# COMAP Galactic Science I: Observations of Spinning Dust Emission at 30 GHz
in Dark Clouds Surrounding the $\lambda$-Orionis Hii Region

Stuart E. Harper,$\\!{}^{1}$, Clive Dickinson,$\\!{}^{1}$ Kieran A.
Cleary,$\\!{}^{2}$ Brandon S. Hensley,$\\!{}^{3}$ Gabriel A.
Hoerning,$\\!{}^{1}$ Roberta Paladini,$\\!{}^{4}$ Thomas J.
Rennie,$\\!{}^{1,5}$ R. Cepeda-Arroita,$\\!{}^{1}$ Delaney A.
Dunne,$\\!{}^{2}$ Hans Kristian Eriksen,$\\!{}^{6}$ Joshua Ott
Gundersen,$\\!{}^{7}$ Håvard T. Ihle,$\\!{}^{6}$ Jonas G. S.
Lunde,$\\!{}^{6}$Roberto Ricci,$\\!{}^{8}$ Jeroen Stil,$\\!{}^{9}$ Nils-Ole
Stutzer,$\\!{}^{6}$ A. R. Taylor,$\\!{}^{10,11,12}$ Ingunn Kathrine Wehus6
1Jodrell Bank Centre for Astrophysics, Department of Physics & Astronomy, The
University of Manchester,
Oxford Road, Manchester, M13 9PL, U.K.
2California Institute of Technology, 1200 E. California Blvd., Pasadena, CA
91125, USA
3Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove
Drive, Pasadena, CA 91109, USA
4Infrared Processing Analysis Center, California Institute of Technology,
Pasadena, CA 91125, USA
5Department of Physics and Astronomy, University of British Columbia,
Vancouver, BC Canada V6T 1Z1, Canada
6Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029
Blindern, N-0315 Oslo, Norway
7Department of Physics, University of Miami, 1320 Campo Sano Avenue, Coral
Gables, FL 33156
8Instituto di Radioastronomia, Bologna, Via Gobetti 101, I-40129, Italy
9Department of Physics and Astronomy, University of Calgary, Alberta, Canada
10Inter-University Institute for Data Intensive Astronomy, Cape Town, South
Africa
11Department of Astronomy, University of Cape Town, South Africa
12Department of Physics and Astronomy, University of the Western Cape, South
Africa E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Anomalous Microwave Emission (AME) is a major component of Galactic emission
in the frequency band 10–60 GHz and is commonly modelled as rapidly rotating
spinning dust grains. The photodissociation region (PDR) at the boundary of
the $\lambda$-Orionis Hii region has been identified by several recent
analyses as one of the brightest spinning dust emitting sources in the sky. We
investigate the Barnard 30 dark cloud, a dark cloud embedded within the
$\lambda$-Orionis PDR. We use total-power observations of Barnard 30 from the
CO Mapping Array Project (COMAP) pathfinder instrument at 26–34GHz with a
resolution of $4.\\!^{\prime}5$ alongside existing data from Planck, WISE,
IRAS, ACT, and the 1.447 GHz GALFACTS survey. We use aperture photometry and
template fitting to measure the spectral energy distribution of Barnard 30. We
find that the spinning dust is the dominant emission component in the 26–34GHz
range at the $7\,\sigma$ level ($S_{30\mathrm{GHz}}=2.85\pm 0.43$ Jy). We find
no evidence that polycyclic aromatic hydrocarbons are the preferred carrier
for the spinning dust emission, suggesting that the spinning dust carriers are
due to a mixed population of very small grains. Finally, we find evidence for
variations in spinning dust emissivity and peak frequency within Barnard 30,
and that these variations are possibly driven by changes in dust grain
population and the total radiation field. Confirming the origin of the
variations in the spinning dust spectrum will require both future COMAP
observations at 15 GHz combined with spectroscopic mid-infrared data of
Barnard 30.

###### keywords:

radio continuum: ISM – infrared: ISM – radiation mechanisms: general – ISM:
clouds – ISM: photodissociation region

††pubyear: 2024††pagerange: COMAP Galactic Science I: Observations of Spinning
Dust Emission at 30 GHz in Dark Clouds Surrounding the $\lambda$-Orionis Hii
Region–A

##  1 Introduction

Anomalous microwave emission (AME) refers to an excess emission at microwave
frequencies that correlates with thermal dust emission at higher frequencies
(see Dickinson et al., 2018, for a review). It was first detected several
decades ago as a new foreground by CMB experiments (Kogut et al., 1996; Leitch
et al., 1997). Since then, AME has been detected from a range of environments,
including dark clouds (e.g., Casassus et al., 2006; Harper et al., 2015; Vidal
et al., 2020), Hii regions (Dickinson et al., 2007; Tibbs et al., 2012a;
Rennie et al., 2022), cirrus dust clouds (Hensley et al., 2016; Harper et al.,
2022), photo-dissociation regions (PDRs) (Casassus et al., 2008), and many
other regions within the Galaxy (Planck Collaboration et al., 2014a; Poidevin
et al., 2023). AME has also had several detections in other galaxies (Murphy
et al., 2010; Hensley et al., 2015; Harper, 2024). The leading model suggests
that AME is generated by the rapid rotation of very small dust grains,
proposed as the spinning dust model by Draine & Lazarian (1998, 1999), and
later refined by the publicly available SpDust code (Ali-Haïmoud et al., 2009;
Silsbee et al., 2011). The exact carrier for spinning dust emission is still
unknown. Polycyclic aromatic hydrocarbons (PAHs) were initially favored as a
carrier due to their prevalence in the interstellar medium (ISM) and being of
the correct physical size needed to produce the observed spectrum (Draine &
Lazarian, 1998). However, there is no strong observational evidence for PAHs
being the favored carrier, implying that spinning dust could be generated by a
continuum of very small dust grains (VSGs), nanograins (Hoang & Lazarian,
2016; Hensley et al., 2016; Ysard et al., 2022), or nanodiamonds (Greaves et
al., 2018), which could be both carbonaceous and silicate in nature.

$\lambda-$Orionis is an O8 III type star in the Collinder-69 cluster that is
surrounded by a well-studied Hii region (Sharpless, 1959) characterised by a
bright radio/optical ionised region at the center surrounded by a prominent IR
photodissociation region (PDR) (Maddalena & Morris, 1987; Lang et al., 2000).
The $\lambda$-Orionis association, located approximately 400 pc away, is
thought to have formed around 5 Myr ago (Murdin & Penston, 1977). The angular
diameter of the $\lambda$-Orionis Hii region is approximately $5^{\circ}$,
making it an ideal target for several low-resolution spinning dust emission
studies (Planck Collaboration et al., 2014a; Bell et al., 2019; Cepeda-Arroita
et al., 2021; Chuss et al., 2022) that found spinning dust to be the dominant
emission mechanism around 30 GHz. The question of the carrier for spinning
dust in this region remains open. PAHs were preferred by the Bayesian analysis
conducted by Bell et al. (2019), while correlations between maps of spinning
dust emission derived from the Planck commander analysis (Planck Collaboration
et al., 2016b) and a map of the $3.3$ $\mu$m PAH feature from COBE/DIRBE data
disfavored PAHs (Chuss et al., 2022). However, these studies were limited to
observations at 1 degree scales, often masking out the brightest spinning dust
regions within the PDR. Fully characterizing the origin of spinning dust
emission within the $\lambda$-Orionis PDR requires arcminute-resolution
observations that can resolve individual clouds.

Figure 1: Location of the Barnard 30 (B30) dark cloud within the
$\lambda$-Orionis PDR. The image is a three-colour composite of the IRAS 100
$\mu$m (red), 60 $\mu$m (green), and 25 $\mu$m (blue) data, smoothed to
$6^{\prime}$ resolution. The location of the $\lambda$-Orionis star is
indicated by the white star. The inset image shows a zoomed in view of the B30
region that was observed by COMAP. The image has dimensions of
$12.\\!\\!^{\circ}5\times 12.\\!\\!^{\circ}5$. The colour map of the image has
had an arcsinh stretch applied.

We use dedicated observations by the CO Mapping Array Project (COMAP)
pathfinder instrument to observe a section of the PDR around $\lambda$-Orionis
at a resolution of $4.\\!^{\prime}5$, between 26 and 34 GHz. The observations
are centred upon the dark cloud Barnard 30 (B30; Dolan & Mathieu, 2001; Koenig
et al., 2015). Figure 1 indicates the location of B30 within the
$\lambda$-Orionis ring as seen in the IRAS 100 $\mu$m map, which is a good
tracer of warm $(T\sim 20$ K) dust. The B30 region was first proposed as a
spinning dust emission candidate by Planck (Planck Collaboration et al.,
2014a), and later confirmed by Cepeda-Arroita et al. (2021) when including 5
GHz C-BASS data. B30 is a bright-rimmed cloud with a PDR facing towards the
$\lambda$-Orionis star. Numerous AME observations have identified PDRs as
strong sources of spinning dust emission (e.g., Casassus et al., 2008), and
the strong environmental variations throughout a PDR make them an excellent
laboratory for the study of variations in spinning dust emissivity with dust
grain population using high resolution radio observations.

This paper is structured as follows: In section 2 we describe the COMAP survey
and all ancillary data used; in section 3 we describe the aperture photometry
method used to measure the integrated flux density of the cloud; in section 4
we describe how template fitting is used to decompose B30; and in section 5 we
present our conclusions.

##  2 Data

In the following sections we describe the COMAP instrument and observations,
and all of the ancillary data used for this analysis. All data are smoothed to
a common resolution of $6^{\prime}$ full-width half-maximum (FWHM).

###  2.1 COMAP

The COMAP instrument is a spectroscopic radiometer with a spectral resolution
of $\sim 2$ MHz between 26 and 34 GHz. The front-end of the instrument
consists of 19 closely-packed left-hand polarised circular feed horns. It is
fielded on a 10.4 m Cassegrain design telescope based at the Owens Valley
Radio Observatory (OVRO) that was previously used as part of the CARMA
experiment (Leighton, 1977). The telescope has a FWHM of $4.\\!^{\prime}5$ at
30 GHz, with optics designed to ensure that the FWHM varies by less than $\pm
4$ per cent across the COMAP band. Each feed horn is separated on the sky by
$12.\\!^{\prime}04$, resulting in 19 simultaneous and independent observations
of the sky.

A single circular polarization of the incoming radiation is amplified by a
cooled low-noise amplifier, then down-converted at ambient temperature before
being split into two 4 GHz bands. These 4 GHz bands are then digitised and
passed to two ROACH-2 spectrometers (Parsons et al., 2008) which perform
sideband separation. For each feed, we obtain four 2 GHz wide sidebands,
sampled once every 20 ms. More details on the COMAP instrument can be found in
(Lamb et al., 2022).

We generally employ the same data reduction methods used in the first COMAP
Galactic science release (Rennie et al., 2022). Here, we provide a brief
overview of the data analysis pipeline and any modifications made. The COMAP
data are initially calibrated by covering the focal plane with a microwave-
absorbing vane of known temperature at the beginning and end of each
observation ($\sim 1$ hour). Subsequently, the data are calibrated onto the
astronomical brightness temperature scale using daily measurements of the
supernova remnants Taurus A (Tau A) and Cassiopeia A (Cas A), along with the
brightness models supplied by the WMAP 7-year release (Weiland et al., 2011).
The overall calibration uncertainty is $3.2\pm 0.1$ per cent.

Following the approach of Rennie et al. (2022), we subtract the mean
atmospheric brightness using an atmospheric slab model and apply a running
median filter to the data. In contrast to the main Galactic science analysis,
we have also implemented a novel continuous-gain correction algorithm capable
of mitigating $1/f$ noise fluctuations by fitting system temperature templates
to each time sample. This method enhances the sensitivity of a substantial
portion of the COMAP continuum data by a factor of two or more. We defer
detailed discussion of this algorithm to a future COMAP publication (Lunde et
al., in prep). The COMAP spectroscopic data for this analysis are averaged
into four 2 GHz bands with central frequencies of 27, 29, 31, and 33 GHz.
Lastly, the final maps are created using an implementation of the destriping
map-making algorithm (e.g., Delabrouille, 1998; Sutton et al., 2010), which is
the same implementation used for the Galactic science data (Rennie et al.,
2022).

###  2.2 COMAP Observations of Barnard 30

Figure 2: Overview of the target B30 cloud at the edge of the
$\lambda$-Orionis Hii region as seen in the COMAP 27 GHz data, smoothed to
$6^{\prime}$. The green region (Full) indicates the region defined as the main
cloud as seen in COMAP, while regions A and B indicate the smaller sub-region
hotspots, respectively. Regions C and D are smaller nearby dust clouds that do
not share the same spectrum as the bulk of the cloud, these are discussed in
section 3. We also mark the location of QSO J030+13, a QSO within the field
and which is discussed in Appendix A. The black arrow indicates the direction
of the central ionizing $\lambda$-Orionis star.

The observed field was a $3\times 3$ deg2 region centred on LDN 1582111R.A.
and Declination of 05:32:00.3, +12:30:28, a dark cloud within Barnard 30. For
the purposes of this analysis, when referring to B30 we mean the entire region
indicated within the inset image of Figure 1, which we break up into several
sub-regions. References to $\lambda$-Orionis refer to both the stellar
association and the larger $\lambda$-Orionis PDR within which B30 is embedded.
Observations were taken between May 2020 and December 2022. The field was
observed for approximately 270 hours. After removing bad observations due to
the proximity of the Sun, bad weather, or instrumental issues we were left
with a total 200 hours of good data. We used the same Lissajous scanning
strategy as for the Galactic plane observations; more details on the scanning
strategy and its benefits are given in (Rennie et al., 2022).

Figure 2 shows the COMAP 27 GHz data smoothed to $6^{\prime}$ to reduce
background noise. The field covers the entire B30 cloud plus one nearby radio
source, QSO J030+13 (see Appendix A for the measured flux densities of this
source at 26–34 GHz). The black arrow indicates the direction of the
$\lambda$-Orionis O8 III type star in Collinder-69 cluster. The apertures
indicate the sub-regions that were used to divide up the data, the details of
which are discussed in section 3.

The white-noise sensitivity of the COMAP maps is approximately 50$\,\mu$K/beam
($\approx 2$–3 mJy/beam) at a resolution of $4.\\!^{\prime}5$ in all the 27 to
33 GHz maps. However, the noise is dominated primarily by large-scale
systematics errors in the data that are mitigated using destriping map-making
and a map-based median filter with a kernel size of $1^{\circ}$ (much larger
than the B30 cloud). In general we will use the COMAP 27 GHz band as the main
dataset for this analysis as the peak brightness temperature of the signal at
27 GHz is approximately 50 per cent higher than in the 33 GHz band.

