | 3 | 2 | 2 | 3 | N
4C+01.19 | a2769 | 209.24 | -4.64 | 3 | 3 | 4 | 3 | 5 | 4 | 4 | 6 | 3 | 2 | 2 | 3 | N
4C+06.28 | a2769 | 209.43 | 7.00 | 2 | 3 | 3 | 3 | 6 | 5 | 5 | 7 | 3 | 2 | 2 | 3 | N
PKS0719+056 | a2769 | 211.43 | 9.23 | 2 | 6 | 6 | 3 | 5 | 3 | 3 | 5 | 3 | 2 | 2 | 3 | N
4C+03.12 | a2769 | 212.82 | 6.78 | 2 | 4 | 4 | 3 | 6 | 6 | 5 | 8 | 3 | 3 | 2 | 3 | N
J071924+021035 | a2769 | 214.18 | 7.22 | 2 | 4 | 3 | 3 | 8 | 6 | 5 | 8 | 3 | 2 | 2 | 3 | N
SRC19 | a3301 | 219.34 | 43.50 | 160 | 175 | 176 | 192 | 1 | 1 | 1 | 1 | 4 | 2 | 2 | 3 | N
Table 1 continued.
| Tc (K) | $\tau_{\sigma}~{}(10^{-3})$ |  |
---|---|---|---|---
Source | 1612∗ | 1666∗ | 1720∗ | 1612 | 1665 | 1667 | 1720 | Notes | Det.
G334.72-0.65 | 503 | 470 | 498 | 54 | 56 | 55 | 58 | 2 (16 km s-1)a | N
G336.49-1.48 | 2339 | 2220 | 2374 | 15 | 15 | 15 | 16 | 1 (-25 km s-1)a | Y
G340.79-1.02 | 1462 | 1406 | 1401 | 20 | 21 | 21 | 23 | 1 (-25 km s-1)a | Y
G344.43+0.05 | 908 | 887 | 898 | 28 | 30 | 29 | 29 | 1 (-67 km s-1)a | Y
G346.52+0.08 | 428 | 405 | 417 | 59 | 60 | 59 | 61 | 2 (2 km s-1)a | Y
G347.75-1.14 | 1427 | 1313 | 1389 | 17 | 18 | 18 | 18 | 3c | Y
G348.44+2.08 | 466 | 415 | 430 | 41 | 45 | 44 | 48 | 3d | N
G350.50+0.96 | 1120 | 1056 | 1143 | 21 | 22 | 22 | 22 | 1 (-11 km s-1)b | Y
G351.56+0.20 | 975 | 1028 | 902 | 26 | 23 | 23 | 29 | 2 (-45 km s-1)b | Y
G351.61+0.17 | 935 | 867 | 905 | 27 | 27 | 27 | 30 | 2 (-45 km s-1)b | Y
G353.41-0.30 | 1286 | 1142 | 1139 | 18 | 23 | 22 | 25 | 1 (-16 km s-1)b | Y
G356.91+0.08 | 582 | 532 | 537 | 38 | 40 | 40 | 42 | 3 | Y
G003.74+0.64 | 394 | 372 | 380 | 43 | 45 | 45 | 45 | 3e, 4f | N
G006.32+1.97 | 471 | 426 | 422 | 31 | 33 | 32 | 37 | 3g,h | N
G007.47+0.06 | 394 | 366 | 398 | 42 | 44 | 42 | 42 | 2 (-18 km s-1)b | Y
Table 2: Detailed information for the continuum sources coinciding with the
sightlines observed by the ATCA examined in this work and their optical depth
sensitivities. ∗Central frequency of zoom band (MHz). The systematically lower
brightness temperatures in the central band are a result of the slightly
larger synthesized beam at this frequency (see text).
Notes: 1\. Hii region near-side, radio recombination line in brackets, 2\. Hii
region far-side, 3\. Extragalactic, 4\. Nearby Hii region.
References: aCaswell1987 (15), bLockman1989 (67), cPetrov2006 (81),
dCondon1998 (17), eGray1994 (45), fWink1982 (102), gHelfand1989 (53),
hGriffith1993 (47). Sources with detections are indicated ‘Y’ and those
without are indicated ‘N’.

##  3 Method practicalities and limitations

In this section we discuss practical details and limitations of the methods
used in this work. We will also discuss the process of Gaussian decomposition
used to obtain our results. This will include details of our use of Amoeba, an
automated Bayesian Gaussian decomposition algorithm developed primarily for
this dataset. Amoeba is described extensively in Petzler2021a (83), and this
section will provide additional details on its use in this work.

Before being decomposed into individual Gaussian components using Amoeba, the
OH data from our on-off observations from the Arecibo telescope were processed
into sets of optical depth and expected brightness temperature spectra (see
Observing OH subsection), following the method of Heiles2003 (51). This method
included a step where the antenna temperatures $T_{\rm a}$ were converted to
brightness temperatures $T_{\rm b}$ by considering the convolution of the
antenna beam with the background continuum source through the following
relation:

$T_{\rm a}=T_{\rm b}\epsilon_{\rm eff},$ (6)

where $\epsilon_{\rm eff}$ is an effective beam efficiency parameter. This
parameter accounts for the efficiency of the main beam and the sidelobes as
they overlap with the background continuum source. Previous surveys of Hi
(Peek2011, 80, GALFA-Hi) apply a single value of $\epsilon_{\rm eff}$, found
by averaging the convolution of the beam efficiency with continuum source size
over the whole survey. The Millennium survey used a similar approach, adopting
an effective beam efficiency of 0.9. Though the OH observed in our data from
Arecibo is likely to be less smoothly distributed than the Hi of the
Millennium survey, in the absence of exact information about that distribution
we adopt the same effective beam efficiency of 0.9. This may lead to an
underestimation of the brightness temperatures $T_{\rm b}$ and hence our
derived excitation temperatures $T_{\rm ex}$, likely by no more than 10%. Our
derived optical depths would be unaffected.

Our method of generating the OH expected brightness temperature spectra
differed slightly from the method used for Hi observations described by
Heiles2003 (51), in that we did not interpolate between the off-source
pointings to determine $T_{\rm exp}$, but rather simply averaged the off-
source brightness temperature spectra. This choice was made because (for a
majority of sightlines) there were not significant differences between the
features seen in the individual off-source brightness temperature spectra.

As noted in the Observations section the on-off method assumes that the OH
optical depths and excitation temperatures, and the diffuse background
continuum brightness temperature are the same in both the on-source and all
the off-source positions. If one or more of these assumptions is incorrect –
i.e. if the OH gas varies in optical depth or excitation temperature across
the on- and off-source pointings or if there is additional continuum behind
any of the off-source positions – then the averaged off-source spectra will
not be a good estimation of the expected brightness temperature spectrum of
the on-source pointing. For the majority of sources presented in this work
(for which the individual off-source pointings were available), there was
little noticeable difference between the individual off-source spectra
surrounding each on-source pointing before the background continuum $T_{\rm
bg}$ had been subtracted. Any variation in the OH gas or continuum between the
off-source pointings in these cases is therefore likely to be small. This is
in contrast to the findings of Liszt1996 (65) who note inconsistencies between
the absorption (‘on-source’) and emission (‘off-source’) spectra of OH.

We did, however, find a small number of sightlines (9, all indicated in Table
1 with asterisks) that did show differences in diffuse background continuum
and/or off-source OH features. For a given transition, variations such as
these affect both the derived optical depth and excitation temperature. In our
data, this resulted in un-physical relationships between either the optical
depth and the expected brightness temperature of the individual transitions
(e.g. positive $\tau_{\nu}$ but $T_{\rm exp}$ implies a negative $T_{\rm ex}$,
or vice-versa), or between the four transitions (e.g. excitation temperatures
that violate the excitation temperature sum rule $\frac{\nu_{1612}}{T_{\rm
ex}(1612)}+\frac{\nu_{1720}}{T_{\rm ex}(1720)}=\frac{\nu_{1665}}{T_{\rm
ex}(1665)}+\frac{\nu_{1667}}{T_{\rm ex}(1667)}$). Amoeba was unable to
construct a model to fit these un-physical features, which remained as
significant residuals of the fits. Since the optical depth spectra tend to
have higher signal-to-noise, these residuals were mostly seen in the expected
brightness temperature spectra (i.e. Amoeba fitted the optical depth spectra
at the expense of residuals to the expected brightness temperature spectra).
However, even if the optical depth spectra were well-fit, the resulting
parameters from the entire sightline were suspect. Therefore, even if the
original individual off-source pointings were not available to us we were
still able to identify this problem in the data. Since sightlines with this
problem represented a small minority of the overall dataset (9 of the 92
observed with Arecibo) the decision was made to exclude these sightlines from
further analysis.

As outlined in the Observing OH subsection we assume that our observations
from the ATCA do not contain any emission from the extended OH cloud or the
diffuse background and are well-described by $T_{\rm b}=T_{\rm
c}(e^{-\tau_{\nu}}-1)$ (i.e. there is no contribution from $T_{\rm ex}$ or
$T_{\rm bg}$ in Eq. 1). If there is contribution from the $T_{\rm ex}$ term
our method will underestimate optical depth. If there is contribution from the
$T_{\rm bg}$ term, optical depth will be overestimated if the actual optical
depth is positive, and underestimated if it is negative. Across the four
transitions this will change the line optical depth ratios, which in most
cases (i.e. where $|T_{\rm ex}|\gg h\nu_{0}/k_{\rm B}=0.08$ K) are expected to
have the relation $\tau_{\rm peak}(1612)+\tau_{\rm peak}(1720)=\frac{\tau_{\rm
peak}(1665)}{5}+\frac{\tau_{\rm peak}(1667)}{9}$, known as the optical depth
sum rule. Amoeba includes a weak prior that penalises deviations from this
relation, but will still fit features that do not adhere to it.

Another challenge that is more relevant for our ATCA observations is the
presence of high-gain OH masers in the primary beam, whose sidelobes may
coincide with our sources. Interferometric maser sidelobes manifest as either
a positive or negative feature in a single transition (the maser transition),
apparent as a feature in the residual of the sum rule. Amoeba is hesitant to
fit such features in a single transition, since the improvement to the
likelihood gained by fitting the feature may not be able to overcome the
penalty from the prior in violating the sum rule to such a degree. Therefore
when we present our fits of our ATCA data in the Results section we include a
plot of the sum rule residuals.

More generally, our assumption that the foreground OH gas is uniform across
the on- and off-source pointings (for both our on-off and our ATCA
observations) is also limited by the fact that molecular gas is clumpy on sub-
parsec scales (below the resolution of our observations). Engelke2019 (37)
addressed this issue, as well as the presence of unresolved structure in the
bright background continuum source. This is a difficult problem to solve
directly without higher resolution observations, but the overall consequence
appears to be that our measurements of optical depth may represent lower
limits rather than their true values.

##  4 Results

Across the 107 sightlines examined in this work (92 with on-off observations
from Arecibo, 15 with optical depth observations from the ATCA), 38 had
detections (27 on-off, 11 optical depth only). We have identified a total of
109 features from these sightlines. 58 of these were from on-off observations,
and therefore include excitation temperatures and column densities. Data
toward 4C+19.19 from project a2769 from Arecibo and towards G340.79-1.02 from
the ATCA are shown with their fitted features in Fig. 5 as typical examples of
the observations examined in this work. The peak optical depth values of these
features are given in Table 3, excitation temperatures in the four ground-
rotational state transitions of features identified from the on-off
observations are shown in Table 4, and the OH column densities in the ground-
rotational state levels (as well as total OH column density) are shown in
Table 5. Data from sightlines with detections are plotted with their
individual features and total fits (and residuals of those fits) in Figs. 17
to 23. The sightlines are organised by Galactic longitude in all tables, and
alphabetically by their background source name in all figures for easy
reference.

|
---|---
Figure 5: Typical examples of data examined in this work from the Arecibo
Radio Telescope (left towards 4C+19.19 from project a2769) and the Australia
Telescope Compact Array (ATCA, right towards G340.79-1.02). Data from Arecibo
(left) consist of 8 spectra plotted in grey: four optical depth ($\tau$)
spectra (at 1612, 1665, 1667 and 1720 MHz) at left and four expected
brightness temperature ($T_{\rm exp}$) spectra at right. Each identified
Gaussian component is indicated in red and the total fit (the sum of Gaussian
components) is shown in blue. The bottom panels then show the residuals of the
total fit in each transition as described in the legend. Data from the ATCA
(right) consist of four optical depth ($\tau$) spectra. In addition to the
residuals of the total fit shown in the fourth panel, these plots also show
the sum rule residual, as described by $\tau_{\rm peak}(1612)+\tau_{\rm
peak}(1720)-\tau_{\rm peak}(1665)/5-\tau_{\rm peak}(1667)/9$.

As described in detail in Petzler2021a (83), Amoeba parameterises individual
Gaussian features in on-off spectra with a set of 6 parameters:
$\boldsymbol{\theta}=[v,$ ${\rm log}_{10}\Delta v,~{}{\rm log}_{10}N_{1},$
$T_{\rm ex}^{-1}(1612),$ $T_{\rm ex}^{-1}(1665),$ $T_{\rm ex}^{-1}(1667)]$.
These are the centroid velocity, $\log$ FWHM, $\log$ column density of OH in
the lowest level of the ground-rotational state, and inverse excitation
temperatures of the 1612, 1665 and 1667 MHz transitions, respectively.
Alternatively (in the case of our ATCA data), if only optical depth spectra
are available Amoeba parameterises an individual Gaussian feature with
$\boldsymbol{\theta}=$ $[v,$ ${\rm log}_{10}\Delta v,$ $\tau_{\rm
peak~{}1}(1612),$ $\tau_{\rm peak~{}1}(1665),$ $\tau_{\rm peak~{}1}(1667),$
$\tau_{\rm peak~{}1}(1720)]$. These are the centroid velocity, $\log$ FWHM,
and the peak optical depth in the 1612, 1665, 1667 and 1720 MHz transitions,
respectively. In both cases these are then sufficient to describe the features
seen in the observed spectra, and the parameters given in Tables 3 to 5.
Therefore, the 68% credibility intervals quoted in these tables for centroid
velocity, $\log$ FWHM, all four peak optical depths for our ATCA data and
$\log$ column density in the lowest energy level for our Arecibo data are
determined from the smallest volume in parameter space that contains 68% of
the converged Markov chains as found by Amoeba, thus representing a $1\sigma$
uncertainty assuming that those distributions are Gaussian. The remaining
parameters and their associated credibility intervals in Tables 3 to 5 are
then derived from those fitted parameters and their credibility intervals. All
Gaussian features identified in this work were accepted if their inclusion
resulted in a Bayes factor of at least 10 compared to a model that did not
include them, in keeping with the standard defined by Jeffreys1961 (56). We
note again here (as discussed in previous sections) that our models assume (in
the case of our on-off spectra) that the OH gas in the on-source position has
the same optical depth and excitation temperature as the gas in the off-source
positions. If this assumption is incorrect, Amoeba will fit a quasi-average
model that best satisfies the available spectra, and any residual signal
(relative to the noise) will decrease the value of the likelihood for that
particular set of parameters, spreading out the model’s posterior distribution
in parameter space and lowering its Bayes factor compared to simpler models.
Therefore both the noise level of the spectra and the validity of our
assumptions will drive the detectability of features and the size of the 68%
credibility intervals of the fitted parameters.

