Faraday Tomography with CHIME: The “Tadpole” Feature G137+7

Abstract

A direct consequence of Faraday rotation is that the polarized radio sky does not resemble the total intensity sky at long wavelengths. We analyze G137+7, which is undetectable in total intensity but appears as a depolarization feature. We use the first polarization maps from the Canadian Hydrogen Intensity Mapping Experiment. Our 400–729 MHz bandwidth and angular resolution, 17 ′ – 30 ′ , allow us to use Faraday synthesis to analyze the polarization structure. In polarized intensity and polarization angle maps, we find a tail extending 10° from the head and designate the combined object, the tadpole . Similar polarization angles, distinct from the background, indicate that the head and tail are physically associated. The head appears as a depolarized ring in single channels, but wideband observations show that it is a Faraday rotation feature. Our investigations of H i and H α find no connections to the tadpole. The tail suggests motion of either the gas or an ionizing star through the interstellar medium; the B2(e) star HD 20336 is a candidate. While the head features a coherent, ∼ −8 rad m ⁻² Faraday depth, Faraday synthesis also identifies multiple components in both the head and tail. We verify the locations of the components in the spectra using QU fitting. Our results show that approximately octave-bandwidth Faraday rotation observations at ∼600 MHz are sensitive to low-density ionized or partially ionized gas, which is undetectable in other tracers.

Full text

Faraday Tomography with CHIME: The “Tadpole”Feature G137+7
Nasser Mohammed
1,2
, Anna Ordog
1,2
, Rebecca A. Booth
3
, Andrea Bracco
4,5
, Jo-Anne C. Brown
3
, Ettore Carretti
6
,
John M. Dickey
7
, Simon Foreman
8
, Mark Halpern
9
, Marijke Haverkorn
10
, Alex S. Hill
1,2
, Gary Hinshaw
11
,
Joseph W. Kania
12,13
, Roland Kothes
2
, T. L. Landecker
2
, Joshua MacEachern
9
, Kiyoshi W. Masui
14,15
,
Aimee Menard
1,2
, Ryan R. Ransom
2,16
, Wolfgang Reich
17
, Patricia Reich
17
, J. Richard Shaw
9
, Seth R. Siegel
18,19,20
,
Mehrnoosh Tahani
21
, Alec J. M. Thomson
22
, Tristan Pinsonneault-Marotte
9
, Haochen Wang
14,15
, Jennifer L. West
2
,
Maik Wolleben
23
, and Dallas Wulf
19,20
CHIME and GMIMS Collaborations
1
Department of Computer Science, Math, Physics, & Statistics, University of British Columbia, Okanagan Campus, Kelowna, BC V1V 1V7, Canada;
nmohamme@student.ubc.ca
2
Dominion Radio Astrophysical Observatory, Herzberg Research Centre for Astronomy and Astrophysics, National Research Council Canada, PO Box 248,
Penticton, BC V2A 6J9, Canada; anna.ordog@ubc.ca
3
Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada
4
INAF—Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
5
Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
6
INAF-Istituto di Radioastronomia, Via Gobetti 101, 40129 Bologna, Italy
7
School of Natural Sciences, University of Tasmania, Hobart, Tas 7000 Australia
8
Department of Physics, Arizona State University, Tempe, AZ 85287, USA
9
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada
10
Department of Astrophysics/IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The Netherlands
11
UBC Vancouver Department of Physics and Astronomy, 6224 Agricultural Rd, Vancouver BC V6T 1Z1, Canada
12
Department of Physics and Astronomy, West Virginia University, P.O. Box 6315, Morgantown, WV 26506, USA
13
Center for Gravitational Waves and Cosmology, West Virginia University, Chestnut Ridge Research Building, Morgantown, WV 26505, USA
14
MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
15
Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
16
Department of Physics and Astronomy, Okanagan College, Kelowna, BC V1Y 4X8, Canada
17
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
18
Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, ON N25 2YL, Canada
19
Department of Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
20
Trottier Space Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7, Canada
21
Banting and KIPAC Fellowships: Kavli Institute for Particle Astrophysics & Cosmology (KIPAC), Stanford University, Stanford, CA 94305, USA
22
ATNF, CSIRO Space & Astronomy, Bentley, WA, Australia
23
Skaha Remote Sensing Ltd., 3165 Juniper Drive, Naramata, BC V0H 1N0, Canada
Received 2024 January 16; revised 2024 May 24; accepted 2024 May 24; published 2024 August 8
Abstract
A direct consequence of Faraday rotation is that the polarized radio sky does not resemble the total intensity sky at
long wavelengths. We analyze G137+7, which is undetectable in total intensity but appears as a depolarization
feature. We use the first polarization maps from the Canadian Hydrogen Intensity Mapping Experiment. Our
400–729 MHz bandwidth and angular resolution, 17
¢
–
3
0
¢
, allow us to use Faraday synthesis to analyze the
polarization structure. In polarized intensity and polarization angle maps, we find a tail extending 10°from the
head and designate the combined object, the tadpole. Similar polarization angles, distinct from the background,
indicate that the head and tail are physically associated. The head appears as a depolarized ring in single channels,
but wideband observations show that it is a Faraday rotation feature. Our investigations of H Iand Hαfind no
connections to the tadpole. The tail suggests motion of either the gas or an ionizing star through the interstellar
medium; the B2(e)star HD 20336 is a candidate. While the head features a coherent, ∼−8 rad m
−2
Faraday depth,
Faraday synthesis also identifies multiple components in both the head and tail. We verify the locations of the
components in the spectra using QU fitting. Our results show that approximately octave-bandwidth Faraday
rotation observations at ∼600 MHz are sensitive to low-density ionized or partially ionized gas, which is
undetectable in other tracers.
Unified Astronomy Thesaurus concepts: Interstellar medium (847);Interstellar magnetic fields (845);Stellar-
interstellar interactions (1576);Radio astronomy (1338);Interstellar dust (836);Interstellar clouds (834);Warm
ionized medium (1788);Polarimetry (1278);Proper motions (1295);Radio interferometry (1346)
1. Introduction
Investigations of the Galactic interstellar medium (ISM)have
revealed the pervasive presence of magnetic fields and ionized
gas (Ferrière 2001). Observations of radio polarization can probe
various scales and phases of the ISM, revealing crucial
information about the interplay of magnetic fields with other
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 https://doi.org/10.3847/1538-4357/ad5099
© 2024. The Author(s). Published by the American Astronomical Society.
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further
distribution of this work must maintain attribution to the author(s)and the title
of the work, journal citation and DOI.
1

energy sources. Deriving the three-dimensional configuration of
the magnetic field from polarization data can be challenging;
nevertheless, recent observations have enabled progress toward a
much clearer picture of the evolution of the ISM and the
formation of clouds and stars (e.g., Tahani et al. 2022a,2022b).
At wavelengths of ∼1–100 cm, polarized radiation largely
arises from synchrotron emission generated by cosmic-ray
electrons as they spiral around magnetic fields. Polarized
radiation beyond the Earth’s atmosphere was first detected by
Westerhout et al. (1962)and Wielebinski et al. (1962)and then
extensively mapped by Brouw & Spoelstra (1976). Recent
surveys of this polarized radiation have Nyquist-sampled wide
areas of the sky in different frequency ranges (Wolleben et al.
2019,2021; Carretti et al. 2019).
Linearly polarized electromagnetic waves undergo Faraday
rotation as they propagate through a magneto-ionic medium.
The resulting change in polarization angle informs us of
electron density and magnetic field strength and direction.
Exploiting this effect, polarized emission from extragalactic
sources propagating through the Galaxy has been used to
measure the two-dimensional distribution of magnetic fields in
the Milky Way and nearby galaxies averaged along the line of
sight (Brown et al. 2003; Taylor et al. 2009; Mao et al. 2012a;
Ordog et al. 2017; Tahani et al. 2018; Van Eck et al. 2021;
Hutschenreuter et al. 2022; Thomson et al. 2023). The Faraday
rotation of the emission of the Galaxy itself is an especially
powerful probe of the diffuse ISM because the emitting cosmic
rays and the Faraday-rotating thermal gas are mixed, where
these emission regions illuminate different Faraday-rotating
regions along the line of sight (e.g., Gaensler et al. 2001; Mao
et al. 2012b; Van Eck et al. 2017).
Faraday rotation probes the convolution of ionized gas
density and the line-of-sight magnetic field; therefore, it is
sensitive to two distinct components of the ISM. The majority
of the ionized gas in the Milky Way ISM is found in the warm
ionized medium (WIM), traced by Hαemission with an
ionization fraction 90% based on observations of the [OI]
λ6300 line (Hausen et al. 2002). However, particularly at low
frequencies 1 GHz, Faraday rotation is sensitive to very small
columns of free electrons and might trace a warm partially
ionized medium (Heiles & Haverkorn 2012)or the low (few
percent; Wolfire et al. 2003; Jenkins 2013)ionization in the
warm neutral medium (Foster et al. 2013; Van Eck et al. 2017;
Bracco et al. 2022). In fact, low-frequency Faraday rotation
observations may not be sensitive to the traditional WIM
(Haffner et al. 2009)at all because the electron density there is
high enough to cause depolarization (DP), even with weak
magnetic fields (Van Eck et al. 2017).
Burn (1966)established the formalism for extracting three-
dimensional information on the diffuse magneto-ionized ISM
with mixed synchrotron emission and Faraday rotation.
However, the technique requires data over a wide range of
wavelength squared (λ
2
), which became feasible only recently
with the advent of radio telescopes equipped with wideband
receivers and modern digital signal processors (Brentjens & de
Bruyn 2005; Heald 2009). Useful λ
2
coverage typically implies
low frequencies and wide bandwidths (ideally octave or more).
The use of Faraday synthesis,
24
a form of Faraday tomography
(Takahashi 2023), enables studies of the large-scale structure of
the magnetic field (Dickey et al. 2019,2022; Erceg et al. 2022),
and also of individual objects and small regions (e.g.,
Schnitzeler et al. 2007; Van Eck et al. 2017,2019; Thomson
et al. 2019,2021). Direct modeling of the spectra of Stokes
parameters Qand U(QU fitting)has proven able to detect
multiple Faraday depth components in Faraday complex
spectra more reliably than Faraday synthesis, but with the
drawbacks of needing considerably longer computational time
for each line of sight and requiring us to assume a Faraday
rotation model (Farnsworth et al. 2011;O’Sullivan et al. 2012;
Ideguchi et al. 2014; Sun et al. 2015). In practice, one often
uses Faraday synthesis to inform the selection of models for
QU fitting.
Here, we study a region, G137+7, first discovered by
Berkhuijsen et al. (1964)in a polarization survey of the northern
sky at 610MHz as a ring of low polarization, 2°in diameter,
centered on ℓ=+137°,b=+7°. It lies in the so-called Fan
region, an area otherwise bright in polarized intensity and
uniform in polarization angle at 408 MHz (Verschuur 1968).
Verschuur (1969)associated it with the star HD 20336 (distance
246 ±20 pc; Gaia Collaboration et al. 2023), suggesting that the
B2(e)star had tunneled its way through a cloud of neutral
hydrogen, disrupting it and ionizing a portion of the hydrogen
gas. Haverkorn et al. (2003)detected this polarized circular object
at 350 MHz, but considered HD 20336 an unlikely progenitor for
the feature on account of the star’s high proper motion of
18 mas yr
−1
being too large to maintain a circular Strömgren
sphere. Instead, they suggest that the structure would be
elongated in the direction opposite to the motion of the star.
Iacobelli et al. (2013)used 150 MHz Faraday synthesis to place
the object at a distance of ∼100 pc, possibly in the wall of the
Local Bubble. The lack of a detectable H II region led to the
suggestion that the source of ionization might be an unidentified
white dwarf. In this paper, we present observations that reveal a
tail-like prominence extending approximately 10°from a
prominent circular region of Faraday rotation, coincident with
the structure studied by earlier authors. This head-tail structure
has led us to name G137+7thetadpole.
The outline of this paper is as follows. In Section 2,wereview
Faraday rotation and Faraday synthesis. In Section 3,wedescribe
the Canadian Hydrogen Intensity Mapping Experiment (CHIME)
data (Section 3.2), the Dominion Radio Astrophysical Observa-
tory (DRAO)Synthesis Telescope (ST)data (Section 3.3),and
published data sets to which we compare the CHIME maps
(Section 3.4). We present the observed features of the tadpole in
Section 4and discuss its origin in Section 5. We summarize the
paper in Section 6. In Appendix A, we present simulations of the
impact of marginally resolved Faraday complexity on Faraday
synthesis observations. In Appendix B, we present our QU-fitting
results.
2. Faraday Rotation and Faraday Synthesis
If a polarized photon is emitted with an intrinsic polarization
angle χ
0
, the polarization angle we measure at wavelength λ
after this signal has been Faraday rotated by the Galactic ISM is
.1
02
cc fl=+·()
The Faraday depth, f,isdefined as (Ferrière et al. 2021)
Blnd
rad m 0.81 cm G pc ,2
e
2emission
observer
3
ò
f
m
=
--
() ·()
24
We mostly adopt the terminology described in Table 1 of Sun et al. (2015):
“Faraday depth,”“Faraday spectrum,”“Faraday synthesis”(Brentjens & de
Bruyn 2005),“RMSF,”“Faraday clean”(Heald 2009), and “3D Faraday
synthesis”(Bell & Enßlin 2012).
2
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