###  2.3 Ancillary Data

We utilise the Planck satellite mission PR3 data release (Planck Collaboration
et al., 2020), which can be accessed via the Planck Legacy
Archive222http://pla.esac.esa.int/pla. We use the Planck bands between 217 and
857 GHz, all smoothed to a common resolution of $6^{\prime}$ to match the
smoothed COMAP data. We do not use the LFI bands, specifically the Planck 28.4
GHz data, as the resolution of this data set is limited to
$32.\\!^{\prime}4$—too coarse to make a direct comparison with the COMAP data
despite the frequency overlap. All the Planck maps were reprojected from a
HEALPix grid (Górski et al., 2005) to a regular Cartesian grid.

We traced the ionised gas associated with $\lambda$-Orionis using both radio
and H$\alpha$ data. The radio data comes from the Galactic Arecibo L-band Feed
Array Continuum Transit Survey (GALFACTS), which was an L-band transit survey
taken between December 2008 and September 2015 using the ALFA receiver
(Taylor, 2013). We used band-averaged GALFACTS data that have an effective
central frequency of 1447 MHz and a resolution of $3.\\!^{\prime}35$. We also
subtract from the GALFACTS map all of the point sources within the field found
in the NRAO VLA Sky Survey (NVSS) catalogue (Condon et al., 1998). We subtract
the background radio sources as we only want to use the GALFACTS data as a
tracer of the radio free-free emission at the COMAP frequencies.

The H$\alpha$ data come from the Virginia Tech Spectral-Line Survey (VTSS)
(Dennison et al., 1998). H$\alpha$ emission is a tracer of ionised gas, and
can be directly related to the brightness of the radio free-free continuum
emission (Draine, 2011). We do not directly use the H$\alpha$ data in this
analysis due to significant dust extinction, but they are used to verify the
observed GALFACTS radio brightness. The H$\alpha$ data have a resolution of
$1.\\!^{\prime}6$.

We also use data from the Green Bank 4.85 GHz Northern sky survey (GB6,
Gregory et al., 1996) to verify the morphology of the free-free emission seen
at 1.447 GHz by GALFACTS. Unfortunately, we cannot directly use the GB6 data
in the analysis due to heavy filtering of the large-scale features (evidenced
by the negatives around the PDR front shown in Figure 3). The GB6 data were
taken from the NASA Skyview website333https://skyview.gsfc.nasa.gov/. The GB6
data have a resolution of $3.\\!^{\prime}5$.

We used the Atacama Cosmology Telescope (ACT) 98 GHz intensity data from the
night-time subset of ACT DR5 (dr5.01, Naess et al., 2020), available on the
NASA Lambda
repository444https://lambda.gsfc.nasa.gov/product/act/actpol_prod_table.html.
We use the ACT 98 GHz data in place of the Planck 143 GHz data as the former
has a resolution of $2^{\prime}$, and the Planck data have a resolution of
$7.\\!\\!^{\prime}3$.

We used the four reprocessed Infrared Astronomical Satellite (IRAS, Neugebauer
et al., 1984) data (IRIS, Miville-Deschênes & Lagache, 2005) maps at $12$,
$25$, $60$, and $100$ $\mu$m. The spatial resolution of IRAS is $\approx
4^{\prime}$. Here we use the IRAS datasets to constrain the turn over in the
thermal dust spectrum that is not measured by the Planck data.

We used all four bands ($3.4$, $4.6$, $12$ and $22$ $\mu$m) from the Wide-
field Infrared Survey Explorer (WISE, Wright et al., 2010). Within the $3.4$
and $12$ $\mu$m bands there are multiple prominent PAH features (e.g. Tielens,
2008), which are a leading candidate for the carrier for spinning dust
emission (Dickinson et al., 2018). While the $4.6$ and $22$ $\mu$m WISE bands
contain no bright PAH features and so can be used to trace small grain
populations. We converted all of the maps from detector units to MJy/sr using
the procedure outlined in Cutri et al. (2012), and applied a $1^{\prime}$
rolling 2D median filter to remove contamination of the diffuse emission due
to stellar sources in the $3.4$ and $4.6$ $\mu$m data.

Figure 3: Grid of multi-frequency maps centred on Barnard 30 in ascending
order of frequency from the top-left to the bottom-right. All maps have been
smoothed to a common resolution of $6^{\prime}$ except for the VTSS and GB6
maps, which are shown at the native resolution of the each survey
($1.\\!^{\prime}6$ and $3.\\!^{\prime}5$, respectively). The white contours
are the COMAP 27 GHz data at levels of 0.5 and 1.6 mK. The width and height of
each panel is $1.\\!\\!^{\circ}$5.

Figure 3 shows all the ancillary data alongside the 27 and 33 GHz COMAP data
all smoothed to $6^{\prime}$. We have overlaid the COMAP 27 GHz contours over
each image for easier comparison. The H$\alpha$, GALFACTS and GB6 maps are
placed in the first two panels as these are tracers of the ionised gas
component being driven by the $\lambda$-Orionis star. We have not corrected
the VTSS data for dust extinction, which is why the GALFACTS and VTSS data are
not identical. All other images increase in frequency from top-left to bottom-
right.

##  3 Aperture Photometry

Table 1: Galactic coordinates and dimensions used for each aperture shown in Figure 2. Note that $\theta$ is given relative to Galactic North.  Region Name | $\ell$ | $b$ | semi-major | semi-minor | $\theta$
---|---|---|---|---|---
| deg. | deg. | arcmin. | arcmin. | deg.
Full | 192.29 | $-11.63$ | 24 | 14 | $-20$
A | 192.03 | $-11.42$ | 14 | 14 | 0
B | 192.18 | $-11.90$ | 14 | 14 | 0
C | 192.60 | $-11.67$ | 14 | 14 | 0
D | 192.53 | $-10.76$ | 14 | 14 | 0
Planck | 192.29 | $-11.63$ | 60 | 30 | $-20$
QSO J0530+11 | 191.36 | -11.03 | 14 | 14 | 0
Table 2: Background aperture descriptions. The central coordinate of each group of background apertures is given in Table 1. $N$ refers to the number of background apertures used to sample the annulus. The final column, $\alpha_{c}$, gives the maximum aperture correction for each configuration. See text for details.  Region Name | N | radius | semi-major | semi-minor | $\alpha_{c}$
---|---|---|---|---|---
|  | arcmin. | arcmin. | arcmin. |
Full | 11 | 8 | 34 | 24 | 1.11
A | 9 | 8 | 24 | 24 | 1.14
B | 9 | 8 | 24 | 24 | 1.14
C | 9 | 8 | 24 | 24 | 1.14
D | 9 | 8 | 24 | 24 | 1.14
Planck | 17 | 10 | 70 | 40 | 1.05
QSO J0530+11 | 9 | 8 | 24 | 24 | 1.14

To measure the integrated flux density $S_{\nu}$ of the cloud we used aperture
photometry. Aperture photometry is defined as

$S_{\nu}=2k_{b}\frac{\nu^{2}}{c^{2}}\int_{\Omega}\left[T(\Omega^{\prime})-\left<T_{\mathrm{bkgd}}\right>\right]\mathrm{d}\Omega^{\prime},$
(1)

where $\Omega$ is the area of the aperture enclosing the source, $T$ is the
source brightness distribution, and $\left<T_{\mathrm{bkgd}}\right>$ is the
average background brightness sampled from a low-brightness region around the
source. In this analysis we used ellipses, defined in Table 1, to measure
source flux density in each region shown in Figure 2. Whereas the background
brightness was sampled from $N_{\mathrm{bkgd}}$ independent circular apertures
that were equally spaced along an ellipse that enclosed the main aperture.
Table 2 defines the path of the background apertures, the radii of each, and
the number ($N$) of background apertures used for each source.

The advantage of calculating the background using many independent apertures
instead of a single annulus is that the background of the source could be
sampled with $N_{\mathrm{bkgd}}(N_{\mathrm{bkgd}}-1)$ independent
configurations. For each configuration we measured the source background
brightness using both the median brightness and a fitted 2D plane. This
resulted in flux density distributions using all median and plane fitted
backgrounds brightness configurations. We found that, except for the 1.4 GHz
radio data, there was no significant (within uncertainties) difference between
the median flux density of both background distributions. As such, we use just
the median flux density of the median background brightness distributions.

The standard method for measuring the uncertainty in the flux density for a
source with a white noise background is

$\sigma_{S}^{2}=\sigma_{\mathrm{annu}}^{2}N_{S}\left[1+\frac{\pi}{2}\frac{N_{S}}{N_{\mathrm{annu}}}\right]+\delta^{2}S^{2}$
(2)

where, $\delta$ represents the calibration uncertainty,
$\sigma_{\mathrm{annu}}$ is the standard deviation of the annulus pixels in
units of Jy/pixel, $N_{S}$ is the number of pixels within the aperture, and
$N_{\mathrm{annu}}$ is the number of background pixels. However, in this case
the background noise in all of the maps was neither Gaussian nor white. As
such we used numerical simulations to calculate the uncertainty in the flux
density by injecting sources of known flux density at 100 random locations
within each map, and measuring the flux density using the same aperture used
in the analysis. In this way we could measure the uncertainty in the flux
density by measuring the standard deviation of the resulting distribution. The
numerically derived uncertainties were found to be consistent with Equation 2
in white noise only simulations. We find that for COMAP, the numerically
derived uncertainties are approximately 10 times higher than those predicted
from the white-noise alone due to a combination of atmospheric and large-scale
noise features in the map. For other datasets, such as WMAP and Planck, we
find that the numerically derived uncertainty is approximately twice what
would be expected from white-noise alone, this difference mostly being driven
by variations in the background emission around B30.

Finally, Table 2 reports the aperture corrections applied to each aperture.
Aperture corrections account for the amount of flux density from the source
that is measured in the background pixels and is then subtracted from the
source flux density. Aperture corrections are a function of the beam used to
smooth the sky signal and the separation of the background pixels from the
aperture pixels. To calculate this we made a mock dataset with the aperture
pixels set to unity and all other pixels set to zero. We smoothed the mock
data to the resolution of $6^{\prime}$ and then measured the flux density
within the aperture as we would in the real data. The aperture correction is
then defined as

$\alpha_{c}=\frac{S_{\mathrm{full}}}{S_{\mathrm{measured}}},$ (3)

where $S_{\mathrm{full}}$ is equal to the input flux density within the
aperture, and $S_{\mathrm{measured}}$ is the flux density measured using our
aperture photometry technique. The reported flux densities are scaled by the
coefficient $\alpha_{c}$. Typical aperture corrections are around $10$ per
cent.

###  3.1 Spectral Fitting

In subsection 3.2 we fit the spectra of the regions, shown in Figure 2,
derived from aperture photometry. We use a four component fit to describe the
spectra defined as:

$S_{\mathrm{tot}}=S_{\mathrm{ff}}+S_{\mathrm{td}}+S_{\mathrm{sd}}+S_{\mathrm{CMB}},$
(4)

where $S_{\mathrm{ff}}$ describes the optically-thin free-free continuum
emission from ionised gas, the thermal dust spectrum is $S_{\mathrm{td}}$,
$S_{\mathrm{sd}}$ is the spinning dust spectrum, and $S_{\mathrm{CMB}}$ is the
integrated flux density of the CMB anisotropies. We do not include any
synchrotron component in the model as previous analyses of the
$\lambda$-Orionis PDR found no evidence for synchrotron emission at
$1^{\circ}$ scales (Planck Collaboration et al., 2014a; Cepeda-Arroita et al.,
2021), and the strong correlation between the optical VTSS H$\alpha$ data with
GALFACTS and GB6 radio data in Figure 3 indicate that the dominant radio
emission is due just to optically thin free-free emission. We also tried
directly subtracting the CMB from each frequency band using the CMB solutions
from Planck (Planck Collaboration et al., 2020) instead of fitting for the CMB
flux density, but found it made little difference to the final result since
the CMB is such a small component at all frequencies except in the ACT 98 GHz
band.

We model the spectrum for optically thin free-free emission using the model
given in Draine (2011),

$T_{\mathrm{ff}}=5.468\times
10^{-2}\left(\frac{T_{e}}{\mathrm{K}}\right)^{-1.5}\left(\frac{\nu}{\mathrm{GHz}}\right)^{-2}\left(\frac{\mathrm{EM}}{\mathrm{pc~{}cm}^{-6}}\right)g(T_{4},\nu_{\mathrm{GHz}}),$
(5)

where $T_{e}$ is the electron temperature and $T_{4}=T_{e}/10^{4}$,
$\mathrm{EM}$ is the emission measure, $g$ is an approximation for the Gaunt
factor given by

$g(T_{4},\nu_{\mathrm{GHz}})=\ln\left(e^{X}+e^{1}\right),$ (6)

where $X=5.960-\sqrt{3}/\pi\ln\left(\nu_{\mathrm{GHz}}T_{4}^{-1.5}\right)$. We
fit only for EM, as EM and $T_{e}$ are degenerate, therefore we fixed the
electron temperature at a typical value for the ISM of $T_{e}=8000$ K
(Paladini et al., 2003).

We fit the thermal dust emission spectrum with a modified black-body spectrum
defined as

$S_{\mathrm{td}}=\tau_{353}\left(\frac{\nu}{353\mathrm{GHz}}\right)^{\beta}B_{\nu}(T_{\mathrm{d}})\Omega,$
(7)

where we fit for the dust optical depth at 353 GHz ($\tau_{353}$), the dust
spectral index ($\beta$), and the effective dust temperature
($T_{\mathrm{d}}$). The other terms are $B_{\nu}$, the Planck function at
temperature $T_{\mathrm{d}}$, and $\Omega$–the solid angle of the aperture.
For the dust emissivity index $\beta$ we used a Gaussian prior of
$N(1.6,0.3)$, and for the dust temperature we used $N(17,10)$, which were
informed by typical all-sky values from Planck Planck Collaboration et al.
(2014b).