Source | Project | $l^{\circ}$ | $b^{\circ}$ | $v$ | $\Delta v$ | $\tau_{\rm peak}\,(10^{-3})$
---|---|---|---|---|---|---
|  |  |  | km s-1 | 1612 | 1665 | 1667 | 1720
G007.47+0.06 | ATCA | 7.47 | 0.06 | -17.86${}^{+3.78}_{-31.30}$ | 0.49${}^{+1.70}_{-0.25}$ | 4.2${}^{+12.5}_{-7.3}$ | 43.2${}^{+67.3}_{-96.9}$ | 8.3${}^{+53.3}_{-9.8}$ | 0.5${}^{+12.9}_{-6.9}$
G007.47+0.06 | ATCA | 7.47 | 0.06 | -14.05${}^{+0.10}_{-0.10}$ | 5.27${}^{+0.82}_{-0.25}$ | 49.4${}^{+5.0}_{-8.1}$ | 175.9${}^{+10.7}_{-51.4}$ | 179.3${}^{+8.7}_{-26.9}$ | 25.0${}^{+5.2}_{-6.0}$
G007.47+0.06 | ATCA | 7.47 | 0.06 | -1.91${}^{+0.17}_{-0.16}$ | 2.68${}^{+0.49}_{-0.40}$ | 26.9${}^{+8.3}_{-8.4}$ | 66.1${}^{+10.5}_{-10.1}$ | 65.8${}^{+8.6}_{-7.3}$ | -1.4${}^{+2.7}_{-8.6}$
G007.47+0.06 | ATCA | 7.47 | 0.06 | 12.36${}^{+0.14}_{-0.12}$ | 3.81${}^{+0.37}_{-0.36}$ | 13.9${}^{+7.2}_{-7.4}$ | 67.6${}^{+8.8}_{-8.1}$ | 84.0${}^{+5.8}_{-6.3}$ | 56.2${}^{+7.0}_{-6.1}$
G007.47+0.06 | ATCA | 7.47 | 0.06 | 16.02${}^{+0.22}_{-0.22}$ | 5.32${}^{+0.74}_{-0.51}$ | -0.7${}^{+2.3}_{-6.1}$ | 86.5${}^{+9.8}_{-7.4}$ | 68.7${}^{+5.7}_{-4.9}$ | 43.1${}^{+6.0}_{-5.8}$
G007.47+0.06 | ATCA | 7.47 | 0.06 | 122.27${}^{+0.19}_{-0.16}$ | 4.99${}^{+0.39}_{-0.43}$ | 2.1${}^{+6.2}_{-2.7}$ | 76.0${}^{+6.4}_{-7.3}$ | 71.9${}^{+6.1}_{-5.4}$ | 17.4${}^{+5.7}_{-6.1}$
SRC44 | a3301 | 68.83 | -3.49 | 6.17${}^{+0.11}_{-0.11}$ | 0.80${}^{+0.03}_{-0.03}$ | -0.2${}^{+0.3}_{-0.2}$ | 9.3${}^{+6.0}_{-3.5}$ | 18.6${}^{+11.9}_{-7.1}$ | 4.2${}^{+2.3}_{-1.3}$
SRC44 | a3301 | 68.83 | -3.49 | 6.28${}^{+0.11}_{-0.11}$ | 2.50${}^{+0.11}_{-0.12}$ | 1.1${}^{+0.2}_{-0.2}$ | 2.9${}^{+0.4}_{-0.5}$ | 8.0${}^{+1.2}_{-1.0}$ | 0.3${}^{+0.0}_{-0.0}$
SRC44 | a3301 | 68.83 | -3.49 | 11.08${}^{+0.11}_{-0.55}$ | 0.72${}^{+0.08}_{-0.08}$ | 0.2${}^{+0.4}_{-0.1}$ | -2.9${}^{+6.5}_{-1.1}$ | -7.9${}^{+15.4}_{-1.6}$ | -1.4${}^{+2.5}_{-0.1}$
SRC44 | a3301 | 68.83 | -3.49 | 11.20${}^{+0.32}_{-0.11}$ | 1.29${}^{+0.07}_{-0.25}$ | -0.1${}^{+0.2}_{-0.3}$ | 7.7${}^{+3.9}_{-3.0}$ | 16.8${}^{+9.1}_{-7.2}$ | 3.7${}^{+1.7}_{-1.1}$
3C417 | a2600 | 73.33 | -5.45 | 9.51${}^{+0.07}_{-0.07}$ | 0.88${}^{+0.06}_{-0.07}$ | 4.2${}^{+2.0}_{-1.8}$ | 40.4${}^{+5.4}_{-5.0}$ | 58.9${}^{+7.5}_{-7.1}$ | 10.5${}^{+0.1}_{-0.1}$
3C417 | a2600 | 73.33 | -5.45 | 9.92${}^{+0.07}_{-0.07}$ | 0.63${}^{+0.02}_{-0.01}$ | 52.0${}^{+8.6}_{-7.6}$ | 75.3${}^{+8.3}_{-8.4}$ | 136.8${}^{+15.6}_{-15.2}$ | -20.0${}^{+3.8}_{-4.7}$
3C417 | a2600 | 73.33 | -5.45 | 10.68${}^{+0.09}_{-0.07}$ | 2.91${}^{+0.10}_{-0.11}$ | 8.0${}^{+0.8}_{-0.8}$ | 14.1${}^{+1.1}_{-1.1}$ | 31.1${}^{+1.5}_{-1.6}$ | -1.6${}^{+0.4}_{-0.4}$
3C092 | a2600 | 159.74 | -18.41 | 8.71${}^{+0.07}_{-0.07}$ | 1.56${}^{+0.07}_{-0.06}$ | 6.6${}^{+1.0}_{-1.0}$ | 11.0${}^{+1.4}_{-1.3}$ | 19.3${}^{+1.6}_{-2.0}$ | -2.2${}^{+0.5}_{-0.5}$
3C092 | a2600 | 159.74 | -18.41 | 8.77${}^{+0.07}_{-0.07}$ | 0.76${}^{+0.01}_{-0.01}$ | 15.1${}^{+2.7}_{-2.4}$ | 63.5${}^{+9.2}_{-7.8}$ | 95.6${}^{+13.3}_{-11.4}$ | 8.3${}^{+0.7}_{-0.4}$
4C+28.11 | a2769 | 166.06 | -17.22 | 6.91${}^{+0.21}_{-0.21}$ | 1.10${}^{+0.05}_{-0.05}$ | 13.6${}^{+1.5}_{-1.5}$ | 29.8${}^{+1.9}_{-1.8}$ | 52.9${}^{+2.1}_{-2.3}$ | -1.7${}^{+0.9}_{-0.9}$
PKS0319+12 | a2769 | 170.59 | -36.24 | 7.73${}^{+0.21}_{-0.21}$ | 1.01${}^{+0.16}_{-0.13}$ | 2.2${}^{+1.5}_{-0.9}$ | 4.6${}^{+2.6}_{-1.7}$ | 6.9${}^{+3.7}_{-2.4}$ | -0.5${}^{+0.3}_{-0.5}$
3C131 | a2600 | 171.44 | -7.80 | 4.56${}^{+0.07}_{-0.07}$ | 0.48${}^{+0.02}_{-0.02}$ | 1.1${}^{+0.5}_{-0.4}$ | 5.0${}^{+0.7}_{-0.6}$ | 9.6${}^{+1.1}_{-1.1}$ | 0.9${}^{+0.2}_{-0.3}$
3C131 | a2600 | 171.44 | -7.80 | 5.71${}^{+0.07}_{-0.08}$ | 3.21${}^{+0.10}_{-0.10}$ | 2.3${}^{+0.2}_{-0.3}$ | 4.1${}^{+0.2}_{-0.2}$ | 7.1${}^{+0.4}_{-0.4}$ | -0.7${}^{+0.2}_{-0.2}$
3C131 | a2600 | 171.44 | -7.80 | 6.59${}^{+0.07}_{-0.07}$ | 0.44${}^{+0.01}_{-0.01}$ | 2.8${}^{+0.6}_{-0.6}$ | 16.3${}^{+1.2}_{-1.1}$ | 25.8${}^{+1.9}_{-1.8}$ | 3.4${}^{+0.2}_{-0.2}$
3C131 | a2600 | 171.44 | -7.80 | 7.23${}^{+0.07}_{-0.07}$ | 0.56${}^{+0.01}_{-0.00}$ | 11.9${}^{+0.6}_{-0.6}$ | 50.2${}^{+1.0}_{-1.1}$ | 83.4${}^{+1.6}_{-1.8}$ | 7.4${}^{+0.2}_{-0.3}$
3C131 | a2600 | 171.44 | -7.80 | 7.48${}^{+0.07}_{-0.07}$ | 1.93${}^{+0.09}_{-0.08}$ | 5.7${}^{+0.8}_{-0.8}$ | 6.4${}^{+0.9}_{-0.9}$ | 10.7${}^{+1.5}_{-1.4}$ | -2.9${}^{+0.4}_{-0.4}$
3C131 | a2600 | 171.44 | -7.80 | 7.79${}^{+0.07}_{-0.07}$ | 0.57${}^{+0.09}_{-0.07}$ | 0.1${}^{+0.2}_{-0.2}$ | -2.4${}^{+0.3}_{-0.2}$ | -3.1${}^{+0.5}_{-0.4}$ | -0.9${}^{+0.1}_{-0.1}$
3C108 | a3301 | 171.47 | -20.70 | 9.42${}^{+0.11}_{-0.11}$ | 1.19${}^{+0.03}_{-0.03}$ | 8.0${}^{+1.0}_{-0.9}$ | 29.9${}^{+2.6}_{-2.3}$ | 31.1${}^{+2.5}_{-2.4}$ | 1.5${}^{+0.2}_{-0.2}$
3C108 | a3301 | 171.47 | -20.70 | 9.74${}^{+0.11}_{-0.11}$ | 0.48${}^{+0.03}_{-0.03}$ | 11.4${}^{+10.5}_{-5.2}$ | 23.1${}^{+17.8}_{-10.2}$ | 31.2${}^{+24.3}_{-13.6}$ | -2.9${}^{+1.4}_{-3.4}$
4C+11.15 | a2769 | 171.98 | -35.48 | 7.18${}^{+0.21}_{-0.21}$ | 0.65${}^{+0.04}_{-0.03}$ | 8.5${}^{+1.7}_{-1.9}$ | 36.2${}^{+3.9}_{-3.7}$ | 64.9${}^{+5.2}_{-5.3}$ | 6.0${}^{+0.6}_{-0.3}$
4C+36.10 | a2769 | 172.98 | 2.44 | -16.74${}^{+0.21}_{-0.21}$ | 2.89${}^{+0.12}_{-0.11}$ | 5.3${}^{+0.8}_{-0.8}$ | 17.2${}^{+0.9}_{-0.9}$ | 29.0${}^{+1.0}_{-1.1}$ | 1.3${}^{+0.5}_{-0.5}$
4C+27.14 | a3301 | 175.46 | -9.96 | 7.19${}^{+0.11}_{-0.11}$ | 1.62${}^{+0.04}_{-0.05}$ | 0.8${}^{+1.7}_{-1.0}$ | 16.0${}^{+1.7}_{-1.7}$ | 36.5${}^{+3.0}_{-1.9}$ | 6.5${}^{+0.5}_{-1.1}$
4C+27.14 | a3301 | 175.46 | -9.96 | 7.89${}^{+0.11}_{-0.11}$ | 0.84${}^{+0.06}_{-0.04}$ | 30.0${}^{+24.0}_{-20.4}$ | 1.1${}^{+3.1}_{-1.7}$ | 15.3${}^{+13.1}_{-10.4}$ | -13.2${}^{+8.0}_{-7.0}$
4C+17.23 | a2769 | 176.36 | -24.24 | 9.35${}^{+0.21}_{-0.21}$ | 0.72${}^{+0.04}_{-0.04}$ | 6.8${}^{+1.3}_{-1.2}$ | 22.2${}^{+2.0}_{-2.0}$ | 44.3${}^{+3.3}_{-3.3}$ | 2.6${}^{+0.4}_{-0.5}$
4C+17.23 | a2769 | 176.36 | -24.24 | 11.42${}^{+0.21}_{-0.21}$ | 0.77${}^{+0.03}_{-0.03}$ | 9.8${}^{+1.5}_{-1.4}$ | 27.5${}^{+2.6}_{-2.4}$ | 51.5${}^{+4.1}_{-3.2}$ | 1.5${}^{+0.5}_{-0.5}$
4C+07.13 | a2769 | 178.87 | -36.27 | 3.48${}^{+0.21}_{-0.21}$ | 1.07${}^{+0.13}_{-0.11}$ | 2.3${}^{+1.7}_{-1.2}$ | 10.3${}^{+3.5}_{-2.6}$ | 14.4${}^{+4.1}_{-3.5}$ | 1.3${}^{+0.3}_{-0.5}$
B0531+2730 | a2769 | 179.87 | -2.83 | 3.04${}^{+0.21}_{-0.21}$ | 0.72${}^{+0.03}_{-0.04}$ | 17.9${}^{+14.6}_{-7.9}$ | -21.3${}^{+21.7}_{-20.4}$ | 92.8${}^{+60.6}_{-34.2}$ | -11.4${}^{+2.9}_{-0.3}$
B0531+2730 | a2769 | 179.87 | -2.83 | 3.17${}^{+0.21}_{-0.21}$ | 0.78${}^{+0.03}_{-0.04}$ | 5.2${}^{+7.0}_{-5.7}$ | 79.6${}^{+63.6}_{-37.9}$ | 20.3${}^{+21.8}_{-20.0}$ | 12.8${}^{+7.9}_{-4.0}$
4C+26.18b | a2769 | 182.36 | -0.62 | -11.93${}^{+0.21}_{-0.21}$ | 1.57${}^{+0.11}_{-0.11}$ | -8.4${}^{+1.0}_{-0.6}$ | 23.3${}^{+7.4}_{-6.2}$ | 41.1${}^{+11.1}_{-10.2}$ | 18.3${}^{+1.7}_{-1.7}$
4C+26.18b | a2769 | 182.36 | -0.62 | -9.99${}^{+0.21}_{-0.28}$ | 2.66${}^{+0.38}_{-0.35}$ | 1.1${}^{+1.3}_{-1.2}$ | 5.5${}^{+1.9}_{-1.6}$ | 14.8${}^{+2.3}_{-1.8}$ | 1.6${}^{+0.7}_{-0.7}$
4C+22.12 | a2769 | 188.07 | 0.04 | -1.62${}^{+0.21}_{-0.21}$ | 0.66${}^{+0.04}_{-0.04}$ | 0.4${}^{+1.2}_{-0.7}$ | 15.2${}^{+9.8}_{-6.2}$ | 31.0${}^{+20.5}_{-12.3}$ | 6.1${}^{+3.0}_{-1.9}$
4C+14.14 | a2769 | 189.04 | -12.85 | 2.60${}^{+0.21}_{-0.21}$ | 3.82${}^{+0.28}_{-0.29}$ | 1.3${}^{+0.6}_{-0.6}$ | 8.4${}^{+0.8}_{-0.9}$ | 16.3${}^{+1.1}_{-0.9}$ | 2.2${}^{+0.4}_{-0.3}$
4C+19.18 | a2769 | 190.09 | -2.17 | -0.62${}^{+0.21}_{-0.21}$ | 2.18${}^{+0.23}_{-0.19}$ | -4.2${}^{+0.9}_{-0.9}$ | 4.7${}^{+1.2}_{-1.2}$ | 13.6${}^{+1.7}_{-1.7}$ | 6.9${}^{+0.6}_{-0.6}$
4C+19.18 | a2769 | 190.09 | -2.17 | 2.39${}^{+0.21}_{-0.21}$ | 1.47${}^{+0.12}_{-0.11}$ | 4.3${}^{+1.1}_{-1.1}$ | 13.6${}^{+1.5}_{-1.4}$ | 29.6${}^{+1.8}_{-1.8}$ | 1.7${}^{+0.6}_{-0.6}$
4C+19.19 | a2769 | 190.13 | -1.64 | 1.12${}^{+0.21}_{-0.21}$ | 1.42${}^{+0.19}_{-0.16}$ | -4.6${}^{+1.2}_{-1.3}$ | 8.0${}^{+6.6}_{-3.3}$ | 15.1${}^{+13.0}_{-6.4}$ | 8.5${}^{+1.4}_{-0.3}$
4C+19.19 | a2769 | 190.13 | -1.64 | 2.70${}^{+0.21}_{-0.21}$ | 3.15${}^{+0.20}_{-0.26}$ | 7.0${}^{+0.9}_{-0.9}$ | 10.1${}^{+1.0}_{-1.1}$ | 19.1${}^{+1.4}_{-1.4}$ | -2.8${}^{+0.5}_{-0.5}$
PKS0528+134 | a2600 | 191.37 | -11.01 | 9.60${}^{+0.07}_{-0.07}$ | 0.90${}^{+0.01}_{-0.01}$ | 5.2${}^{+0.6}_{-0.6}$ | 25.4${}^{+1.6}_{-1.6}$ | 46.2${}^{+2.8}_{-2.7}$ | 5.0${}^{+0.0}_{-0.0}$
4C+16.15b | a2769 | 193.64 | -1.53 | 11.88${}^{+0.21}_{-0.21}$ | 0.87${}^{+0.06}_{-0.05}$ | 5.6${}^{+1.0}_{-1.1}$ | 24.0${}^{+1.5}_{-1.5}$ | 43.2${}^{+2.3}_{-2.3}$ | 4.0${}^{+0.5}_{-0.5}$
3C158 | a2769 | 196.64 | 0.17 | 3.14${}^{+0.21}_{-0.21}$ | 0.98${}^{+0.14}_{-0.15}$ | 0.5${}^{+1.5}_{-0.7}$ | 7.6${}^{+11.0}_{-4.5}$ | 8.4${}^{+11.6}_{-4.9}$ | 1.9${}^{+2.0}_{-0.7}$
Table 3: Fitted centroid velocity, FWHM and peak optical depth of the features identified in this work. Columns give the targeted background source of each sightline, the project name, Galactic longitude and latitude, centroid velocity $v$, FWHM $\Delta v$, and peak optical depth (10-3) at 1612, 1665, 1667 and 1720 MHz. The uncertainties of all parameters are the 68% credibility intervals, except in the case of centroid velocity, where this interval is replaced with the channel width if the channel width is greater than the 68% credibility interval Petzler2021a (83). Source | Project | $l^{\circ}$ | $b^{\circ}$ | $v$ | $\Delta v$ | $\tau_{\rm peak}\,(10^{-3})$
---|---|---|---|---|---|---
|  |  |  | km s-1 | 1612 | 1665 | 1667 | 1720
4C+14.18 | a2600 | 196.98 | 1.10 | 4.28${}^{+0.07}_{-0.07}$ | 0.55${}^{+0.05}_{-0.05}$ | 0.2${}^{+0.4}_{-0.2}$ | 4.7${}^{+5.6}_{-2.7}$ | 10.2${}^{+13.0}_{-5.7}$ | 1.9${}^{+2.3}_{-1.0}$
4C+14.18 | a2600 | 196.98 | 1.10 | 4.94${}^{+0.07}_{-0.07}$ | 1.84${}^{+0.04}_{-0.03}$ | 3.5${}^{+0.3}_{-0.3}$ | 11.9${}^{+0.5}_{-0.5}$ | 16.5${}^{+0.6}_{-0.7}$ | 0.7${}^{+0.1}_{-0.1}$
4C+14.18 | a2600 | 196.98 | 1.10 | 7.39${}^{+0.07}_{-0.07}$ | 0.81${}^{+0.04}_{-0.03}$ | 2.8${}^{+0.6}_{-0.6}$ | 6.8${}^{+1.1}_{-1.0}$ | 8.7${}^{+1.3}_{-1.2}$ | -0.4${}^{+0.2}_{-0.3}$
4C+14.18 | a2600 | 196.98 | 1.10 | 16.49${}^{+0.07}_{-0.07}$ | 1.29${}^{+0.09}_{-0.09}$ | -0.5${}^{+0.5}_{-0.4}$ | 5.1${}^{+0.8}_{-0.7}$ | 10.6${}^{+1.7}_{-1.5}$ | 2.7${}^{+0.1}_{-0.2}$
4C+14.18 | a2600 | 196.98 | 1.10 | 17.59${}^{+0.07}_{-0.07}$ | 0.70${}^{+0.06}_{-0.06}$ | 1.2${}^{+0.7}_{-0.5}$ | 4.9${}^{+1.7}_{-1.3}$ | 10.9${}^{+3.7}_{-2.8}$ | 1.0${}^{+0.1}_{-0.0}$
4C+14.18 | a2600 | 196.98 | 1.10 | 18.40${}^{+0.22}_{-0.18}$ | 3.76${}^{+0.26}_{-0.36}$ | 2.3${}^{+0.4}_{-0.4}$ | 1.9${}^{+0.4}_{-0.3}$ | 3.4${}^{+0.5}_{-0.4}$ | -1.4${}^{+0.3}_{-0.3}$
4C+14.18 | a2600 | 196.98 | 1.10 | 31.98${}^{+0.07}_{-0.07}$ | 0.42${}^{+0.86}_{-0.01}$ | 4.3${}^{+2.0}_{-1.0}$ | 21.6${}^{+12.3}_{-5.6}$ | 37.2${}^{+21.1}_{-9.9}$ | 4.2${}^{+2.8}_{-1.2}$
4C+14.18 | a2600 | 196.98 | 1.10 | 32.33${}^{+0.07}_{-0.33}$ | 1.19${}^{+0.08}_{-0.80}$ | 1.3${}^{+0.5}_{-1.0}$ | 6.2${}^{+1.9}_{-7.5}$ | 11.4${}^{+2.6}_{-14.3}$ | 1.2${}^{+0.2}_{-2.1}$
