# First Extragalactic Detection of Thermal Hydroxyl (OH) 18cm Emission in M31
Reveals Abundant CO-faint Molecular Gas

Michael P. Busch Department of Astronomy & Astrophysics, University of
California, San Diego, 9500 Gilman Drive, San Diego, CA 92093, USA Michael P.
Busch<EMAIL_ADDRESS>
###### Abstract

The most abundant interstellar molecule, molecular Hydrogen (H2), is
practically invisible in cold molecular clouds. Astronomers typically use
carbon monoxide (CO) to trace the bulk distribution and mass of H2 in our
galaxy and many others. CO observations alone fail to trace a massive
component of molecular gas known as “CO-dark” gas. We present an ultra
sensitive pilot search for the 18cm hydroxyl (OH) lines in the Andromeda
Galaxy (M31) with the 100m Robert C. Byrd Green Bank Telescope. We
successfully detected the 1667 and 1665 MHz OH in faint emission. The
1665/1667 MHz line ratio is consistent with the characteristic 5:9 ratio
associated with local thermodynamic equilibrium (LTE). To our knowledge, this
is the first detection of non-maser 18cm OH emission in another galaxy. We
compare our OH and HI observations with archival CO (1-0) observations. Our OH
detection position overlaps with the previously discovered Arp Outer Arm in
CO. Our best estimates show that the amount of H2 traced by OH is 140% higher
than the amount traced by CO in this sightline. We show that the amount of
dark molecular gas implied by dust data supports this conclusion. We conclude
that the 18cm OH lines hold promise as a valuable tool for mapping of the “CO-
dark” and “CO-faint” molecular gas phase in nearby galaxies, especially with
upcoming multi-beam, phased-array feed receivers on radio telescopes which
will allow for drastically improved mapping speeds of faint signals.

Andromeda Galaxy (39); Radio astronomy (1338); Interstellar medium (847);
Interstellar clouds (834); Interstellar molecules (849)

††facilities: Robert C. Byrd Green Bank Telescope††software: astropy (The
Astropy Collaboration et al., 2013); scipy (Virtanen et al., 2020), lmfit
(Newville et al., 2014)

##  1 Introduction

The hydroxyl radical (OH) was the first molecule discovered in the radio
regime in absorption towards Cas A 60 years ago (Weinreb et al., 1963). There
was initial optimism at the time that OH would serve as a tracer for the bulk
of H2 in the galaxy. It was quickly discovered that this would be incredibly
difficult due to the complex excitation of the four $\Lambda$-doubling ground-
state lines (1612, 1665, 1667 and 1720 MHz), and the faintness of the emission
signal (Barrett, 1967). Surveys for OH in our own Galaxy revealed that
absorption measurements were far more successful than emission due to the
typically low excitation temperature (a few K above background continuum and
CMB) of the 18cm OH lines. The first major survey for OH was carried out by
Goss (1968) in absorption. Shortly after the discovery of OH 18 cm absorption,
Weaver et al. (1965) announced the detection of OH 18 cm emission. Surveys for
OH emission from the OH 18cm lines tended to be relatively faint and was
difficult to detect using the receiver technology of the time (Penzias, 1964),
although thermal (or “normal”) emission from OH was eventually announced
(Heiles, 1968). The discovery of the masing phenomenon of OH molecules
captured attention as a brighter target for observational OH work (Wilson &
Barrett, 1968; Baan & Haschick, 1987). Meanwhile, millimetre emission from the
CO molecule, first detected by Wilson et al. (1970) took over as the choice
tracer for H2 in the Galaxy, owing to its brightness and abundance (for a
review see e.g. Bolatto et al., 2013; Heyer & Dame, 2015).

Attempts to detect OH emission in external galaxies have historically
struggled with the weak strength of the signal and limitations of receiver
technology at the time. The first systematic search for OH in 63 nearby spiral
galaxies was led by Schmelz & Baan (1988) using the 305m Arecibo Observatory.
There was an early search for OH in the Large Magellanic Cloud (LMC) using the
Parkes 64m Telescope (Radhakrishnan, 1967). The detection of OH maser emission
from OH/IR stars in the LMC (Wood et al., 1986) prompted additional searches
for OH masers in the Magellanic clouds (Wood et al., 1992). The now well known
and incredibly bright OH megamaser phenomenon was first discovered in Arp 220
(Baan & Haschick, 1987), and was recently revisited with much higher angular
resolution data (Baan et al., 2023). A large absorption survey of OH in the
Magellanic systems is expected to be carried out by GASKAP this decade (Dickey
et al., 2013). A recent search for OH absorption using the FAST telescope by
Zheng et al. (2020) failed to detect any extragalactic OH absorption sources,
but placed stringent upper limits, and also reviewed the existing literature
on extragalactic OH absorption sources. Of note, one of the earliest searches
for extragalactic OH using the Effelsberg 100m telescope successfully observed
thermal OH in absorption in M82 (Nguyen-Q-Rieu et al., 1976). More recently,
masing 1720 MHz OH emission was detected in a galaxy at $z$ = 0.247 in the
MeerKAT Absorption Line Survey (Combes et al., 2021).