To model the spinning dust emission we use a warm neutral medium (WNM)
template spectrum generated using the SpDust (Ali-Haïmoud et al., 2009) code
using the WNM parameters defined in Draine & Lazarian (1998). The template
spectrum is normalised relative to the brightness at 30 GHz. The fitted
function for the spinning dust emission in then

$S_{\mathrm{sd}}=A_{\mathrm{sd}}\frac{f(\nu\nu_{p}/\nu_{\mathrm{sd}})}{f(\nu_{r}\nu_{p}/\nu_{\mathrm{sd}})},$
(8)

where we fit for the spectral flux density at 30 GHz ($A_{\mathrm{sd}}$), and
the spectrum peak frequency ($\nu_{\mathrm{sd}}$). The term $\nu_{p}$ is the
numerically derived peak of the spinning dust spectrum, and $\nu_{r}$ is the
reference frequency of 30 GHz. For this analysis we have used a Gaussian prior
on $\nu_{\mathrm{sd}}$ of $N(30\,\mathrm{GHz},10\,\mathrm{GHz})$, to help
constrain the spinning dust peak to make up for the lack of data around 15 and
60 GHz. The detailed choice of the spinning dust template does not
significantly impact the results, and similar fits are obtained for cold
neutral medium models (CNM). We do not use a fixed log-normal distribution, as
has been used in other analyses (e.g., Cepeda-Arroita et al., 2021), as we do
not have sufficient sampling in frequency space to be able to constrain the
width of the log-normal, but by using the SpDust WNM model the width of the
spectrum is already fixed to a physically motivated value.

The final model we fit for is the integrated flux density from the cosmic
microwave background anisotropies. We modelled these as

$S_{\mathrm{CMB}}=A_{\mathrm{CMB}}B_{\nu}(T_{\mathrm{CMB}})\Omega\times
10^{6},$ (9)

where $A_{\mathrm{CMB}}$ is the mean CMB anisotropies amplitude in $\mu$K,
$B_{\nu}$ is the Planck function at temperature $T_{\mathrm{CMB}}$, and
$\Omega$ is the solid angle of the aperture.

In summary, we performed an MCMC fit to the flux densities measured in the
apertures defined by Regions Full, A, B, C, and D—given in Table 3. Fits were
performed between 1 and 3000 GHz resulting in 11 data points. We fitted for
seven free parameters: $\tau_{353}$, $T_{\mathrm{d}}$, $\beta$, $\mathrm{EM}$,
$A_{\mathrm{sd}}$, $\nu_{\mathrm{sd}}$, and $A_{\mathrm{CMB}}$—given in Table
4. We do not account for the correlated noise between the COMAP bands, however
this should not have significant impact on the overall uncertainties as
discussed in section 3.

For the MCMC analysis we use the affine invariant Markov chain Monte Carlo
ensemble sampler (emcee) package (Foreman-Mackey et al., 2013). We used a
total of 100 walkers, with chain lengths of 3000, and a burn-in of 1000.
Chains were initialised using least-squares fits to the spectrum. We checked
that all chains were converged using the Rubin-Gelman statistic. If after 3000
steps a chain was not converged, we reinitialised the chain using the average
value of the converged chains. This was not required for most regions, except
Region D, which required four reinitalisations before all chains were
converged (giving an effective chain length of 12000).

###  3.2 Integrated Flux Density

Table 3: Flux densities for each region shown in Figure 2 and described in Table 1. The flux densities are measured using aperture photometry and the uncertainties are calculated using bootstrapping and include calibration uncertainties. Survey | Frequency |  Full Region | Region A | Region B | Region Planck | Region C | Region D
---|---|---|---|---|---|---|---
| [GHz] | [Jy] | [Jy] | [Jy] | [Jy] | [Jy] | [Jy]
GALFACTS | 1.447 | 0.53 $\pm$ 0.39 | 0.25 $\pm$ 0.32 | 0.24 $\pm$ 0.25 | 3.2 $\pm$ 1.3 | 0.54 $\pm$ 0.11 | 0.45 $\pm$ 0.10
COMAP | 27 | 2.84 $\pm$ 0.25 | 1.41 $\pm$ 0.2 | 1.42 $\pm$ 0.2 | 7.4 $\pm$ 1.3 | 0.62 $\pm$ 0.32 | 0.56 $\pm$ 0.15
COMAP | 29 | 2.93 $\pm$ 0.23 | 1.34 $\pm$ 0.22 | 1.38 $\pm$ 0.22 | 7.1 $\pm$ 1.2 | 0.48 $\pm$ 0.29 | 0.66 $\pm$ 0.13
COMAP | 31 | 3.19 $\pm$ 0.26 | 1.5 $\pm$ 0.23 | 1.45 $\pm$ 0.22 | 10.3 $\pm$ 1.3 | 0.4 $\pm$ 0.44 | 0.73 $\pm$ 0.21
COMAP | 33 | 2.89 $\pm$ 0.28 | 1.35 $\pm$ 0.22 | 1.16 $\pm$ 0.2 | 7.8 $\pm$ 1.5 | 0.27 $\pm$ 0.38 | 0.65 $\pm$ 0.2
ACT | 98 | 3.46 $\pm$ 0.22 | 2.06 $\pm$ 0.15 | 0.83 $\pm$ 0.23 | 6.75 $\pm$ 0.95 | 1.07 $\pm$ 0.58 | 0.47 $\pm$ 0.18
Planck | 217 | 57.5 $\pm$ 8.5 | 37.1 $\pm$ 7.9 | 13.4 $\pm$ 5.9 | 178 $\pm$ 13 | 23 $\pm$ 11 | 5.6 $\pm$ 1.4
Planck | 353 | 211 $\pm$ 40 | 137 $\pm$ 37 | 54.0 $\pm$ 23.0 | 678 $\pm$ 50 | 79 $\pm$ 36 | 22.2 $\pm$ 7.1
Planck | 545 | 710 $\pm$ 110 | 450 $\pm$ 120 | 199 $\pm$ 65 | 2310 $\pm$ 170 | 250 $\pm$ 110 | 79 $\pm$ 31
Planck | 857 | 2060 $\pm$ 330 | 1340 $\pm$ 370 | 590 $\pm$ 220 | 7020 $\pm$ 500 | 750 $\pm$ 410 | 310 $\pm$ 100
IRAS $100\,\mu$m | 3000 | 2200 $\pm$ 220 | 1340 $\pm$ 220 | 830 $\pm$ 180 | 6540 $\pm$ 750 | 900 $\pm$ 410 | 500 $\pm$ 150
IRAS $60\,\mu$m | 5000 | 833 $\pm$ 44 | 464 $\pm$ 72 | 395 $\pm$ 70 | 2650 $\pm$ 150 | 380 $\pm$ 130 | 215 $\pm$ 49
IRAS $25\,\mu$m | 12000 | 225 $\pm$ 19 | 108 $\pm$ 22 | 112 $\pm$ 15 | 676 $\pm$ 37 | 77 $\pm$ 36 | 51 $\pm$ 14
WISE $22\,\mu$m | 13600 | 194 $\pm$ 17 | 93 $\pm$ 19 | 98 $\pm$ 14 | 626 $\pm$ 75 | 78 $\pm$ 38 | 36 $\pm$ 15
IRAS $12\,\mu$m | 25000 | 144 $\pm$ 14 | 64 $\pm$ 15 | 71 $\pm$ 13 | 431 $\pm$ 29 | 76 $\pm$ 34 | 35.7 $\pm$ 8.6
WISE $12\,\mu$m | 25000 | 183 $\pm$ 28 | 70 $\pm$ 22 | 93 $\pm$ 18 | 762 $\pm$ 75 | 56 $\pm$ 25 | 42 $\pm$ 14
WISE $4.6\,\mu$m | 64900 | 3.7 $\pm$ 0.3 | 1.6 $\pm$ 0.4 | 1.6 $\pm$ 0.3 | 10.3 $\pm$ 0.5 | 1.5 $\pm$ 0.4 | 0.8 $\pm$ 0.2
WISE $3.4\,\mu$m | 88200 | 8.7 $\pm$ 0.9 | 4.4 $\pm$ 0.7 | 3.6 $\pm$ 0.7 | 29.7 $\pm$ 2.3 | 3.4 $\pm$ 1.0 | 3.3 $\pm$ 0.6
Figure 4: Best-fitting spectrum to Region Full in Figure 2. The black line indicates the integrated spectrum, while each component is shown by the dashed lines. The amplitude of the CMB ($A_{\mathrm{CMB}}$) in this fit is negative, so we show the absolute value of the CMB fit using a dotted line. The $1\sigma$ uncertainties in the model are shown by the grey highlighted region. Bands at wavelengths below 100 $\mu$m were excluded from the fit. The inset axis shows the residual spinning dust flux density in the COMAP bands with the best-fitting spinning dust model. Table 4: Best-fitting parameters for each region. Uncertainties are taken from the standard deviation of the posterior distributions—such as those in Figure 5. The spectral index of the thermal dust has Gaussian prior of $N(1.6,0.3)$ based on average all-sky values from Planck (Planck Collaboration et al., 2014b). The peak frequency of the spinning dust used a Gaussian prior of $N(30\,\mathrm{GHz},10\,\mathrm{GHz})$.  Region | $\tau_{353}$ | $T_{\mathrm{d}}$ | $\beta$ | EM | $A_{\mathrm{sd}}$ | $\nu_{\mathrm{sd}}$ | $A_{\mathrm{CMB}}$
---|---|---|---|---|---|---|---
| $\times 10^{-6}$ | [K] |  | [cm-6 pc] | [Jy] | [GHz] | [$\mu$K]
Full | $67.0\pm 19.0$ | $17.8\pm 2.3$ | $1.54\pm 0.20$ | $71\pm 47$ | $2.85\pm 0.43$ | $32.3\pm 5.9$ | $-17\pm 35$
Planck | $37.8\pm 9.3$ | $18.0\pm 2.3$ | $1.49\pm 0.20$ | $57\pm 29$ | $7.30\pm 1.40$ | $33.2\pm 6.4$ | $-48\pm 23$
A | $75.0\pm 26.0$ | $17.5\pm 2.5$ | $1.57\pm 0.21$ | $62\pm 44$ | $1.32\pm 0.26$ | $31.6\pm 6.7$ | $-13\pm 38$
B | $23.0\pm 12.0$ | $19.2\pm 3.5$ | $1.58\pm 0.27$ | $86\pm 50$ | $1.19\pm 0.25$ | $29.0\pm 6.5$ | $-10\pm 28$
C | $41.0\pm 28.0$ | $17.9\pm 4.6$ | $1.54\pm 0.27$ | $99\pm 37$ | $0.27\pm 0.20$ | $29.6\pm 9.3$ | $-19\pm 39$
D | $9.9\pm 5.1$ | $20.6\pm 4.9$ | $1.51\pm 0.27$ | $87\pm 34$ | $0.41\pm 0.17$ | $32.7\pm 8.3$ | $-11\pm 18$

Figure 4 shows the best-fitting model of Equation 4 to the photometry data
measured within Region Full shown in Figure 2, and Figure 5 shows the
posterior distributions. Table 3 gives the measured flux densities at each
frequency. Figure 4 also shows the model residuals normalised by the
uncertainties in each flux density. The dust emitting at frequencies above the
IRAS 100 $\mu$m band are much more susceptible to stochastic heating that is
not well described by a single-temperature modified black-body spectrum. These
bands are therefore excluded from the fit (shown as hollow markers). The model
is most uncertain between 50–100 GHz due to a lack of data at the required
angular resolution at these frequencies.

Figure 5: Posterior distributions for each fitted parameter for the spectrum
of Region Full shown in Figure 4. Contours are shown at $1$ and $2\sigma$.

The best-fitting models for each of the three regions are given in Table 4.
The uncertainties in the table are the standard deviations of each parameter’s
posterior distribution. Spinning dust is detected at a high significance of
$7\sigma$ in the Full region. This corresponds to a total fraction of AME at
30 GHz of $86.0\pm 0.08$ per cent.

The uncertainties in Figure 4 are calculated by measuring the distribution of
flux densities when moving the aperture within the field, as discussed in
section 3. The $\chi^{2}$ of the residuals for the fit are $\chi^{2}=1.54$
with a reduced $\chi^{2}_{r}=0.39$ (4 degrees-of-freedom). The small
$\chi^{2}_{r}$ is because we do not account for the correlations in the
uncertainties. For COMAP, the noise between frequency bands is highly
correlated ($\approx 90$ %), meaning we should really only consider COMAP to
be a single data point in Figure 4. If we do this the degrees-of-freedom
becomes approximately unity, and the reduced $\chi^{2}_{r}$ becomes $1.54$. We
also do not model how the background emission is correlated between bands in
the sub-mm and infrared bands, and in Figure 4 we show these as entirely
independent uncertainties. This has the effect of increasing the effective
uncertainties of the model fit, and to decrease the $\chi^{2}$ of the fit.

We used the Bayesian information criterion (BIC) to compare models with and
without a spinning dust component. With spinning dust the model
$\mathrm{BIC}_{\mathrm{sd}}=111$, while without spinning dust
$\mathrm{BIC}_{\mathrm{ff}}=145$. For hierarchical models, the lower BIC value
is favoured if the difference is greater than 5. In the case the difference is
$\Delta\mathrm{BIC}=34$ suggesting the data strongly favour the inclusion of
an spinning dust component (Hilbe et al., 2017).

####  3.2.1 Comparison with Planck

The Region Planck aperture was chosen to encompass all of the emission seen
within the COMAP data so that it can be directly compared with the flux
density measured in the Planck survey of Galactic spinning dust emission
regions (Planck Collaboration et al., 2014a). The Planck analysis used a
$1^{\circ}$ radius aperture at $1^{\circ}$ resolution, and reported a flux
density of $7.6\pm 1.0$ Jy at 28.4 GHz for the B30 region, while we find
(scaling the value from Table 4) a flux density of $6.8\pm 1.4$ Jy at 28.4 GHz
(we do not account for colour corrections in this comparison as they are
negligible). This implies that most of the emission seen in the lower
resolution Planck 28.4 GHz data is due to spinning dust emission within the
B30 cloud that is seen by COMAP. This is approximately twice the flux density
measured within the tighter aperture that just captures the flux from the
central cloud, which has a flux density of $S_{\mathrm{Full}}=2.68\pm 0.37$ Jy
at 28.4 GHz (again, scaling the value from Table 4). This implies that
approximately half of the spinning dust emission within B30, when measured at
$1^{\circ}$ scales, is due to a diffuse component outside of the Region Full
aperture shown in Figure 2.