where n
e
is the electron density of the ISM, and we are
projecting the magnetic field, B, along our line of sight, dl.
There is a Fourier transform-like relationship between the
observable complex polarization
25
PQiU
2
l=+
˜() and the
Faraday spectrum Ff
˜()
, which is recoverable through a process
known as Faraday synthesis (Burn 1966; Brentjens & de
Bruyn 2005). The polarized intensity at each Faraday depth is
pI Q U
22
fffº+() () (), where p(f)is the fractional
polarization and Iis the total intensity. The Faraday spectrum
is the spectrum of polarized intensity as a function of Faraday
depth for each line of sight. A weighting function W(λ
2
)
introduces a rotation measure spread function (RMSF),
R
f
˜()
,
the Fourier transform of W(λ
2
). Gaps in W(λ
2
)result in
sidelobes in
R
f
˜()
. Utilizing polarization data over a wide range
of wavelengths allows the creation of a (complex)Faraday
depth cube of Fℓ b,,f
˜(
)
for Galactic coordinates (ℓ,b).
The Faraday depth resolution, measured as the FWHM of the
main lobe of
R
Rff=() ∣
˜()
∣
, can be approximated as
(Schnitzeler et al. 2009)
3.8 3
max
2
min
2
df ll
»-()
for reference wavelength λ
0
(the wavelength to which the
polarization angles are derotated; Brentjens & de Bruyn 2005,
Equations (25)–(26)) set to the average λ
2
in the band (as we do
in this paper). The largest-scale feature in Faraday depth space
that is not depolarized is (Brentjens & de Bruyn 2005)
.4
max scale
min
2
fp
l
»
-()
Rudnick & Cotton (2023)argue that setting λ
0
=0 recovers
additional information and modifies Equations (3)and (4), but
we use traditional Faraday synthesis in this work.
3. Data and Instruments
3.1. CHIME and Global Magneto-ionic Medium Survey
Surveys
This work is a part of the Global Magneto-Ionic Medium
Survey (GMIMS), a collaboration using telescopes in the
Northern and Southern hemispheres to obtain all-sky diffuse
polarization maps with frequency coverage and resolution
designed to, in combination, be sensitive to large Faraday depth
scales (100 rad m
max scale 2
f
~
--)with fine sensitivity to small
Faraday depth structures (δf∼10 rad m
−2
). This requires
frequency coverage from ∼300–1800 MHz with thousands of
frequency channels. GMIMS also requires sensitivity to all
spatial scales above the resolution limit, which prefers the use
of single-antenna telescopes. GMIMS low-band south
(300–480 MHz using the Murriyang Telescope at the Parkes
Observatory; Wolleben et al. 2019)and high-band north
(1280–1750 MHz using the John A. Galt Telescope at DRAO;
Wolleben et al. 2021)data products are public. This work uses
prerelease data from the low-band north survey using CHIME
at DRAO. The CHIME instrument is described in detail by
CHIME Collaboration (2022). The CHIME data pipeline,
including RFI excision, complex gain calibration, averaging
over redundant baselines, and stacking over sidereal days, is
described in CHIME Collaboration (2023). The CHIME/
GMIMS low-band north polarization data set will be described
in detail elsewhere (CHIME & GMIMS Collaborations 2024,
in preparation, hereafter “CHIME/GMIMS survey paper”).We
present a brief overview of the data and processing steps here.
3.2. CHIME/GMIMS Low-band North
We use all-sky diffuse polarization data from CHIME for
polarization observations of the tadpole feature and as the basis
for Faraday synthesis of the region. CHIME consists of four
stationary parallel cylindrical reflectors, measuring 1024
frequency channels across its range of 400–800 MHz. Oriented
north–south, each 100 ×20m
2
cylinder has 256 dual-polariza-
tion linear feeds (Xand Y)spaced every 30 cm along the central
78m of the focal line. CHIME observes the entire meridian at
any given moment with baselines from 0.3–78 m, mapping the
northern sky every sidereal day. This gives the telescope the
ability to collect data at a range of angular scales, resulting in
an effective angular resolution of approximately
3
0
¢
at
400 MHz (Masui et al. 2019). We exclude autocorrelations of
feeds with themselves. As an interferometer, CHIME is
missing the very largest scales corresponding to baselines
<0.3m or angular scales 50°. A future survey with the DRAO
15 m Telescope (A. Ordog et al. 2024, in preparation)will
provide the largest scales for the final GMIMS low-band north
data product.
We generate full sky maps known as ringmaps by
performing a one-dimensional Fourier transform on ∼21 s
samples of the visibilities in the north–south direction along the
meridian. As the sky passes through the primary beam, we
sample the full range of right ascension values with these one-
dimensional images each sidereal day, which we combine to
produce the full map. We employ stacked ringmaps, using
nighttime-only visibilities from 102 nights of data collected
from 2019 January to November. The CHIME beam profile,
which is declination dependent and somewhat different in the
XX and YY polarizations due to the cylindrical and stationary
design of the telescope, is one of our largest uncertainties; for
this reason, in this paper, we report CHIME data in jansky per
beam rather than brightness temperature units and confine
ourselves to a relatively small declination range at a low zenith
angle (21°)where the beam is nearly constant.
The ringmaps we use do not have beam deconvolution
applied. There are small artifacts in the image, resulting from
this, which we describe in Section 4.5; however, their presence
is not detrimental to studying structures on the scale of several
degrees, such as the tadpole. In this analysis, we use the
400–729 MHz subset of the full CHIME band, as the highest
frequencies are contaminated by aliasing, which makes the
maps unreliable in the region of interest.
3.2.1. Polarization Angle Calibration
To calibrate CHIME polarization angles UQ0.5 tan 1
cº-(
)
(calculated using the full ±πrange accounting for the signs of U
and Q), we rely only on CHIME co- and cross-polar data
products and two key assumptions: that Stokes V=0(averaged
over right ascension at every declination), and that the gain
difference ΔGbetween the Xand Ypolarizations is small.
Because of the declination-dependent beam properties of
CHIME, we calibrate each declination in the raw maps using
data within a 1°strip, centered on that declination, and covering
25
We use a tilde to indicate complex values.
3
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

the full right ascension range. We focus on the narrow
declination range around G137+7, +60°δ70°. This covers
zenith angles 11°–21°, a region in which the CHIME beam
model is best (CHIME Collaboration 2022,2023).
We represent the co-polar power from the orthogonal feeds
as XX
CC
¢¢
(east–west feeds)and
Y
Y
CC
¢¢
(north–south feeds)and
the (complex)cross-polar term as XY
CC
¢¢
. We use the stacked
XX
CC
¢¢
,
Y
Y
CC
¢¢
, and XY
CC
¢¢
ringmaps. Here, X
C
and Y
C
refer to the
CHIME coordinate system (CHIME Collaboration 2022),in
which the naming of the variables Xand Yis interchanged from
the IAU convention (IAU 1973).(The spherical CHIME
cosmology X
C
and Y
C
coordinate system used here is also
different from the Cartesian CHIME/Fast Radio Burst (FRB)
coordinate system; CHIME/FRB Collaboration 2021.)The
prime notation indicates detected values after passing through
the full CHIME system, so the observed Stokes vector is
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟

I
Q
U
V
YY XX
YY XX
YX
YX
M
0.5
0.5
Re
Im
5
CC C C
CC C C
CC
CC
¢º
¢¢
¢
¢
=
¢¢
+¢¢
¢¢
-¢¢
¢¢
-¢¢
=
()
()
()
()
()
for Müller matrix Mand true sky Stokes vector