The recent renewed interest in searching for OH emission is partly due to the
utility of OH to trace the “CO-dark” molecular gas. It was originally
discovered by Wannier et al. (1993) that OH emission can arise at cloud edges,
where no corresponding CO emission was detected. The observational discovery
of “dark gas”, a massive diffuse ISM gas phase seemingly not traced by HI or
CO, but implied to exist by indirect total gas tracers like $\gamma$-rays and
dust (Grenier et al., 2005; Wolfire et al., 2010; Planck Collaboration et al.,
2011; Murray et al., 2018) prompted others to consider the OH emission as a
tracer for a diffuse molecular gas phase not traced by CO. The first modern
and sensitive blind search for OH emission from the quiescent ISM by Allen et
al. (2012) demonstrated that OH emission was ubiquitous, and commonly not
accompanied by CO emission. A wealth of research has also demonstrated the
existence of “CO-dark” molecular gas: the C[II]$\lambda$158um line has been
used to trace the “CO-dark” H2 (Pineda et al., 2013; Madden et al., 2020;
Chevance et al., 2020; Bigiel et al., 2020; Schneider et al., 2023),
simulations of molecular cloud formation and photodissociation region modeling
on cloud and galactic scales (Seifried et al., 2019; Nickerson et al., 2019;
Inoguchi et al., 2020; Skalidis et al., 2022), and molecular absorption of
other tracers such as CH (Jacob et al., 2019, 2021, 2022), HF (Kavak et al.,
2019), and HCO+ (Liszt et al., 2019; Rybarczyk et al., 2022; Liszt & Gerin,
2023).

Figure 1: The derived mass surface density map of dust from Draine et al.
(2014). The spectroscopic measurement of 18cm OH discussed in this paper is
shown at (J2000) $0^{h}39^{m}32^{s}$$+40^{\circ}26^{\prime}$ as a magenta open
circle, approximately 62’ from the nucleus, aligned with the major axis of the
galaxy. The yellow open circle is the sightline with a non-detection at
(J2000) $0^{h}40^{m}24^{s}$$+40^{\circ}28^{\prime}$.

The SPLASH survey mapped OH in the galactic plane with the Parkes 64m
telescope and greatly improved our understanding of the distribution of OH in
the Galaxy (Dawson et al., 2014). OH was widely observed in all four ground
state transitions. The OH profiles remain difficult to interpret because of
the low excitation temperatures and non-uniformity and brightness of the
continuum temperature towards the inner galaxy, leading to a mix of absorption
and emission profiles along the line of sight. However, a large amount of
observational knowledge concerning the anomalous excitation (Petzler et al.,
2020, 2021) and catalogs of OH masers have been generated (Dawson et al.,
2022).

The observational situation for OH is remarkably different towards the outer
galaxy, where the ambient radio continuum temperatures are uniformly low
(within 1K of TCMB). Faint OH emission (Tmb $<$ 0.05K) has been repeatedly
detected in sensitive blind OH emission surveys, which are usually in the
“main-line” LTE ratio (1665/1667, 5:9) (Allen et al., 2012, 2015; Busch et
al., 2019). The weaker “satellite” lines (1612, 1720 MHz, 1:1 ratio in LTE)
are routinely too faint to detect. In reality, there are commonly departures
from the LTE ratio in the satellite lines of interstellar OH. The 1720 MHz
line can sometimes be slightly anomalously emitting (Allen et al., 2015), even
if the main-lines are in the LTE 5:9 ratio. This behaviour may be tracing
shocks moving through the ISM leading to compression and increased collisional
excitation (Lockett et al., 1998), or be indicative of the slightly anomalous
ambient excitation temperatures of the satellite lines–as the SPLASH survey
observed widespread diffuse weakly-masing 1720 MHz emission, even across
entire clouds which are not near supernova remnants (Dawson et al., 2014).

Altogether, OH has been demonstrated to trace the “CO-dark” H2 in diffuse
clouds (Barriault et al., 2010; Cotten et al., 2012; Engelke & Allen, 2018,
2019; Allen et al., 2015; Busch et al., 2019), in the envelopes of giant
molecular clouds (Wannier et al., 1993), in absorption sightlines across the
sky (Li et al., 2015, 2018; Petzler et al., 2023), and more recently in a
thick “CO-dark” molecular gas “disk” of ultra-diffuse H2 (nH $\sim$ 5 $\times$
10-3 cm-3) in the outer galaxy (Busch et al., 2021). Potentially related,
broad faint HCO+ absorption coincident with HI absorption with no
corresponding CO emission or absorption was also recently discovered in
several sightlines (Rybarczyk et al., 2022). HCO+ and OH optical depths have
been shown to be tightly correlated in diffuse gas regimes (Liszt & Lucas,
1996). A similar discovery of very broad Galactic OH emission and HCO+
absorption was presented back in 2010 by Liszt et al. (2010) towards one
sightline.

We present here, to our knowledge, the first detection of thermal OH emission
in another Galaxy, M31. We stress that by “thermal”, we mean strictly that the
1665:1667 MHz emission is in the 5:9 LTE line ratio. The 1720 MHz line is
undetected, which is consistent with the LTE ratio. As the 1720 MHz line would
be nine times weaker than the 1667 MHz line with the LTE ratio, any such
emission would be below our current sensitivity limits. The 1612 MHz line is
not recovered because of radio frequency interference (RFI) at the Green Bank
Observatory. There is no evidence that the emission is caused by unresolved
masing sources in the beam, for which the line strengths would not be in the
LTE ratio.