One issue when comparing with the $1^{\circ}$ resolution Planck analysis is
that its $1^{\circ}$ radius aperture is much larger than is possible for the
COMAP data and so would have integrated a larger fraction of the surrounding
free-free emission alongside the spinning dust component. In Planck
Collaboration et al. (2014a) the average emission measure within the measured
aperture was $\mathrm{EM}=8\pm 6$ pc cm-6. We can use this, along with the
reported spinning dust flux density of $7.6\pm 1.0$ Jy, to estimate the
fraction of spinning dust emission to the total emission at 28.4 GHz. We find
that the Planck spinning dust flux density ratio is $80\pm 14$ per cent, while
we found the ratio with the Planck region aperture to be much higher at $95\pm
3$ per cent. This difference is driven by the fact we are using a slightly
smaller aperture that integrates less of the $\lambda$-Orionis Hii region, and
shows that the Planck analysis underestimated the fraction of the emission
from B30 that is due to spinning dust emission.

####  3.2.2 Comparison of GALFACTS with VTSS

In Table 3 we show that the 1.447 GHz GALFACTS data within the Full, A and B
aperture regions is consistent with noise. Looking at the GALFACTS data in
Figure 3 it is clear that there is a free-free background that forms a
gradient across the region.

Within the measured apertures free-free emission does not make a significant
contribution. This is also clear if one compares the GALFACTS and COMAP data
in Figure 3, there is no clear correlation between the two data sets. In
Region Full the spinning dust emission detected at 30 GHz is approximately
$7\sigma$ above the radio free-free emission predicted by the GALFACTS
data—meaning the GALFACTS data would need to be almost an order-of-magnitude
brighter to match the flux density we see at 30 GHz.

We can cross-check the calibration of the GALFACTS data by comparing it to the
VTSS H$\alpha$ data. Both H$\alpha$ and radio free-free emission are generated
by the same ionised gas and a direct relationship between the H$\alpha$
intensity and free-free brightness is expected (Draine, 2011). Although we do
not correct for dust absorption, significant H$\alpha$ extinction is only
apparent for certain regions within B30 but since we are only interested in
the average relationship between the radio and H$\alpha$ emission over the
whole region the impact of dust absorption should be minimal. We measured the
gradient between between the VTSS and GALFACTS data within the common pixels
shown in Figure 3 and found $I(\mathrm{H}\alpha)/T_{\mathrm{ff}}=5.88\pm 0.04$
mK/R, while the expected ratio at 1.447 GHz (assuming an electron temperature
between 5000–10000 K) is $I(\mathrm{H}\alpha)/T_{\mathrm{ff}}=3.0$–$6.6$ mK/R
(e.g., Dickinson et al., 2003). Therefore, the free-free level is consistent
between the radio and optical data.

Table 5: Derived values from the photometry and model fits of the different regions shown in Figure 2. The second and third columns are the spinning dust emissivity relative to the fitted spinning dust brightness at 30 GHz, the fourth column is the average relative interstellar radiation field (ISRF) in the region, and columns five and six are the ratios of the flux densities between the WISE 12 and 4.6 $\mu$m bands and the WISE 22 $\mu$m band. Region | T30GHz/$\tau_{353}$ | T30GHz/IRAS100μm | $G$ | $\alpha^{22\mu\mathrm{m}}_{4.6\mu\mathrm{m}}$ | $f^{\mathrm{PAH}}_{12\mu\mathrm{m}}$ | $f^{\mathrm{PAH}}_{3.4\mu\mathrm{m}}$
---|---|---|---|---|---|---
| [K] | [$\mu$K/(MJy/sr)] |  |  |  |
Full | $22.1\pm 5.0$ | $53.0\pm 10.0$ | $1.1\pm 0.8$ | $-2.55\pm 0.08$ | $0.31\pm 0.07$ | $0.24\pm 0.06$
Planck | $16.9\pm 3.6$ | $40.7\pm 9.5$ | $1.2\pm 0.8$ | $-2.59\pm 0.09$ | $0.20\pm 0.04$ | $0.19\pm 0.05$
A | $15.6\pm 5.0$ | $41.0\pm 11.0$ | $1.0\pm 0.8$ | $-2.58\pm 0.22$ | $0.37\pm 0.20$ | $0.19\pm 0.11$
B | $43.0\pm 21.0$ | $59.0\pm 18.0$ | $1.7\pm 1.7$ | $-2.65\pm 0.16$ | $0.29\pm 0.10$ | $0.25\pm 0.12$
C | $5.7\pm 5.4$ | $11.4\pm 9.6$ | $1.1\pm 1.6$ | $-2.55\pm 0.46$ | $0.29\pm 0.23$ | $0.26\pm 0.22$
D | $39.0\pm 23.0$ | $29.0\pm 15.0$ | $2.5\pm 3.2$ | $-2.39\pm 0.41$ | $0.24\pm 0.18$ | $0.13\pm 0.12$

####  3.2.3 Differences Between Region A and B

Figure 6: Best-fitting spectra to Region A (top) and Region B (bottom) in
Figure 2. The black line indicates the integrated spectrum, while each
component is shown by the dashed lines. The $1\sigma$ uncertainties in the
model are shown by the grey highlighted region. Bands at wavelengths below 100
$\mu$m were excluded from the fit.

In Figure 6 we show the spectra for both Region A and Region B, which are the
two bright spinning dust emitting hot spots in the COMAP data. Comparing these
to Figure 4 it is clear that all three spectra are very similar, with the same
spinning dust emission peak brightness, and free-free radio background. The
largest difference in both spectra comes from the measurements of the thermal
dust emission—in Region B this is more than a factor of two lower than in
Region A. However, as illustrated by the figures and Table 3, the far-infrared
(FIR) data at 100 and 60 $\mu$m and the mid-infrared (MIR) data at
$\lambda<25$ $\mu$m are consistent within uncertainties. This is also clear in
Figure 3 where the relative brightness of Region A is much brighter than
Region B, but in the mid-infrared bands this difference between Region A and B
becomes less apparent—similar to what is seen in the COMAP data.

How can we explain why the flux density of the spinning dust emission and MIR
data are equal in Region A and B, while the sub-mm thermal dust flux densities
vary by a factor of two? It suggests that the total dust column, as traced by
the thermal dust emission, is not an accurate tracer of the spinning dust
carriers at parsec scales. We know that Region A has a much higher dust column
density than Region B, both from the peak in the Planck bands shown in Figure
3, which is a known cold clump (Planck Collaboration et al., 2016c), and from
other observations that have identified cold cores within the region
(Kauffmann et al., 2008). Therefore the spinning dust carriers must be part of
the lower density, warm dust phase within B30, which is better traced by the
FIR and MIR data.

In Table 5 we provide several statistics derived from the photometry and the
model fits. The first two columns of Table 5 show the spinning dust emissivity
derived for both the brightness of spinning dust emission at 30 GHz over
$\tau_{353}$ and the IRAS 100 $\mu$m flux density. It is useful to compare the
30 GHz flux densities with the dust optical depth at 353 GHz ($\tau_{353}$),
which is thought to be one of the best direct tracers of the total dust column
along a line-of-sight (Planck Collaboration et al., 2016a).

Typical values for the emissivity of spinning dust relative to $\tau_{353}$
ranges from $5-25$ K at 28.4 GHz, with higher values in denser molecular cloud
regions such as Perseus or $\rho$-Ophiuchus (Planck Collaboration et al.,
2011b) and lower values in lower density high-latitude cirrus dust clouds
(Harper et al., 2022). We find that at 28.4 GHz the spinning dust emissivity
per unit $\tau_{353}$ is statistically consistent between all regions. The
Full region has an emissivity of $20.1\pm 4.8$ K, while Region A and B have
emissivities of $14.9\pm 5.0$ K and $44.0\pm 21.0$ K, respectively (these are
scaled from the 30 GHz values given in Table 5).

When deriving the spinning dust emissivity relative to IRAS 100 $\mu$m data,
we find that the two regions are more consistent ($41\pm 11$ and $59\pm 18$
$\mu$K/(MJy/sr), respectively). However, both regions have an emissivity that
is higher than any other observed PDR associated with spinning dust emission
measured to date, which typically have values between 10 and 25
$\mu$K/(MJy/sr) (e.g., Casassus et al., 2006; Dickinson et al., 2007; Planck
Collaboration et al., 2011b).

In Table 4 we can see that the average dust temperature within Region A is
lower than in Region B, which, assuming both clouds have similar grain
populations, implies that Region B has a more intense total interstellar
radiation field (ISRF). We give estimates of the ISRF ($G_{0}$) in Table 5
using

$G_{0}=\left(\frac{T_{d}}{17.5\mathrm{K}}\right)^{4+\beta},$ (10)

where $\beta$ and $T_{\mathrm{d}}$ are given in Table 4. Region A has a lower
average $G_{0}$ than Region B, implying there is more shielding in this region
that could lead to grain coagulation and depletion of the smallest grains that
are carriers of spinning dust emission.

Finally, in Table 5 we estimate the PAH emission fraction in each region. We
do this by fitting for a power-law between the 4.6 and 22 $\mu$m bands, as
both of these bands are free of bright PAH features and should be dominated by
the continuum background (however these bands may contain ionic PAH features
that we are not accounting for here). This gives us a function for the
continuum background of
$S_{\mathrm{c}}(\lambda)=S_{22\mu\mathrm{m}}\left(\frac{22\,\mu\mathrm{m}}{4.6\,\mu\mathrm{m}}\right)^{\alpha}$,
where the $\alpha$ values are given in Table 5. The fraction of PAHs is then
defined as

$f_{\lambda}^{\mathrm{PAH}}=1-\frac{S_{\lambda}}{S_{\mathrm{c}}(\lambda)},$
(11)

where $S_{\lambda}$ is the flux measured in either the 3.6 or 12 $\mu$m WISE
bands. We find that both regions do contain a significant PAH fraction,
between 20 and 40 per cent depending on the region and WISE band used.
However, we do not find that the PAH fraction is significantly different
between both regions.

####  3.2.4 Region C and Region D

Figure 7: Best-fitting spectra to Region C (top) and Region D (bottom) in
Figure 2. The black line indicates the integrated spectrum, while each
component is shown by the dashed lines. The $1\sigma$ uncertainties in the
model are shown by the grey highlighted region. Bands at wavelengths below 100
$\mu$m were excluded from the fit.

In Figure 7 we show the spectra for both Region C and Region D, two additional
sub-regions of B30. Region C is known to have significant low-mass star
formation and multiple young-stellar objects (YSOs), proto-brown dwarfs, and
prestellar cores have been identified (Huélamo et al., 2017; Barrado et al.,
2018). The region protrudes inward towards the $\lambda$-Orionis star, and as
such has the most intense ISRF (as seen by $G_{0}$ in Table 5 and
$T_{\mathrm{d}}$ in Table 4), and the highest background contamination due to
radio free-free emission—Region C can be seen as an absorption feature within
the VTSS data shown in Figure 3. However, in terms of the dust column, Region
C is similar to both regions A and B (see $\tau_{353}$ in Table 4) yet the
spinning dust flux density in this region is significantly lower and is
consistent with zero. In fact, the BIC for the spectrum including spinning
dust emission shown in Figure 7 is $\mathrm{BIC}=17$ and without spinning dust
emission it is $\mathrm{BIC}=12$, which strongly suggests that the no spinning
dust model is preferred.

Region D is a smaller cloud separate from the main B30 complex. It is
coincident with a faint (0.072 Jy at 1.4 GHz) radio source (Healey et al.,
2009), contains some low-mass star formation, and the lowest thermal dust
optical depth of all of the regions. Although it is fainter than the main
cloud in all bands, this region has the same spinning dust emissivity per
$\tau_{353}$ (Table 5) as Region B, but the same spinning dust emissivity per
$I(100\mu\mathrm{m})$ as Region A. The implication being that the spinning
dust carriers are likely traced by the warmer, FIR and MIR dust population in
this region rather than the total thermal dust population (as traced by
$\tau_{353}$).

##  4 Template Fitting

As well as looking at the integrated flux density of B30, we use a template
fitting or correlation analysis to decompose the COMAP bands into the
constituent emission components—free-free and dust emission. Template fitting
methods have been used extensively for studying diffuse Galactic emission
(e.g. Kogut et al., 1996; de Oliveira-Costa et al., 1997; Davies et al., 2006;
Peel et al., 2012; Harper et al., 2022). The template fitting method assumes
that the data can be decomposed into a linear combination of spatial templates
as

$\mathbf{d}=\mathbf{A}\mathbf{s}+\mathbf{n},$ (12)

where $\mathbf{d}$ is the data, $\mathbf{A}$ is the template matrix,
$\mathbf{s}$ is the vector of template coefficients, and $\mathbf{n}$ is the
noise vector. The maximum likelihood estimate of the template coefficients are
then solved for by

$\mathbf{s}=\left(\mathbf{A}^{T}\mathbf{N}^{-1}\mathbf{A}\right)^{-1}\mathbf{A}^{T}\mathbf{N}^{-1}\mathbf{d},$
(13)

where $\mathbf{N}$ is the noise covariance matrix. The noise covariance matrix
is defined as $\mathbf{N}=\langle\mathbf{n}\mathbf{n}^{T}\rangle$. Nominally
the uncertainties in $\mathbf{s}$ can be found by taking the trace of
$\left(\mathbf{A}^{T}\mathbf{N}^{-1}\mathbf{A}\right)$, however, for this
analysis we use the same technique described in Harper et al. (2022), where
the uncertainties are bootstrapped by resampling the template region.
Uncertainties for the template fitting results include only the statistical
uncertainties due to the noise in each map, and the calibration uncertainty of
each map. The template fitting uncertainties are often much smaller than the
uncertainties in the aperture photometry as they do not include photometry
errors due to the background emission.

For this analysis we only fit two templates to each map: a dust template and a
geometric offset. We do not fit directly for the free-free emission because
the level of free-free contamination at 30 GHz is small, this is evident in
Figure 3 where the morphology of the central B30 cloud as seen at 30 GHz has
very little correlation with the free-free emission seen by GALFACTS, GB6 or
the H$\alpha$ data. As the free-free is so low at 30 GHz, we found that
fitting for it directly introduces systematic biases in the derived dust
template coefficients that vary depending on the dust template used.
Specifically, the correlation between dust and free-free emission is positive
when using the Planck bands and negative for the IRAS bands, resulting in a
change in the expected free-free brightness by up to 50 per cent. Therefore to
account for the free-free contribution in the COMAP bands we subtract the
GALFACTS 1.447 GHz data scaled by a typical optically thin free-free spectrum
of

$T_{\mathrm{ff}}=T_{\mathrm{GALFACTS}}\left(\frac{1.447}{\nu_{\mathrm{GHz}}}\right)^{-2.1},$
(14)

where $T_{\mathrm{ff}}$ is the expected free-free contribution at frequency
$\nu_{\mathrm{GHz}}$, and $T_{\mathrm{GALFACTS}}$ are the GALFACTS pixel
brightnesses.