. This follows
the IAU convention with linear position angles increasing
counterclockwise when looking at the source (IAU 1973).
Using linear feeds to measure Stokes Qrequires the careful
subtraction of two large numbers (the autocorrelations),
whereas Stokes Uinvolves measuring the small cross-
correlation. For calibration of Qand U, we perform data-based
estimates of the cross terms in Mfollowing Heiles (2002). First,
we assume that the difference in gains G
X
and G
Y
is small
enough to approximate ΔG=(G
Y
−G
X
)/(G
Y
+G
X
)=1. We
calculate the average ΔGat each declination and frequency
from a linear regression of
Y
Y
CC
¢¢
as a function of XX
CC
¢¢
, using
data within a 1°decl. bin (overlapping bins centered on each
declination)and covering the full 24 hr R.A. range. Over the
declination range of the tadpole region (45°–80°)and the
frequencies used in this analysis, we find the mean and median
of ΔGto be −0.43 and −0.38, respectively, with 73% of
declinations and unflagged frequencies having |ΔG|<0.5.
Although this does not strictly satisfy ΔG=1, it is sufficiently
small, so the defined ΔGterm dominates over second-order
corrections. The gain difference is dominated by differences in
the beam solid angle between the two polarizations due to the
asymmetric design of the CHIME telescope. We then apply this
declination- and frequency-dependent ΔGto correct for
leakage between Stokes Iand Q,
/
/
QQIG
G
2
12 6
2
=¢-¢D
-D() ()
Stokes Uand Vare measured from the cross-correlation
products. We assume that 〈V〉=0 from the sky in diffuse
emission because synchrotron emission in low-density astro-
physical environments does not produce circular polarization.
Leakage between Vand Uarises from phase offsets. We
measure a mean phase shift 〈ψ〉(δ,ν)at each declination and
frequency, assuming that 〈V〉=0 and calculate
UU Vcos sin . 7yy= ¢ áñ+ ¢ áñ ()
The 〈V〉=0 assumption leads to high-quality fits even in FRB
observations, where the assumption has less clear physical
justification than in the diffuse polarized emission we
investigate (Mckinven et al. 2023).Wefind that the phase
shift is linear in frequency, consistent with a cable delay
τ=〈ψ〉/2πν ∼1 ns for the diffuse emission, as Mckinven et al.
(2021, their Appendix A)found in CHIME/FRB data.
In Figure 1, we compare the calibrated data to the Dwingeloo
telescope survey at 610 MHz in the Fan region (Brouw &
Spoelstra 1976). There is a strong correlation between Dwingeloo
Uand CHIME Uand Dwingeloo Qand CHIME Qin those
directions for which there is Dwingeloo data, with correlation
coefficient Rvalues of 0.91 for U−Uand0.89forQ−Q
comparisons. This is a significant improvement from the
uncalibrated correlation coefficients of 0.76 and 0.59, respec-
tively. We find a remaining leakage of up to 20% in Stokes Q
based on unresolved point source measurements. Using the mean
orthogonal distance between each point and the fitted line, we find
that noise from CHIME and Dwingeloo data describes ≈70% of
the scatter in Figure 1. The polarization angle correlation, also
shown in Figure 1, is also improved through calibration, and most
outliers are points with low polarized intensity (yellow dots),
where the uncertainty in derived χis high.
We show the resulting CHIME Qand Umaps, with the
χ=0 reference axis rotated to the north Galactic pole, in
Figure 2. While Stokes Ito Qleakage does exist in our data, the
tadpole structure cannot simply be the result of leakage.
Although there is total intensity emission over the entire Fan
region, including the tadpole, this emission is featureless on
small scales and thus cannot produce spurious polarization
matching the tadpole in morphology. Furthermore, the tadpole
cannot be the product of Stokes Iemission originating at large
angular distances (such as the Galactic plane)and seen in far
sidelobes. While the far sidelobes have poor polarization
properties, their polarization averages to low values over
sizable areas. Moreover, with linear feeds, leakage from Iis
primarily into Q, not U(in the native equatorial coordinates of
CHIME), but the tadpole is already evident in Stokes Uin
equatorial coordinates (not shown).
The slopes of U−Uand Q−Qinform the calculation
of the beam solid angle in converting jansky per beam to
brightness temperature units. From these slopes, we deduce that
1 Jy beam
−1
corresponds to 1.79K. The effective area of
CHIME is, therefore, 4900 m
2
at 610 MHz, confirming that, in
our application, CHIME acts like a large single-antenna
telescope. This paper focuses on Faraday rotation effects,
meaning that the primary data product is the polarization angle
and its variation with frequency. Absolute calibration of the
amplitude scale is thus of minor significance for the present
work, and we report intensities in units of jansky per beam,
leaving a more careful conversion to temperature units for the
CHIME/GMIMS survey paper.
The CHIME observations were made in 2019, at solar
minimum. Only nighttime data were used. The observations
were not corrected for Faraday rotation in the ionosphere, but we
expect the effect to be smaller than 1 rad m
−2
, with an rms value
of 0.3 rad m
−2
. The result is a small decrease in polarized
intensity since we averaged together observations from different
nights.
3.2.2. Faraday Synthesis on CHIME Data
We apply Faraday synthesis to the Stokes Qand Ucubes
from the calibrated CHIME polarization data in Galactic
coordinates using RMTools_3D in the RM-Tools software
4
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

package (Purcell et al. 2020). We show images of the main
products of Faraday synthesis in Figure 3, and the magnitude of
the RMSF along with frequency and λ
2
coverage in Figure 4.
For each pixel in the maps, we calculate the dirty Faraday
spectrum out to ±200 rad m
−2
sampled every 0.5 rad m
−2
. This
extent in fis sufficient to include the major structures without
being dominated by sidelobes. We do not convolve the CHIME
data to a common resolution prior to Faraday synthesis, as this
may be unreliable due to uncertainties in the synthesized beam
shape. With the resolution only varying between 30~
¢
(at
400 MHz)and 17~
¢
(at 729 MHz), structures on the scale of
the tadpole (several degrees)are largely unaffected.
The 400–729 MHz frequency coverage yields δf=9.7 rad m
−2
and 19 rad m
max scale 2
f
=
--. With max scal
e
d
ff<-,weexpect
CHIME data to resolve somewhat extended Faraday depth
structures. For all lines of sight in the tadpole region
(Section 4.2), we apply the RM-Tools implementation of the
RM-CLEAN algorithm (Heald 2009)to reduce the sidelobes in the
spectra, using a CLEAN threshold of 0.2 Jy beam
−1
basedonan
estimate of the noise in the dirty spectra. We present CLEANed
spectra in Section 4.2 below.
Using the rmtools_peakfitcube algorithm in RM-
Tools, we obtain the peak Faraday depth and its associated
error for every spectrum along all lines of sight. The resulting
map is shown in Figure 3(b). We use peak Faraday depths
rather than a first moment (Dickey et al. 2019)to focus on the
Faraday depth of the brightest feature in each line of sight
rather than a weighted mean Faraday depth in Faraday complex
regions.
We show the integrated polarized intensity across the
Faraday depth spectra as a zero moment map in Figure 3(a).
A polarization angle map derotated to χ
0
by the peak Faraday
depth at each pixel is shown in Figure 3(c).
3.3. DRAO Synthesis Telescope Observations
We use new and previously published polarized continuum
and H Iobservations from the DRAO ST (Landecker et al.
2000). The ST continuum observations combine four 7.5 MHz-
wide frequency channels within a 35 MHz bandpass centered
on 1420.4 MHz to measure Stokes Qand Uusing dual circular
polarization feeds. The ST H Iobservations are produced by a
256-channel spectrometer with a velocity range between 211
and 1.32 km s
−1
spectral resolution. Existing observations
come from the Canadian Galactic plane survey (CGPS; Taylor
et al. 2003; Landecker et al. 2010), covering Galactic latitudes
of −3°<b<+5°. We use a variety of ST fields observed and
calibrated in the same manner as CGPS fields for a number of
projects, some previously published (West et al. 2007; Kothes
et al. 2014), and some unpublished, covering +5°<b<+12°.
In all ST polarized continuum observations, single-channel
1410 MHz polarization observations from the Effelsberg Med-
ium-Latitude Survey (EMLS; Uyanıker et al. 1998,1999;Reich
et al. 2004, P. Reich et al. 2024, in preparation.)provide single-
antenna information. The EMLS data are based on Effelsberg
100 m Telescope observations from latitude |b|<20°, observed
mostly in blocks 7°×7°in size but with many exceptions to
avoid strong source complexes at the map boundaries. Emission
exceeding the map size is missing and was restored by
combining with the northern-sky Galt Telescope survey
(Wolleben et al. 2006). We then combine this single-antenna
data with the ST 1420 MHz data as follows. First, we mosaicked
the ST fields together following Taylor et al. (2003). Then, we
convolve the ST data to 10.′4, slightly larger than the 9 35
EMLS resolution. We then subtract the convolved ST data
(Stokes Qand Useparately)from the EMLS data; the residual is
Figure 1. Comparisons between the Dwingeloo (Brouw & Spoelstra 1976)
absolutely calibrated Qand Uobservations in the Fan region (120°ℓ180°,
−2°b30°)at 610 MHz and CHIME 614 MHz. All data points show a
Dwingeloo pointing and the median of corresponding CHIME data within the
Dwingeloo beam. The color bar is the CHIME polarized intensity for these
points. For Stokes Qand U, the Dwingeloo data are shown in brightness
temperature units and CHIME data in jansky per beam.
5
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