##  2 Observations and Data

Table 1: GBT L-band (1.15-1.73 GHz) Observing Parameters Project Code | AGBT20A_556
---|---
Observing Dates | 2020-06-04 to 2020-07-21
Backend | VEGAS (Prestage et al., 2015)
Polarizations | X,Y (linear)
Spectral Windows | 4
Central Frequencies (MHz) | 1420.40, 1617.40, 1666.40, 1720.53
Pointing Source | 0114+4823
Bandwith (MHz) | 16.875
Spectral Resolution (KHz) | 1.03
Integration time per spectral dump (s) | 5
Beam Size (’) | 7.6

###  2.1 M31 Blind Pilot Survey Construction

We chose two positions in M31 to observe for OH 18 cm emission, at $\alpha$ =
$0^{h}39^{m}32^{s}$, $\delta$ = $+40^{\circ}26^{\prime}$ (J2000), and at
$\alpha$ = $0^{h}40^{m}24^{s}$, $\delta$ = $+40^{\circ}28^{\prime}$ (J2000).
Both of these positions are approximately 62’ from the nucleus, corresponding
to a distance from the center of $\sim 13$ kpc. This pilot survey was blind in
the sense that we did not point towards any previously known astronomical
object, such as HII regions, supernova remnants, a potential absorption
source, etc. The goal was to attempt to observe quiescent diffuse molecular
gas on a large physical scale. We did however choose these sightlines for
several other reasons. First, these sightlines contain relatively bright HI
emission, which may increase the likelihood of detecting an OH emission signal
at the same coordinates, since recent OH surveys in our Galaxy have
demonstrated that HI and OH brightness temperatures are correlated, at least
until the HI becomes optically thick (Allen et al., 2012, 2013, 2015; Busch et
al., 2021). Secondly, these two sightlines are spatially separated from the
bulk of the CO emission in M31, between 8-11 kpc, as presented in (Dame et
al., 1993) and any OH detections could be indicative of “CO-dark” or “CO-
faint” molecular gas at large galactic radii (Wannier et al., 1993; Grenier et
al., 2005; Wolfire et al., 2010; Li et al., 2015, 2018), giving us the
opportunity to learn more about molecular gas in regions of galaxies where
there is an absence of, or very faint, CO emission. Third, we wanted to
optimize the detectability of faint OH emission. The continuum temperature at
radio wavelengths is typically quite low at large galactic radii, just above
TCMB. Generally, this is below the observed range of excitation temperatures
of the OH lines ($\approx$ 4-10K) (Li et al., 2018; Engelke & Allen, 2018;
Petzler et al., 2023). Background continuum temperatures above this range
could result in a mix of absorption and emission in the main OH lines, or no
detections at all if the continuum temperatures become approximately equal to
the OH excitation temperature.

After 21.26 hours of the exploratory search program, faint OH emission was
significantly detected in the first planned sightline ($\alpha$ =
$0^{h}39^{m}32^{s}$, $\delta$ = $+40^{\circ}26^{\prime}$ (J2000), the magenta
aperture in Fig.1), which had the higher peak brightness temperature in HI
(Tmb = 30K). We then spent the rest of the observing time searching for OH in
a nearby sightline ($\alpha$ = $0^{h}40^{m}24^{s}$, $\delta$ =
$+40^{\circ}28^{\prime}$ (J2000), the yellow circle in Fig. 1) with the hope
of detecting OH in another position. The second sightline had a peak
brightness temperature in HI of Tmb = 13K. A total of 37.30 hours of
integration time was spent on this sightline; there was no statistically
significant detection of OH at 1665, 1667 or 1720 MHz. The lack of a secondary
OH detection implies that the OH detection in the primary sightline is not an
unknown instrumental effect of the telescope or receiver which might have
introduced a spurious signal. The spectra of both sightlines are shown in Fig
3.

###  2.2 Green Bank Telescope Observations

Observations were made with the Robert C. Byrd Green Bank Telescope (GBT)
located in West Virginia within the National Radio Quiet Zone, using the
Gregorian receiver system operating in the frequency band 1.15-1.73 GHz
($L$-band). Observing parameters are summarized in Table 1. We observed for
21.26 hours at $\alpha$ = $0^{h}39^{m}32^{s}$, $\delta$ =
$+40^{\circ}26^{\prime}$ (J2000) and for 37.30 hours at $\alpha$ =
$0^{h}40^{m}24^{s}$, $\delta$ = $+40^{\circ}28^{\prime}$ (J2000). The
observations took place from June 2020 to July 2020. The signal is fed to the
control by an IF system. The signal from the IF was copied and directed at 4
sections of the GBT spectrometer, centered on 1420.40 MHz, 1617.40 MHz,
1666.40 MHz, and 1720.530 MHz. In order to maximize on-signal observing time
we employed in-band frequency-switching by $\pm$2 MHz (O’Neil, 2002), such
that the expected science signal appears in both switching cycles, but in
different channel numbers. The spectra from both switching cycles are
therefore shifted and inverted before subtraction to average the science
signal from both switching cycles. The IF band width was 16.875 MHz, chosen in
order to minimize the possibility of harmful radio interference, and to make
it possible to observe the OH main line 1665 MHz and 1667 MHz spectra on the
same IF band. The frequencies observed also covered the OH satellite lines at
1612 MHz and 1720 MHz, although the 1612 MHz spectra suffer frequent transient
baseline ripples from radio interference. We simultaneously observed the HI 21
cm line at 1420 MHz. Each pointing is made up of a sum of multiple 10-minute
scans. The receiver is a single-beam, dual polarization instrument with an
effective system temperature in the range of 16 - 20 K, depending on the
weather, elevation of the pointing and background continuum emission. The FWHM
of the GBT point-spread function at 18 cm is 7.6’. The antenna efficiency of
the GBT in this frequency band is $\eta$ = 0.95, as determined by NRAO
staff111https://www.gb.nrao.edu/GBT/Performance/PlaningObservations.htm, hence
the antenna and main-beam brightness temperatures are virtually identical
($T_{mb}=T_{A}/0.95$). The pointing of the telescope was calibrated at the
start of each observing session. The GBT project number for the data presented
in this paper is AGBT20A_556.