The final step before template fitting the data was to fit a 2D Gaussian model
to a source in Region C seen in the sub-mm, FIR, and MIR bands as the aperture
photometry suggests it does not have a spinning dust component (as discussed
in section 3). Subtracting out the source, rather than just masking it,
ensures that there is not a large negative systematic in the residual maps
after removing the free-free model and best-fitting dust models from the COMAP
data.

###  4.1 Spectral Models

The natural units for the template fitting analysis are in units of K per unit
dust template. However, we convert these into units of MJy/sr per MJy/sr dust
template so that we can use the same dust models described in subsection 3.1.

To model the template fitted dust coefficients we used

$\mathbf{S}_{\mathrm{d}}=\mathbf{S}_{\mathrm{td}}+\mathbf{S}_{\mathrm{sd}},$
(15)

where $\mathbf{S}_{\mathrm{td}}$ and $\mathbf{S}_{\mathrm{sd}}$ are the same
as given in Equation 7 and Equation 8, respectively.

We use only positivity priors on the spinning dust amplitude and thermal dust
optical depth. For the dust temperature we use a uniform prior of
$0<T_{D}<100$ K. For $\beta$ we use a Gaussian prior of $N(1.6,0.3)$, where
the mean of the prior is $\beta=1.6$, which Planck found to be the all-sky
average value (Planck Collaboration et al., 2014b).

###  4.2 Fitted Template Coefficients

Figure 8: The COMAP 27 GHz data with free-free emission subtracted. The
contours are from the IRAS 100 $\mu$m data at 30, 40, 50, 60, and 70 MJy sr-1.
The boxed regions indicate the areas used for the template fitting analysis.
The areas of both Region A and B are $0.\\!\\!^{\circ}5\times
0.\\!\\!^{\circ}35$.  Figure 9: Best-fitting spectrum to the IRAS 100 $\mu$m
dust template coefficients for Region Full shown in Figure 8. The black line
indicates the integrated spectrum, while each component is shown by the dashed
lines. The $1\sigma$ uncertainties in the model are shown by the grey
highlighted region—in this case these are smaller than the line width of the
black line. Bands at wavelengths shorter than 100 $\mu$m were excluded from
the fit. The inset axis shows the residual template coefficients in the COMAP
bands after subtracting the best-fitting thermal dust model. Table 6: Best-
fitting spinning dust and thermal dust model parameters to the dust template
coefficients for the Full region in Figure 8. The spectral index
$\alpha^{27\mathrm{GHz}}_{33\mathrm{GHz}}$ is measured within the COMAP band
from the fitted dust template coefficients in flux density units. The Pearson
correlations at 27 and 33 GHz are given by $r_{27\mathrm{GHz}}$ and
$r_{33\mathrm{GHz}}$, respectively.

Frequency | Wavelength | $S_{30\mathrm{GHz}}$ | Peak Frequency | $\beta$ | $T_{d}$ | $\alpha^{27\mathrm{GHz}}_{33\mathrm{GHz}}$ | $r_{27\mathrm{GHz}}$ | $r_{33\mathrm{GHz}}$
---|---|---|---|---|---|---|---|---
[̇GHz] |  | [$\mu$K/(MJy/sr)] | [GHz] |  | [K] |  |  |
98 | 3.1mm | $22560\pm 590$ | $33.7\pm 2.5$ | $1.58\pm 0.02$ | $18.1\pm 0.2$ | $0.62\pm 0.34$ | $0.88^{0.89}_{0.87}$ | $0.88^{0.89}_{0.87}$
353 | 0.8mm | $271.5\pm 9.3$ | $35.4\pm 2.6$ | $1.65\pm 0.02$ | $17.3\pm 0.2$ | $1.14\pm 0.43$ | $0.80^{0.81}_{0.79}$ | $0.90^{0.91}_{0.89}$
545 | 0.6mm | $79\pm 3$ | $35\pm 3$ | $1.65\pm 0.02$ | $17.3\pm 0.2$ | $1.10\pm 0.60$ | $0.80^{0.82}_{0.79}$ | $0.90^{0.91}_{0.89}$
857 | 0.3mm | $27.3\pm 0.9$ | $35.2\pm 2.5$ | $1.65\pm 0.02$ | $17.4\pm 0.2$ | $1.20\pm 0.40$ | $0.82^{0.83}_{0.81}$ | $0.91^{0.92}_{0.90}$
3000 | 100$\mu$m | $32.4\pm 0.5$ | $33.0\pm 1.5$ | $1.61\pm 0.03$ | $18.1\pm 0.2$ | $0.60\pm 0.20$ | $0.95^{0.96}_{0.94}$ | $0.94^{0.95}_{0.93}$
5000 | 60$\mu$m | $103.7\pm 1.7$ | $30.2\pm 1.1$ | $1.57\pm 0.04$ | $18.7\pm 0.3$ | $0.17\pm 0.24$ | $0.96^{0.97}_{0.95}$ | $0.87^{0.88}_{0.86}$
12000 | 25$\mu$m | $362\pm 9$ | $29.2\pm 1.5$ | $1.55\pm 0.07$ | $19.1\pm 0.5$ | $-0.14\pm 0.33$ | $0.93^{0.94}_{0.92}$ | $0.81^{0.82}_{0.79}$
13600 | 22$\mu$m | $384\pm 8$ | $30.4\pm 1.4$ | $1.57\pm 0.06$ | $18.8\pm 0.4$ | $0.19\pm 0.27$ | $0.93^{0.94}_{0.92}$ | $0.86^{0.87}_{0.84}$
25000 | 12$\mu$m | $474\pm 11$ | $30.2\pm 1.7$ | $1.57\pm 0.06$ | $18.9\pm 0.4$ | $0.14\pm 0.33$ | $0.91^{0.92}_{0.90}$ | $0.82^{0.83}_{0.81}$
64900 | 4.6$\mu$m | $21230\pm 530$ | $29.8\pm 1.6$ | $1.56\pm 0.06$ | $18.8\pm 0.5$ | $0.04\pm 0.30$ | $0.93^{0.94}_{0.92}$ | $0.82^{0.84}_{0.81}$
88200 | 3.4$\mu$m | $11440\pm 310$ | $29.0\pm 1.5$ | $1.55\pm 0.06$ | $19.1\pm 0.5$ | $-0.20\pm 0.30$ | $0.94^{0.95}_{0.93}$ | $0.81^{0.83}_{0.80}$

  * a

The spinning dust emissivity per unit 353 GHz dust opacity is $10.55\pm 0.36$.

Table 7: Best-fitting spinning dust and thermal dust model parameters to the
dust template coefficients for the Region A in Figure 8. The spectral index
$\alpha^{27\mathrm{GHz}}_{33\mathrm{GHz}}$ is measured within the COMAP band
from the fitted dust template coefficients in flux density units. The Pearson
correlations at 27 and 33 GHz are given by $r_{27\mathrm{GHz}}$ and
$r_{33\mathrm{GHz}}$, respectively.

Frequency | Wavelength | $S_{30\mathrm{GHz}}$ | Peak Frequency | $\beta$ | $T_{d}$ | $\alpha^{27\mathrm{GHz}}_{33\mathrm{GHz}}$ | $r_{27\mathrm{GHz}}$ | $r_{33\mathrm{GHz}}$
---|---|---|---|---|---|---|---|---
[̇GHz] |  | [$\mu$K/(MJy/sr)] | [GHz] |  | [K] |  |  |
98 | 3.1mm | $18410\pm 590$ | $28.3\pm 1.7$ | $1.60\pm 0.04$ | $17.92\pm 0.36$ | $-0.31\pm 0.37$ | $0.88^{0.89}_{0.87}$ | $0.84^{0.86}_{0.82}$
353 | 0.8mm | $216\pm 9.5$ | $32.6\pm 3.0$ | $1.67\pm 0.02$ | $16.81\pm 0.22$ |  $0.54\pm 0.56$ | $0.77^{0.79}_{0.75}$ | $0.87^{0.89}_{0.85}$
545 | 0.6mm | $63\pm 3$ | $32.7\pm 3.0$ | $1.68\pm 0.02$ | $16.82\pm 0.2$ |  $0.59\pm 0.49$ | $0.77^{0.79}_{0.75}$ | $0.87^{0.89}_{0.86}$
857 | 0.3mm | $22.0\pm 0.9$ | $32.5\pm 2.7$ | $1.68\pm 0.02$ | $16.83\pm 0.2$ |  $0.53\pm 0.48$ | $0.78^{0.79}_{0.75}$ | $0.88^{0.89}_{0.87}$
3000 | 100$\mu$m | $30.1\pm 0.8$ | $29.5\pm 1.6$ | $1.64\pm 0.04$ | $17.71\pm 0.24$ | $-0.03\pm 0.30$ | $0.93^{0.94}_{0.92}$ | $0.94^{0.95}_{0.93}$
5000 | 60$\mu$m | $95.9\pm 2.4$ | $28.2\pm 1.6$ | $1.56\pm 0.07$ | $18.61\pm 0.62$ | $-0.45\pm 0.37$ | $0.94^{0.95}_{0.93}$ | $0.87^{0.88}_{0.86}$
12000 | 25$\mu$m | $422\pm 12$ | $28.0\pm 1.6$ | $1.56\pm 0.11$ | $18.84\pm 0.88$ | $-0.53\pm 0.43$ | $0.93^{0.94}_{0.92}$ | $0.84^{0.86}_{0.82}$
13600 | 22$\mu$m | $459\pm 13$ | $28.8\pm 1.7$ | $1.61\pm 0.09$ | $18.4\pm 0.68$ | $-0.32\pm 0.41$ | $0.92^{0.93}_{0.91}$ | $0.87^{0.89}_{0.86}$
25000 | 12$\mu$m | $622\pm 18$ | $29.1\pm 1.9$ | $1.61\pm 0.09$ | $18.31\pm 0.69$ | $-0.22\pm 0.43$ | $0.90^{0.91}_{0.89}$ | $0.87^{0.88}_{0.85}$
64900 | 4.6$\mu$m | $25220\pm 640$ | $28.6\pm 1.6$ | $1.59\pm 0.08$ | $18.37\pm 0.65$ | $-0.51\pm 0.43$ | $0.93^{0.94}_{0.92}$ | $0.87^{0.88}_{0.85}$
88200 | 3.4$\mu$m | $14620\pm 330$ | $28.5\pm 1.4$ | $1.58\pm 0.10$ | $18.61\pm 0.83$ | $-0.51\pm 0.37$ | $0.95^{0.96}_{0.94}$ | $0.88^{0.89}_{0.86}$

  * a

The spinning dust emissivity per unit 353 GHz dust opacity is $8.05\pm 0.35$.

Table 8: Best-fitting spinning dust and thermal dust model parameters to the
dust template coefficients for the Region B in Figure 8. The spectral index
$\alpha^{27\mathrm{GHz}}_{33\mathrm{GHz}}$ is measured within the COMAP band
from the fitted dust template coefficients in flux density units. The Pearson
correlations at 27 and 33 GHz are given by $r_{27\mathrm{GHz}}$ and
$r_{33\mathrm{GHz}}$, respectively.

Frequency | Wavelength | $S_{30\mathrm{GHz}}$ | Peak Frequency | $\beta$ | $T_{d}$ | $\alpha^{27\mathrm{GHz}}_{33\mathrm{GHz}}$ | $r_{27\mathrm{GHz}}$ | $r_{33\mathrm{GHz}}$
---|---|---|---|---|---|---|---|---
[̇GHz] |  | [$\mu$K/(MJy/sr)] | [GHz] |  | [K] |  |  |
98.0 | 3.1mm | $29280\pm 550$ | $33.3\pm 1.8$ | $1.52\pm 0.02$ | $19.1\pm 0.3$ | $0.61\pm 0.25$ | $0.92^{0.93}_{0.91}$ | $0.94^{0.95}_{0.93}$
353.0 | 0.8mm | $386\pm 9$ | $34.7\pm 2.3$ | $1.58\pm 0.02$ | $18.6\pm 0.2$ | $0.7\pm 0.26$ | $0.90^{0.91}_{0.89}$ | $0.94^{0.95}_{0.93}$
545.0 | 0.6mm | $112\pm 3$ | $35.1\pm 2.5$ | $1.58\pm 0.02$ | $18.6\pm 0.2$ | $0.71\pm 0.35$ | $0.90^{0.91}_{0.88}$ | $0.94^{0.95}_{0.93}$
857.0 | 0.3mm | $36.5\pm 0.8$ | $34.4\pm 2.2$ | $1.58\pm 0.02$ | $18.6\pm 0.1$ | $0.62\pm 0.27$ | $0.90^{0.92}_{0.89}$ | $0.95^{0.96}_{0.94}$
3000.0 | 100$\mu$m | $34.1\pm 0.6$ | $32.1\pm 1.4$ | $1.57\pm 0.03$ | $18.9\pm 0.2$ | $0.45\pm 0.20$ | $0.96^{0.97}_{0.95}$ | $0.96^{0.97}_{0.95}$
5000.0 | 60$\mu$m | $107.2\pm 1.5$ | $31.0\pm 1.1$ | $1.55\pm 0.03$ | $19.1\pm 0.2$ | $0.30\pm 0.20$ | $0.97^{0.98}_{0.96}$ | $0.94^{0.95}_{0.93}$
12000.0 | 25$\mu$m | $351\pm 4$ | $30.7\pm 0.7$ | $1.55\pm 0.03$ | $19.1\pm 0.2$ | $0.28\pm 0.12$ | $0.98^{0.99}_{0.97}$ | $0.95^{0.96}_{0.94}$
13600.0 | 22$\mu$m | $356\pm 4$ | $31.1\pm 0.8$ | $1.56\pm 0.03$ | $19.0\pm 0.2$ | $0.37\pm 0.16$ | $0.98^{0.99}_{0.97}$ | $0.96^{0.97}_{0.95}$
25000.0 | 12$\mu$m | $444\pm 6$ | $31.0\pm 1.0$ | $1.56\pm 0.04$ | $19.0\pm 0.3$ | $0.35\pm 0.17$ | $0.97^{0.98}_{0.96}$ | $0.95^{0.96}_{0.94}$
64900.0 | 4.6$\mu$m | $20030\pm 290$ | $30.9\pm 1.0$ | $1.55\pm 0.03$ | $19.1\pm 0.3$ | $0.31\pm 0.18$ | $0.97^{0.98}_{0.96}$ | $0.94^{0.95}_{0.93}$
88200.0 | 3.4$\mu$m | $10770\pm 130$ | $30.4\pm 0.8$ | $1.54\pm 0.03$ | $19.1\pm 0.3$ | $0.21\pm 0.15$ | $0.98^{0.99}_{0.97}$ | $0.94^{0.95}_{0.93}$

  * a

The spinning dust emissivity per unit 353 GHz dust opacity is $16.89\pm 0.41$.