the large-scale structure missed in the ST data (Reich et al.
1990). Finally, we add the residual to the original ST data to
produce Qand Uimages, including scales from 1
¢
to the full sky.
This technique is somewhat different from that used for the
CGPS, where ST+EMLS data were combined in Fourier space
(Landecker et al. 2010), but produces very similar results. We
refer to this combined data set of interferometric observations
from the ST with single-antenna data from the Effelsberg and
Galt telescopes as “ST+EMLS,”and show the resulting
polarized intensity and polarization angles maps for the tadpole
region in Figures 5(i)and (j).
In our ST atomic hydrogen observations, we incorporate the
HI4PI Survey of H I21 cm brightness temperature, with an
angular resolution of 16 2, velocity coverage of 600 km s
−1
,
and spectral resolution of 1.49 km s
−1
(HI4PI Collaboration
et al. 2016), to provide the majority of the single-antenna
information. The fields we incorporated that were previously
processed for the CGPS used the DRAO 26 m data to provide
short-spacing information on account of HI4PI being unavail-
able at the time. We process a wider field of view for the H I
observations than for the polarized continuum observations—
covering Galactic latitudes of −4°<b<+12°and longitudes
of 126°<l<149°—to highlight typical fluctuations seen
across the diffuse neutral medium (see Section 5.1). For each
ST field in this region, we determine continuum emission by
averaging the H Ichannels void of 21 cm emission, then
subtracting this to isolate only H Iemission. We calibrate,
merge short-spacing and ST data, and mosaic the H Ifields by
the same procedure used for the CGPS Taylor et al. (2003).
This results in the H Ibrightness temperature map, which we
refer to as “ST+HI4PI.”
3.4. Ancillary Data Sources
We use data from the Westerbork Synthesis Radio Telescope
(WSRT)at 150 MHz (Bernardi et al. 2009; Iacobelli et al.
2013, provided by M. Iacobelli, 2023, private communication)
and 350 MHz (Haverkorn et al. 2003)to supplement discus-
sions of observed DP. We summarize the observing parameters
for all four polarization data sets used in this paper in Table 1.
The five channels in the 350 MHz data are not sufficient for
Faraday synthesis, measuring only the rotation measure
RM =dχ/dλ
2
. For the 150 MHz data, only post-Faraday
synthesis data are available, so we cannot show single-
frequency images or perform QU fitting on these data. We
show the WSRT polarized intensity and polarization angle
maps in Figures 5(a)–(d).
We use the Wisconsin H-Alpha Mapper (WHAM)survey of
Hαemission to study ionized hydrogen in the region (Haffner
et al. 2003,2010). WHAM has an angular resolution of 1°and
provides a kinematically resolved map of Hαemission within
≈100 km s
−1
of the local standard of rest (LSR)with 12 km s
−1
spectral resolution.
4. Features of the Tadpole
4.1. Morphology in Single-frequency Images
We show images of the tadpole region in Qand Uat 614 MHz
in Figure 2, image products derived from Faraday synthesis with
CHIME in Figure 3,andpI and χfrom the polarization data sets
described above, covering 150–1420 MHz, in Figure 5.The
tadpole is immediately apparent in the single-channel CHIME Q
and Uimages in Figure 2with a circular feature we call the head
near (ℓ,b)=(137°,+7°)and a tail extending to the right as far
as (127°,+6°),mostclearlyinU. The structure as a whole
strongly resembles the larval stage of amphibians, leading us to
nickname it the tadpole. We use the name “G137+7”to refer to
the circular region first identified by Verschuur (1968), and the
name tadpole to describe the entire feature, including the tail.
The head (G137+7)is the feature that has been studied since
Verschuur (1968); it is visible in all channels in Figure 5.
At 150 MHz (Figures 5(a)(b)), the head is evident as a large,
diffuse structure in pI. There is a circular pattern to the
polarization angles, suggesting rapid wrapping through π
radians as one moves outward radially from the center of
the head.
At 350 MHz (Figures 5(c),(d)), the head appears as a ring in pI
(Figure 5(c)). Haverkorn et al. (2003)measured RM =−8radm
−2
in the center of the head. At this frequency, the head is also a ring
in χ, with approximately two full rotations through πradians in the
radial direction. This is consistent with the RM changing from
−8radm
−2
in the center of the head to 0 rad m
−2
outside the head,
Figure 2. Images of the tadpole region in Stokes Qand Uat 614 MHz in Galactic coordinates. The “×”markers indicate the position of B2(e)star HD 20336
(the ×near the center of the circular tadpole head)as well as the selected spectra shown in Figure 7. The thin black line represents the LSR-corrected proper motion of
HD 20336, projected backward in time over 3 Myr, with each dot representing 1 Myr. The translucent lines represent the error cone, which is dominated by the
uncertainty in the LSR correction.
6
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

which would correspond to an angle change Δχ=fλ
2
=6
radians. Haverkorn et al. (2003)point out an elongated structure of
high pI extending northwest, which they say does not necessarily
have the same origin as the ring; this is evident in both pI
(Figure 5(c)) and χ(Figure 5(d)). This appears to be the tail.
At 410 MHz in the CHIME pI data, the clearest signature of
the head is a narrow ring of low polarized intensity, which
extends in a nearly complete circle. At 614 MHz, there is a
similar ring of low polarized intensity, but only in a semicircle
on the left (east)side of the head. This feature is one beam
wide, a clear signature of beam DP, with the polarization angle
changing within the beam such that there is destructive
interference, reducing the polarized intensity (Sokoloff et al.
1998; Gaensler et al. 2001). The same feature is evident in pI
from the Faraday synthesis products in Figure 3, but it does not
stand out as much: by using information at a wide range of λ
2
,
the Faraday synthesis product is less sensitive to beam DP than
single-frequency images. Furthermore, if the depolarized ring
arises from beam DP, we would not expect to see it in the
ST+EMLS data, due to the significantly smaller beam
(
1
¢
compared to
3
0
¢
). This is, in fact, the case in Figure 5(i):
none of the head, the depolarized ring, or the tail is evident
in pI.
In polarization angle, the 410 MHz CHIME data show a
clear wrap through πradians moving radially from the center of
the head to outside the ring (Figure 5(f)). The tail of the tadpole
stands out clearly, especially as a polarization angle feature in
Figure 3(c)and Figures 5(f),(h). The tadpole, both head and
tail, is also visible at 1420 MHz in the ST+EMLS polarization
angle image (Figure 5(j)), despite not being evident in pI. The
large-scale structure at 1420 MHz is similar to that observed in
CHIME 614 MHz polarization angle (Figure 5(h)), where the χ
Figure 3. Maps of products of Faraday synthesis generated from the
400–729 MHz channels of CHIME. (a)Moment zero integrated polarized
intensity. (b)Faraday depth of highest peaks of the Faraday depth spectra. (c)
The derotated polarization angle (i.e., the angle at the point of emission). The
“×”markers are as in Figure 2.
Figure 4. Top: magnitude of the RMSF for the full CHIME frequency range
(black lines), the usable CHIME frequency channels (cyan line), and the full
WSRT 150 MHz frequency range (magenta line). See Table 1. Bottom: usable
CHIME frequencies, W(λ
2
)(bottom axis)or W(ν)(top axis). The WSRT
RMSF shown here assumes full frequency coverage from 138–156 MHz
because we have no record of the missing frequencies.
7
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

Figure 5. The tadpole depicted in polarized intensity (left)and polarization angle (right). From top to bottom: (a),(b)Bernardi et al. (2009)Faraday synthesis data at
frequencies ∼150 MHz with the WSRT at f=−2 rad m
−2
(a frequency data cube is unavailable),(c),(d)Haverkorn et al. (2003)single-frequency polarized intensity
and polarization angle at 349MHz, CHIME data at (e),(f)410 MHz and (g),(h)614 MHz, and (i),(j)1.4 GHz DRAO ST+EMLS data. “×”markers are as in
Figure 2. Beams are shown within each image. Beams for the WSRT and ST+EMLS data are too small to be easily visible (see Table 1).
8
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

values agree in sign with that of ST+EMLS. The values of |χ|
are smaller at 1420 MHz than at 614 MHz, which is consistent
with the expected reduction in Faraday rotation at higher
frequencies. We note some smaller structures on sub-tadpole
scales in ST+EMLS data not present in CHIME, which may
arise from probing larger physical depths at a higher frequency
and with a much smaller beam, combining to yield a more
distant polarization horizon (Uyanıker et al. 2003). In contrast,
although the WSRT data have an angular resolution on the
order of magnitude of the ST+EMLS data, the larger λ
2
means
we expect the polarization horizon to be closer, possibly
probing physical depths more similar to CHIME than to the
ST+EMLS.
4.2. Faraday Depths
While the tadpole is prominent in polarization angle images, it
does not stand out from the background in total intensity in
single-channel images. Previous studies (Haverkorn et al. 2003;
Bernardi et al. 2009;Iacobellietal.2013)found the head to show
strong negative Faraday rotation peaking at f≈−8radm
−2
.The
data sets used in these studies and their observing parameters are
listed in Table 1.
We show pI images at f=−15, −7, and −3radm
−2
using
CHIME and WSRT 150 MHz data in Figure 6. In both data sets,
the head stands out as a strong feature in pI at −7radm
−2
with
little surrounding emission. Furthermore, in both data sets the
head appears to be a DP feature in pI at −3radm
−2
, but with
differing morphology; in WSRT, the entire region of the head
shows little or no polarized intensity, while there is a ring of
polarized intensity outside the head. This suggests pure Faraday
rotation: the polarized intensity is moved from f=−3to
−7radm
−2
. At CHIME frequencies, the −3radm
−2
image
shows a narrow depolarized ring immediately outside the head,
but it lacks the clearly defined region of bright emission we find
in WSRT. At f=−15 rad m
−2
, a structure appears in the
CHIME data, which is absent in the WSRT data. The tail of the
tadpole stands out from its surroundings at this Faraday depth,
with the bright emission extending partway around the head,
tracing the depolarized ring that appears at the other two Faraday
depths shown. The tail also appears as reduced pI at
f=−7radm
−2
in CHIME data.
We show Faraday spectra at three positions—one in the
head, one in the tail, and a background position—in Figure 7
for CHIME and 150 MHz WSRT data. In the head, we find
multiple peaks in both data sets. In the 150 MHz data, there are
peaks at ≈−8, −4, and 0 rad m
−2
, with polarized intensities of
∼5, 4, and 6 Jy beam
−1,
respectively. In CHIME data, there is
also a Faraday depth peak at f≈−8 rad m
−2
with
pI ≈1.3 Jy beam
−1
, while a secondary peak is at +5 rad m
−2
with pI ≈0.4 Jy beam
−1
. There is no evidence of a peak near
−4 rad m
−2
. However, with δf=9.7 rad m
−2
in the CHIME
data, we would not expect to resolve two peaks separated by
≈4 rad m
−2
. In the tail, we see two peaks in both the CHIME
and 150 MHz data at f≈−2 and −14 rad m
−2
(pI ≈1.75 and
0.35 Jy beam
−1
), and f≈−4 and −12 rad m
−2
(pI ≈3.4 and
1.8 Jy beam
−1
)respectively. The CHIME peaks in both the
head and tail are separated by close to δf, suggesting that the
separation of the peaks may be an artifact of the RMSF and
may not be physically meaningful, as we discuss in Section 4.3
below. Off-tadpole, we find only one peak in the CHIME data
at f≈−2 rad m
−2
with pI ≈1.35 Jy beam
−1
. There is a bump
in the spectrum seen at ∼10 rad m
−2
; however, this bump does
not coincide with any notable peak in the 150 MHz data.
Rather, we find two peaks at f≈−2 and −8 rad m
−2
with
polarized intensities ≈4 and 3 Jy beam
−1
, respectively.
Plotting the fitted peak Faraday depth values (as described in
Section 3.2.2)in Galactic coordinates gives the map shown in
Figure 3(b). This image lets us view the Faraday depth
morphology of the region more effectively. In this image, the
head of the tadpole is clearly visible, showing significant
negative Faraday depths (around −7to−8 rad m
−2
)compared
to the surrounding region (around −1 rad m
−2
). In contrast with
the single-frequency images (Stokes Qand Uin Figure 2and
polarization angle in Figure 5)the tail of the tadpole does not
stand out in peak Faraday depth.
4.3. Faraday Complexity
Using the peak Faraday depths in Figure 3(b), we derotated
the observed polarization angle to the nominal intrinsic angle
by rearranging Equation (1). The result, shown in Figure 3(c),
reveals the tail as a distinct feature, separate from its
background, and spatially uniform in polarization angle. If
the tadpole is solely a Faraday rotation phenomenon, with a
single Faraday-simple feature representing each line of sight,
we would not expect it to be visible in a map of derotated χ.
The fact that it does appear means that either the tadpole
contributes significant polarized emission distinct from its
surroundings, or there is Faraday complexity along the lines of
sight passing through it. The latter possibility is strongly
suggested by the sample Faraday depth spectra in Figure 7and
the image slices shown in Figure 6.
The separation of the two peaks in the tail in the CHIME data,
≈12 rad m
−2
, is close to the separation between the main lobe
and first sidelobe of the RMSF, which suggests the influence of
Table 1
Observing Parameters
Bernardi et al. (2009), Iacobelli et al. (2013)Haverkorn et al. (2003)This Paper This Paper, Landecker et al. (2010)
Instrument WSRT WSRT CHIME ST+EMLS
Observed field ∼12°×12°∼7°×7°all-sky Galactic plane plus 20°×7°extension
Frequencies 138–156 MHz 341–375 MHz 400–729 MHz 1.4 GHz
Channels 2048 ×9.8 kHz 5 ×5 MHz 844 ×390 kHz 1 ×35 MHz
λ
2
coverage 3.7–4.7 m
2
0.64–0.77 m
2
0.17–0.56 m
2
0.04 m
2
δf(equation 3)3.8 rad m
−2
29 rad m
−2
9.7 rad m
−2
n/a
max scale
f-(Equation 4)0.8 rad m
−2
n/a 19 rad m
−2
n/a
Angular resolution 2′×2.′25.′0×5517»
¢
to
3
0
¢
1~
¢
Baselines 36–2760 m 36–2760 m 0.3–80 m 0–614 m
Note. Haverkorn et al. (2003)fitRM=dχ/d(λ
2
)without Faraday synthesis and thus have no ability to separate multiple Faraday depth components.
9
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