###  2.3 Archival CO Data

We compare our OH observations with archival CO (1-0) observations taken with
the 1.2 m telescope at the Harvard Center for Astrophysics (CFA) (Dame et al.,
1993). This is the only available CO survey of M31 that has overlapping data
with our survey. This CO survey has observed all of M31 out to a radius of at
least 15 kpc and has a similar beamsize at 8.7’ to the GBT beam at OH (7.6’),
and it is extremely sensitive, at an rms of 18mk per 1.3 km/s channel. The
extraction position of the spectra is shown on the integrated CO map in Fig.
6.

###  2.4 Data Reduction

The HI observations are checked for RFI in each 10 minute scan and then
averaged together. A polynomial of order two is fit to 100 km/s on either side
of the HI signal and subtracted. The data are smoothed by Gaussian convolution
and decimated by 5 channels and the final velocity resolution is 1 km/s and
the root-mean-squre noise per channel is 4 mK. For the OH observations, each
10 minute scan in each linear polarization is reviewed for the presence of
interference or other instrumental problems. In general, there are no major
sources of radio frequency interference (RFI) near the 1667, 1665 or 1720 MHz
lines. Unfortunately there are large amounts of RFI near the 1612 MHz line,
which render it unusable.

Before smoothing and decimation, the noise is in the spectrum is approximately
5mK, the spectral resolution is 1.88 kHz corresponding to a velocity
resolution of 0.34 km/s. The resultant noise per channel is 0.4 mK at the
final chosen velocity smoothing of 3.88 km/s, which corresponds to a spectral
resolution of 22.24 kHz. The noise levels agree very well with the radiometer
equation for the integration times and channel bandwith, which is a good
confirmation that we are not overfitting the background in the signal-free
baseline regions.

After averaging all scans, the final spectra are smoothed by Gaussian
convolution, with decimation, by 27 channels to a velocity resolution of 3.88
km/s to decrease rms noise per channel. An order 4 polynomial baseline was
subtracted from the final baseline by fitting 100 km/s on either side of the
expected signal. The boundaries for the baseline fitting followed the extent
of the HI emission. This was done using the usual baseline fitting procedures
in GBTIDL, such at setregion, nfit and baseline (Garwood et al., 2006).

Initial inspection of the CO spectra at our detection position revealed a
broad CO signal coincident with the OH and HI spectra. This was determined to
be at least part of the previously discovered Arp Outer Arm S5 in CO in Dame
et al. (1993). We smoothed the CO signal with a convolution to a Gaussian
kernel and decimated by 3 channels to a corresponding velocity resolution of
1.7 km/s using scipy (Virtanen et al., 2020). This decreased the resulting rms
in the spectra to 3mK per 1.7 km/s channel. The reprocessing confirmed the
existence of broad, faint CO emission at the target position, with peak Tmb of
17 $\pm$ 3 mK. The original CO data and the reprocessed data and Gaussian fit
are shown in Fig. 5.

Figure 2: 21cm HI and three 18cm OH lines overplotted. The scale on the left
axis is for the OH data while the right is for HI. The OH spectra were
smoothed to 3.88 km/s per channel to achieve necessary S/N, whereas the HI
spectrum was smoothed to 1 km/s. The dashed line corresponds to $\pm$
1-$\sigma$ statistical noise, $\Delta$ Tmb $\sim$ 0.4mK. The steep drop off at
the edge of the bandpass at -650 km/s in the 1667 MHz spectra is an artifact
of baseline subtraction on the bandpass shape. Gaussian fits to each line are
overplotted in dashed lines with a 1-$\sigma$ confidence band. In the case of
the HI line, two Gaussian components were fit. The best fit parameters are
reported in Table 2.

##  3 Results

Our most significant result is the detection of thermal 18cm OH emission in
another galaxy for the first time, an optically thin radio wavelength tracer
of H2.

###  3.1 Features of the HI and OH Line Profiles

The observed HI and OH spectra from the GBT are displayed in Figure. 2. The
peak of the OH emission at 1667 MHz is 2.4 mK, whereas the peak of the 1665
MHz emission is is 1.5mK, close to the expected LTE ratio of the lines. The
1612 MHz line is unusable due to RFI at Green Bank. We do not detect any
emission, or absorption, in the 1720 MHz line. This is expected for LTE
conditions: if the 1720 MHz emission were in the LTE ratio (1:5:9:1 for
1612:1665:1667:1720 MHz), then the peak 1720 MHz emission would be buried in
the noise, as Tmb,1720 = $T_{mb,1667}$/9 $\sim$ 0.3 mK. As the rms noise per
channel is about 0.4 mK, it is consistent with the LTE interpretation for 1720
MHz emission to be absent at the sensitivity of the observations presented
here.

The statistical error in W(OH) is calculated as the square root of the number
of channels (Nchan $\sim$ 100) in the profile integral times the 1-$\sigma$
baseline rms. The rms is calculated by the stats routine in GBTIDL between
-900 km/s and -600 km/s (where no signal is present). Typical rms values
calculated this way are approximately 0.4 mK, with a slight dependence on the
order of baseline polynomial subtracted.

We analyze the HI and OH profiles by fitting a Gaussian profile to each line
to derive the following line parameters: peak brightness, line width, line
center, and their corresponding statistical uncertainties. We performed the
line integrals directly on the data which in practice is a sum of channels
multiplied by the channel width in km/s:

$\mathrm{W(OH)}=\sum T_{mb}\times\Delta V$ (1)

The Gaussian profiles are fit to the data using lmfit (Newville et al., 2014)
and the results are reported in Table 2. In the case of the HI profile, two
Gaussians are fit as it seems there is a narrow and broad component. The
central velocity and velocity dispersion of the lines are overall similar to
each other, indicating that the emission likely arises from gas that is
associated with each other. We do note that the broad component of HI is
offset from the peak of OH, whereas the the narrow component has the same
central velocity of the OH.