Figure 8 shows the COMAP 27 GHz data after subtracting a scaled version of the
GALFACTS data to remove the free-free component. The three marked regions in
the figure show the pixels that were used to perform the template fitting
analysis. Region Full is a $0.\\!\\!^{\circ}5\times 0.\\!\\!^{\circ}7$ box
centred on $(\ell,b)=(192.\\!\\!^{\circ}3,-11.\\!\\!^{\circ}6)$ contains the
whole of the B30 cloud, while Region A and B are $0.\\!\\!^{\circ}5\times
0.\\!\\!^{\circ}35$ boxes centred on
$(\ell,b)=(192.\\!\\!^{\circ}3,-11.\\!\\!^{\circ}425)$ and
$(\ell,b)=(192.\\!\\!^{\circ}3,-11.\\!\\!^{\circ}775)$, respectively. The
Region A and Region B pixel selections were optimised such that they could be
described by a single dust tracer with a single value for the spinning dust
emissivity.

Table 6, Table 7, and Table 8 give the best-fitting spinning dust and thermal
dust model parameters for each dust tracer for the Full region, Region A, and
Region B as indicated in Figure 8. We also give the COMAP in-band spectral
index, and the Pearson correlation at 27 and 33 GHz. The best-fitting model to
the IRAS $100$ $\mu$m template coefficients spectrum is shown in Figure 9.

####  4.2.1 COMAP and Dust Tracer Correlations

Figure 10: Pearson correlation coefficient spectrum between each dust tracer
and the free-free subtracted COMAP data for Region A, B, and Full. The top
panel shows the Pearson coefficients for the COMAP 27 GHz data, and the bottom
panel shows the Pearson coefficients for the COMAP 33 GHz data.

At present the exact carrier for spinning dust is not known, and is one of the
major questions facing spinning dust emission studies (Dickinson et al.,
2018). For example, the Planck sub-mm bands trace the large dust grain
population in thermal equilibrium, while the FIR and MIR emission trace
smaller grain populations that undergo stochastic heating events, and in the
MIR there are several strong PAH features. Correlation analyses have been used
successfully in the past to study spinning dust emission, but no strong
conclusion has been drawn about the carrier of spinning dust emission (Hensley
et al., 2016; Bell et al., 2019; Cepeda-Arroita et al., 2021).

In Figure 10 we show the Pearson correlation coefficients between the free-
free corrected COMAP 27 and 33 GHz data and the Planck, IRAS, and WISE maps.
Both figures show the correlations measured in Region Full, Region A, and
Region B (as shown in Figure 8). If we first look at the Full region at 27 GHz
(the circle markers) we can see that in the sub-mm Planck bands the
correlation is lowest, it rises to a peak in the FIR around 100 $\mu$m and
then drops again in the MIR, with a slight increase in the WISE 3.4 $\mu$m
band. At 33 GHz we see again the correlation increasing from the sub-mm to the
FIR, but there is a larger drop in the MIR correlation to less than 90 per
cent from the 90 per cent correlation seen at 27 GHz. This difference is not
simply due to the decreased sensitivity of the 33 GHz band relative to the 27
GHz data, as this would result in a uniform decrease in correlation with all
of the dust tracers, which is not observed. The change in correlation across
the band is also not due to contributions of vibrational thermal dust emission
in the higher frequency COMAP bands as this is still negligible at this
frequency. Rather, this suggests that between 27 and 33 GHz we are seeing a
change in the nature of the spinning dust carrier.

Figure 10 also shows the correlation coefficients for the individual sub-
regions A and B. We see that Region A is similar to the overall region
correlations. The dust correlations in Region B are considerably different to
those in Region A and the region overall. We can see that at 27 GHz there is
the same rise in correlation at sub-mm wavelengths, but this time the peak in
the correlation is in the IRAS and WISE 25/22 $\mu$m MIR bands, with a small
fall in correlation at 12 and 4.6 $\mu$m before rising again at 3.4 $\mu$m.
While at 33 GHz, Region B shows no significant preference for any particular
dust tracer.

How can the differences between Regions A and B be explained? One possibility
is that the dust grain size distribution between Region A and B are
significantly different. We know from the spinning dust model (Ali-Haïmoud et
al., 2009) that the smallest dust grains have the highest spinning dust
emissivity, and also have spectral energy distributions that peak at higher
frequencies. So, if Region A has a depletion of smaller grains, we would
expect to see a lower spinning dust peak frequency, and a lower spinning dust
emissivity—this is exactly what we have measured.

Using the best-fitting values to the template fitting spectrum for Region A
(Table 7) and Region B (Table 8), we do find evidence that the grain size
distribution and thus the spinning dust carriers change between Region A and
B. First, looking at the spinning dust peak frequencies using the 100 $\mu$m
IRAS data as a dust tracer we find Region A has a peak at $27.32\pm 0.97$ GHz,
while in Region B it peaks at $32.3\pm 1.8$ GHz. Second, if we use the
spinning dust brightness per unit 353 GHz optical depth as a proxy for
emissivity, we find in Region A the spinning dust emissivity is $8.05\pm 0.35$
K, while in Region B it is more than twice as high at $16.89\pm 0.41$ K. Both
the difference in peak frequency and spinning dust emissivity match the
spinning dust model predictions for a depletion of the smallest grain
population. The depletion of small grains in Region A could be due to grain
coagulation occurring within the known cold clump (Planck Collaboration et
al., 2016c) and denser central cold core L1582 (Kauffmann et al., 2008) within
Region A. Further, previous dedicated observations of cold cores by CARMA at
30 GHz (Tibbs et al., 2011) have shown that most of these high density
environments are not strong emitters of spinning dust emission.

Figure 11: Ratio of best-fitting 27 GHz template coefficients in Region B over
Region A.

In Figure 11 we show how the ratio of the fitted template coefficients at 27
GHz in Region B over A varies with dust tracer. We find that the Region B
template coefficients are twice those in Region A in the sub-mm, and this
ratio slowly decreases down to the MIR where the template coefficients in
Region A are 20 per cent brighter than those in Region B.

The high ratio in the sub-mm emissivities between Region B and A is due to the
change in the dust population grain size distribution, as discussed earlier.
The smallest grains that are the most emissive spinning dust carriers are
being depleted within Region A due to the high density environment of the cold
clump. Such an effect has been observed several times previously, for example
from the survey of cores with the CARMA telescope (Tibbs et al., 2016). Also,
several studies have shown that denser environments generally have lower
spinning dust emissivities relative to sub-mm bands (Vidal et al., 2011;
Planck Collaboration et al., 2014a), which is consistent with the idea that
the small grains responsible for spinning dust emission are being depleted in
Region A.

The explanation for why the 30 GHz emission per unit MIR brightness in Region
A is apparently higher than in Region B can also be explained by the higher
density environment surrounding the cold clump. In the higher density region
of Region A, there will be more shielding from the incident radiation field
from $\lambda$-Ori, decreasing the total ISRF. This has little effect on the
emission seen in the sub-mm as these frequencies generally trace the larger
grain population that are in thermal equilibrium and as such the flux density
is only weakly dependent on the ISRF, e.g. $I_{\nu}\propto
U^{\frac{1}{4+\beta}}$. Meanwhile, the MIR traces grain populations that are
not in thermal equilibrium, and as such are much more sensitive to the ISRF
such that $I_{\nu}\propto U$ (Draine, 2011).

If the environments in Region A and B were similar, we would expect that the
ratio of the flux densities in the sub-mm over the MIR should be constant.
However, using the 353 GHz and 22 $\mu$m fluxes from Table 3, we find that the
flux density ratios for Region A and B are: $1.5\pm 0.5$ and $0.6\pm 0.2$
respectively. This implies that, if the MIR grains were subject to the same
total radiation field in Region A as they are in B, we would expect the MIR
emission to be three times higher in Region A than is observed. Therefore the
apparent increase in 27 GHz emission per unit MIR brightness in Region A is
due to decrease in MIR emissivity per grain due to the decreased ISRF within
Region A.

To summarise, we find that Region A and Region B have different spinning dust
template coefficients (i.e., spinning dust brightness per unit dust tracer),
which is due to differences in the dust populations in both regions. The most
likely explanation for why Region A has lower spinning dust template
coefficients for all dust tracers is because Region A contains fewer small
grains than Region B, which, from the spinning dust models (Ali-Haïmoud et
al., 2009), is expected to reduce the spinning dust emissivity and peak
frequency. However, we cannot entirely rule out that these differences are due
to other factors such as differences in environment or dust grain dipole
moments. If there are fewer small dust grains in Region A, one possible
explanation for this is that the small grains are coagulating within the cold
clump region resulting in the small grains being depleted. To confirm this we
will need spectroscopic MIR observations to find direct evidence of small
grain depletion. Potentially this could be done with the James Webb Space
Telescopes (JWST) MIR instrument similar to recent JWST observations of the
Orion bar (Berné et al., 2022).

####  4.2.2 Comparisons with Other Work

There have been several other studies of the correlation between spinning dust
emission and dust tracers around the $\lambda$-Orionis PDR at $1^{\circ}$
resolution (Bell et al., 2019; Cepeda-Arroita et al., 2021; Chuss et al.,
2022). These studies looked at the correlation between maps of spinning dust
of the entire PDR derived from per pixel parametric fitting of multiple
$1^{\circ}$ resolution surveys. Both lower resolution studies of the
$\lambda$-Orionis PDR found that spinning dust best correlated with 857 GHz
data, with a Spearman correlation of $r_{\mathrm{857GHz}}\approx 0.9$ and a
sharp decline in correlation in the FIR, reaching $r_{60\mu\mathrm{m}}\approx
0.4$.

We do not observe a sharp decline in the correlation around 60 $\mu$m for B30,
but in fact find that that the spinning dust correlation peaks in the FIR.
Both Bell et al. (2019) and Cepeda-Arroita et al. (2021) attribute the drop in
correlation at 60 $\mu$m to stochastically heated small grains, that are not
in thermal equilibrium, not being good carriers of spinning dust emission.
However, this is not true for B30. A potential reason is that the spinning
dust emissivity is varying significantly around the $\lambda$-Orionis PDR due
to variations in environment and dust grain size distribution. It has been
noted for some time that the spinning dust emissivity relative to FIR data can
exhibit large variations due to environment (Tibbs et al., 2012b). We see this
effect when we measure Region Full, as shown in Figure 10, there is a sharp
drop in the FIR/MIR at 33 GHz when measuring Region Full. We also tried
measuring larger regions, and found that the correlation for FIR/MIR decreases
as you increase the area fitted by the template fitting analysis. While noise
could be responsible for the observed decrease in correlation, another
possibility is variations in the spinning dust emissivity. Thus the results of
the low resolution analysis may be driven by large variations in spinning dust
emissivity, which is more sensitive at FIR/MIR bands as these bands are more
sensitive to environmental factors such as the ISRF and dust temperature.

####  4.2.3 Template Fitting Residuals

Figure 12: 27 GHz residuals after subtracting the free-free background and
best-fitting template fitted dust model using the Region B template
coefficients. Dust maps subtracted, from left to right are: Planck 353 GHz,
IRAS 100 $\mu$m, and WISE 22 $\mu$m. The white contours show the COMAP 27 GHz
data, while the gray contours show the morphology of the dust tracers. Each
panel has dimensions of $1.\\!\\!^{\circ}5\times 1.\\!\\!^{\circ}5$.

In Figure 12 we show the residual 27 GHz data after subtracting the free-free
background using GALFACTS and the best-fitting template fitted dust model
using Planck 353 GHz, IRAS 100 $\mu$m, and WISE 22 $\mu$m. We have used the
template coefficients fitted to Region B to highlight the impact of the cold
clump and the changes in an extension we have labelled on the WISE 22 $\mu$m
map as the North West Arm.

We can see from the residual using the Planck 353 GHz data that the sub-mm
data are not a good tracer of the 27 GHz emission. There is both a positive
residual in Region B, indicating a poor fit, and that in the region around
both the Cold Clump and the North West Arm in Region A, there is a clear
negative or over-subtraction. Additionally, there is a gradient running from
left to right across the image, with a positive residual that is tracing the
edge of the free-free emission seen at 1.4 GHz. We are seeing this effect as
the sub-mm data is insensitive to the total radiation field that is driven by
$\lambda$-Orionis, which implies that the spinning dust emission per grain is
higher in regions towards the irradiated edge of the PDR, and decreases in
either more shielded regions (i.e., within the cold clump), or in regions
farther away from $\lambda$-Orionis.

In the the right-most panel of Figure 12 we show the residual after
subtracting the WISE 22 $\mu$m data. In this panel we can see that the
residual in Region B is much closer to zero. However, the residuals around the
cold clump and the North West arm are positive, i.e., the spinning dust
emission per unit MIR brightness is higher in Region A, which is what we also
see in Figure 11 showing the ratio of the template coefficients in Region B
over A. This further supports the earlier discussion that the MIR grains are
emitting less in Region A (and the North West arm feature) due to the
increased dust column density and the resulting decrease in the ISRF in this
region.

The centre panel shows the FIR IRAS 100 $\mu$m residual. In this residual map
we can see that the residuals are much closer to zero across the whole field,
with a small excess in Region B, and small over subtraction around the cold
clump. We also see the gradient from left to right that we see in all three
residuals. FIR emission is sensitive to both the total radiation field and the
dust column along a line-of-sight, and has only a small contribution from
stochastically heated grains. Interestingly, spinning dust models do not
predict any significant change in spinning dust emissivity with dust
temperature (Ali-Haïmoud et al., 2009), so the high correlation with FIR
tracers, which are very sensitive to dust temperature, is surprising. However,
this suggests that the depletion of the spinning dust carriers in regions with
lower temperature is directly proportional to the decrease in FIR emission due
to the dust temperature. Unfortunately, without spectroscopic observations of
the dust population in B30, it hard to make a definitive statement about
relationship between dust grain population and temperature.