4C+13.32 | a2769 | 197.15 | -0.85 | -5.65${}^{+0.01}_{-0.01}$ | 6.01${}^{+0.29}_{-0.25}$ | 4.9${}^{+3.4}_{-2.0}$ | 12.8${}^{+9.0}_{-5.1}$ | 24.0${}^{+15.8}_{-9.7}$ | 0.4${}^{+0.2}_{-0.2}$
4C+13.32 | a2769 | 197.15 | -0.85 | -0.35${}^{+0.11}_{-0.11}$ | 1.02${}^{+0.11}_{-0.10}$ | 0.0${}^{+0.1}_{-0.0}$ | 2.2${}^{+5.8}_{-1.6}$ | 6.0${}^{+16.1}_{-4.4}$ | 1.3${}^{+4.4}_{-1.0}$
4C+13.32 | a2769 | 197.15 | -0.85 | 4.46${}^{+0.11}_{-0.11}$ | 1.20${}^{+0.07}_{-0.07}$ | -0.4${}^{+0.2}_{-0.1}$ | 3.6${}^{+5.8}_{-2.2}$ | 8.6${}^{+14.1}_{-5.3}$ | 2.1${}^{+2.5}_{-0.9}$
4C+13.32 | a2769 | 197.15 | -0.85 | 6.99${}^{+0.25}_{-0.20}$ | 2.21${}^{+0.74}_{-0.45}$ | 1.6${}^{+1.3}_{-0.8}$ | 1.0${}^{+1.1}_{-0.6}$ | 2.4${}^{+1.6}_{-1.2}$ | -1.1${}^{+0.5}_{-0.9}$
4C+13.32 | a2769 | 197.15 | -0.85 | 9.50${}^{+0.21}_{-0.21}$ | 1.15${}^{+0.08}_{-0.08}$ | 0.7${}^{+0.7}_{-0.4}$ | 4.0${}^{+4.4}_{-2.2}$ | 7.0${}^{+7.4}_{-3.7}$ | 0.9${}^{+1.0}_{-0.4}$
4C+17.41 | a2769 | 201.13 | 16.42 | 0.23${}^{+0.21}_{-0.21}$ | 1.38${}^{+0.24}_{-0.17}$ | 3.4${}^{+1.2}_{-1.1}$ | 9.1${}^{+1.6}_{-1.7}$ | 18.9${}^{+2.1}_{-2.2}$ | 0.6${}^{+0.5}_{-0.6}$
4C+17.41 | a2769 | 201.13 | 16.42 | 1.89${}^{+0.21}_{-0.21}$ | 0.73${}^{+0.06}_{-0.06}$ | 11.7${}^{+1.8}_{-1.8}$ | 28.7${}^{+2.5}_{-2.4}$ | 51.2${}^{+2.9}_{-3.0}$ | -0.2${}^{+0.9}_{-0.9}$
4C+04.22 | a2769 | 205.41 | -4.43 | 11.92${}^{+0.21}_{-0.21}$ | 0.71${}^{+0.06}_{-0.07}$ | 7.7${}^{+2.1}_{-1.7}$ | 17.0${}^{+2.8}_{-2.7}$ | 38.1${}^{+5.1}_{-4.4}$ | 0.0${}^{+0.7}_{-0.9}$
4C+04.22 | a2769 | 205.41 | -4.43 | 13.33${}^{+0.11}_{-0.11}$ | 0.92${}^{+0.08}_{-0.07}$ | 10.6${}^{+1.9}_{-2.1}$ | 17.8${}^{+2.7}_{-2.7}$ | 38.8${}^{+5.1}_{-5.1}$ | -2.5${}^{+1.0}_{-0.7}$
J134217-040725 | a3301 | 205.58 | -4.14 | 9.19${}^{+0.09}_{-0.09}$ | 1.20${}^{+0.04}_{-0.04}$ | 7.9${}^{+1.2}_{-1.2}$ | 23.6${}^{+2.4}_{-2.4}$ | 41.0${}^{+3.6}_{-3.9}$ | 1.4${}^{+0.3}_{-0.3}$
4C+04.24 | a2769 | 205.92 | -3.57 | 9.39${}^{+0.03}_{-0.03}$ | 1.25${}^{+0.07}_{-0.07}$ | 7.3${}^{+1.3}_{-1.2}$ | 23.7${}^{+2.1}_{-2.0}$ | 45.3${}^{+3.3}_{-3.0}$ | 2.5${}^{+0.4}_{-0.5}$
G336.49-1.48 | ATCA | 336.49 | -1.48 | -23.32${}^{+0.16}_{-0.14}$ | 4.06${}^{+0.21}_{-0.15}$ | 12.9${}^{+5.0}_{-4.1}$ | 130.4${}^{+3.7}_{-5.0}$ | 175.9${}^{+5.0}_{-5.2}$ | 42.0${}^{+5.2}_{-4.1}$
G336.49-1.48 | ATCA | 336.49 | -1.48 | -20.44${}^{+0.09}_{-0.09}$ | 2.43${}^{+0.27}_{-0.12}$ | 92.3${}^{+3.7}_{-3.3}$ | 130.0${}^{+5.5}_{-8.4}$ | 143.7${}^{+11.2}_{-15.3}$ | -57.4${}^{+7.7}_{-9.4}$
G336.49-1.48 | ATCA | 336.49 | -1.48 | -14.25${}^{+0.12}_{-0.12}$ | 2.37${}^{+0.31}_{-0.23}$ | 11.1${}^{+3.4}_{-3.0}$ | 29.8${}^{+3.9}_{-3.4}$ | 34.8${}^{+4.2}_{-3.5}$ | -1.0${}^{+1.7}_{-3.0}$
G340.79-1.02 | ATCA | 340.79 | -1.02 | -29.22${}^{+0.09}_{-0.09}$ | 2.56${}^{+0.11}_{-0.12}$ | 67.5${}^{+3.9}_{-3.9}$ | 149.5${}^{+5.1}_{-5.3}$ | 35.9${}^{+5.1}_{-5.0}$ | -34.5${}^{+4.6}_{-4.2}$
G340.79-1.02 | ATCA | 340.79 | -1.02 | -26.44${}^{+0.09}_{-0.09}$ | 2.37${}^{+0.06}_{-0.04}$ | -53.7${}^{+3.9}_{-4.4}$ | 267.5${}^{+6.1}_{-6.2}$ | 226.2${}^{+5.1}_{-4.6}$ | 140.0${}^{+4.6}_{-4.9}$
G340.79-1.02 | ATCA | 340.79 | -1.02 | -19.50${}^{+0.10}_{-0.11}$ | 1.91${}^{+0.50}_{-0.31}$ | 0.9${}^{+2.8}_{-2.1}$ | 40.0${}^{+6.0}_{-5.7}$ | 38.4${}^{+5.7}_{-5.5}$ | 1.6${}^{+4.5}_{-2.5}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -67.57${}^{+0.09}_{-0.09}$ | 5.41${}^{+0.18}_{-0.18}$ | -30.0${}^{+3.7}_{-3.4}$ | 129.1${}^{+4.7}_{-5.1}$ | 139.4${}^{+4.6}_{-4.9}$ | 68.3${}^{+4.0}_{-4.8}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -62.70${}^{+0.09}_{-0.09}$ | 1.55${}^{+0.12}_{-0.10}$ | -29.0${}^{+13.1}_{-10.7}$ | -65.6${}^{+24.0}_{-29.7}$ | 133.9${}^{+8.1}_{-8.5}$ | 22.0${}^{+11.6}_{-11.9}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -61.64${}^{+0.09}_{-0.09}$ | 1.98${}^{+0.16}_{-0.13}$ | -80.0${}^{+9.4}_{-7.6}$ | 228.9${}^{+9.6}_{-12.2}$ | 3.5${}^{+12.8}_{-5.4}$ | 93.7${}^{+7.5}_{-8.2}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -22.45${}^{+0.09}_{-0.09}$ | 1.34${}^{+0.12}_{-0.11}$ | 103.1${}^{+8.9}_{-8.0}$ | -18.8${}^{+13.5}_{-13.3}$ | 24.1${}^{+9.0}_{-7.7}$ | 1.4${}^{+9.1}_{-3.4}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -21.91${}^{+0.12}_{-0.12}$ | 4.25${}^{+0.34}_{-0.28}$ | 87.0${}^{+7.5}_{-6.6}$ | 31.9${}^{+7.3}_{-7.2}$ | 61.9${}^{+5.6}_{-5.4}$ | 24.8${}^{+4.5}_{-6.0}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -17.90${}^{+0.19}_{-0.23}$ | 3.09${}^{+0.70}_{-0.52}$ | 48.4${}^{+4.8}_{-4.8}$ | 15.2${}^{+6.3}_{-5.6}$ | 29.5${}^{+6.2}_{-5.6}$ | 8.5${}^{+5.4}_{-7.2}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -5.31${}^{+0.09}_{-0.09}$ | 0.50${}^{+0.06}_{-0.04}$ | 12.0${}^{+9.6}_{-10.8}$ | -209.9${}^{+17.5}_{-15.2}$ | -15.5${}^{+13.0}_{-10.2}$ | 8.6${}^{+10.5}_{-8.7}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -3.79${}^{+0.09}_{-0.09}$ | 0.80${}^{+0.06}_{-0.06}$ | 22.0${}^{+7.8}_{-9.9}$ | -146.7${}^{+13.6}_{-12.6}$ | -80.3${}^{+8.1}_{-8.1}$ | 13.7${}^{+8.4}_{-10.3}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -2.30${}^{+0.09}_{-0.09}$ | 0.90${}^{+0.05}_{-0.05}$ | 16.0${}^{+8.1}_{-9.6}$ | -399.5${}^{+12.6}_{-15.6}$ | -43.6${}^{+8.6}_{-8.2}$ | 0.7${}^{+7.0}_{-5.6}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -1.55${}^{+0.09}_{-0.09}$ | 0.50${}^{+0.04}_{-0.05}$ | 2.4${}^{+10.7}_{-3.6}$ | 300.7${}^{+23.1}_{-22.3}$ | 20.4${}^{+9.7}_{-10.6}$ | 0.1${}^{+5.1}_{-8.7}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | -0.79${}^{+0.09}_{-0.09}$ | 0.43${}^{+0.06}_{-0.05}$ | 1.2${}^{+6.7}_{-3.2}$ | -220.8${}^{+20.4}_{-22.4}$ | -1.1${}^{+5.0}_{-9.4}$ | 7.3${}^{+8.8}_{-6.8}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | 1.38${}^{+0.16}_{-0.21}$ | 0.33${}^{+0.15}_{-0.13}$ | 3.8${}^{+12.0}_{-5.3}$ | 22.4${}^{+17.3}_{-16.8}$ | 1.6${}^{+8.8}_{-3.4}$ | 0.3${}^{+6.0}_{-8.6}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | 5.39${}^{+0.09}_{-0.09}$ | 1.19${}^{+0.20}_{-0.13}$ | 18.3${}^{+7.6}_{-7.5}$ | 161.3${}^{+13.3}_{-14.7}$ | 26.6${}^{+6.8}_{-7.3}$ | -1.5${}^{+3.1}_{-9.7}$
G344.43+0.05 | ATCA | 344.43 | 0.05 | 14.79${}^{+0.09}_{-0.09}$ | 3.11${}^{+0.20}_{-0.21}$ | 130.2${}^{+5.5}_{-5.0}$ | -1.0${}^{+7.1}_{-5.9}$ | -0.9${}^{+2.1}_{-4.6}$ | -0.2${}^{+2.1}_{-4.2}$
G346.52+0.08 | ATCA | 346.52 | 0.08 | 3.30${}^{+0.25}_{-0.21}$ | 6.65${}^{+0.57}_{-0.49}$ | 19.9${}^{+6.2}_{-6.6}$ | 143.0${}^{+9.6}_{-9.2}$ | 109.7${}^{+6.3}_{-6.8}$ | 26.6${}^{+7.9}_{-7.4}$
G346.52+0.08 | ATCA | 346.52 | 0.08 | 6.90${}^{+0.16}_{-0.18}$ | 3.65${}^{+0.51}_{-0.41}$ | 19.7${}^{+8.6}_{-8.8}$ | 156.0${}^{+11.9}_{-10.9}$ | 88.4${}^{+8.3}_{-8.6}$ | 10.1${}^{+10.4}_{-9.4}$
G347.75-1.14 | ATCA | 347.75 | -1.14 | -36.77${}^{+73.74}_{-23.18}$ | 1.54${}^{+0.53}_{-1.32}$ | 12.6${}^{+6.7}_{-12.1}$ | 25.1${}^{+9.8}_{-42.9}$ | 37.9${}^{+8.9}_{-38.1}$ | 1.3${}^{+7.1}_{-3.0}$
G350.50+0.96 | ATCA | 350.50 | 0.96 | -10.74${}^{+0.09}_{-4.37}$ | 2.34${}^{+0.10}_{-1.44}$ | -16.7${}^{+17.1}_{-10.7}$ | -53.0${}^{+65.4}_{-48.6}$ | 166.0${}^{+9.5}_{-161.8}$ | 81.2${}^{+11.6}_{-69.3}$
G350.50+0.96 | ATCA | 350.50 | 0.96 | -10.53${}^{+0.09}_{-0.09}$ | 2.72${}^{+0.05}_{-0.04}$ | -19.3${}^{+10.3}_{-10.4}$ | 356.3${}^{+45.9}_{-43.8}$ | 177.3${}^{+130.3}_{-11.7}$ | 90.6${}^{+61.4}_{-11.1}$
G350.50+0.96 | ATCA | 350.50 | 0.96 | -3.62${}^{+0.09}_{-0.09}$ | 2.30${}^{+0.20}_{-0.16}$ | -0.9${}^{+2.2}_{-5.2}$ | 59.9${}^{+5.5}_{-5.3}$ | 59.7${}^{+4.2}_{-4.4}$ | 18.6${}^{+5.0}_{-5.2}$
G350.50+0.96 | ATCA | 350.50 | 0.96 | 6.69${}^{+0.09}_{-0.09}$ | 1.67${}^{+0.21}_{-0.21}$ | 24.0${}^{+4.9}_{-4.9}$ | 36.1${}^{+6.2}_{-5.7}$ | 43.1${}^{+5.6}_{-5.2}$ | 0.6${}^{+3.3}_{-2.4}$
Table 3 continued.
Source | Project | $l^{\circ}$ | $b^{\circ}$ | $v$ | $\Delta v$ | $\tau_{\rm peak}\,(10^{-3})$
---|---|---|---|---|---|---
|  |  |  | km s-1 | 1612 | 1665 | 1667 | 1720
G351.56+0.20 | ATCA | 351.56 | 0.20 | -93.20${}^{+0.49}_{-0.31}$ | 4.84${}^{+1.01}_{-1.37}$ | 0.6${}^{+2.9}_{-1.9}$ | 26.1${}^{+6.8}_{-4.8}$ | 37.9${}^{+6.4}_{-3.9}$ | 12.5${}^{+3.9}_{-4.4}$
G351.56+0.20 | ATCA | 351.56 | 0.20 | -45.18${}^{+0.19}_{-0.20}$ | 4.20${}^{+0.54}_{-0.50}$ | 22.4${}^{+5.3}_{-5.7}$ | 47.5${}^{+6.3}_{-7.4}$ | 55.1${}^{+7.1}_{-6.4}$ | -1.1${}^{+3.3}_{-6.3}$
G351.56+0.20 | ATCA | 351.56 | 0.20 | -40.62${}^{+0.30}_{-0.30}$ | 8.24${}^{+0.66}_{-0.59}$ | -30.6${}^{+4.9}_{-4.0}$ | 71.3${}^{+4.5}_{-4.3}$ | 71.4${}^{+4.8}_{-5.1}$ | 57.6${}^{+4.3}_{-3.8}$
G351.56+0.20 | ATCA | 351.56 | 0.20 | -36.77${}^{+0.49}_{-0.52}$ | 6.75${}^{+0.81}_{-0.90}$ | -21.4${}^{+4.2}_{-4.7}$ | 30.6${}^{+3.9}_{-4.1}$ | 39.3${}^{+3.8}_{-3.8}$ | 18.8${}^{+4.6}_{-3.7}$
G351.56+0.20 | ATCA | 351.56 | 0.20 | -7.63${}^{+0.09}_{-0.09}$ | 0.76${}^{+0.10}_{-0.08}$ | 0.1${}^{+3.2}_{-4.2}$ | 125.0${}^{+10.6}_{-10.7}$ | 3.8${}^{+9.6}_{-4.1}$ | 1.4${}^{+8.2}_{-3.3}$
G351.56+0.20 | ATCA | 351.56 | 0.20 | 0.09${}^{+0.09}_{-0.09}$ | 0.71${}^{+0.08}_{-0.07}$ | 8.2${}^{+9.8}_{-8.1}$ | -137.0${}^{+12.3}_{-10.6}$ | 8.1${}^{+10.2}_{-7.8}$ | 0.3${}^{+5.1}_{-6.3}$
G351.56+0.20 | ATCA | 351.56 | 0.20 | 6.90${}^{+0.09}_{-0.09}$ | 1.88${}^{+0.20}_{-0.22}$ | 13.7${}^{+5.8}_{-7.2}$ | 27.0${}^{+5.9}_{-5.8}$ | 60.4${}^{+5.6}_{-4.9}$ | 1.1${}^{+5.7}_{-2.7}$
G351.61+0.17 | ATCA | 351.61 | 0.17 | -43.39${}^{+0.38}_{-0.40}$ | 8.51${}^{+0.98}_{-1.21}$ | 6.5${}^{+4.3}_{-5.0}$ | 55.4${}^{+4.2}_{-4.5}$ | 62.3${}^{+3.6}_{-4.2}$ | 20.6${}^{+4.3}_{-4.0}$
G351.61+0.17 | ATCA | 351.61 | 0.17 | -7.93${}^{+0.09}_{-0.09}$ | 0.50${}^{+0.03}_{-0.04}$ | 0.6${}^{+4.2}_{-4.7}$ | 215.1${}^{+14.9}_{-15.4}$ | 2.6${}^{+10.4}_{-3.1}$ | 0.2${}^{+5.7}_{-5.8}$
G351.61+0.17 | ATCA | 351.61 | 0.17 | -0.07${}^{+0.09}_{-0.09}$ | 0.38${}^{+0.06}_{-0.05}$ | 0.7${}^{+8.5}_{-4.6}$ | -162.1${}^{+18.5}_{-19.2}$ | 1.2${}^{+8.7}_{-5.3}$ | 1.3${}^{+8.5}_{-3.3}$
G353.41-0.30 | ATCA | 353.41 | -0.30 | -94.54${}^{+0.09}_{-0.09}$ | 3.03${}^{+0.16}_{-0.15}$ | 94.3${}^{+3.8}_{-4.1}$ | -0.4${}^{+4.5}_{-4.8}$ | 0.7${}^{+2.6}_{-1.6}$ | -0.1${}^{+2.2}_{-3.2}$
G353.41-0.30 | ATCA | 353.41 | -0.30 | -58.88${}^{+13.22}_{-0.14}$ | 1.67${}^{+0.27}_{-1.41}$ | 59.6${}^{+9.1}_{-59.9}$ | 2.3${}^{+22.9}_{-8.8}$ | -0.4${}^{+5.5}_{-4.7}$ | 0.6${}^{+6.7}_{-5.8}$
G353.41-0.30 | ATCA | 353.41 | -0.30 | -19.10${}^{+0.09}_{-0.09}$ | 1.55${}^{+0.03}_{-0.03}$ | 26.8${}^{+4.5}_{-5.5}$ | -308.0${}^{+7.0}_{-8.4}$ | 25.7${}^{+5.3}_{-5.7}$ | -290.4${}^{+7.2}_{-5.8}$
G353.41-0.30 | ATCA | 353.41 | -0.30 | -14.40${}^{+0.09}_{-0.09}$ | 5.31${}^{+0.11}_{-0.10}$ | -59.5${}^{+2.7}_{-2.6}$ | 182.8${}^{+4.1}_{-3.9}$ | 98.4${}^{+3.4}_{-3.8}$ | 117.9${}^{+3.4}_{-3.5}$
G356.91+0.08 | ATCA | 356.91 | 0.08 | -75.58${}^{+0.38}_{-0.33}$ | 5.76${}^{+1.08}_{-0.76}$ | 0.2${}^{+2.2}_{-3.0}$ | 34.8${}^{+7.3}_{-5.5}$ | 60.8${}^{+6.0}_{-5.7}$ | 12.4${}^{+5.9}_{-8.6}$
G356.91+0.08 | ATCA | 356.91 | 0.08 | -4.90${}^{+0.10}_{-0.10}$ | 2.44${}^{+0.25}_{-0.25}$ | -11.0${}^{+9.7}_{-7.7}$ | 59.0${}^{+10.5}_{-10.4}$ | 83.4${}^{+7.9}_{-6.8}$ | 41.3${}^{+7.7}_{-7.2}$
G356.91+0.08 | ATCA | 356.91 | 0.08 | 4.71${}^{+0.12}_{-0.11}$ | 2.83${}^{+0.34}_{-0.28}$ | 43.7${}^{+7.7}_{-6.8}$ | 58.6${}^{+8.6}_{-7.9}$ | 71.6${}^{+6.9}_{-7.4}$ | 2.8${}^{+8.2}_{-3.2}$