The integrated line emission values, W(OH), from -600 km/s to -500 km/s are
0.056 $\pm$ 0.008 K km/s and 0.039 $\pm$ 0.008 K km/s for the 1667 and 1665
MHz lines respectively. This corresponds to a S/N of 7 for W(OH1667) and 5 for
W(OH1665). In LTE, the ratio between the brightness temperatures vary between
1.8 for optically thin conditions to 1 for infinite optical depths (Tang et
al., 2017). The profile integrals of the OH 1667 and 1665 MHz lines appear to
be consistent in the LTE ratio as we calculate R = $\int\ T_{67}\ dv/\int\
T_{65}\ dv$ = 1.4 $\pm$ 0.34.

|
---|---
Figure 3: Both sightlines discussed in this paper. OH was detected at the
coordinates presented in the left panel. No significant OH signal was detected
in the right panel (the 1667 MHz line is shown). Both OH spectra were reduced
using the same procedures discussed in Section 2. The observed GBT HI spectra
for both positions are also overplotted. The dashed line corresponds to $\pm$
1-$\sigma$ statistical noise, $\Delta$ Tmb $\sim$ 0.4mK.

###  3.2 Column Densities of HI and OH

The beam-averaged column density of HI can be calculated in the optically thin
assumption by (e.g. Dickey & Benson, 1982). The optically thin assumption
leads to a lower limit for the HI column density. On the physical scale
discussed in this paper, this is likely a safe assumption and we are not
missing a large opaque fraction of HI. Under another assumption that the spin
temperature is much larger than the continuum background at 21cm (Ts $>>$ Tc),
the column density can be calculated directly from the measured $T_{b}$:

$N(\mathrm{HI})=C_{0}\ \int\Delta T_{b}(v)dv;$ (2)

where the constant $C_{0}$ is 1.82 $\times 10^{18}$ $\mathrm{cm^{-2}}$. The
beam-averaged column density, $N$(OH), along the line of sight is calculated
by (e.g. Liszt et al., 2010; Allen et al., 2012, 2015; Busch et al., 2019):

$N(\mathrm{OH})=C_{0}\left[\frac{T_{ex}}{T_{ex}-T_{c}}\right]\int\Delta
T_{b}(v)dv;$ (3)

where $\Delta T_{b}(v)$ is the (main beam) brightness temperature of the OH
emission profile from the cloud as observed in one of the 18-cm OH
transitions, minus an estimate of the underlying radio continuum brightness at
the same radial velocity, $T_{ex}$ is the excitation temperature for either
the 1667 or 1665 line, $T_{c}$ is the brightness of the continuum emission at
1666 MHz incident on the back surface of the cloud, and the integration over
velocity includes all the molecular emission thought to arise in that
particular cloud. The prefactor, Tex/Tex-TC is usually called the ’background
correction’ factor, and a larger contrast between Tex and TC would lower the
uncertainty in the column density correction. Unfortunately the excitation
temperatures for the 18cm OH lines are usually seen to have excitation
temperatures within a few kelvin of the background continuum temperature. The
observed range is usually between 4-10K with the typical values being around
4-5K. (Liszt & Lucas, 1996; Li et al., 2015; Petzler et al., 2023).

We require a reasonable measurement of the continuum temperature, Tc in order
to calculate the OH column density. The usual prescription is to find a
continuum survey at a similar frequency, assume a spectral index and
extrapolate to the continuum at 18cm (Nguyen et al., 2018). We use the 20.5cm
(1462 MHz) Effelsburg+VLA continuum survey of M31 presented in Beck et al.
(1998). Inspecting their Figure 4 continuum map, we adopt an average intensity
of 1 mJy/beam. Using the angular resolution of 45”, we transform this to
temperature and then use the following equation to calculate TC at 18cm (1666
MHz) assuming a standard spectral index of -2.8 (Nguyen et al., 2018):

$T_{c,1666}=T_{CMB}+T_{C,1462}(1666/1462)^{-2.8}$ (4)

This results in a TC of 3.28 K. The rms noise in the continuum map near the
map edges is stated to be $\approx$ 150 $\mu$Jy, and the corresponding error
in TC is negligible.

We have to assume an excitation temperature of the OH lines in the absence of
emission/absorption pairs or further information. The distribution of Tex
presented in Li et al. (2015), which samples diffuse absorption sightlines in
the Milky Way, is an appropriate starting point. We take Tex = 5K and 6K for
1667 and 1665 MHz lines respectively, as these lines have been shown to have
different excitation temperatures by about 1K (Engelke & Allen, 2018). The
limit in which Tex $>>$ TC is also a useful lower limit of $N$(OH). The
constant $C_{0}$ is $2.257\times 10^{14}$ cm-2 for the 1667 MHz line. The
value of $C_{0}$ for the 1665 MHz line is $4.0\times 10^{14}$ cm-2.

We compute the HI column densities for both fit Gaussian components
separately, we call broad and narrow corresponding to their fit velocity
widths (FWHM of 40.6 and 22.6 km/s respectively). Using the above quantities,
the computed HI column density is $N$(HIbroad) = 1.24 $\pm$ 0.01 $\times$ 1021
cm-2 and $N$(HInarrow) = 6.26 $\pm$ 0.01 $\times$ 1021 cm-2, where the error
is statistical. The column density of OH calculated from the 1667 MHz line is
$N$(OH) = 3.7 $\pm$ 0.4 $\times$ 1013. The column density calculated from the
1665 MHz line is $N$(OH) = 3.8 $\pm$ 0.7 $\times$ 1013 cm2, which is
statistically consistent with the 1667 MHz derived column density. We
calculate the abundance ratio of OH/HI as 6 $\times$ 10-8, where we use the
narrow component of the HI only.