Finally, the North West arm is seen in both the Planck 353 GHz as a negative,
and the WISE 22 $\mu$m data as a positive residual. This feature can be seen
in all of the maps shown in Figure 3, and its location relative to COMAP
shifts from being to the right of the COMAP data in the Planck sub-mm bands,
to aligning with COMAP in the FIR, and then to the left of COMAP in the MIR.
This is a classic feature of a PDR, as different grain size populations emit
in different infrared bands, with smaller grains emitting in the MIR in
regions with higher total radiation fields, and larger grains emitting in the
FIR/sub-mm as the grains become more shielded. The fact the FIR residual in
the North West arm is consistent with zero in Figure 12, is a strong indicator
that the spinning dust emission is predominantly associated with the dust
population that is also emitting in the FIR. The fact that this region is also
well modelled by the template coefficient fitted to Region B, suggests that
the same dust population is emitting in both the North West arm and Region B.

####  4.2.4 Spinning Dust Emissivity and Spectrum

A way to determine the origin of spinning dust within a region is to look at
the spinning dust emissivity defined as the spinning dust emission brightness
at a given frequency per unit dust tracer. Common dust tracers that are used
include the IRAS 100 $\mu$m map, the optical depth at 353 GHz, the total
integrated dust radiance, and MIR data containing PAH features (Dickinson et
al., 2018). Each of these are tracers of different dust populations, and are
susceptible to different environmental conditions.

We compared the ratios of spinning dust emission to the dust optical depth at
353 GHz and to emission at 100 $\mu$m for Region A and Region B to ratios from
the literature. We find that Region B is typical of most spinning dust
emitting regions, with a spinning dust brightness per unit 353 GHz optical
depth of $16.89\pm 0.41$ K, and a ratio to $I_{100\mu\mathrm{m}}$ of $34.11\pm
0.58$ $\mu$K/(MJy/sr). For reference the Perseus and $\rho$-Ophiuchus clouds
have ratios of $16.4\pm 3.1$ K, and $24.3\pm 4.0$ $\mu$K/(MJy/sr) and $14.2\pm
4.0$ K, and $9.6\pm 2.1$ $\mu$K/(MJy/sr), respectively (Planck Collaboration
et al., 2011b). Both of these regions are star forming regions and are
associated with PDRs. Comparing the ratios of the Region B template
coefficients to those of Perseus and $\rho$-Ophiuchus, we find that per unit
$\tau_{353}$ (i.e., the total dust column) these regions are very similar,
however for FIR $I_{100\mu\mathrm{m}}$ emission the ratio of Region B to
Perseus is 1.2, while for $\rho$-Ophiuchus it is 3.6. It is not entirely
unexpected that there is a larger scatter in the relative brightness to FIR
tracers, as far FIR emission is more dependent on the local radiation field
(Tibbs et al., 2012b). However, this does imply that, since the emission per
grain is the same in all of these PDRs, that spinning dust emission can
originate in a range of environmental conditions and is not sensitive to the
range of environmental differences between these regions.

We find that the peak frequency of spinning dust is around 30 GHz for the
whole cloud, with a peak frequency slightly below 30 GHz in Region A, and
slightly above 30 GHz in Region B. We have limited data to constrain the peak
of the spinning dust spectrum in B30 (data at 15 GHz and 50 to 60 GHz would
greatly help), however we can use the COMAP in-band spectral indices, given in
Table 7 and Table 8, to see that for Region A the in-band spectral index is
consistent with zero implying we are near to the peak. For Region B, the
spectrum is rising with a significance between 2 and 3$\sigma$, depending on
the dust template, which is what is driving the slightly higher peak
frequency—however, we cannot rule out a higher peak frequency in Region B
entirely with COMAP alone. The peak frequency of both Region A and B are
consistent with typical spinning dust peak frequencies associated with PDRs
(e.g., Perseus and $\rho$-Ophiuchus (Planck Collaboration et al., 2011b)), but
also the typical peak frequencies from surveys of spinning dust emitting
regions within the Galaxy that are likely associated with PDR environments
(Planck Collaboration et al., 2014a; Tramonte et al., 2023).

The most well-studied source of spinning dust emission however comes from
high-latitude spinning dust clouds, where strong correlations between between
microwave and FIR data has been well-known since the earliest AME studies
(Banday et al., 2003; Davies et al., 2006). The best-fitting template
coefficients of these high-latitude clouds are $14.0\pm 0.4$ $\mu$K/(MJy/sr)
relative to $I_{100\mu\mathrm{m}}$, and $5.8\pm 0.2$ K relative to
$\tau_{353}$ (Harper et al., 2023), which are a factor of 2.4 and 2.9 lower
than the template coefficients measured in Region B, and 1.4 and 2.4 times
lower than in Region A. Clearly this suggests that the dust grain population
and environment in high-latitude cirrus clouds is very different to that in
B30 and other PDR regions. The lower emissivity and peak frequency in the
high-latitude clouds suggests that there is a depletion of smaller grain sizes
in these regions, similar to what we are finding in Region A. Spinning dust
emission in high-latitude clouds have also been shown to not strongly
correlate with PAH fraction (Hensley et al., 2016, 2022). Considering that
both environments can produce spinning dust emission, and that we see no
strong preference that the COMAP data correlate with MIR bands that have PAH
feature contamination, this suggests that PAHs are not required for spinning
dust emission and may not be the primary spinning dust carrier.

There have also been a number of measurements of AME regions that have defined
the spinning dust emission per unit IRAS 100 $\mu$m brightness at resolutions
comparable to COMAP. For example, six Hii regions measured by the Cosmic
Background Interferometer (CBI) at 31 GHz found average emissivities of
$3.3\pm 1.7$ $\mu$K/(MJy/sr), except for RCW49 that had an emissivity of
$13.6\pm 4.2$ (Dickinson et al., 2007). Nine other Hii regions surveyed by
(Todorović et al., 2010) found an average emissivity of $3.9\pm 0.8$
$\mu$K/(MJy/sr). The CBI was also used to measure the emissivity of two Lynds
dark clouds LDN 1622 (Casassus et al., 2006) and LDN 1621 (Dickinson et al.,
2010), and found emissivities of $21.3\pm 0.6$ and $18.1\pm 4.4$
$\mu$K/(MJy/sr), respectively. Finally, the Perseus molecular cloud, when
measured by high resolution observations tends to yield emissivities that are
significantly lower than those found by Planck at low resolutions. In summary,
all of these values are much lower than the emissivity of B30 in either Region
A or B by 50 per cent or more. However, the emissivity that we measure for B30
is consistent with that found by Planck at $1^{\circ}$ resolution. The main
difference between COMAP and previous high-resolution measurements of spinning
dust regions is that all previous observations used interferometric
observations, while COMAP is a single-dish total power telescope. This means
COMAP does not filter out extended emission, and so the difference in spinning
dust emissivity indicates that a significant proportion of the total spinning
dust emission originates in the more diffuse, extended phases of the ISM.

##  5 Conclusions

B30 is a sub-region of the PDR bounding the edge of the $\lambda$-Orionis Hii
region. The B30 region has been studied several times at $1^{\circ}$
resolution (Planck Collaboration et al., 2014a; Bell et al., 2019; Cepeda-
Arroita et al., 2021) and was identified as a promising spinning dust emitting
candidate. In this paper we have presented $4.\\!^{\prime}5$ resolution
observations from COMAP, which, combined with ancillary data from GALFACTS,
ACT, Planck, IRAS, and WISE, have revealed B30 to be one of the cleanest
examples of spinning dust detected to date.

We have studied B30, and sub-regions within B30, using both aperture
photometry and template fitting and find that $86.0\pm 0.08$ per cent of the
emission at 30 GHz is due to spinning dust, which we detect above the free-
free background with $7\sigma$ significance. Using template fitting we have
identified that the spinning dust emission is best traced with the FIR and MIR
data at wavelengths less than 100 $\mu$m, with a weak preference for the 60
$\mu$m band. However, we find there is no preference for MIR bands that
contain PAH features, raising further doubts about an association between
spinning dust emission and PAHs.

We have also found evidence of variations of spinning dust emissivity within
B30. Region B has a higher spinning dust emissivity per 353 GHz optical depth
than Region A, when using the dust optical depth as a tracer, while Region A
is slightly brighter per unit MIR brightness. We suggest that the difference
in emissivity per dust grain in Region A is due to differences in the dust
grain population in both regions. We suggest that the most likely explanation
is that Region A has a smaller population of the smallest dust grains than
Region B, which is predicted by spinning dust models to result in lower
spinning dust emissivity and peak frequency just as we have measured in B30
(Ali-Haïmoud et al., 2009). A possible reason for the depletion of small
grains in Region A could be because of coagulation of small grains in to
larger grains within the high density cold clump within Region A. However, we
cannot rule out that the differences in the spinning dust emissivity between
Region A and B are not due to other effects, such as: differences grain dipole
moments, or environmental factors. Certainly we know that environmental
factors must be making an impact as we find the MIR and FIR emissivities are
also different in Region A and B, with Region A having less MIR emission per
unit dust column that is likely due to a lower total ISRF due to increased
shielding from the higher density environment. Ultimately, to fully understand
the physics of what is happening within B30 will require spectroscopic
observations to quantify the dust grain population. This could be achieved
using JWST MIRI observations similar to those recently undertaken of the Orion
bar (Berné et al., 2022).

To conclude, these new observations of B30 within the $\lambda$-Orionis ring
by the COMAP Pathfinder are revealing new possibilities in understanding the
physics of spinning dust emission. Further studies of spinning dust regions
with COMAP are planned in the near future by extending the Galactic plane
survey presented in Rennie et al. (2022), as well as further targets including
the Perseus molecular cloud, the Andromeda galaxy, and the California nebula.
Finally, these observations highlight the critical importance of single-dish,
rather than interferometric, observations to measure spinning dust emission.
This is because we find most of the spinning dust emission is in the diffuse
ISM, and not compact sources, which can be filtered out by interferometric
observations. As for B30, we intend to revisit this analysis in the future
using planned 15 GHz COMAP observations (Cleary et al., 2022; Breysse et al.,
2022), which will allow for more detailed modelling of the spinning dust
spectrum and lead to a more definitive answer to the question of what is the
carrier of spinning dust in B30.

## Acknowledgements

SEH and CD acknowledge funding from an STFC Consolidated Grant (ST/P000649/1)
and a UKSA grant (ST/Y005945/1) funding LiteBIRD foreground activities.

This material is based upon work supported by the National Science Foundation
under Grant Nos. 1517108, 1517288, 1517598, 1518282, 1910999 and 2206834, as
well as by the Keck Institute for Space Studies under “The First Billion
Years: A Technical Development Program for Spectral Line Observations”.

This work was carried out in part at Jet Propulsion Laboratory, California
Institute of Technology, under a contract with the National Aeronautics and
Space Administration.

We acknowledge support from the Research Council of Norway through grants
251328 and 274990, and from the European Research Council (ERC) under the
Horizon 2020 Research and Innovation Program (Grant agreement No. 772253
bits2cosmology and 819478 Cosmoglobe).

## Data Availability

The COMAP 27, 29, 31, and 33 GHz maps of Barnard 30 used in this analysis can
be made available upon request to the authors.