G356.91+0.08 | ATCA | 356.91 | 0.08 | 9.81${}^{+67.06}_{-0.29}$ | 2.23${}^{+0.57}_{-2.00}$ | 1.5${}^{+7.1}_{-4.9}$ | 42.7${}^{+12.4}_{-97.8}$ | 53.1${}^{+12.5}_{-54.2}$ | 24.2${}^{+10.4}_{-23.2}$
Table 3 continued.
Source | Project | $l^{\circ}$ | $b^{\circ}$ | $v$ | $\Delta v$ |  $T_{\rm ex}$ (K)
---|---|---|---|---|---|---
|  |  |  | km s-1 | 1612 | 1665 | 1667 | 1720
SRC44 | a3301 | 68.83 | -3.49 | 6.17 | 0.80 | -30.52${}^{+88}_{-19.61}$ | 3.00${}^{+0.93}_{-0.60}$ | 2.63${}^{+0.87}_{-0.52}$ | 1.38${}^{+0.26}_{-0.21}$
SRC44 | a3301 | 68.83 | -3.49 | 6.28 | 2.50 | 9.72${}^{+1.94}_{-1.50}$ | 19.43${}^{+2.80}_{-2.15}$ | 12.61${}^{+1.18}_{-1.30}$ | 33.05${}^{+3.19}_{-3.12}$
SRC44 | a3301 | 68.83 | -3.49 | 11.08 | 0.72 | 2.48${}^{+10.79}_{-1.15}$ | -0.56${}^{+1.63}_{-0.34}$ | -0.44${}^{+1.35}_{-0.20}$ | -0.23${}^{+1.02}_{-0.12}$
SRC44 | a3301 | 68.83 | -3.49 | 11.20 | 1.29 | -9.20${}^{+28.20}_{-7.05}$ | 0.86${}^{+0.21}_{-0.15}$ | 0.64${}^{+0.20}_{-0.13}$ | 0.36${}^{+0.04}_{-0.05}$
3C417 | a2600 | 73.33 | -5.45 | 9.51 | 0.88 | 7.94${}^{+5.14}_{-2.15}$ | 4.30${}^{+0.27}_{-0.24}$ | 5.27${}^{+0.29}_{-0.26}$ | 3.43${}^{+0.26}_{-0.25}$
3C417 | a2600 | 73.33 | -5.45 | 9.92 | 0.63 | 1.10${}^{+0.08}_{-0.08}$ | 3.75${}^{+0.13}_{-0.13}$ | 3.91${}^{+0.12}_{-0.13}$ | -2.92${}^{+0.38}_{-0.40}$
3C417 | a2600 | 73.33 | -5.45 | 10.68 | 2.91 | 2.98${}^{+0.25}_{-0.22}$ | 8.57${}^{+0.51}_{-0.47}$ | 7.13${}^{+0.22}_{-0.20}$ | -15.18${}^{+2.68}_{-4.23}$
3C092 | a2600 | 159.74 | -18.41 | 8.71 | 1.56 | 4.59${}^{+0.71}_{-0.54}$ | 13.97${}^{+1.53}_{-1.41}$ | 14.54${}^{+1.35}_{-0.93}$ | -14.68${}^{+2.65}_{-4.11}$
3C092 | a2600 | 159.74 | -18.41 | 8.77 | 0.76 | 2.62${}^{+0.27}_{-0.23}$ | 3.19${}^{+0.18}_{-0.20}$ | 3.84${}^{+0.20}_{-0.22}$ | 5.05${}^{+0.04}_{-0.12}$
4C+28.11 | a2769 | 166.06 | -17.22 | 6.91 | 1.10 | 2.89${}^{+0.34}_{-0.29}$ | 6.72${}^{+0.41}_{-0.41}$ | 6.93${}^{+0.26}_{-0.25}$ | -24.55${}^{+8.49}_{-27.01}$
PKS0319+12 | a2769 | 170.59 | -36.24 | 7.73 | 1.01 | 1.91${}^{+0.77}_{-0.62}$ | 4.63${}^{+1.44}_{-1.29}$ | 5.75${}^{+1.66}_{-1.46}$ | -8.89${}^{+4.10}_{-8.15}$
3C131 | a2600 | 171.44 | -7.80 | 4.56 | 0.48 | 3.93${}^{+2.00}_{-1.13}$ | 4.53${}^{+0.37}_{-0.36}$ | 4.29${}^{+0.35}_{-0.28}$ | 4.98${}^{+2.21}_{-0.95}$
3C131 | a2600 | 171.44 | -7.80 | 5.71 | 3.21 | 3.02${}^{+0.33}_{-0.26}$ | 8.83${}^{+0.46}_{-0.43}$ | 9.25${}^{+0.40}_{-0.35}$ | -10.47${}^{+1.77}_{-2.94}$
3C131 | a2600 | 171.44 | -7.80 | 6.59 | 0.44 | 4.29${}^{+1.02}_{-0.66}$ | 3.77${}^{+0.16}_{-0.16}$ | 4.29${}^{+0.17}_{-0.17}$ | 3.79${}^{+0.30}_{-0.31}$
3C131 | a2600 | 171.44 | -7.80 | 7.23 | 0.56 | 3.69${}^{+0.18}_{-0.17}$ | 4.49${}^{+0.07}_{-0.07}$ | 4.89${}^{+0.07}_{-0.06}$ | 6.27${}^{+0.26}_{-0.23}$
3C131 | a2600 | 171.44 | -7.80 | 7.48 | 1.93 | 0.79${}^{+0.07}_{-0.06}$ | 3.33${}^{+0.28}_{-0.26}$ | 3.90${}^{+0.29}_{-0.27}$ | -1.54${}^{+0.11}_{-0.13}$
3C131 | a2600 | 171.44 | -7.80 | 7.79 | 0.57 | 8.26${}^{+4.94}_{-26.70}$ | -1.93${}^{+0.38}_{-0.55}$ | -2.90${}^{+0.66}_{-0.89}$ | -1.05${}^{+0.06}_{-0.02}$
3C108 | a3301 | 171.47 | -20.7 | 9.42 | 1.19 | 4.07${}^{+0.40}_{-0.34}$ | 5.60${}^{+0.29}_{-0.30}$ | 9.72${}^{+0.48}_{-0.46}$ | 23.62${}^{+4.42}_{-3.64}$
3C108 | a3301 | 171.47 | -20.7 | 9.74 | 0.48 | 0.85${}^{+0.25}_{-0.27}$ | 2.06${}^{+0.59}_{-0.56}$ | 2.88${}^{+0.73}_{-0.74}$ | -3.40${}^{+1.41}_{-1.25}$
4C+11.15 | a2769 | 171.98 | -35.48 | 7.18 | 0.65 | 3.65${}^{+0.98}_{-0.56}$ | 4.38${}^{+0.40}_{-0.37}$ | 4.42${}^{+0.29}_{-0.26}$ | 5.46${}^{+0.40}_{-0.59}$
4C+36.10 | a2769 | 172.98 | 2.44 | -16.74 | 2.89 | 5.40${}^{+0.92}_{-0.72}$ | 8.62${}^{+0.51}_{-0.47}$ | 9.28${}^{+0.38}_{-0.35}$ | 23.13${}^{+13.61}_{-5.90}$
4C+27.14 | a3301 | 175.46 | -9.96 | 7.19 | 1.62 | 75.92${}^{+52.70}_{-292}$ | 18.63${}^{+2.24}_{-1.74}$ | 14.69${}^{+0.80}_{-1.04}$ | 9.47${}^{+1.90}_{-0.64}$
4C+27.14 | a3301 | 175.46 | -9.96 | 7.89 | 0.84 | 0.10${}^{+0.04}_{-0.02}$ | 6.60${}^{+4.33}_{-13.36}$ | 1.86${}^{+0.65}_{-0.37}$ | -0.12${}^{+0.02}_{-0.04}$
4C+17.23 | a2769 | 176.36 | -24.24 | 9.35 | 0.72 | 3.10${}^{+0.58}_{-0.46}$ | 4.86${}^{+0.39}_{-0.37}$ | 4.41${}^{+0.26}_{-0.27}$ | 8.58${}^{+2.00}_{-1.30}$
4C+17.23 | a2769 | 176.36 | -24.24 | 11.42 | 0.77 | 2.40${}^{+0.34}_{-0.26}$ | 4.34${}^{+0.34}_{-0.28}$ | 4.24${}^{+0.19}_{-0.21}$ | 16.53${}^{+8.07}_{-4.52}$
4C+07.13 | a2769 | 178.87 | -36.27 | 3.48 | 1.07 | 3.25${}^{+3.00}_{-1.23}$ | 3.75${}^{+0.83}_{-0.79}$ | 4.85${}^{+0.91}_{-0.80}$ | 5.91${}^{+3.93}_{-1.56}$
B0531+2730 | a2769 | 179.87 | -2.83 | 3.04 | 0.72 | 1.53${}^{+0.54}_{-0.47}$ | -6.25${}^{+396}_{-3.84}$ | 2.75${}^{+0.56}_{-0.66}$ | -2.41${}^{+0.02}_{-0.63}$
B0531+2730 | a2769 | 179.87 | -2.83 | 3.17 | 0.78 | 4.08${}^{+1.87}_{-36.41}$ | 1.44${}^{+0.57}_{-0.42}$ | 9.80${}^{+491}_{-3.82}$ | 1.84${}^{+0.10}_{-0.39}$
4C+26.18b | a2769 | 182.36 | -0.62 | -11.93 | 1.57 | -2.38${}^{+0.54}_{-0.56}$ | 4.69${}^{+0.65}_{-0.82}$ | 4.55${}^{+0.46}_{-0.64}$ | 1.23${}^{+0.01}_{-0.10}$
4C+26.18b | a2769 | 182.36 | -0.62 | -9.99 | 2.66 | 14.70${}^{+7.80}_{-151}$ | 15.18${}^{+6.19}_{-3.62}$ | 10.16${}^{+1.20}_{-1.06}$ | 10.48${}^{+7.93}_{-3.21}$
4C+22.12 | a2769 | 188.07 | 0.04 | -1.62 | 0.66 | 15.72${}^{+11.00}_{-32.70}$ | 2.36${}^{+0.65}_{-0.68}$ | 2.03${}^{+0.50}_{-0.60}$ | 1.21${}^{+0.11}_{-0.26}$
4C+14.14 | a2769 | 189.04 | -12.85 | 2.60 | 3.82 | 7.86${}^{+7.47}_{-2.47}$ | 6.20${}^{+0.71}_{-0.55}$ | 5.75${}^{+0.30}_{-0.35}$ | 4.86${}^{+0.80}_{-0.68}$
4C+19.18 | a2769 | 190.09 | -2.17 | -0.62 | 2.18 | -2.37${}^{+0.48}_{-0.72}$ | 11.44${}^{+3.61}_{-2.30}$ | 6.87${}^{+0.76}_{-0.67}$ | 1.61${}^{+0.16}_{-0.16}$
4C+19.18 | a2769 | 190.09 | -2.17 | 2.39 | 1.47 | 4.41${}^{+1.41}_{-0.87}$ | 7.13${}^{+0.82}_{-0.71}$ | 5.93${}^{+0.33}_{-0.33}$ | 11.52${}^{+5.33}_{-2.86}$
4C+19.19 | a2769 | 190.13 | -1.64 | 1.12 | 1.42 | -1.25${}^{+0.55}_{-1.01}$ | 4.05${}^{+1.04}_{-1.12}$ | 3.57${}^{+0.83}_{-1.00}$ | 0.79${}^{+0.10}_{-0.22}$
4C+19.19 | a2769 | 190.13 | -1.64 | 2.70 | 3.15 | 2.25${}^{+0.27}_{-0.21}$ | 7.88${}^{+0.76}_{-0.57}$ | 7.71${}^{+0.45}_{-0.39}$ | -5.94${}^{+0.84}_{-1.11}$
PKS0528+134 | a2600 | 191.37 | -11.01 | 9.60 | 0.90 | 4.25${}^{+0.48}_{-0.38}$ | 4.47${}^{+0.19}_{-0.17}$ | 4.44${}^{+0.16}_{-0.16}$ | 4.67${}^{+0.11}_{-0.13}$
4C+16.15b | a2769 | 193.64 | -1.53 | 11.88 | 0.87 | 4.40${}^{+1.07}_{-0.69}$ | 5.25${}^{+0.35}_{-0.33}$ | 5.26${}^{+0.27}_{-0.26}$ | 6.42${}^{+0.84}_{-0.77}$
3C158 | a2769 | 196.64 | 0.17 | 3.14 | 0.98 | 8.07${}^{+5.06}_{-23.59}$ | 3.08${}^{+1.75}_{-1.36}$ | 4.93${}^{+2.56}_{-2.11}$ | 2.53${}^{+0.03}_{-0.85}$
4C+14.18 | a2600 | 196.98 | 1.10 | 4.28 | 0.55 | 3.04${}^{+1.57}_{-24.37}$ | 0.80${}^{+0.40}_{-0.30}$ | 0.62${}^{+0.29}_{-0.26}$ | 0.40${}^{+0.12}_{-0.16}$
4C+14.18 | a2600 | 196.98 | 1.10 | 4.94 | 1.84 | 3.30${}^{+0.24}_{-0.24}$ | 4.99${}^{+0.15}_{-0.16}$ | 6.54${}^{+0.20}_{-0.20}$ | 17.12${}^{+4.04}_{-2.33}$
4C+14.18 | a2600 | 196.98 | 1.10 | 7.39 | 0.81 | 1.53${}^{+0.26}_{-0.22}$ | 3.20${}^{+0.31}_{-0.31}$ | 4.62${}^{+0.39}_{-0.39}$ | -10.11${}^{+3.42}_{-8.92}$
4C+14.18 | a2600 | 196.98 | 1.10 | 16.49 | 1.29 | -11.67${}^{+536}_{-5.72}$ | 5.77${}^{+0.46}_{-0.47}$ | 4.88${}^{+0.39}_{-0.37}$ | 2.24${}^{+0.29}_{-0.23}$
4C+14.18 | a2600 | 196.98 | 1.10 | 17.59 | 0.70 | 2.97${}^{+1.69}_{-0.84}$ | 3.71${}^{+0.62}_{-0.59}$ | 3.05${}^{+0.50}_{-0.46}$ | 3.80${}^{+0.28}_{-0.42}$
4C+14.18 | a2600 | 196.98 | 1.10 | 18.40 | 3.76 | 1.46${}^{+0.20}_{-0.16}$ | 8.49${}^{+1.14}_{-0.92}$ | 9.09${}^{+0.76}_{-0.74}$ | -2.38${}^{+0.29}_{-0.36}$
4C+14.18 | a2600 | 196.98 | 1.10 | 31.98 | 0.42 | 3.57${}^{+0.93}_{-0.84}$ | 3.65${}^{+1.06}_{-0.26}$ | 3.83${}^{+1.16}_{-0.28}$ | 3.91${}^{+0.75}_{-1.31}$
4C+14.18 | a2600 | 196.98 | 1.10 | 32.33 | 1.19 | 3.52${}^{+1.55}_{-0.84}$ | 3.79${}^{+0.58}_{-0.77}$ | 3.69${}^{+0.48}_{-0.56}$ | 3.97${}^{+0.40}_{-0.26}$
Table 4: Fitted excitation temperatures of features identified in this work. Columns give the background source, project name, Galactic longitude and latitude, centroid velocity $v$, FWHM $\Delta v$, and excitation temperatures at 1612, 1665, 1667 and 1720 MHz. The uncertainties are 68% credibility intervals. Source | Project | $l^{\circ}$ | $b^{\circ}$ | $v$ | $\Delta v$ |  $T_{\rm ex}$ (K)
---|---|---|---|---|---|---
|  |  |  | km s-1 | 1612 | 1665 | 1667 | 1720
4C+13.32 | a2769 | 197.15 | -0.85 | -5.65 | 0.78 | 1.21${}^{+0.33}_{-0.32}$ | 2.31${}^{+0.61}_{-0.62}$ | 2.29${}^{+0.63}_{-0.56}$ | 15.25${}^{+4.03}_{-2.45}$
4C+13.32 | a2769 | 197.15 | -0.85 | -0.35 | 1.02 | 2.54${}^{+24.45}_{-1.31}$ | 0.23${}^{+0.31}_{-0.10}$ | 0.11${}^{+0.20}_{-0.06}$ | 0.08${}^{+0.13}_{-0.04}$
4C+13.32 | a2769 | 197.15 | -0.85 | 4.46 | 1.20 | -6.94${}^{+3.64}_{-15.72}$ | 4.42${}^{+2.35}_{-1.98}$ | 3.24${}^{+1.79}_{-1.49}$ | 1.53${}^{+0.08}_{-0.52}$
4C+13.32 | a2769 | 197.15 | -0.85 | 6.99 | 2.21 | 2.35${}^{+0.93}_{-0.92}$ | 18.97${}^{+12.75}_{-8.94}$ | 14.59${}^{+6.17}_{-4.89}$ | -3.56${}^{+1.37}_{-1.23}$
4C+13.32 | a2769 | 197.15 | -0.85 | 9.50 | 1.15 | 6.45${}^{+5.22}_{-2.61}$ | 5.56${}^{+2.37}_{-2.23}$ | 5.68${}^{+2.08}_{-2.22}$ | 5.02${}^{+0.98}_{-1.96}$
4C+17.41 | a2769 | 201.13 | 16.42 | 0.23 | 1.38 | 2.48${}^{+1.17}_{-0.64}$ | 4.68${}^{+0.97}_{-0.75}$ | 4.14${}^{+0.44}_{-0.42}$ | 15.81${}^{+509}_{-7.87}$
4C+17.41 | a2769 | 201.13 | 16.42 | 1.89 | 0.73 | 1.86${}^{+0.31}_{-0.24}$ | 3.86${}^{+0.32}_{-0.31}$ | 3.98${}^{+0.20}_{-0.20}$ | -120.31${}^{+99}_{-150}$
4C+04.22 | a2769 | 205.41 | -4.43 | 11.92 | 0.71 | 2.37${}^{+0.58}_{-0.45}$ | 5.43${}^{+0.81}_{-0.63}$ | 4.45${}^{+0.40}_{-0.39}$ | 2751.44${}^{+2773}_{-2725}$
4C+04.22 | a2769 | 205.41 | -4.43 | 13.33 | 0.92 | 1.43${}^{+0.26}_{-0.19}$ | 4.27${}^{+0.49}_{-0.50}$ | 3.65${}^{+0.31}_{-0.35}$ | -6.20${}^{+1.29}_{-3.23}$
J134217-040725 | a3301 | 205.58 | -4.14 | 9.19 | 1.20 | 2.55${}^{+0.35}_{-0.28}$ | 4.36${}^{+0.30}_{-0.30}$ | 4.58${}^{+0.27}_{-0.26}$ | 15.01${}^{+4.68}_{-3.13}$
4C+04.24 | a2769 | 205.92 | -3.57 | 9.39 | 1.25 | 2.72${}^{+0.48}_{-0.38}$ | 4.31${}^{+0.35}_{-0.31}$ | 4.10${}^{+0.23}_{-0.23}$ | 8.59${}^{+2.22}_{-1.38}$
Table 4 continued.
Source | Project | $l^{\circ}$ | $b^{\circ}$ | $v$ | $\Delta v$ | N1 | N2 | N3 | N4 | NOH
---|---|---|---|---|---|---|---|---|---|---
|  |  |  | km s-1 | log10 cm-2
SRC44 | a3301 | 68.83 | -3.49 | 6.17 | 0.80 | 12.25${}^{+0.13}_{-0.10}$ | 12.46${}^{+0.13}_{-0.10}$ | 12.24${}^{+0.13}_{-0.10}$ | 12.45${}^{+0.13}_{-0.10}$ | 12.96${}^{+0.13}_{-0.10}$
SRC44 | a3301 | 68.83 | -3.49 | 6.28 | 2.50 | 13.05${}^{+0.03}_{-0.04}$ | 13.27${}^{+0.03}_{-0.04}$ | 13.04${}^{+0.03}_{-0.04}$ | 13.27${}^{+0.03}_{-0.04}$ | 13.77${}^{+0.03}_{-0.04}$
SRC44 | a3301 | 68.83 | -3.49 | 11.08 | 0.72 | 10.97${}^{+0.42}_{-0.33}$ | 11.27${}^{+0.34}_{-0.24}$ | 11.03${}^{+0.33}_{-0.22}$ | 11.35${}^{+0.22}_{-0.17}$ | 11.79${}^{+0.31}_{-0.22}$