Table 2: Gaussian Fit Parameters and Profile Integrals Towards Source M31-540 Line Description |  $v_{LSR}$ (km/s) | FWHM (km/s) | Tpeak (K) |  $W$ (K km/s) | S/N
---|---|---|---|---|---
HI 21cm (Narrow) | -544.09 $\pm$ 0.22 | 22.58 $\pm$ 0.77 | 14.32 $\pm$ 0.88 | 344 $\pm$ 32 | 10.75
HI 21cm (Broad) | -531.71 $\pm$ 0.71 | 40.61 $\pm$ 0.56 | 15.80 $\pm$ 0.72 | 683 $\pm$ 33 | 20.69
CO(J=1-0) | -548.44 $\pm$ 0.54 | 18.63 $\pm$ 1.28 | 0.017 $\pm$ 0.004 | 0.29 $\pm$ 0.02 | 14.5
OH 1667 MHz | -543.64 $\pm$ 0.94 | 24.15 $\pm$ 2.23 | 0.0024 $\pm$ 0.0004 | 0.057 $\pm$ 0.0077 | 7.3
OH 1665 MHz | -545.55 $\pm$ 1.84 | 24.54 $\pm$ 4.34 | 0.0014 $\pm$ 0.0004 | 0.040 $\pm$ 0.0079 | 5.7
OH 1720 MHz | -554.71 $\pm$ 4.80 | 22.77 $\pm$ 11.32 | 0.0009 $\pm$ 0.0004 | 0.00059 $\pm$ 0.0078 | 0.076

##  4 Discussion

Figure 4: HI, OH and CO for the sightline discussed in this paper, transformed
into proton (atomic hydrogen for HI, molecular hydrogen for OH, CO) column
density per channel (Np). We use the Galactic X(CO) value suggested from
Bolatto et al. (2013). The abundance ratio of
$N(\mathrm{OH})/N(\mathrm{{H_{2}}})$ = 1 $\times$ 10-7 was used to convert the
OH 1667 line to a proton column. This could also be labeled as hydrogen nuclei
column density per channel. We present two choices of Tex, where 5K is a
somewhat standard choice, and 10K can be considered a lower limit to OH column
densities, as most observed values of Tex for the 1667 MHz OH line fall
between 4-10K with an average value around 4-5K.

###  4.1 Comparing the Gas Mass Traced by HI, CO and OH

Recent studies have suggested a correlation between faint optically thin HI
and faint optically thin OH emission on large spatial scales (Allen et al.,
2012, 2013; Busch et al., 2021). A corollary was discussed in Allen et al.
(2012) from the data presented from that survey that related the main-beam
temperature of HI and OH (1667 MHz) as Tmb(OH) = 1.5 $\times$ 10-4 Tmb(HI),
with a scatter of 3mK. This relation seems to hold for Tmb(HI) $<$ 60K, above
which the HI saturates, but OH temperature continues to rise because it
remains optically thin. As discussed in section 2, this relation guided our
exploratory search. The relationship predicts a peak OH signal of 2.6 $\pm$ 3
mK in the sightline without a detection, which is consistent with no signal,
so perhaps this is not surprising. The sightline with the OH detection was
chosen because the predicted peak signal here is 5.3 $\pm$ 3mK. In building
further extragalactic OH searches, this relationship should be consulted and
refined. It is especially unknown how this relationship differs with
metallicity, which should be a topic of further research.

In order to compare the gas masses traced by HI, CO and OH, we must first
adopt suitable conversion factors for each gas tracer. For OH, we need the
abundance ratio of OH/H2 to convert our $N$(OH) to $N$(H2). In this diffuse
molecular gas regime we can start by adopting a reasonable estimate for the
value for the OH/H2 abundance ratio. We adopt the median literature value of 1
$\times$ 10-7 (Liszt & Lucas, 1996; Wiesemeyer et al., 2016; Rugel et al.,
2018; Jacob et al., 2019). While chemical model calculations tend to produce
abundance ratios of varying values over a range of cloud parameter space
(8$\times 10^{-9}$ to 4$\times 10^{-6}$), observations of the abundance ratio
cluster fairly tightly around 1 $\times$ 10-7 (Nguyen et al., 2018). Given the
size of the resolution element, the median literature value for the ratio is
likely a fair approximation because we are averaging over many different
environments. This value for the abundance ratio appears to hold for
$N(\mathrm{OH})$ values as low as $\sim$ a few $\times$ 1012 cm-2 (Jacob et
al., 2019). Most of the literature values were derived for local, solar
metallicity gas. The metallicity in M31 at the galactic radius discussed here
($\sim$ 13 kpc) is statistically consistent with solar metallicity (Sanders et
al., 2012). Note here also that we do not correct by the inclination of the
galaxy, so values are beam-averaged along the line of sight.

As OH is almost always optically thin, we can directly calculate the column
density and transform this into a column of H2. Using the updated Cepheid
distance to M31, $D=761\pm 11$ kpc Li et al. (2021). Then we can calculate the
total mass in the enclosed beam via the equation:

$M_{\mathrm{H_{2}}}=N(\mathrm{H_{2}})\ A_{\mathrm{H_{2}}}\mu\ m_{\mathrm{H}}$
(5)

where $N(\mathrm{H_{2}})$ is the traced H2 column. A${}_{\mathrm{H_{2}}}$ is
the physical area covered by the GBT beam (which is related to the GBT solid
angle and distance to M31 by: A${}_{H_{2}}$ = $\Omega\ d^{2}$), $\mu$ is the
molecular weight which we set to 2 and for now ignore contribution to the mass
by helium, and mH is the weight of the hydrogen atom.