the λ
2
coverage. In this context, the Faraday complexity is a true
feature but unresolved or marginally resolved. We address this
issue in Appendix A, concluding that while the presence of
multiple peaks in the Faraday spectra is real, the positions of two
peaks separated by δfare modified by the Faraday synthesis
process, as was first demonstrated by Sun et al. (2015).QU
fitting is less subject to this issue; in most but not all cases, QU
fitting recovers the true Faraday depths of multiple screens even
when separated by δf. We investigate the validity of the
secondary peaks further in the following section.
4.4. QU Fitting
In the CHIME Faraday depth spectra, a secondary peak at
f≈−14 rad m
−2
appears as a coherent structure along the tail.
Given the proximity of this feature to the first sidelobe of the
RMSF (Figure 4), it is necessary to investigate the validity of
these secondary peaks. To this end, we employed QU fitting,
using the qufit package in RM-Tools, with the PyMul-
tiNest nested sampler. We examined 51 representative lines
of sight throughout the head and tail of the tadpole and in the
surrounding region. We tested four models: screens at one and
two Faraday depths (1FDand2FD), with and without beam
DP. The fractional polarization for this set of models is given by
pP
Ipe e ,8
k
ki22
0, 22
kk k
0, 224
å
ll
== cfl sl+-
˜( ) ˜() ()
()
where σ
k
is the standard deviation of Faraday depths within the
beam, the subscript 0 refers to quantities at the source of
emission, and the subscript krefers to the individual Faraday
depth components (primary and secondary in our models). The
Figure 6. Images of polarized intensity at f=−15 rad m
−2
(a),(b),−7 rad m
−2
(c),(d), and −3 rad m
−2
(e),(f)from CHIME 400–729 MHz data (left)and WSRT
150 MHz data (right). Note that the fainter loop above and to the left of the head, visible in all three CHIME channels but most clearly at −7 rad m
−2
, is a grating lobe
artifact; see Section 4.5.
10
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

e2k
2
4
sl-factor represents beam DP caused by any unresolved
variation of fwithin the beam. Beam DP can be caused
by unresolved turbulent cells or a gradient of facross the
beam. Setting σ
k
to zero produces the corresponding Faraday
screen(s)with no beam DP, while setting p
0,k
to zero for k>1
produces the one-component model.
For the nested sampling, we used uniform distributions of
priors for all parameters, with f
k
ä[−50, 50]rad m
−2
,
p
0,k
ä[0, 1],χ
0,k
ä[0°, 180°], and σ
k
ä[0, 100]rad m
−2
.We
also constrained the Faraday depths and fractional polarizations
such that |f
1
−f
2
|100 rad m
−2
and ∑
k
p
0,k
1. Following
Thomson et al. (2021), we use the Bayesian evidence to
determine the best-fit models, as described in Appendix B.
For the three representative lines of sight shown in Figure 7,
we found a two-component model with independent beam DP
factors for each component to be the best fit(the full form of
Equation (8)), although the primary and secondary components
of the off-tadpole and head points respectively have low DP.
By contrast, both components for the line of sight through the
tail exhibit significant DP. The results of this model and best-fit
parameters are summarized in Table 2and Figure 8(orange
lines)for these three sample lines of sight, and the fvalues are
marked by vertical lines in Figure 7. Figure 8also shows the
three other models we tested for those lines of sight. A
comparison of the models is presented in detail in Appendix B.
Note that the ripples seen in the data in Figure 8that are not
fitted by the models are the well-known 30 MHz CHIME ripple
caused by reflections between the cylinders and the focal line
(CHIME Collaboration 2022,2023). The Faraday depths for all
51 lines of sight tested are shown in Figure 9, with the
background images indicating the first (top panel)and second
(bottom panel)peaks from the Faraday depth cube, and the
colors of the 51 points indicating the corresponding QU-fitted
Faraday depths from the two-component model with DP.
In the head of the tadpole, most of the 18 tested lines of sight
have a primary component near −7 rad m
−2
(Figure 9, top
panel), with some lines of sight having a weak secondary
component (mostly less than p=0.1; Figure 9, bottom panel).
Since this secondary component is relatively weak, the head is
mostly well-fit with a one-component model with DP. In the
tail of the tadpole, a two-component model (with DP)is
consistently the best-fit model across the 18 lines of sight
tested, in contrast to the surroundings for which several of the
15 tested lines of sight are adequately described by a one- or
two-component screen (without DP). Although the tail does not
stand out from its surroundings in terms of the primary
component (which is mostly between −2 and 0 rad m
−2
in both
the tail and the off-tadpole region),itdoes have a relatively
coherent secondary component between −14 and −11 rad m
−2
,
which the surroundings lack. This is the secondary component
that also appears in the Faraday depth spectra, although in some
cases, it is shifted slightly in Faraday depth due to the
interaction of the components with the RMSF (see Sun et al.
2015, and Appendix A).
We note that the purpose of the models we chose to test was to
confirm the Faraday depth values of the primary and secondary
peaks in the spectra derived using Faraday synthesis. As we can
see from large values of the Bayes odds ratios listed for the
models in Appendix B,thetrue description of the tadpole lines
of sight is likely more complicated than this set of models.
4.5. Artifacts
The CHIME maps are sensitive to structures on a wide range
of angular scales. Some artifacts are described in detail in
Figure 7. Faraday spectra (magnitudes)from CHIME 400–729 MHz (black solid lines)and WSRT 150MHz (blue dotted–dashed lines)for lines of sight on the
tadpole head, tail, and in the surrounding region. These lines of sight correspond to the markers shown in Figure 2and elsewhere. Dashed and dotted vertical lines
show the peaks f
1
and f
2
from QU fitting (see Section 4.4). The intensity scale on the left applies to CHIME data; the intensity scale on the right applies to
WSRT data.
Table 2
Results of QU Fitting for Representative Lines of Sight
Location ℓ,bp
1
f
1
χ
0,1
σ
1
p
2
f
2
χ
0,2
σ
2
(rad m
−2
)(rad m
−2
)(rad m
−2
)(rad m
−2
)
Head 137.1°, 7.1°0.46 −7.5 1°1.4 0.08 3.0 65°0.02
Tail 133.9°, 6.7°0.47 −1.4 163°1.3 0.15 −12.5 112°2.0
Off 134.9°, 9.6°0.26 −1.3 176°0.03 0.11 7.4 106°1.3
Note. Parameters refer to variables in Equation (8). Faraday depth values are bolded for ease of comparison with Faraday synthesis results.
11
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