SRC44 | a3301 | 68.83 | -3.49 | 11.20 | 1.29 | 11.83${}^{+0.12}_{-0.21}$ | 12.01${}^{+0.11}_{-0.21}$ | 11.79${}^{+0.11}_{-0.21}$ | 11.95${}^{+0.10}_{-0.20}$ | 12.51${}^{+0.11}_{-0.21}$
3C417 | a2600 | 73.33 | -5.45 | 9.51 | 0.88 | 13.09${}^{+0.06}_{-0.07}$ | 13.30${}^{+0.06}_{-0.07}$ | 13.08${}^{+0.06}_{-0.07}$ | 13.30${}^{+0.06}_{-0.07}$ | 13.81${}^{+0.06}_{-0.07}$
3C417 | a2600 | 73.33 | -5.45 | 9.92 | 0.63 | 13.15${}^{+0.04}_{-0.05}$ | 13.40${}^{+0.05}_{-0.05}$ | 13.14${}^{+0.04}_{-0.05}$ | 13.39${}^{+0.05}_{-0.05}$ | 13.89${}^{+0.04}_{-0.05}$
3C417 | a2600 | 73.33 | -5.45 | 10.68 | 2.91 | 13.45${}^{+0.02}_{-0.03}$ | 13.68${}^{+0.02}_{-0.03}$ | 13.45${}^{+0.02}_{-0.03}$ | 13.67${}^{+0.02}_{-0.03}$ | 14.18${}^{+0.02}_{-0.03}$
3C092 | a2600 | 159.74 | -18.41 | 8.71 | 1.56 | 13.28${}^{+0.02}_{-0.03}$ | 13.51${}^{+0.03}_{-0.03}$ | 13.28${}^{+0.02}_{-0.03}$ | 13.51${}^{+0.03}_{-0.03}$ | 14.01${}^{+0.02}_{-0.03}$
3C092 | a2600 | 159.74 | -18.41 | 8.77 | 0.76 | 13.09${}^{+0.04}_{-0.04}$ | 13.32${}^{+0.04}_{-0.04}$ | 13.08${}^{+0.04}_{-0.04}$ | 13.31${}^{+0.04}_{-0.04}$ | 13.82${}^{+0.04}_{-0.04}$
4C+28.11 | a2769 | 166.06 | -17.22 | 6.91 | 1.10 | 13.24${}^{+0.02}_{-0.02}$ | 13.47${}^{+0.02}_{-0.02}$ | 13.24${}^{+0.02}_{-0.02}$ | 13.47${}^{+0.02}_{-0.02}$ | 13.97${}^{+0.02}_{-0.02}$
PKS0319+12 | a2769 | 170.59 | -36.24 | 7.73 | 1.01 | 12.24${}^{+0.12}_{-0.14}$ | 12.47${}^{+0.12}_{-0.14}$ | 12.23${}^{+0.12}_{-0.14}$ | 12.46${}^{+0.12}_{-0.14}$ | 12.97${}^{+0.12}_{-0.14}$
3C131 | a2600 | 171.44 | -7.80 | 4.56 | 0.48 | 11.94${}^{+0.03}_{-0.04}$ | 12.17${}^{+0.04}_{-0.04}$ | 11.94${}^{+0.03}_{-0.04}$ | 12.16${}^{+0.04}_{-0.04}$ | 12.67${}^{+0.04}_{-0.04}$
3C131 | a2600 | 171.44 | -7.80 | 5.71 | 3.21 | 12.96${}^{+0.02}_{-0.02}$ | 13.19${}^{+0.02}_{-0.02}$ | 12.96${}^{+0.02}_{-0.02}$ | 13.19${}^{+0.02}_{-0.02}$ | 13.69${}^{+0.02}_{-0.02}$
3C131 | a2600 | 171.44 | -7.80 | 6.59 | 0.44 | 12.34${}^{+0.02}_{-0.02}$ | 12.56${}^{+0.03}_{-0.03}$ | 12.33${}^{+0.02}_{-0.02}$ | 12.55${}^{+0.03}_{-0.03}$ | 13.06${}^{+0.03}_{-0.03}$
3C131 | a2600 | 171.44 | -7.80 | 7.23 | 0.56 | 13.01${}^{+0.01}_{-0.01}$ | 13.23${}^{+0.01}_{-0.01}$ | 13.00${}^{+0.01}_{-0.00}$ | 13.22${}^{+0.01}_{-0.01}$ | 13.73${}^{+0.01}_{-0.01}$
3C131 | a2600 | 171.44 | -7.80 | 7.48 | 1.93 | 12.52${}^{+0.05}_{-0.05}$ | 12.77${}^{+0.05}_{-0.05}$ | 12.51${}^{+0.04}_{-0.05}$ | 12.76${}^{+0.05}_{-0.05}$ | 13.26${}^{+0.05}_{-0.05}$
3C131 | a2600 | 171.44 | -7.80 | 7.79 | 0.57 | 11.33${}^{+0.10}_{-0.12}$ | 11.58${}^{+0.10}_{-0.12}$ | 11.35${}^{+0.10}_{-0.11}$ | 11.59${}^{+0.10}_{-0.12}$ | 12.08${}^{+0.10}_{-0.12}$
3C108 | a3301 | 171.47 | -20.70 | 9.42 | 1.19 | 13.20${}^{+0.03}_{-0.03}$ | 13.43${}^{+0.03}_{-0.03}$ | 13.20${}^{+0.03}_{-0.03}$ | 13.42${}^{+0.03}_{-0.03}$ | 13.93${}^{+0.03}_{-0.03}$
3C108 | a3301 | 171.47 | -20.70 | 9.74 | 0.48 | 12.26${}^{+0.13}_{-0.17}$ | 12.50${}^{+0.15}_{-0.18}$ | 12.24${}^{+0.13}_{-0.17}$ | 12.49${}^{+0.14}_{-0.17}$ | 12.99${}^{+0.14}_{-0.17}$
4C+11.15 | a2769 | 171.98 | -35.48 | 7.18 | 0.65 | 12.91${}^{+0.03}_{-0.03}$ | 13.14${}^{+0.03}_{-0.03}$ | 12.91${}^{+0.03}_{-0.03}$ | 13.13${}^{+0.03}_{-0.03}$ | 13.64${}^{+0.03}_{-0.03}$
4C+36.1 | a2769 | 172.98 | 2.44 | -16.74 | 2.89 | 13.54${}^{+0.02}_{-0.02}$ | 13.76${}^{+0.02}_{-0.02}$ | 13.53${}^{+0.01}_{-0.02}$ | 13.76${}^{+0.02}_{-0.02}$ | 14.26${}^{+0.02}_{-0.02}$
4C+27.14 | a3301 | 175.46 | -9.96 | 7.19 | 1.62 | 13.59${}^{+0.01}_{-0.01}$ | 13.81${}^{+0.01}_{-0.01}$ | 13.59${}^{+0.01}_{-0.01}$ | 13.81${}^{+0.01}_{-0.01}$ | 14.31${}^{+0.01}_{-0.01}$
4C+27.14 | a3301 | 175.46 | -9.96 | 7.89 | 0.84 | 11.70${}^{+0.14}_{-0.31}$ | 12.25${}^{+0.20}_{-0.39}$ | 11.69${}^{+0.13}_{-0.30}$ | 12.23${}^{+0.20}_{-0.38}$ | 12.65${}^{+0.18}_{-0.37}$
4C+17.23 | a2769 | 176.36 | -24.24 | 9.35 | 0.72 | 12.79${}^{+0.03}_{-0.03}$ | 13.02${}^{+0.03}_{-0.03}$ | 12.79${}^{+0.03}_{-0.03}$ | 13.01${}^{+0.03}_{-0.03}$ | 13.52${}^{+0.03}_{-0.03}$
4C+17.23 | a2769 | 176.36 | -24.24 | 11.42 | 0.77 | 12.87${}^{+0.03}_{-0.02}$ | 13.09${}^{+0.03}_{-0.03}$ | 12.86${}^{+0.03}_{-0.02}$ | 13.08${}^{+0.03}_{-0.03}$ | 13.59${}^{+0.03}_{-0.02}$
4C+7.13 | a2769 | 178.87 | -36.27 | 3.48 | 1.07 | 12.52${}^{+0.08}_{-0.09}$ | 12.74${}^{+0.08}_{-0.09}$ | 12.51${}^{+0.08}_{-0.09}$ | 12.74${}^{+0.08}_{-0.09}$ | 13.24${}^{+0.08}_{-0.09}$
B0531+2730 | a2769 | 179.87 | -2.83 | 3.04 | 0.72 | 12.89${}^{+0.11}_{-0.14}$ | 13.14${}^{+0.12}_{-0.14}$ | 12.89${}^{+0.11}_{-0.14}$ | 13.12${}^{+0.11}_{-0.14}$ | 13.63${}^{+0.11}_{-0.14}$
B0531+2730 | a2769 | 179.87 | -2.83 | 3.17 | 0.78 | 12.85${}^{+0.12}_{-0.15}$ | 13.06${}^{+0.12}_{-0.16}$ | 12.83${}^{+0.11}_{-0.15}$ | 13.05${}^{+0.11}_{-0.15}$ | 13.56${}^{+0.11}_{-0.15}$
4C+26.18b | a2769 | 182.36 | -0.62 | -11.93 | 1.57 | 13.14${}^{+0.07}_{-0.11}$ | 13.34${}^{+0.07}_{-0.11}$ | 13.13${}^{+0.06}_{-0.11}$ | 13.33${}^{+0.07}_{-0.11}$ | 13.85${}^{+0.07}_{-0.11}$
4C+26.18b | a2769 | 182.36 | -0.62 | -9.99 | 2.66 | 13.25${}^{+0.07}_{-0.07}$ | 13.47${}^{+0.07}_{-0.07}$ | 13.25${}^{+0.07}_{-0.07}$ | 13.47${}^{+0.07}_{-0.07}$ | 13.97${}^{+0.07}_{-0.07}$
4C+22.12 | a2769 | 188.07 | 0.04 | -1.62 | 0.66 | 12.28${}^{+0.10}_{-0.15}$ | 12.49${}^{+0.10}_{-0.15}$ | 12.26${}^{+0.09}_{-0.15}$ | 12.47${}^{+0.09}_{-0.15}$ | 12.99${}^{+0.09}_{-0.15}$
4C+14.14 | a2769 | 189.04 | -12.85 | 2.60 | 3.82 | 13.20${}^{+0.03}_{-0.04}$ | 13.42${}^{+0.03}_{-0.04}$ | 13.19${}^{+0.03}_{-0.04}$ | 13.41${}^{+0.03}_{-0.04}$ | 13.92${}^{+0.03}_{-0.04}$
4C+19.18 | a2769 | 190.09 | -2.17 | -0.62 | 2.18 | 12.97${}^{+0.05}_{-0.05}$ | 13.18${}^{+0.05}_{-0.05}$ | 12.97${}^{+0.05}_{-0.05}$ | 13.17${}^{+0.05}_{-0.05}$ | 13.69${}^{+0.05}_{-0.05}$
4C+19.18 | a2769 | 190.09 | -2.17 | 2.39 | 1.47 | 13.06${}^{+0.03}_{-0.04}$ | 13.28${}^{+0.04}_{-0.04}$ | 13.05${}^{+0.03}_{-0.04}$ | 13.27${}^{+0.03}_{-0.04}$ | 13.78${}^{+0.03}_{-0.04}$
4C+19.19 | a2769 | 190.13 | -1.64 | 1.12 | 1.42 | 12.57${}^{+0.17}_{-0.18}$ | 12.75${}^{+0.18}_{-0.20}$ | 12.56${}^{+0.17}_{-0.17}$ | 12.74${}^{+0.18}_{-0.19}$ | 13.27${}^{+0.18}_{-0.19}$
4C+19.19 | a2769 | 190.13 | -1.64 | 2.70 | 3.15 | 13.30${}^{+0.03}_{-0.05}$ | 13.54${}^{+0.03}_{-0.05}$ | 13.30${}^{+0.03}_{-0.05}$ | 13.53${}^{+0.03}_{-0.05}$ | 14.03${}^{+0.03}_{-0.05}$
PKS0528+134 | a2600 | 191.37 | -11.01 | 9.60 | 0.90 | 12.91${}^{+0.02}_{-0.02}$ | 13.14${}^{+0.02}_{-0.02}$ | 12.91${}^{+0.02}_{-0.02}$ | 13.13${}^{+0.02}_{-0.02}$ | 13.64${}^{+0.02}_{-0.02}$
4C+16.15b | a2769 | 193.64 | -1.53 | 11.88 | 0.87 | 12.94${}^{+0.03}_{-0.03}$ | 13.17${}^{+0.03}_{-0.03}$ | 12.94${}^{+0.03}_{-0.03}$ | 13.16${}^{+0.03}_{-0.03}$ | 13.67${}^{+0.03}_{-0.03}$
3C158 | a2769 | 196.64 | 0.17 | 3.14 | 0.98 | 12.26${}^{+0.20}_{-0.27}$ | 12.48${}^{+0.19}_{-0.27}$ | 12.25${}^{+0.19}_{-0.26}$ | 12.47${}^{+0.19}_{-0.27}$ | 12.98${}^{+0.19}_{-0.27}$
4C+14.18 | a2600 | 196.98 | 1.10 | 4.28 | 0.55 | 11.22${}^{+0.17}_{-0.23}$ | 11.41${}^{+0.16}_{-0.22}$ | 11.18${}^{+0.15}_{-0.21}$ | 11.35${}^{+0.12}_{-0.21}$ | 11.90${}^{+0.15}_{-0.21}$
4C+14.18 | a2600 | 196.98 | 1.10 | 4.94 | 1.84 | 12.94${}^{+0.01}_{-0.01}$ | 13.17${}^{+0.01}_{-0.01}$ | 12.93${}^{+0.01}_{-0.01}$ | 13.16${}^{+0.01}_{-0.01}$ | 13.67${}^{+0.01}_{-0.01}$
4C+14.18 | a2600 | 196.98 | 1.10 | 7.39 | 0.81 | 12.15${}^{+0.04}_{-0.05}$ | 12.38${}^{+0.04}_{-0.05}$ | 12.14${}^{+0.04}_{-0.04}$ | 12.37${}^{+0.04}_{-0.05}$ | 12.88${}^{+0.04}_{-0.05}$
4C+14.18 | a2600 | 196.98 | 1.10 | 16.49 | 1.29 | 12.48${}^{+0.06}_{-0.06}$ | 12.69${}^{+0.06}_{-0.07}$ | 12.47${}^{+0.06}_{-0.06}$ | 12.68${}^{+0.06}_{-0.07}$ | 13.20${}^{+0.06}_{-0.07}$
4C+14.18 | a2600 | 196.98 | 1.10 | 17.59 | 0.70 | 12.01${}^{+0.09}_{-0.10}$ | 12.23${}^{+0.09}_{-0.10}$ | 12.00${}^{+0.09}_{-0.10}$ | 12.22${}^{+0.09}_{-0.10}$ | 12.73${}^{+0.09}_{-0.10}$
4C+14.18 | a2600 | 196.98 | 1.10 | 18.40 | 3.76 | 12.70${}^{+0.05}_{-0.07}$ | 12.94${}^{+0.05}_{-0.07}$ | 12.69${}^{+0.05}_{-0.07}$ | 12.93${}^{+0.05}_{-0.07}$ | 13.43${}^{+0.05}_{-0.07}$
4C+14.18 | a2600 | 196.98 | 1.10 | 31.98 | 0.42 | 12.42${}^{+0.09}_{-0.04}$ | 12.64${}^{+0.09}_{-0.03}$ | 12.41${}^{+0.09}_{-0.03}$ | 12.64${}^{+0.09}_{-0.03}$ | 13.15${}^{+0.09}_{-0.03}$
4C+14.18 | a2600 | 196.98 | 1.10 | 32.33 | 1.19 | 12.35${}^{+0.05}_{-0.07}$ | 12.57${}^{+0.05}_{-0.07}$ | 12.34${}^{+0.05}_{-0.07}$ | 12.56${}^{+0.05}_{-0.07}$ | 13.07${}^{+0.05}_{-0.07}$
Table 5: Fitted column densities of features identified in this work. Columns give the background source of each sightline, project name, Galactic longitude and latitude, centroid velocity $v$, FWHM $\Delta v$, and column densities of the hyperfine levels of the OH ground-rotational state (where N1 is the lowest level) and the total OH column density. The uncertainties are the 68% credibility intervals. Source | Project | $l^{\circ}$ | $b^{\circ}$ | $v$ | $\Delta v$ | N1 | N2 | N3 | N4 | NOH
---|---|---|---|---|---|---|---|---|---|---
|  |  |  | km s-1 | log10 cm-2
4C+13.32 | a2769 | 197.15 | -0.85 | -5.65 | 0.78 | 12.27${}^{+0.11}_{-0.12}$ | 12.50${}^{+0.11}_{-0.13}$ | 12.25${}^{+0.10}_{-0.12}$ | 12.49${}^{+0.10}_{-0.12}$ | 12.99${}^{+0.11}_{-0.12}$
4C+13.32 | a2769 | 197.15 | -0.85 | -0.35 | 1.02 | 10.62${}^{+0.36}_{-0.26}$ | 10.71${}^{+0.26}_{-0.19}$ | 10.47${}^{+0.24}_{-0.17}$ | 10.40${}^{+0.01}_{-0.14}$ | 11.17${}^{+0.24}_{-0.16}$
4C+13.32 | a2769 | 197.15 | -0.85 | 4.46 | 1.20 | 12.18${}^{+0.18}_{-0.25}$ | 12.39${}^{+0.18}_{-0.26}$ | 12.18${}^{+0.18}_{-0.25}$ | 12.38${}^{+0.17}_{-0.25}$ | 12.90${}^{+0.18}_{-0.25}$
4C+13.32 | a2769 | 197.15 | -0.85 | 6.99 | 2.21 | 12.52${}^{+0.17}_{-0.24}$ | 12.75${}^{+0.18}_{-0.24}$ | 12.52${}^{+0.17}_{-0.24}$ | 12.75${}^{+0.17}_{-0.24}$ | 13.25${}^{+0.17}_{-0.24}$
4C+13.32 | a2769 | 197.15 | -0.85 | 9.50 | 1.15 | 12.31${}^{+0.13}_{-0.22}$ | 12.53${}^{+0.13}_{-0.22}$ | 12.30${}^{+0.12}_{-0.22}$ | 12.52${}^{+0.12}_{-0.22}$ | 13.03${}^{+0.13}_{-0.22}$
4C+17.41 | a2769 | 201.13 | 16.42 | 0.23 | 1.38 | 12.67${}^{+0.06}_{-0.07}$ | 12.90${}^{+0.07}_{-0.07}$ | 12.67${}^{+0.06}_{-0.07}$ | 12.89${}^{+0.07}_{-0.07}$ | 13.40${}^{+0.07}_{-0.07}$
4C+17.41 | a2769 | 201.13 | 16.42 | 1.89 | 0.73 | 12.81${}^{+0.03}_{-0.04}$ | 13.04${}^{+0.03}_{-0.04}$ | 12.80${}^{+0.03}_{-0.04}$ | 13.03${}^{+0.03}_{-0.04}$ | 13.54${}^{+0.03}_{-0.04}$
4C+4.22 | a2769 | 205.41 | -4.43 | 11.92 | 0.71 | 12.72${}^{+0.05}_{-0.06}$ | 12.95${}^{+0.05}_{-0.06}$ | 12.72${}^{+0.05}_{-0.06}$ | 12.94${}^{+0.05}_{-0.06}$ | 13.45${}^{+0.05}_{-0.06}$
4C+4.22 | a2769 | 205.41 | -4.43 | 13.33 | 0.92 | 12.75${}^{+0.05}_{-0.06}$ | 12.99${}^{+0.05}_{-0.06}$ | 12.74${}^{+0.04}_{-0.06}$ | 12.98${}^{+0.05}_{-0.06}$ | 13.48${}^{+0.05}_{-0.06}$
J134217-040725 | a3301 | 205.58 | -4.14 | 9.19 | 1.20 | 12.99${}^{+0.03}_{-0.03}$ | 13.22${}^{+0.03}_{-0.03}$ | 12.99${}^{+0.03}_{-0.03}$ | 13.21${}^{+0.03}_{-0.03}$ | 13.72${}^{+0.03}_{-0.03}$
4C+4.24 | a2769 | 205.92 | -3.57 | 9.39 | 1.25 | 13.01${}^{+0.03}_{-0.03}$ | 13.24${}^{+0.03}_{-0.03}$ | 13.00${}^{+0.03}_{-0.03}$ | 13.23${}^{+0.03}_{-0.03}$ | 13.74${}^{+0.03}_{-0.03}$
Table 5 continued.