The variation of Tex in diffuse clouds has been observationally constrained;
the distribution of Tex as presented in Li et al. (2018) is a good starting
assumption when we lack coincident absorption and emission profiles. In
addition, there was the recent determination of Tex = 5.1 $\pm$ 0.2K in front
of the W5 star forming region using the novel ’continuum background’ method
(Engelke & Allen, 2018). Since we detect emission, we know that Tex has to be
higher than the continuum temperature in this region, 3.28K. We therefore take
a range of Tex = 5 $\pm$ 0.5K as a sensible approximation. The approximation
of Tex $\gg$ Tc is also a suitable lower limit to the OH column density as the
background correction factor goes to unity.

We calculate the inferred N(H2) column density for this sightline from the CO
data. The CO-derived N(H2,CO) is 5.8 $\pm$ 0.4 $\times$ 1019 using the typical
value of X(CO) of $2\times 10^{20}$ (Bolatto et al., 2013).

The mass of $H_{2}$ traced by OH is then 1.1-1.6 $\times$ 107 M⊙, with the
range arising from the choice of Tex between 4.5-5.5 K. For comparison, the
amount of mass traced by HI in this same sightline is 3.3 $\pm$ 0.01 $\times$
107 M⊙, the error in the HI calculation is statistical. These estimates
suggest there is about 3 times more atomic mass than molecular mass in this
sightline. If we were using CO data alone, the same estimate would suggest
that there is 15 times more atomic mass than molecular. Transforming all gas
tracers to physical units (proton column density per channel, or hydrogen
nuclei per channel) is demonstrated in Fig.4. This exercise gives a
visualization on the range of “CO-faint” (we say “faint” here as opposed to
“dark” because CO is detected) molecular gas that is traced by OH, which is
dependent on the assumed Tex.

###  4.2 Calibration of OH/H2 by Dust Emission on kpc Scales

We can use dust data available on M31 to estimate the total neutral gas column
density (Nguyen et al., 2018) to calibrate the abundance ratio of OH/H2. The
procedure for calibrating the abundance ratio in this way is as follows: first
we obtain an estimate for the dust mass in our observed region (Md), apply a
dust-to-gas mass ratio (Md/MH) to obtain an estimate of the total hydrogen gas
mass, subtract the contribution of the gas mass by atomic hydrogen (as
measured from the $N$(HI) data), and then assume the residual amount of gas
mass is molecular. We use the dust models of dust emission from Draine et al.
(2014) to calculate this quantity. Usually, this calibration is done on much
smaller spatial scales than we are discussing here (Nguyen et al., 2018), but
since we are averaging over many different environments we may be averaging
over dust systematics as well. The diameter of our resolution element is 1.67
kpc at the distance of M31 (Li et al., 2021), resulting in an area of 2.2
kpc2. We obtain the dust map shown in Fig.1 and measure the median dust
surface mass density in an aperture the size of the GBT beam (7.6’) at our OH
detection coordinates. We correct the map to the updated Cepheid distance of
$D=761\pm 11$ kpc (Li et al., 2021), which introduces a small correction by a
few percent.

The resulting median dust surface mass density in the aperture is 2.5 $\times$
105 M⊙/kpc2. We use the Md/MH prescription from Equation 8 in Draine et al.
(2014) for our distance from the the center of M31 of 13 kpc. We divide the
dust surface mass density by this ratio (0.0079) to obtain the gas surface
mass density and further divide by the proton mass to obtain NH, the column
density of hydrogen nuclei. This procedure results in a NH of 4 $\times$ 1021
cm-2. We then use the corresponding HI column density (uncorrected for optical
depth effects, as the correction from Braun et al. (2009) seemed to
overestimate HI as it was incompatible with the gas mass predicted by dust by
an order of magnitude) from the Braun et al. (2009) HI map, as the dust map
from Draine et al. (2014) used this map to infer their dust models. The HI
column density, N(HI), measured in the same aperture towards the OH detection
coordinates is approximately 3 $\times$ 1021 cm-2. We then subtract this from
the total hydrogen nuclei column density inferred from dust (NH), and assume
the rest of the hydrogen nuclei is molecular (H2). This results in a N(H2) of
5 $\times$ 1020 cm-2. Finally, we can calibrate the N(OH)/N(H2) abundance
ratio with this result. The corresponding values for Tex = 5, 10K are 1
$\times$ 10-7 and 4 $\times$ 10-8 respectively. These results are consistent
with the range of literature values and seem to assure us our assumed value of
1 $\times$ 10-7. We should also consider if there is a correction for opaque
HI inside the beam, at large galactic radii the correction for optically thick
HI is expected to be quite low(Koch et al., 2021), and optically thick HI has
not been able to reconcile the observed mass of “dark gas” previously (Murray
et al., 2018). As a check, a generous 30$\%$ correction to the N(HI) used to
subtract from the dust results in a N(H2) of 7.6 $\times$ 1019 cm-2 and a
abundance ratio of 7 $\times$ 10-8, which is still consistent with literature
values of the abundance ratio.