## References

  * Abdo et al. (2010) Abdo A. A., et al., 2010, ApJ, 716, 30
  * Ackermann et al. (2011) Ackermann M., et al., 2011, ApJ, 741, 30
  * Ali-Haïmoud et al. (2009) Ali-Haïmoud Y., Hirata C. M., Dickinson C., 2009, MNRAS, 395, 1055
  * Banday et al. (2003) Banday A. J., Dickinson C., Davies R. D., Davis R. J., Górski K. M., 2003, MNRAS, 345, 897
  * Barrado et al. (2018) Barrado D., et al., 2018, A&A, 612, A79
  * Becker et al. (1991) Becker R. H., White R. L., Edwards A. L., 1991, ApJS, 75, 1
  * Bell et al. (2019) Bell A. C., Onaka T., Galliano F., Wu R., Doi Y., Kaneda H., Ishihara D., Giard M., 2019, PASJ, p. 110
  * Bennett et al. (1986) Bennett C. L., Lawrence C. R., Burke B. F., Hewitt J. N., Mahoney J., 1986, ApJS, 61, 1
  * Berné et al. (2022) Berné O., et al., 2022, PASP, 134, 054301
  * Breysse et al. (2022) Breysse P. C., et al., 2022, ApJ, 933, 188
  * Cara & Lister (2008) Cara M., Lister M. L., 2008, ApJ, 674, 111
  * Casassus et al. (2006) Casassus S., Cabrera G. F., Förster F., Pearson T. J., Readhead A. C. S., Dickinson C., 2006, ApJ, 639, 951
  * Casassus et al. (2008) Casassus S., et al., 2008, MNRAS, 391, 1075
  * Cepeda-Arroita et al. (2021) Cepeda-Arroita R., et al., 2021, MNRAS, 503, 2927
  * Chuss et al. (2022) Chuss D. T., Hensley B. S., Kogut A. J., Guerra J. A., Nofi H. C., Siah J., 2022, ApJ, 940, 59
  * Cleary et al. (2022) Cleary K. A., et al., 2022, ApJ, 933, 182
  * Condon et al. (1998) Condon J. J., Cotton W. D., Greisen E. W., Yin Q. F., Perley R. A., Taylor G. B., Broderick J. J., 1998, AJ, 115, 1693
  * Cooper et al. (2007) Cooper N. J., Lister M. L., Kochanczyk M. D., 2007, ApJS, 171, 376
  * Cutri et al. (2012) Cutri R. M., et al., 2012, Explanatory Supplement to the WISE All-Sky Data Release Products, Explanatory Supplement to the WISE All-Sky Data Release Products
  * Davies et al. (2006) Davies R. D., Dickinson C., Banday A. J., Jaffe T. R., Górski K. M., Davis R. J., 2006, MNRAS, 370, 1125
  * Delabrouille (1998) Delabrouille J., 1998, A&AS, 127, 555
  * Dennison et al. (1998) Dennison B., Simonetti J. H., Topasna G. A., 1998, Publications Astronomical Society of Australia, 15, 147
  * Dickinson et al. (2003) Dickinson C., Davies R. D., Davis R. J., 2003, MNRAS, 341, 369
  * Dickinson et al. (2007) Dickinson C., Davies R. D., Bronfman L., Casassus S., Davis R. J., Pearson T. J., Readhead A. C. S., Wilkinson P. N., 2007, MNRAS, 379, 297
  * Dickinson et al. (2010) Dickinson C., et al., 2010, MNRAS, 407, 2223
  * Dickinson et al. (2018) Dickinson C., et al., 2018, New Astron. Rev., 80, 1
  * Dodson et al. (2008) Dodson R., et al., 2008, ApJS, 175, 314
  * Dolan & Mathieu (2001) Dolan C. J., Mathieu R. D., 2001, AJ, 121, 2124
  * Draine (2011) Draine B. T., 2011, Physics of the Interstellar and Intergalactic Medium. Princeton University Press
  * Draine & Lazarian (1998) Draine B. T., Lazarian A., 1998, ApJ, 494, L19
  * Draine & Lazarian (1999) Draine B. T., Lazarian A., 1999, ApJ, 512, 740
  * Foreman-Mackey et al. (2013) Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125, 306
  * Górski et al. (2005) Górski K. M., Hivon E., Banday A. J., Wandelt B. D., Hansen F. K., Reinecke M., Bartelmann M., 2005, ApJ, 622, 759
  * Greaves et al. (2018) Greaves J. S., Scaife A. M. M., Frayer D. T., Green D. A., Mason B. S., Smith A. M. S., 2018, Nature Astronomy, 2, 662
  * Gregory & Condon (1991) Gregory P. C., Condon J. J., 1991, ApJS, 75, 1011
  * Gregory et al. (1996) Gregory P. C., Scott W. K., Douglas K., Condon J. J., 1996, ApJS, 103, 427
  * Harper (2024) Harper S. E. e. a., 2024, MNRAS, in prep.
  * Harper et al. (2015) Harper S. E., Dickinson C., Cleary K., 2015, MNRAS, 453, 3375
  * Harper et al. (2022) Harper S. E., et al., 2022, MNRAS, 513, 5900
  * Harper et al. (2023) Harper S. E., et al., 2023, MNRAS, 523, 3471
  * Healey et al. (2007) Healey S. E., Romani R. W., Taylor G. B., Sadler E. M., Ricci R., Murphy T., Ulvestad J. S., Winn J. N., 2007, ApJS, 171, 61
  * Healey et al. (2009) Healey S. E., Fuhrmann L., Taylor G. B., Romani R. W., Readhead A. C. S., 2009, AJ, 138, 1032
  * Hensley et al. (2015) Hensley B., Murphy E., Staguhn J., 2015, MNRAS, 449, 809
  * Hensley et al. (2016) Hensley B. S., Draine B. T., Meisner A. M., 2016, ApJ, 827, 45
  * Hensley et al. (2022) Hensley B. S., Murray C. E., Dodici M., 2022, ApJ, 929, 23
  * Hilbe et al. (2017) Hilbe J. M., de Souza R. S., Ishida E. E. O., 2017, Bayesian Models for Astrophysical Data Using R, JAGS, Python, and Stan. Cambridge University Press, doi:10.1017/CBO9781316459515
  * Hoang & Lazarian (2016) Hoang T., Lazarian A., 2016, ApJ, 821, 91
  * Horiuchi et al. (2004) Horiuchi S., et al., 2004, ApJ, 616, 110
  * Hovatta et al. (2008) Hovatta T., Nieppola E., Tornikoski M., Valtaoja E., Aller M. F., Aller H. D., 2008, A&A, 485, 51
  * Huélamo et al. (2017) Huélamo N., et al., 2017, A&A, 597, A17
  * Kauffmann et al. (2008) Kauffmann J., Bertoldi F., Bourke T. L., Evans N. J. I., Lee C. W., 2008, A&A, 487, 993
  * Kellermann et al. (2004) Kellermann K. I., et al., 2004, ApJ, 609, 539
  * Koay et al. (2011) Koay J. Y., et al., 2011, AJ, 142, 108
  * Koenig et al. (2015) Koenig X., Hillenbrand L. A., Padgett D. L., DeFelippis D., 2015, AJ, 150, 100
  * Kogut et al. (1996) Kogut A., Banday A. J., Bennett C. L., Gorski K. M., Hinshaw G., Smoot G. F., Wright E. I., 1996, ApJ, 464, L5
  * Kovalev et al. (2005) Kovalev Y. Y., et al., 2005, AJ, 130, 2473
  * Kuehr et al. (1981) Kuehr H., Witzel A., Pauliny-Toth I. I. K., Nauber U., 1981, A&AS, 45, 367
  * Lamb et al. (2022) Lamb J. W., et al., 2022, ApJ, 933, 183
  * Lang et al. (2000) Lang W. J., Masheder M. R. W., Dame T. M., Thaddeus P., 2000, A&A, 357, 1001
  * Laurent-Muehleisen et al. (1997) Laurent-Muehleisen S. A., Kollgaard R. I., Ryan P. J., Feigelson E. D., Brinkmann W., Siebert J., 1997, A&AS, 122, 235
  * Lee et al. (2017) Lee J. A., Sohn B. W., Jung T., Byun D.-Y., Lee J. W., 2017, ApJS, 228, 22
  * Leighton (1977) Leighton R. B., 1977, Millimeter-wave antenna design, Final Report California Inst. of Tech., Pasadena.
  * Leitch et al. (1997) Leitch E. M., Readhead A. C. S., Pearson T. J., Myers S. T., 1997, ApJ, 486, L23
  * Linford et al. (2012) Linford J. D., Taylor G. B., Romani R. W., Helmboldt J. F., Readhead A. C. S., Reeves R., Richards J. L., 2012, ApJ, 744, 177
  * Lister et al. (2011) Lister M. L., et al., 2011, ApJ, 742, 27
  * Lister et al. (2015) Lister M. L., Aller M. F., Aller H. D., Hovatta T., Max-Moerbeck W., Readhead A. C. S., Richards J. L., Ros E., 2015, ApJ, 810, L9
  * Maddalena & Morris (1987) Maddalena R. J., Morris M., 1987, ApJ, 323, 179
  * Massardi et al. (2009) Massardi M., López-Caniego M., González-Nuevo J., Herranz D., de Zotti G., Sanz J. L., 2009, MNRAS, 392, 733
  * Miville-Deschênes & Lagache (2005) Miville-Deschênes M., Lagache G., 2005, ApJS, 157, 302
  * Murdin & Penston (1977) Murdin P., Penston M. V., 1977, MNRAS, 181, 657
  * Murphy et al. (2010) Murphy E. J., et al., 2010, ApJ, 709, L108
  * Naess et al. (2020) Naess S., et al., 2020, J. Cosmology Astropart. Phys., 2020, 046
  * Neugebauer et al. (1984) Neugebauer G., et al., 1984, ApJ, 278, L1
  * Nieppola et al. (2011) Nieppola E., Tornikoski M., Valtaoja E., León-Tavares J., Hovatta T., Lähteenmäki A., Tammi J., 2011, A&A, 535, A69
  * Paladini et al. (2003) Paladini R., Burigana C., Davies R. D., Maino D., Bersanelli M., Cappellini B., Platania P., Smoot G., 2003, A&A, 397, 213
  * Parsons et al. (2008) Parsons A., et al., 2008, PASP, 120, 1207
  * Peel et al. (2012) Peel M. W., Dickinson C., Davies R. D., Banday A. J., Jaffe T. R., Jonas J. L., 2012, MNRAS, 424, 2676
  * Petrov et al. (2007) Petrov L., Hirota T., Honma M., Shibata K. M., Jike T., Kobayashi H., 2007, AJ, 133, 2487
  * Planck Collaboration et al. (2011a) Planck Collaboration et al., 2011a, A&A, 536, A15
  * Planck Collaboration et al. (2011b) Planck Collaboration et al., 2011b, A&A, 536, A20
  * Planck Collaboration et al. (2014a) Planck Collaboration et al., 2014a, A&A, 565, A103
  * Planck Collaboration et al. (2014b) Planck Collaboration et al., 2014b, A&A, 571, A11
  * Planck Collaboration et al. (2016a) Planck Collaboration et al., 2016a, A&A, 586, A132
  * Planck Collaboration et al. (2016b) Planck Collaboration et al., 2016b, A&A, 594, A10
  * Planck Collaboration et al. (2016c) Planck Collaboration et al., 2016c, A&A, 594, A28
  * Planck Collaboration et al. (2020) Planck Collaboration et al., 2020, A&A, 641, A1
  * Poidevin et al. (2023) Poidevin F., et al., 2023, MNRAS, 519, 3481
  * Rennie et al. (2022) Rennie T. J., et al., 2022, ApJ, 933, 187
  * Richards et al. (2014) Richards J. L., Hovatta T., Max-Moerbeck W., Pavlidou V., Pearson T. J., Readhead A. C. S., 2014, MNRAS, 438, 3058
  * Rickett et al. (2006) Rickett B. J., Lazio T. J. W., Ghigo F. D., 2006, ApJS, 165, 439
  * Sharpless (1959) Sharpless S., 1959, ApJS, 4, 257
  * Shimmins et al. (1975) Shimmins A. J., Bolton J. G., Wall J. V., 1975, Australian Journal of Physics Astrophysical Supplement, 34, 63
  * Silsbee et al. (2011) Silsbee K., Ali-Haïmoud Y., Hirata C. M., 2011, MNRAS, 411, 2750
  * Stanghellini et al. (1998) Stanghellini C., O’Dea C. P., Dallacasa D., Baum S. A., Fanti R., Fanti C., 1998, A&AS, 131, 303
  * Sutton et al. (2010) Sutton D., et al., 2010, MNRAS, 407, 1387
  * Taylor (2013) Taylor A. R., 2013, IOP Conference Series: Materials Science and Engineering, 44, 012019
  * Tibbs et al. (2011) Tibbs C. T., et al., 2011, MNRAS, 418, 1889
  * Tibbs et al. (2012a) Tibbs C. T., et al., 2012a, ApJ, 754, 94
  * Tibbs et al. (2012b) Tibbs C. T., Paladini R., Dickinson C., 2012b, Advances in Astronomy, 2012, 124931
  * Tibbs et al. (2016) Tibbs C. T., et al., 2016, MNRAS, 456, 2290
  * Tielens (2008) Tielens A. G. G. M., 2008, ARA&A, 46, 289
  * Todorović et al. (2010) Todorović M., et al., 2010, MNRAS, 406, 1629
  * Tramonte et al. (2023) Tramonte D., et al., 2023, MNRAS, 519, 3432
  * Vidal et al. (2011) Vidal M., et al., 2011, MNRAS, 414, 2424
  * Vidal et al. (2020) Vidal M., Dickinson C., Harper S. E., Casassus S., Witt A. N., 2020, MNRAS, 495, 1122
  * Vollmer et al. (2008) Vollmer B., Krichbaum T. P., Angelakis E., Kovalev Y. Y., 2008, A&A, 489, 49
  * Weiland et al. (2011) Weiland J. L., et al., 2011, ApJS, 192, 19
  * White & Becker (1992) White R. L., Becker R. H., 1992, ApJS, 79, 331
  * Wiren et al. (1992) Wiren S., Valtaoja E., Terasranta H., Kotilainen J., 1992, AJ, 104, 1009
  * Wright & Otrupcek (1990) Wright A., Otrupcek R., 1990, PKS Catalog (1990, p. 0
  * Wright et al. (2010) Wright E. L., et al., 2010, AJ, 140, 1868
  * Ysard et al. (2022) Ysard N., Miville-Deschênes M. A., Verstraete L., Jones A. P., 2022, A&A, 663, A65
  * Zavala & Taylor (2004) Zavala R. T., Taylor G. B., 2004, ApJ, 612, 749
  * de Oliveira-Costa et al. (1997) de Oliveira-Costa A., Kogut A., Devlin M. J., Netterfield C. B., Page L. A., Wollack E. J., 1997, ApJ, 482, L17

##  Appendix A QSO J0530+13

Figure 13: Best-fit power law spectrum to QSO J0530+13 (NVSS J053056+133155) as measured in the COMAP and GALFACTS maps. The grey points are ancillary data from the literature taken from the NED extragalactic database, indicating significant time variability. Ancillary data from: Shimmins et al. (1975); Kuehr et al. (1981); Bennett et al. (1986); Wright & Otrupcek (1990); Becker et al. (1991); Gregory & Condon (1991); Wiren et al. (1992); White & Becker (1992); Laurent-Muehleisen et al. (1997); Condon et al. (1998); Stanghellini et al. (1998); Horiuchi et al. (2004); Kellermann et al. (2004); Zavala & Taylor (2004); Kovalev et al. (2005); Rickett et al. (2006); Cooper et al. (2007); Healey et al. (2007); Petrov et al. (2007); Cara & Lister (2008); Dodson et al. (2008); Hovatta et al. (2008); Vollmer et al. (2008); Massardi et al. (2009); Abdo et al. (2010); Ackermann et al. (2011); Koay et al. (2011); Lister et al. (2011); Nieppola et al. (2011); Planck Collaboration et al. (2011a); Linford et al. (2012); Richards et al. (2014); Lister et al. (2015); Lee et al. (2017). Table 9: Flux densities measured in the COMAP and GALFACTS maps using the aperture given in Table 1.  Frequency | Flux Density
---|---
GHz | Jy
1.447 | $1.70\pm 0.10$
27 | $1.20\pm 0.10$
29 | $1.30\pm 0.10$
31 | $1.30\pm 0.10$
33 | $1.30\pm 0.10$

Figure 13 shows the spectrum of a radio source QSO J0530+13 that is near to
the main cloud, but is just outside of the region shown in Figure 2. QSO
J0530+13 is a well known variable, flat-spectrum QSO at a redshift of
$z=2.070$ (Dodson et al., 2008). We give the flux densities measured by COMAP
and GALFACTS in Table 9. We find that the flux densities measured by COMAP are
consistent with other measurements in the literature, albeit COMAP estimates
are among the lower measurements for the source at 30 GHz. The fitted spectral
index in Figure 13 is $\alpha=-0.11\pm 0.03$, however this clearly is not an
accurate model of the true source spectrum as can be seen by the the other
available literature values (grey points) taken from the NASA/IPAC
Extragalactic Database (NED555https://ned.ipac.caltech.edu).