Figs. 6 to 8 illustrate the distributions of the key parameters (FWHM, column
density, optical depth and excitation temperature) of our fits. The
distribution of FWHM (shown on a log scale in the left panel of Fig. 6)
suggests a log-normal distribution with a mean of 1.5 km s-1 and a 68%
confidence interval bound by $0.7-3.4$ km s-1. The distribution of total OH
column density (shown in the right panel of Fig. 6) suggests a typical OH
column density of $\approx 10^{13.5}$cm-2. The detection limit for OH column
density is difficult to estimate with consistency as it depends not only on
the noise level and channel width of the optical depth and expected brightness
temperature spectra but on the excitation temperatures in the four
transitions. However, with estimates of ‘typical’ excitation temperatures
$T_{\rm ex}\approx 2-5$ K (see Fig. 8) we can estimate a detection limit of
$N_{\rm OH}\approx 10^{12.5}-10^{13}{\rm cm}^{-2}$, which is consistent with
the distribution in Fig. 6. This therefore implies that our detections are
incomplete and the typical column density of OH could be lower.

|
---|---
Figure 6: Distribution of FWHM (left) and total OH column density (right)
found from the sightlines examined in this paper. Note that the FWHM
distribution has bin widths of equal $\log_{10}{\rm km\,s}^{-1}$. The leftmost
bin in the column density plot contains all values below $N_{\rm OH}=10^{12}$
cm-2. The vertical axes show counts.