##  5 Conclusion

We have detected statistically significant extragalactic emission from faint,
thermal (non-maser, LTE-like) interstellar OH for the first time. The emission
is detected in the southern disk of M31 using ultra sensitive GBT observations
towards one sightline aligned with the major axis, $\sim$ 62’ from the nucleus
of the galaxy. A non-detection is also presented which suggests that the
detection presented is not an otherwise unknown instrumental artifact. The
velocity structure of the OH follows closely that of the narrow HI component
and broad faint CO, implying the existence of molecular gas on the same
spatial scale as the atomic gas traced by a portion of the HI. We derived
Gaussian line profile parameters to the observed OH and HI data. We also
calculated the profile integrals of the OH 1667 and 1665 line and found that
they are in the LTE ratio. We compared the OH data with archival CO data from
(Dame et al., 1993). The corresponding estimates for H2 column density traced
by CO is 5.8 $\pm$ 0.4$\times$ 1019 using the standard X(CO) conversion with
the estimated 30% error (Bolatto et al., 2013). OH appears to trace 140% more
than CO in the same sightoine. When we use dust as a total neutral gas column
tracer we calibrate the OH/H2 abundance ratio between 1 $\times$ 10-7 and 4
$\times$ 10-8 respectively, the range arising from the choice of excitation
temperature.

Single dish radio telescopes with ample observing time at cm wavelengths (cm
observations can normally be completed in any weather and any time of day)
could systematically map the distribution of the 18cm OH emission in local
group galaxies at large galactic radii, where the continuum temperature is
only slightly above $T_{CMB}$. On the other hand, we may also expect to map
out the absorption of 18cm OH towards the inner disks of these galaxies due to
increased synchotron emission, which can be interpreted under slightly
different assumptions. While CO will undoubtedly remain our brightest general
tracer of H2 in the Galaxy and beyond, mapping OH will drastically improve our
understanding of the distribution and mass of the “CO-dark” gas phase. Single-
beam L-band (cm) instruments would potentially require a prohibitive amount of
time to survey local group galaxies at the 18 OH. New multi-beam phased array
feeds (e.g. Roshi et al., 2018; Pingel et al., 2021) will drastically improve
mapping speeds for large single-dish telescopes by orders of magnitude. In the
near future, these instruments will be able to map the distribution of 18cm OH
to trace the “CO-dark” gas, as long as sufficient sensitivities are achieved
(Trms $<$ 1mK). The amount of molecular gas revealed by these new OH
observations are significant, between 140% more than the CO in this sightline.
These estimates are similar in magnitude to the “CO-dark” gas estimates from
$\gamma$-ray observations (Grenier et al., 2005) in the Milky Way’s halo. It
is still unclear if such a correction could be appropriately applied to the
current CO maps of M31 and more observations are warranted. Mapping the
distribution of OH would complement existing CO maps in the local group to
help accurately understand the total accounting of the molecular phase of the
ISM.

Michael P. Busch is supported by an NSF Astronomy and Postdoctoral Fellowship
under award AST-2202373. We would like to thank Tom Dame for delivering the
M31 CFA CO data in a digital format in private communication. We would also
like to thank long-time collaborators Dave E. Hogg and Philip Engelke for
sharing insightful scientific conversations and discourse. We want to thank
and remember the late Ronald J. Allen for their mentorship and for the initial
conception of this experiment. Thanks to the Allen family for their kindness
and support. We would like to thank Karin Sandstrom and Josh Peek for
comments, suggestions and guidance. We would also like to thank Joanne Dawson,
Anita Petzler, David Neufeld, Michael Rugel, and Arshia Jacob for lively
conversations about the OH molecule, its excitation mechanisms and how to
observe it. The authors acknowledge Interstellar Institute’s programs “II4”,
“II5”, and “II6” and the Paris-Saclay University’s Institut Pascal for hosting
discussions that nourished the development of the ideas behind this work.

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##  Appendix A Archival CO Data

In this appendix we present the archival CO data, both the spectrum of the
original and reprocessed data, and the approximate location of the extraction
from the original CO data cube, which in the coordinates used of Dame et al.
(1993) are approximately at $X$,$Y$ = [-62.4’, 1.8’], where these are offsets
from the center of M31. These offsets were calculated by calculating the
offset from the Arp Outer Arm S5 to the OH detection source coordinates. The
location of the Arp Outer Arm S5 in CO at $X$,$Y$ = [-63’, 0’] (Dame et al.
(1993), Table 1), is calculated with a directional offset of 63’ to the J2000
center of M31 at a position angle of $\theta$ = 37.7∘. There is an offset of
approximately $\sim$ 2’ to the NW as defined in Dame et al. (1993). While
offset from the CO peak at the Arp Outer Arm S5, it still lies within the GBT
beam. The results from the Gaussian fit to the CO data are reported in Table
2.

Figure 5: The original CO spectrum extracted from the M31 CFA CO data cube
(Dame et al., 1993) with the reprocessed spectrum overplotted. The dashed
horizontal black lines represent the 1-$\sigma$ rms of noise of 0.003K. The
dashed red line is a Gaussian fit to the reprocessed data, the Gaussian fit
parameters are reported in Table. 2. Figure 6: The integrated CO map from Dame
et al. (1993) with the position of the OH detection sightline highlighted with
the magenta aperture. The white aperture is the location of the Arp Outer Arm
S5, previously discovered in CO, which coincides with our OH detection. The
aperture is approximately the beamsize of the GBT (7.6’), where the CO
spectrum from Fig. 5 is extracted from. The $X$ and $Y$ are rectangular
offsets from $\alpha$ = $0^{h}40^{m}$, $\delta$ = $+41^{\circ}$ (1950), with
$X$ increasing toward the northeast along the major axis of M31 at a position
angle of 37.7∘.