CHIME Collaboration (2022). One is evident in the single
diagonal stripe in the top left corner of Figures 2and 3, which
is a line at the right ascension of Tau A. Curved striations, seen
in the Stokes Qand Uimages (Figure 2)and the Faraday
synthesis images (Figure 3), correspond to fixed zenith angles
(or, equivalently, declinations). Point sources appear as a single
point with bright copies at the same declination on either side
of the source due to grating lobes, resulting in an apparent triple
source. The sources themselves appear in Stokes Qin
equatorial coordinates due to leakage, with symmetric side-
lobes, while in Stokes Uonly the asymmetric sidelobes, with
opposite signs, appear. In the Galactic coordinates shown in
this paper, leakage sources appear in both Qand U, along with
their sidelobes.
Grating lobes also appear for larger-scale structures, having a
slight effect on the appearance of the images of the tadpole
region. In the CHIME 410 MHz pI map in Figure 5, a copy of
the head of the tadpole can be seen as an outline that stands out
in polarized intensity, centered on ℓ≈138°.5, b≈8°. 5. The
location and the separation between this and the center of the
head agree with the position of the grating lobes in relation to
the main lobes of the point sources. This ghost copy of the
tadpole also appears in the 410 MHz polarization angle image
in Figure 5, is generally more apparent at the lower frequencies,
and is quite evident in the Faraday depth slices shown in
Figure 6.
There is also declination-dependent striping, which appears as
curved stripes in Galactic coordinates in Figure 2and other
images, although it is much less pronounced in angle images and
Faraday synthesis products. This arises from crosstalk between
adjacent feeds (CHIME Collaboration 2022,Figure18).We
could remove the striping using image processing techniques,
but this cosmetic improvement to the images is unnecessary for
our science. Ultimately, the inclusion of the DRAO 15 m survey
(A. Ordog et al. 2024, in preparation)will allow us to exclude
baselines 5 m from the final CHIME-GMIMS data product; we
expect this to considerably reduce this striping.
5. The Origin of the Tadpole
5.1. Neutral Hydrogen Structure
We turn our investigation to an analysis of the general
structure of neutral hydrogen in the Galaxy’s ISM in the Fan
region. We use DRAO ST+HI4PI H Iobservations described
in Section 3.3 and shown in Figure 10 for this purpose. We
searched the ST+HI4PI data cube at velocities corresponding
to the Local, Perseus, and Outer spiral arms (Reid et al. 2014)
for emission features with a morphological resemblance to the
tadpole but were unable to find any. The tadpole most likely
lies within the Local Arm, corresponding to |V
LSR
|30 km s
−1
for H Iemission. Under this assumption, its physical scale is
reasonable; at outer-arm distances, the head would be 170 pc in
diameter. As discussed by Haverkorn et al. (2003), this is
implausibly large for a single-star ionized region or any other
Faraday-rotating feature. Moreover, if the tadpole is local, there
will be polarized emission arising at larger distances, which can
be Faraday rotated.
In an attempt to identify the structure of G137+7 in neutral
hydrogen observations in regions of excess, or lack of,
hydrogen, Verschuur (1969)made “relative intensity”profiles
Figure 8. Best-fit models from QU fitting for the lines of sight shown in Figure 7. The panels show Q/I(a)−(c),U/I(d)−(f)and the fractional polarized intensity,
p(g)–(i). Black points represent the data. The blue dotted–dashed line is the one-component model (1FD), the green dashed line is the two-component model (2FD),
the magenta dotted line is the one-component model with beam DP (1FD+DP), and the orange solid line is the two-component model with beam DP (2FD+DP). The
fast ripples in the data (an instrumental effect)are not fitted by the models.
12
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

of H Iat each velocity interval (using data from Heiles 1967).
These relative intensity profiles came from drawing a baseline
through the mean levels at the two highest and two lowest
declinations from the scans. Then, the baselines were
subtracted from the H Idata to create profiles to show
abundances or deficiencies in H I. From this, Verschuur
(1969)identified H Ideficiencies at velocities between −16
and −4kms
−1
that coincide with the structure G137+7in
polarization maps.
We attempted to replicate the findings of Verschuur (1969),
now using the ST+HI4PI data. The ST+HI4PI data has an
angular resolution of1
¢
, an improvement on the 12
¢
resolution
of Heiles (1967), and both surveys have a spectral resolution of
roughly 1 km s
−1
. Searching the entire cube after subtraction,
we note a weak deficit of H Iat −11.4 km s
−1
roughly
coincident with the tail, showing a drop in H Iof ∼50 percent
relative to the immediate surroundings. However, this deficit
does not match the morphology of the tail, and dips in H I
intensity at this scale are very common in the HI4PI data for
this area, as seen in Figure 10. We do not regard this as a
significant feature.
5.2. Ionized Hydrogen Structure
Hαprofiles offer a means to probe the distribution of ionized
gas (Haffner et al. 2003). The WHAM survey provides us with
a kinematically resolved map of the Hαemission in the
Galaxy, within approximately 100 km s
−1
of our LSR. Areas
rich in ionized gas signify an enhanced population of free
electrons, which play a crucial role in the Faraday rotation
mechanism.
Local Arm Hαdata from the WHAM survey is shown in
Figure 11, where the tadpole feature does not coincide with any
region of bright Hαemission. We searched the rest of the
channels in the data cube and found no correspondences. The
regions bright in Hαemission that are seen in Figure 11 are
from documented features, namely, the three H II regions W3,
W4, and W5 near 134°ℓ142°and b≈+1°.
We consider the possibility that the tail is primarily due to
residual ionization from a past ionization source, such as a
passing hot star. If the WIM is 8000 K, the recombination
Figure 9. Results of QU fitting along representative lines of sight in the tadpole
region, compared to Faraday synthesis results. The background images show
the Faraday depth of the brightest peak in the Faraday spectrum (top panel)and
the second-brightest peak (bottom panel)at each pixel. The circles show the
Faraday depths derived from QU fitting (f
1
in the top panel, f
2
in the bottom
panel)in 51 directions in and around the tadpole. A mask is applied in the
bottom panel to exclude peaks in the spectra below the CLEAN threshold
(0.2 Jy beam
−1
; grayed out regions)and QU-fitted components below p=0.1
(missing points).
Figure 10. HIimage from ST+HI4PI at Local Arm velocity of −11.4 km s
−1
.
Superimposed is a contour from the CHIME polarization angle representing the
tadpole region. The “×”markers are as in Figure 2. In parts of the image where
ST data are not available (mostly at b>+12°), we use HI4PI data instead.
Figure 11. Hαimage from the WHAM survey at the Local Arm velocity of
−10.2 km s
−1
. The contour is as in Figure 10; the “×”markers are as in
Figure 2.
13
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

coefficient to energy levels n2isα
(2)
≈3.04 ×10
−13
cm
3
s
−1
(Haffner et al. 2003; Draine 2011). The recombination time is
tn
re
21
a»-
()
() . If we assume an electron density n
e
=0.1 cm
−3
(Hill et al. 2008), this gives a recombination time of ∼1Myr.
Under the assumption that the ionizing source has traveled along
the path laid out tail-to-head, then ∼1 Myr ago, the star was in
the middle of the current location of the tail (ℓ≈132°).The
angular separation of the center of the head and halfway along
the tail is about 5°, meaning the ionizing source would have a
proper motion of ∼20 mas yr
−1
in this model. The thinning of
the tail with increasing distance from the head is consistent with
this recombination scenario.
5.3. Proper Motions of Candidate Stars
Previous studies of feature G137+7 considered the circular
region to be a result of a Strömgren sphere of the B2(e)star
HD 20336, or alternatively, a relic Strömgren sphere from the
white dwarf WD 0314+64, both of which lay within the head
of the tadpole (Verschuur 1968; Iacobelli et al. 2013).
We hypothesize that the tail of the tadpole is a trail of
ionized gas behind a suitable star, and should indicate motion
related to the feature, potentially in the fashion suggested by
Haverkorn et al. (2003)with an elongated Strömgren sphere.
The tail may be similar to tails associated with planetary
nebulae (Ransom et al. 2010,2015), yielding estimates of the
timescales for the interactions of planetary nebulae and the
ISM. For a star to be considered a strong candidate for the
tadpole, the characteristics we observe require it to be a hot star
(Type O or B)with a proper motion comparable to our
calculations based on the recombination time (see Section 5.2)
and direction aligned with the orientation of the tail.
We check to see whether the motion of HD 20336 meets these
criteria. We overlay the inferred positions over the past 3 Myr of
HD 20336 given the sky-projected space velocity calculated from
Gaia proper motion values (Gaia Collaboration et al. 2023),
corrected for the LSR (e.g., Soderblom et al. 1989;Ransometal.
2015)given by Huang (2015)atop Figure 2. The orientation of
the tadpole is just outside the error cone of the trajectory we
determined for HD 20336, suggesting that an association is
possible but not definitive. The error in the path of HD 20336 is
largely from the uncertainty in the LSR. The orientation of the tail
parallel to the Galactic plane also suggests motion in the plane, as
might be expected for a star. Similar corrected space velocity
values were calculated for WD 0314+64, finding a proper
motion path that agreed less well with the tail. The angular
velocities of the B2(e)star and white dwarf are 9.98 ±0.02 and
159.4 ±0.1 mas yr
−1,
respectively. The high angular velocity of
the white dwarf rules it out based on the timescale estimates we
find for the tail in Section 5.2 (unless n
e
∼1cm
−3
,whichismuch
higher than typical in the WIM);however,theB2(e)star’s
angular velocity is of the same order of magnitude as our
estimates—a result consistent with the star causing the feature.
Using the Gaia database, we searched
26
for any other candidate
stars that could cause the Faraday rotation feature (Anderson
et al. 2024). We identified no new candidates from this query.
5.4. Faraday Depth and Electron Column
We can make sense of the absence of the tadpole in both
the ST+HI4PI H Iand WHAM surveys by considering that
the strongest observed Faraday rotation in the head is
f≈−8radm
−2
. This requires free electrons that would
have been ionized from neutral hydrogen in the ISM. Here,
we assume that a change in the electron density, not a change
in the magnetic field, is the dominant factor in the change
in f. This would leave a deficit in the neutral hydrogen
column density, N(HI), but as demonstrated above, we do
not observe this. The magnitude of change in the H Idensity
needed to produce the observed Faraday depth can be estimated
using (from Equation (2)) f=0.81 ·n
e
B
∥
L. Using the
Faraday depth from the head of the tadpole and the
canonical total magnetic field strength in the Solar neighborhood
of 6 μG(Haverkorn 2015), the change needed in the column
density of free electrons is
n
LB1.5 10 cm
e18 612
~´ ~
--
B1.4 pc cm
613
--, or an emission measure of nds
E
Me
2
ò
º
=
nL L L B2 1 pc pc cm
e21
626
~---
(
)() . Here, we define B
6
≡
B
||
/6μG;
B
13
6=if a 6 μGfield is randomly distributed
among three orthogonal components.
If the free electrons arose from the ionization of existing
neutral hydrogen, this would result in a decrease in N(HI)of
B1.5 10 cm
18 612
~´ --. This is small compared to the typical
N(HI)10
20
cm
−2
near the plane (less than 3% in the case of
B
13
6=)and thus would be impossible to see as a deficit in
HImaps. An emission measure of ≈2pccm
−6
would be
detectable in Hαemission (Haffner et al. 2003); if the path
length of ionized gas were L3 pc, the emission measure
would be less than the 3σsensitivity of the WHAM survey
(EM ∼0.3 pc cm
−6
). Therefore, Faraday rotation would be
sensitive to a change in electron column density that could not
be detected in other tracers even if there were no change in the
magnetic field. Because we would not expect to detect a change
in n
e
Lin other tracers, we cannot readily distinguish between a
change in the electron column and a change in B
||
. The motion
of ionized gas may distort the magnetic field lines, changing
their orientation with respect to the line of sight, which can also
lead to a gradient in Faraday depth, a so-called magnetic wake
(Ransom et al. 2010).
6. Summary and Future Prospects
In this paper, we have presented the first polarization maps
from CHIME in what will be a component of the GMIMS low-
band north all-sky survey. The wide bandwidth at relatively
low frequencies (400–729 MHz)gives us a Faraday depth
resolution, which is roughly half the largest scale we are
sensitive to, enabling investigation of Faraday complexity. We
analyzed a relatively small region of the sky where the
emission is bright and instrumental properties are best under-
stood; in future work, we will expand the use of CHIME data to
analyze the large-scale structure of the Galactic magnetic field.
The polarized structure that we refer to as the tadpole is
composed of a circular head centered on ℓ=137°,b=+7°
roughly 2°in diameter, with a tail extending about 10°to
ℓ=127°. The entire feature has an observed polarization angle
rotated significantly compared to the surrounding sky due to
Faraday rotation. The largest Faraday depth |f|is in the head of
the tadpole, with values as large as −8radm
−2
. The tail appears
as a second Faraday depth component at ≈−12 rad m
−2
.The
tail has been hinted at previously but is very clear both in single-
channel polarization angle images and in Faraday depth images
with CHIME. Similarly, what we identify as the head has been
seen primarily as a DP feature in the past. With the angular and
26
We used the capabilities of a natural language model to construct ADQL
search queries of the Gaia archive (OpenAI 2023).
14
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