Fig. 7 shows the distribution of peak optical depths across the four OH
ground-rotational state transitions. All detections are optically thin
($\tau_{\rm peak}\ll 1$) with approximately log-normal distributions. As would
be expected from their relative transition strengths, the satellite lines have
the lowest magnitude peak optical depths and the 1667 MHz line has the
highest. The trends in optical depth are examined more closely in the
following section. Fig. 8 shows the distribution of excitation temperature
across the four transitions. The main-line excitation temperatures show a
similar, roughly normal distribution centred at approximately 4 K, while the
satellite lines tend towards slightly lower values of about 3 K. The satellite
lines (and particularly the 1720 MHz transition) are more often inverted (i.e.
$T_{\rm ex}<0$) than the main lines. These trends are also examined more
closely in the following section.

|
---|---
Figure 7: Distribution of main-line (left) and satellite-line (right) peak optical depth found from the sightlines examined in this paper. The vertical axes show counts. |
---|---
Figure 8: Distribution of main-line (left) and satellite-line (right)
excitation temperatures found from the sightlines examined in this paper. The
vertical axes show counts.

##  5 Analysis

As briefly outlined in the Observing OH subsection, this work represents an
unprecedented analysis of OH in the diffuse ISM due primarily to our Gaussian
decomposition algorithm (Petzler2021a, 83, Amoeba). Generally speaking, other
works tend to fit features in each transition separately NguyenQRieu1976 (76,
26, 16, 65, 88, 62), or solve all spectra simultaneously but channel-by-
channel rather than component-by-component (Crutcher1977, 19, 20, e.g.). For
this reason, we will discuss here the broad trends described by these earlier
works, as a more detailed sightline-by-sightline comparison of measurements
like optical depth, excitation temperature and column density is not strictly
valid given the vast differences in our analyses.

Figs. 17 to 23 (with representative examples shown in Fig. 5) show the results
of the Gaussian decomposition of our spectra using Amoeba Petzler2021a (83).
For sightlines observed with the ATCA (Figs. 21 and 22) these plots show
optical depth vs velocity for the four OH ground-rotational transitions in
grey with the individual Gaussian components in red and the total fit in blue.
The residuals of the total fits are shown in the fifth panel, and the sixth
panel shows the residual of the optical depth sum rule:

$\tau_{\rm peak}(1612)+\tau_{\rm peak}(1720)-\tau_{\rm peak}(1665)/5-\tau_{\rm
peak}(1667)/9$

in black. The optical depth sum rule will hold when $|T_{\rm ex}|\gg
h\nu_{0}/k_{\rm B}=0.08$, so features seen in the sum rule residuals indicate
features for which $|T_{\rm ex}|\lesssim 0.08\,$K or, more likely, places
where maser sidelobes have contaminated the ATCA spectra. When analysing
optical depth spectra only, Amoeba includes an a priori distribution where
deviations from the sum rule are expected to have a standard deviation of 0.5.
This is intended as a weakly-informative prior, and is therefore much larger
than the standard deviation of $\sim 10^{-3}$ that we found from our on-off
observations (where Amoeba does not assume that $|T_{\rm ex}|\gg
h\nu_{0}/k_{\rm B}$). As a consequence of this prior, Amoeba will tend not to
fit signal caused by single-transition maser emission or other anomalies seen
in only one transition, but will still be able to fit features that depart
moderately from the optical depth sum rule. With this prior the fitted
components from our ATCA observations yield a distribution of sum rule
residuals with a standard deviation of 0.05. Any significant departures from
the sum rule evident in our ATCA data are described in the Appendix.

The sightlines with on-off observations (Figs. 17 to 20 and 23) are generally
well-fit, as evidenced by the lack of significant features in the residuals.
Some minor exceptions can be seen in the observations towards SRC44 (Fig. 23)
and 3C417 (Fig. 17) with residuals seen in the expected brightness temperature
at 1720 MHz, and PKS0528+134 (Fig. 23) and 4C+14.18 (Fig. 18) with residuals
seen at 1612 MHz. We note that all of these features are seen in the residuals
of the expected brightness temperatures for the satellite-line transitions,
which across all observations tend to have the lowest signal-to-noise ratios.
Amoeba assumes that the OH gas seen in the on-source and off-source positions
have the same column densities in each of the four ground-rotational state
levels as well as the same velocity dispersion. Therefore we interpret this
lack of significant features in the residuals of the fits as validation of the
underlying assumptions of Amoeba. We do not find evidence that OH has a
significant ‘multi-phase’ structure that would result in it having
significantly different excitation in these positions, contrary to the finding
of Liszt1996 (65).

We note the detection of four satellite-line ‘flips’: two that have already
been reported in Petzler2020 (82) towards G340.79-1.02 (at $-29.22$ and
$-26.44$ km s-1, see Fig. 21) and G353.41-0.30 (at $-19.10$ and $-14.40$ km
s-1, see Fig. 22), and two that are new detections towards 4C+19.19 (at 1.12
and 2.70 km s-1, see Fig. 19) and 4C+14.18 (at 16.49 and 18.40 km s-1, see
Fig. 18). Petzler2020 (82) suggested that this profile type – where the
satellite lines show paired emission and absorption that then flip orientation
across a closely blended feature – generally indicates molecular gas on either
side of a shock front. The flips towards G340.79-1.02 and G353.41-0.30 show
the more common velocity orientation of the flip, with the 1720 MHz stimulated
emission seen at more negative velocities. These two sightlines are also
associated on the sky and in velocity with known Hii regions (G340.780-01.022
at $-25$ km s-1 Caswell1987 (15) and G353.408-00.381 at $-15.7$ km s-1
Quireza2006 (85), respectively), which Petzler2020 (82) argue implies that an
associated shock front is expanding from those Hii regions towards the
observer. In their picture, the 1720 MHz-emitting gas is on the inside of the
shock and collides with the 1612 MHz-emitting gas in the surrounding molecular
cloud: the enhanced radiation from the Hii region and the surrounding dust
inverts the 1612 MHz line in the surrounding molecular cloud while the heating
and compression from the shock switches off the 1612 MHz emission and inverts
the 1720 MHz line.

On the other hand, the two new flips towards 4C+19.19 ($l^{\circ}=190.13$,
$b^{\circ}=-1.64$) and 4C+14.18 ($l^{\circ}=196.98$, $b^{\circ}=1.10$) have
the opposite velocity orientation and no clear Hii association. Petzler2020
(82) reported three such flips, all within the Taurus molecular cloud complex
(and near to these two new detections though not in the same complex), towards
G172.80-13.24 (Xu2016, 108, at 5.3 and 6.8 km s-1), G173.40-13.26
(Ebisawa2019, 30, at 5 and 8 km s-1) and G175.83-9.36 (4C+27.14 from project
a2600 at 7.1 and 7.8 km s-1, GNOMES collaboration). This third flip was
observed twice in the data set examined in this paper, once in the a2600
project and once in a3301. The flip was visually apparent in the a2600 data,
but this work fit the newer, higher signal-to-noise data from a3301 (which was
not yet available at the time Petzler2020 (82) was published) and a flip was
not found. Petzler2020 (82) propose that these flips, and by extension these
two new detections towards 4C+19.19 and 4C+14.18, are not indicative of an
enhanced radiation field or a shock, but may represent some other type of bulk
motions such as the large shell proposed by Bialy2021 (4).

###  5.1 Optical depth and excitation temperature relationships

The relationships between main-line and satellite-line peak optical depths
across the four OH ground-rotational transitions are shown in Figs. 9 and 11
respectively. Similarly, the relationships between main-line and satellite-
line excitation temperatures are shown in Figs. 10 and 12. Overall we find
that while the excitation temperatures of the main lines are similar (median
$|\Delta T_{\rm ex}({\rm main})|=0.6\,$K, 84% show $|\Delta T_{\rm ex}({\rm
main})|<2\,$K), those of the satellite lines show that the gas is generally
not in LTE. In this subsection we will focus first on trends seen in the main
lines, then on those seen in the satellite lines before commenting on the
implications of both.

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Figure 9: Distribution of peak optical depths in the ‘main’ lines at 1665 and
1667 MHz. Features identified from our ‘on-off’ data (from Arecibo) are shown
in blue while our ‘optical depth only’ data (from the ATCA) are shown in red.
The rectangle in the left plot indicates the area enlarged in the plot on the
right. The grey reference lines indicate the axes and where $\tau_{\rm
peak}(1667)=\frac{9}{5}\tau_{\rm peak}(1665)$, which is the expected
relationship between $\tau_{\rm peak}(1667)$ and $\tau_{\rm peak}(1665)$ when
in local thermodynamic equilibrium (LTE), though adherence to this ratio is
not sufficient evidence to conclude LTE. The error bars indicate the 68%
credibility intervals. Figure 10: Relationship between the OH ‘main-line’
excitation temperatures found from the sightlines examined in this paper. The
red reference line indicates where the two excitation temperatures are equal,
and the error bars indicate the 68% credibility intervals.

Fig. 9 shows a significant difference in main-line peak optical depth
relationship between our on-off data (shown in blue) and our optical-depth
only data (shown in red). The features identified in our on-off data tend to
have a main-line optical depth ratio of $5:9$ which is the expected ratio in
the case of local thermodynamic equilibrium (LTE). LTE would also imply that
the excitation temperatures of the main lines are equal, and they do tend
towards similar values when we compare the main-line excitation temperatures
in Fig. 10 (recall that we were unable to calculate excitation temperatures
from our optical depth only data). The main-line excitation temperatures had a
median difference of $|\Delta T_{\rm ex}({\rm main})|=0.6\,$K, and 84% show
$|\Delta T_{\rm ex}({\rm main})|<2\,$K.

On the other hand, features identified in our optical depth only data from the
ATCA have main-line peak optical depths that show little discernible pattern
aside from a slight tendency (seen in the right panel of Fig. 9) to have
higher 1665 MHz peak optical depth than that expected in LTE. Measurements of
main-line optical depths from Li2018 (62) show a pattern that is not
inconsistent with this – there is a slight skew towards higher peak optical
depth in the 1665 MHz transition – but the trend is much less pronounced. We
note that Li2018 (62) fit the main lines separately but did utilise on-off
measurements. This trend, along with others noted in this subsection, are
likely only apparent due to the large number of sightlines analysed in this
work as well as our simultaneous fitting method, which is inherently more
sensitive to lower optical depths.