Faraday depth resolution of CHIME, we clearly identify it as a
Faraday rotation feature, recovering most of the power that is
depolarized with poorer angular or Faraday depth resolution.
The presence of a tail suggests motion along its direction
through the ISM. The proper motion of HD 20336 is
marginally consistent with the orientation of the tail. The
tadpole is not seen in maps of neutral or ionized hydrogen
column density, although our estimates suggest that the amount
of gas necessary to undergo ionization, resulting in the
observed Faraday rotation magnitude, falls below the sensitiv-
ity threshold of Hαand H Isurveys, especially given the
intensity of surrounding emission. We find the recombination
time for the ionized electrons to be ∼1 Myr, and with this
estimate, we derive a proper motion of the (unknown)ionizing
source of ∼20 mas yr
−1
, which is on the order of magnitude of
the B2(e)star’s velocity. Although this is suggestive evidence,
we cannot be certain that the B2(e)star is linked to the tadpole.
The CHIME Stokes Qand Ucubes covering the 400
−729 MHz range comprise the primary data set used in this
study. This frequency coverage yields a Faraday depth
resolution of 9.7 rad m
−2
, resolving the maximum fscale of
∼19 rad m
−2
. Given the asymmetries present in the main lobes
of some of the spectra we observe on or near the tadpole
feature, exploring this region with improved fresolution
combined with sensitivity to extended features will be valuable.
In the longer term, we will be able to combine fresolution
and improved spatial resolution with the advent of the
upgraded DRAO ST, which will cover 400–1800 MHz at 1
¢
resolution (compared to the single-frequency channel available
from the current ST). The single-channel 1
¢
-resolution χmap
from the DRAO ST+EMLS in Figure 5already reveals an
abundance of structures on scales much smaller than the size of
the tadpole, and investigating these in fspace with high
resolution may provide further insights into the nature of the
overall structure. Other future studies may also include
exploring potential correlations between the tadpole Faraday
structure and thermal dust emission features in three-dimen-
sional dust maps.
There are three factors in this study that CHIME makes
possible. First, for the purpose of this study, CHIME is
effectively a large single antenna, with sensitivity to large
structures, coupled with better angular resolution than the single
antennas that have been used for polarimetry in this frequency
range. Second, the wide bandwidth and many frequency
channels enable Faraday synthesis with 2
max scale
f
d
f
»
-,
comfortably resolving the maximum scale. Third, the polarized
sky is Nyquist sampled. This powerful combination has revealed
an extended and Faraday complex structure in G137+7, a region
that has been a curiosity for six decades.
Acknowledgments
This paper relies on observations obtained using telescopes
located at the Dominion Radio Astrophysical Observatory,
which is located on the traditional, ancestral, and unceded
territory of the syilx people. We benefitenormouslyfromthe
stewardship of the land by the syilx Okanagan Nation and the
radio frequency interference environment protection work by the
syilx Okanagan Nation and DRAO. We acknowledge the DRAO
staff, especially K. Phillips and B. Robert, for their work on the
site and the telescopes used in this work. DRAO is a national
facility operated by the National Research Council Canada.
CHIME is funded by grants from the Canada Foundation for
Innovation (CFI)2012 Leading Edge Fund (Project 31170),the
CFI 2015 Innovation Fund (Project 33213), and by contributions
from the provinces of British Columbia, Québec, and Ontario.
Additional support was provided by the University of British
Columbia, McGill University, and the University of Toronto.
CHIME also benefits from several NSERC Discovery Grants,
including RGPIN-2020-05035 and 569654. This research was
enabled in part by support provided by the Digital Research
Alliance of Canada.
A.S.H. and A.O. acknowledge Interstellar Instituteʼs pro-
gram “II6”and the Paris-Saclay University Institut Pascal for
hosting discussions that nourished the development of the ideas
behind this work, especially with R. A. Benjamin. We thank
R. Mckinven for useful discussions about instrumental polar-
ization in CHIME/FRB data. We also acknowledge helpful
discussions with W. Raja. We thank the anonymous referee for
a careful and constructive report, which led to an improved
paper.
N.M. was supported by an Undergraduate Research Award
from the UBC Okanagan Irving K. Barber Faculty of Science
and an NSERC Undergraduate Student Research Award. A.O.
is partly supported by the Dunlap Institute at the University of
Toronto. A.B. acknowledges financial support from the INAF
initiative “IAF Astronomy Fellowships in Italy,”grant name
MEGASKAT. M. Haverkorn acknowledges funding from the
European Research Council (ERC)under the European
Union’s Horizon 2020 research and innovation program (grant
agreement No. 772663). We acknowledge the support of
NSERC, funding reference number 569654. K.W.M. holds the
Adam J. Burgasser Chair in Astrophysics and is supported by
NSF grants (2008031, 2018490). M.T. is supported by the
Banting Fellowship (Natural Sciences and Engineering
Research Council Canada)hosted at Stanford University.
Data Availability
FITS files containing the CHIME data products, Stokes I,Q,
U,andVas a function of frequency and Faraday depth for the
regions shown in this paper, are available through the Canadian
Astronomical Data Centre (CHIME & GMIMS collaborations
2024):doi:10.11570/24.0001.
Facilities: CHIME, DRAO:Synthesis Telescope, Effelsberg.
Software: Astropy (Astropy Collaboration et al. 2022);
ch_pipeline;Matplotlib (Hunter 2007);NumPy;RM-
Tools (Purcell et al. 2020).
Appendix A
Resolved and Unresolved Faraday Components in Faraday
Synthesis
In this appendix, we model the impact of resolved and
unresolved Faraday depth components on Faraday synthesis
spectra, similar to the analysis of Sun et al. (2015), but covering
the much broader λ
2
range corresponding to the CHIME
frequency coverage. We create a model with Faraday depth
components f
k
with polarization fractions p
0,k
emitted at
polarization angles χ
0,k
. The observed complex polarization is
then given by Equation (8). We performed a series of
simulations with the inputs listed in Table A1. We set
σ
k
=0 rad m
−2
in all cases; making σ
k
nonzero produces
results that are similar to reducing p
0,k
for each component. We
15
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

then performed Faraday synthesis on the resulting P2
l
˜(
)
spectra
and CLEANed the spectra to a threshold of pI =0.2 in the
arbitrary units used in these figures, producing the Faraday
depth spectra shown in Figure A1. We used complete
frequency coverage from 400–729 MHz in running these
simulations, an idealized version of the portion of the CHIME
data used in this paper, with the FWHM of R(f)being
δf=9.7 rad m
−2
. Accounting for the gaps in our frequency
coverage produces additional sidelobes in the dirty spectrum
but does not change the qualitative picture.
First, in Figure A1(a), we show a model with a single
component at f=−5 rad m
−2
. The dirty spectrum is an exact
replica of the RMSF, shifted to the input Faraday depth.
Cleaning removes the sidelobes effectively.
Next, in Figure A1(b), we show cases in which there are two
components that are separated by 4 rad m
−2
, which is
Table A1
Model Parameters Shown in Figure A1
Model p
0,1
If
1
σ
0,1
χ
0,1
p
0,2
If
2
σ
0,2
χ
0,2
0 1.0 −5 rad m
−2
0.0 rad m
−2
0°0.0 LLL
1 1.0 −2 rad m
−2
0.0 rad m
−2
0°1.0 2 rad m
−2
0.0 rad m
−2
0°
2 1.0 −5 rad m
−2
0.0 rad m
−2
0°1.0 5 rad m
−2
0.0 rad m
−2
0°
3 1.0 −10 rad m
−2
0.0 rad m
−2
0°1.0 10 rad m
−2
0.0 rad m
−2
0°
4 1.0 −2 rad m
−2
0.0 rad m
−2
0°1.0 2 rad m
−2
0.0 rad m
−2
45°
5 1.0 −2 rad m
−2
0.0 rad m
−2
0°1.0 2 rad m
−2
0.0 rad m
−2
90°
6 1.0 −2 rad m
−2
0.0 rad m
−2
0°0.5 2 rad m
−2
0.0 rad m
−2
0°
7 1.0 −2 rad m
−2
0.0 rad m
−2
0°0.5 2 rad m
−2
0.0 rad m
−2
45°
8 1.0 −2 rad m
−2
0.0 rad m
−2
0°0.5 2 rad m
−2
0.0 rad m
−2
90°
Note. Input parameters used with Equation (8)to create Figure A1.
Figure A1. Output of models from Table A1. Vertical dotted lines show the input Faraday depths f
1
and f
2
. We show dirty (dotted–dashed lines)and clean (solid
lines)spectra for a few cases but clean spectra only in most cases to reduce clutter. (a)Our control model with one component at −5 rad m
−2
.(b)Models 1–3 with two
components separated by 4, 10, and 20 rad m
−2
.(c)Models 1, 4, and 5, with two components separated by 4 rad m
−2
, which is not resolved by the RMSF. We show
the same model but with χ
2
ranging from 0 (model 1, as in panel (b)to 90°(model 5).(d)Models 6–8, with two components separated by 4 rad m
−2
, which is not
resolved by the RMSF. The second component has reduced pI. As in models 1, 3, and 4, we show the same model but with χ
2
ranging from 0 (model 5)to 90°
(model 7).
16
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