Our data set from the ATCA differs from our on-off spectra both in the method
by which features were identified (as described in the Method practicalities
and limitations section), but also in the location of the lines-of-sight: our
ATCA sightlines are in the Plane and towards the Galactic centre. It is
therefore unclear which of these may be responsible for the differences seen
in the main-line peak optical depth relationships. If we assume the latter
case then we may conclude that deviations from the expected LTE ratio – often
referred to as ‘main-line anomalies’ – are more common in the Plane and
towards the Galactic centre. Such main-line anomalies have been well-
documented (Crutcher1977, 19, 20, e.g.) and indicate (as outlined in the
Introduction) either a radiation field that differs significantly from a
Planck distribution (such as from warm dust) or collisional excitations from
particles that differ significantly from a Maxwellian distribution (such as
from particle flows). Elaborating on the previous brief introduction, these
conditions provide a significant difference in the energy budget between
excitations into the upper and lower halves of the lambda doublets of the
higher rotational states of OH. Then as these excited molecules cascade back
into the ground-rotational state they remain on their respective side of the
rotational ladder, but also remain on either the top or the bottom of the
lambda doublet due to selection rules. Therefore any imbalance in the number
of excitations into, say, the upper half of the lambda doublet in the infrared
transitions into higher rotational states will result in a similar imbalance
in the upper half of the lambda doublet in the ground-rotational state. This
imbalance could be sufficient to invert one or both of the main-line
transitions, but it could also result in the observed divergence from the LTE
ratio. For example, in the presence of an infrared radiation field with
sufficiently steep (negative) spectral profile, there will be fewer photons
available at high energies compared to low energies. Therefore, transitions
into the lower half of the lambda doublets of excited rotational states will
be more common than transitions into the upper halves. As these OH molecules
cascade back into the ground-rotational state they will tend to over-populate
the lower levels of the ground-rotational state, thus sub-thermally exciting
all four ground-rotational state transitions, and more particularly the 1665
MHz transition (and the 1720 MHz transition, though we discuss this later) as
its lower level has fewer sub-levels Elitzur1976etal (34). This sub-thermal
excitation could then lead to the systematically higher peak optical depths in
the 1665 MHz transition as seen in the right panel of Fig. 9. We also note
that we have identified 16 features for which either one or both of the main
lines have a negative optical depth, implying that those lines are inverted,
and all but 3 of these are from our sightlines observed with the ATCA and are
therefore located in the Plane and towards the Galactic centre. From these it
appears that inversions of the 1665 MHz line are more common than those of the
1667 MHz line, and in cases where the 1667 MHz line is inverted it is more
common for the 1665 MHz line to also be inverted, though the small sample size
is insufficient to draw significant conclusions from these trends.

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Figure 11: Distribution of peak optical depths in the ‘satellite’ lines at
1612 and 1720 MHz. The rectangle in the left plot indicates the area enlarged
in the plot on the right. The grey reference lines indicate the axes and where
$\tau_{\rm peak}(1612)=\tau_{\rm peak}(1720)$, which is the expected
relationship between $\tau_{\rm peak}(1612)$ and $\tau_{\rm peak}(1720)$ when
in local thermodynamic equilibrium. The error bars indicate the 68%
credibility intervals. Figure 12: Relationship between the OH ‘satellite-line’
excitation temperatures found from the sightlines examined in this paper. The
red reference line indicates where the two excitation temperatures are equal,
and the error bars indicate the 68% credibility intervals.

Turning our attention now to the satellite lines, we see no tendency towards
the expected LTE ratio of $1:1$, and the satellite-line excitation
temperatures (see the right panel of Fig. 8, noting that these represent on-
off observations only) are clearly unequal. This is consistent with the
findings of nearly all previous works that have measured satellite-line
optical depths.

Looking closer at the relationship between satellite-line optical depths (see
Fig. 11), we note that while it is most common for both to be positive (63/109
points are found in the first quadrant of Fig. 11), it is more common for the
1720 MHz transition to have a negative optical depth (27/109) than it is for
the 1612 MHz line (19/109). Negative optical depths imply a population
inversion. This is consistent with works such as Turner1982 (96) and
Dawson2022 (22) who note that inversions of the 1720 MHz line are ubiquitous
in the ISM. However, we note that in the case of our sightlines observed with
the ATCA (in the Plane and towards the Galactic centre) this trend disappears
and it is marginally more common for the 1612 MHz line to have a negative
optical depth (12/51) compared to the 1720 MHz line (9/51). We also note that
in these cases the 1612 MHz line tends towards more negative optical depths
than the 1720 MHz, a possible indication that it is more strongly inverted
(though not conclusively as this could be a column density effect).

Continuing from the previous brief introduction, satellite line inversions are
caused by an imbalance in cascades into the ground-rotational state from the
first and second excited rotational states Elitzur1976 (35). Collisions can
selectively excite into just the first excited rotational level but not the
second, which then leads to an enhancement of cascade pathways into the $F=2$
levels of the ground-rotational state and inversion of the 1720 MHz line
Elitzur1976 (35). On the other hand, an enhanced radiation field can excite OH
into both the first and second excited rotational states, which will cascade
into the $F=1$ and $F=2$ levels of the ground-rotational state equally. In
this case, since the $F=1$ levels have a lower degeneracy ($g=3$) than the
$F=2$ levels ($g=5$), this mechanism can invert the 1612 MHz line
Elitzur1976etal (34). However, at the low column densities identified in this
work ($N_{\rm OH}\lesssim 10^{15}{\rm cm}^{-2}$) this mechanism is generally
disrupted because the cascade from the second-excited rotational level becomes
optically thin. This disruption can then allow the 1720 MHz line to invert but
only weakly Elitzur1992 (33). At these low column densities the 1612 MHz line
is able to weakly invert ($|\tau_{\rm peak}|\lesssim 0.02$) in gas with low
number density (Petzler2020, 82, $n_{\rm OH}\lesssim 10^{3}$cm-3). Therefore
while we may speculate that the gas hosting the 1612 MHz inversion has a low
number density, the cause of the 1720 MHz inversions is less clear.

Overall, as noted by nearly all works who have measured all four OH ground-
rotational state transitions, it is much more likely for the satellite lines
to be inverted than the main lines. However, this trend becomes much less
significant when we consider only our sightlines observed with the ATCA. As
previously mentioned, these observations differ from our Arecibo observations
in two key ways: the locations of the sightlines were in the Plane towards the
Galactic centre, but were also analysed differently as they only consisted of
optical depth spectra. In addition, when we sub-divide our data set in this
way we become increasingly limited in our conclusions due to small sample size
effects. We therefore cautiously summarise that while non-LTE excitations of
OH (as primarily evidenced by the behaviour of the satellite line peak optical
depths) are clearly the norm in the diffuse ISM, these trends appear more
pronounced along sightlines toward the Galactic centre. Further, the precise
excitation mechanisms that dominate this non-LTE behaviour also appear to be
different towards the Galactic centre.

###  5.2 Comparison of OH and Hi CNM component parameters

A selection of the sightlines in this work with OH detections had previously
been observed in Hi absorption as part of the Millennium survey Heiles2003
(51). The CNM components from these sightlines (a total of 327 components)
were identified by Nguyen2019 (74) as part of the GNOMES collaboration, and
these are compared to our OH fits in Figs. 24 to 27 in the Appendix. In this
work we wish to draw comparisons between the properties of OH as obtained from
our fits and any associated CNM gas. We therefore attempted to match our OH
features (in velocity) to the CNM components identified by Nguyen2019 (74) for
each sightline. This was done via a by-eye comparison of the OH feature
centroid velocities to those of the CNM components identified by Nguyen2019
(74).

In all cases the FWHM of OH detections in this work overlapped in velocity
with the FWHM of Hi absorption features identified by Nguyen2019 (74). In many
cases (i.e. 4C+17.23 in Fig. 25, 4C+28.11 in Fig. 26) there is a clear
association between a given OH feature and an individual CNM component (i.e.
the two components line up in velocity with no other nearby features).
However, in other cases (e.g. 3C092 in Fig. 24, 4C+11.15 in Fig. 25) the
association with an individual CNM component is more ambiguous. In addition,
the process by which Nguyen2019 (74) fit the CNM components was restricted by
consideration of the complimentary Hi emission data and physical constraints
(i.e. spin temperature) on the resulting components (Heiles2003, 51, for
details see). Therefore at times the Hi CNM fits may be too conservative for a
feature-by-feature comparison with OH. For example the very high signal-to-
noise of the Hi data towards 3C131 (see Fig. 24) may justify a more complex
fit to the feature at 5 km s-1 which may yield better matches to the complex
OH fit from this work. Given the CNM fits as they are, we have several
instances where we must choose between one or more potential CNM components
for a given OH feature (e.g. 4C+17.41 in Fig. 25), in which case we used our
judgement to match either the closest component in velocity, or the more
narrow CNM component. Additionally, there were several instances where we
matched one or more OH component to the same CNM component (e.g. 4C+04.22 in
Fig. 24). This process resulted in a total of 43 matches between 43 OH
components and 26 Hi CNM components. These matches are summarised in Table 6.

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Figure 13: Left: relationship between line-of-sight integrated H2 column
density (found from $N_{\rm H_{2}}=10^{7}N_{\rm OH}$) and total H column
density (found from $N_{\rm H}=N_{\rm H\textsc{i}}({\rm CNM})+N_{\rm
H\textsc{i}}({\rm WNM})+2N_{\rm H_{2}}$) for each sightline with both OH and
Hi observations from this work (blue), and from Bellomi2020 (3). Right:
relationship between OH column density and Hi CNM column density for matching
OH and Hi features. The detection limits in both plots are estimated from the
$2\times$ rms noise in our optical depth data, the median excitation
temperatures determined from our sightlines with detections and a feature
width of 0.3 km s-1 (i.e. three times our typical channel width): grey arrows
indicate the upper limit, under which detections may be missing.

UV studies of H2 indicate that the molecular gas fraction $f_{\rm
H_{2}}=2N_{\rm H_{2}}/(N_{\rm H\textsc{i}}+2N_{\rm H_{2}})$ sharply increases
at a total gas column density of $N_{\rm H}=N_{\rm H\textsc{i}}+2N_{\rm
H_{2}}\approx 10^{21}$ cm-2 Savage1977 (90, 86, 40), at which point the total
Hi column density is expected to saturate in the Milky Way galaxy Reach1994
(87, 70, 28, 2, 59, 66) and in other galaxies Wong2002 (107, 7, 60, 106). At
this Hi column density (in solar metallicity environments) there is sufficient
dust shielding for H2 to persist. Beyond this limit any additional Hi will be
converted to H2.

Bellomi2020 (3) illustrated this transition in what they term a ‘kingfisher’
diagram, shown in the left panel of Fig. 13. Their data was a selection of
those included in Gudennavar2012 (48), and included direct measurements of H2
from UV absorption lines, thus was able to probe much lower molecular column
densities than this work. In Fig. 13 we show the data from Bellomi2020 (3) in
red which illustrate the atomic-to-molecular transition evident from N${}_{\rm
H}\approx 10^{20}$ to $10^{21}$cm-2. Also included in this plot (in blue) are
the results from this work. The total molecular column density per sightline
from this work was found from the sum of the column densities of individual OH
components along each sightline, then converted to $N_{\rm H_{2}}$ using the
relative abundance of OH to H2 of 10-7 Nguyen2018 (75), against total hydrogen
column density found from the sum of the column densities of all WNM and CNM
components (taken from Nguyen2018 (75)) along each sightline plus twice the
computed H2 column density. The detection limit of our data shown in Fig. 13
was estimated from the $2\times$ rms noise in our optical depth data, the
median excitation temperatures determined from our sightlines with detections
and a feature width of 0.3 km s-1 (i.e. three times our typical channel
width).

We can see from Fig. 13 that our detections represent lines of sight with
total $N_{\rm H_{2}}$ much higher than that at which the atomic-to-molecular
transition is seen to occur. Our detections also fall in a region of the
kingfisher plot where there is not a strong relationship between the molecular
and total column density. Therefore it is not surprising that we do not see a
relationship between $N_{\rm H_{2}}$ and $N_{\rm H}$ in our data. We also do
not see a relationship when we compare individual matched features’ Hi and OH
column densities, as illustrated on the right panel in Fig. 13.

There are some significant differences between Hi CNM components with
associated OH and those without. The histograms shown in Fig. 14 compare the
distributions of the Hi CNM components with an associated OH component (red)
and without such an association (blue) across Hi CNM peak optical depth and
column density. In both cases these two distributions differ significantly,
with components associated with OH tending towards higher values of both
parameters. The significance of these different distributions was measured via
the Kolmogorov-Smirnov test, which resulted in a p-value for the CNM peak
optical depth distributions of $3\times 10^{-6}$, and 0.02 for the column
density distributions.

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Figure 14: Normalised histograms showing the distribution of $\log_{10}$ peak
Hi CNM optical depth (left) and $\log_{10}$ Hi CNM column density (right) of
Hi CNM features found by Nguyen2019 (74) both with (red) and without (blue) a
matching OH component. Both sets of distributions differ significantly, with a
Kolmogorov-Smirnov p-value of $3\times 10^{-6}$ for peak Hi CNM optical depth,
and 0.02 for Hi CNM column density.

Though Fig. 14 implies that CNM clouds with higher peak optical depth or
column density are more likely to contain detectable OH, the lack of a clear
linear relationship between OH and CNM column density (see right panel of Fig.
13) does not imply that CNM clouds with higher peak optical depth or column
density contain more OH. Instead, these data suggest the existence of a
threshold CNM optical depth or column density under which any OH will not be
detected, but over which there is not then a linear relationship between how
much OH (and by extension, H2) will form. Again, this is consistent with the
findings of Bellomi2020 (3).

Focusing on this apparent tendency of OH to be more readily detectable in
clouds with higher peak Hi CNM optical depth or column density, we naturally
would like to establish if this is due to OH at lower peak Hi CNM optical
depth or column density being undetectable or whether it is due to it being
absent. In other words, is the apparent lack of OH ‘real’ or a symptom of our
sensitivity? Bearing in mind the complexities of detectibility discussed in
previous sections, generally speaking the strongest influence on whether or
not an OH feature is detected is the signal to noise ratio of the 1667 MHz
peak optical depth (which will in turn generally depend on the brightness of
the background continuum) as it tends to have the highest signal-to-noise
ratio of the 8 spectra comprising each sightline, followed by that of the 1665
MHz peak optical depth. Fig. 15 shows the relationships between these key
parameters that drive detectability (main-line optical depth) and Hi CNM peak
optical depth and column density. Detection limits are indicated by grey
vertical lines that connect the $\pm 2\sigma$ values for spectra for which a
match for a CNM component was not found (thus indicating the range for which
detections may be missing). We estimated the OH peak optical depth detection
limits to be approximately equal to twice the standard deviation of the noise
in the optical depth spectra based on the findings of Petzler2021a (83) that
for spectra with a signal-to-noise ratio of 2 Amoeba is able to recover 90% of
features present in on-off data.

From Fig. 15 there does not appear to be a trend of decreasing main-line peak
optical depths (and therefore decreasing detectablility) at lower peak Hi CNM
optical depth or column density. This is of course not definitive evidence
that the OH is absent as it is still possible that the pattern we see in Fig.
14 is a reflection of the detectability of the OH due to the complex nature of
the relationship between the abundance of OH (i.e. its column density) and its
optical depth. However, if we were to go so far as to assume that the
differences in the distributions with and without OH detections seen in Fig.
14 are real, we may attribute this to the shielding of the Hi gas: at higher
Hi CNM peak optical depth and column density molecular gas will be shielded