unresolved (model 1); separated by 10 rad m
−2
, which is
marginally resolved (model 2), and separated by 20 rad m
−2
,
more than twice δf(model 3). In the resolved case (model 3),
two peaks appear at their input Faraday depths. Sidelobes are
present but removed precisely by cleaning, leaving two peaks
that closely resemble Gaussians. We performed the same
experiment with a wide range of input angles χ
0,2
; there is no
appreciable change in the resulting Faraday spectrum. For the
Δf=10 rad m
−2
case (model 2), there is a flattened appear-
ance to the blended peaks in the Faraday spectrum. There are
two peaks, but they are separated by ≈8 rad m
−2
, less than the
separation of the input Faraday depths. Lastly, in the
unresolved case (Δf=4 rad m
−2
; model 1), there are two
distinct peaks but they are separated by ≈9 rad m
−2
.
In Figure A1(c), we again show two components with equal
polarized intensity separated by 4 rad m
−2
, which is not
resolved by the RMSF. Model 1, with the same χ
0
in both
components, is as in Figure A1(b). When the two components
are emitted at different angles (45°different in model 3 and 90°
different in model 4), we see only a single component centered
between the two input components. These two peaks are true
features in that they correspond to two distinct but unresolved
input components, but their observed Faraday depths are not
accurate. Instead, the Faraday depths of the observed peaks are
separated by ≈δf. Because these peaks represent true features,
they are not removed by RM-CLEAN, but their position is also
not changed (or perhaps changed very slightly). In contrast, the
sidelobes at ±15 and ±23 rad m
−2
are removed by RM-
CLEAN.
In Figure A1(d), we show a similar experiment but the
intensity of one of the input components is reduced by 50%. In
the in-phase model (model 5), the two peaks remain present
and remain pushed out to be separated by ≈δf. In the out-of-
phase models (6 and 7), only one peak is evident, centered at
the intensity-weighted mean of the two input components.
We ran models of types 1, 4, and 5 (equal input polarized
intensities with three different angular separations of the
components), but now for a range of input Faraday depth
separations between the components and then determined the
separation of the peaks in Faraday spectra. We show the results
in Figure A2 (similar to Figure 4 of Sun et al. 2015, but with a
denser sampling of Δf).AtΔf12 rad m
−2
, the components
are resolved by Faraday synthesis and the output peaks
correspond well with the input peaks. We do not observe
peaks in the Faraday spectrum, which are appreciably closer
than the FWHM of R(f), 9.7 rad m
−2
.
What causes the observed peaks in the Faraday spectrum to
be at separations wider than the input values? This is a DP
effect. Absent DP, we would expect two unresolved compo-
nents to appear in a single, broadened Gaussian-like form.
When the Faraday-rotated emission from the two components
is out of phase, DP occurs. With two Faraday screens of equal
pI, the Faraday spectrum Ff
˜()
is the sum of two copies of the
RMSF with centroids separated by f
2
−f
1
. The imaginary part
of
R
f
˜()
is antisymmetric, so for certain separations of f
1
and
f
2
, the imaginary parts of the copies of
R
f
˜()
interfere and
depolarize. From these investigations, we conclude that
Faraday synthesis results should be interpreted with caution
when the spacing of peaks is δf(Equation (3)), in agreement
with the similar results at higher frequencies presented by Sun
et al. (2015). In this case, QU fitting, which is less sensitive to
this type of interaction between Faraday depth components,
should be used to refine the results.
Appendix B
QU-fitting Results
Here, we present a comparison between the Faraday
synthesis and QU-fitting results for the CHIME data in terms
of the Faraday depth spectra, along with a comparison of the
four models tested. For the three lines of sight shown in
Figures 6and 7, we determine the complex polarized fraction,
p2
l
˜()
, from the best-fit parameters resulting from QU fitting for
the four models we tested: one- and two-component Faraday
screens (1 FD and 2 FD), with and without beam DP. These are
shown in Figure 8for comparison in the λ
2
domain. In Figure 9
we show the Faraday depths derived from the two-component
model that includes beam DP, 2 FD +DP.
We apply Faraday synthesis to each model p2
l
˜()
determined
from QU fitting. We show the resulting Faraday depth spectra,
compared to the spectra derived from the data p2
l
˜()
in
Figures B1–B3. For all three lines of sight, the two-component,
beam-depolarized model (2FD+DP)spectrum agrees well
with the spectrum derived from the data p2
l
˜()
. Note that small
discrepancies between the data spectra shown in Figure 7and
the spectra shown here arise because the latter were calculated
from Q/Iand U/I(no spectral index)rather than Qand U
(including spectral index)as were used for the main analysis.
The off-tadpole line of sight shown in Figure B3(d)is an
example of the type of scenario described in Appendix Aand
depicted in Figure A1(d)(model 8), in which two Faraday
depth components (denoted by the vertical black lines in both
of the two-component models)become slightly shifted with
respect to each other through the Faraday synthesis process.
In Table B1, we summarize the best-fit parameters of all
models for these three lines of sight, along with the Bayesian
Figure A2. Output separation of Faraday depth components (calculated using
Faraday synthesis)as a function of the input separation of Faraday depth
components in the simulation. The dashed line shows a 1:1 line, and the dotted
box shows the FWHM of R(f)(9.7 rad m
−2
). We ran this experiment for
1<f<20 rad m
−2
in 0.1 rad m
−2
increments; outputs for which there are not
separate peaks in the output Faraday spectrum are blank.
17
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

evidence, Z, and the Bayes odds ratio, Zln
D
()
, to quantify
the comparison between the models. We compare all models,
m, to 2 FD +DP, which has the highest value of ln(Z), such
that
ZZ Zln ln ln . B1
m2FDDPm
D= -
+
() ( ) () ()
Figure B1. Results of QU fitting used as input to Faraday synthesis for a line of sight on the head of the tadpole for the four models described in Section 4.4. Blue lines
represent the magnitudes of the spectra derived from applying Faraday synthesis to the CHIME p2
l
˜()
data. Orange lines are the magnitudes of the spectra derived
from applying Faraday synthesis to the model p2
l
˜()
determined from QU fitting. Solid (dashed)lines represent clean (dirty)spectra. Vertical, black dotted lines
indicate the locations of the QU-fitted Faraday depth components, and the black dot indicates the polarized fraction corresponding to that component.
Figure B2. Results of QU fitting used as input to Faraday synthesis for a line of sight on the tail of the tadpole. See Figure B1 for a full description.
18
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

For the selected points in the head and tail of the tadpole, a
two-component beam-depolarized model (2FD+DP)is
clearly the best fit, while for the selected off-tadpole point a
two-component model without DP (2FD)may be sufficient
within the set of models explored here. As noted in Section 4.4,
a full description of the lines of sight toward the tadpole likely
includes more complexity than this basic set of models. The
primary Faraday depth components, f
1
, are reasonably
consistent between these models, while in the head and tail
of the tadpole, the secondary component, f
2
, is strongly
dependent on whether or not beam DP is included in the model.
ORCID iDs
Nasser Mohammed https://orcid.org/0009-0008-1224-0382
Anna Ordog https://orcid.org/0000-0002-2465-8937
Rebecca A. Booth https://orcid.org/0000-0001-5181-6673
Andrea Bracco https://orcid.org/0000-0003-0932-3140
Jo-Anne C. Brown https://orcid.org/0000-0003-4781-5701
Ettore Carretti https://orcid.org/0000-0002-3973-8403
John M. Dickey https://orcid.org/0000-0002-6300-7459
Simon Foreman https://orcid.org/0000-0002-0190-2271
Mark Halpern https://orcid.org/0000-0002-1760-0868
Marijke Haverkorn https://orcid.org/0000-0002-5288-312X
Figure B3. Results of QU fitting used as input to Faraday synthesis for a line of sight in the off-tadpole region. See Figure B1 for a full description.
Table B1
QU-fitting Results for Representative Lines of Sight
Location ℓ,bModel Zln() ZlnD(
)
p
1
f
1
χ
0,1
σ
1
p
2
f
2
χ
0,2
σ
2
(×10
3
)(×10
3
)(rad m
−2
)(rad m
−2
)(rad m
−2
)(rad m
−2
)
Head 137°,7°1FD −53.4 37.5 0.4 −7.5 2°.0
2FD −27.0 11.1 0.6 −5.9 143°. 8 0.4 −4.2 9°.6
1FD+DP −27.7 11.8 0.5 −7.6 2°. 4 1.4
2FD+DP −15.9 0.0 0.5 −7.5 0°. 6 1.4 0.1 3.0 65°. 3 0.02
Tail 134°, 6.5°1FD −57.3 49.2 0.4 −1.4 162°.7
2FD −13.4 5.3 0.6 −2.4 15°. 7 0.4 −4.0 152°.2
1FD+DP −16.7 8.6 0.6 −1.6 164°. 9 1.6
2FD+DP −8.1 0.0 0.5 −1.4 163°. 2 1.3 0.2 −12.5 112°. 5 2.0
Off 135°,9°1FD −14.9 9.8 0.3 −1.9 8°.8
2FD −5.7 0.6 0.3 −1.6 1°. 5 0.1 8.1 93°.2
1FD+DP −14.9 9.8 0.3 −1.9 8°. 8 0.18
2FD+DP −5.1 0.0 0.3 −1.3 175°. 5 0.03 0.1 7.4 106°. 3 1.3
19
The Astrophysical Journal, 971:100 (20pp), 2024 August 10 Mohammed et al.

Alex S. Hill https://orcid.org/0000-0001-7301-5666
Gary Hinshaw https://orcid.org/0000-0002-4241-8320
Joseph W. Kania https://orcid.org/0000-0002-3354-3859
Roland Kothes https://orcid.org/0000-0001-5953-0100
T. L. Landecker https://orcid.org/0000-0003-1455-2546
Joshua MacEachern https://orcid.org/0000-0001-8064-6116
Kiyoshi W. Masui https://orcid.org/0000-0002-4279-6946
Aimee Menard https://orcid.org/0009-0007-6503-1501
Ryan R. Ransom https://orcid.org/0000-0003-2469-1611
Wolfgang Reich https://orcid.org/0000-0002-5313-6409
Patricia Reich https://orcid.org/0009-0006-8615-8352
J. Richard Shaw https://orcid.org/0000-0002-4543-4588
Seth R. Siegel https://orcid.org/0000-0003-2631-6217
Mehrnoosh Tahani https://orcid.org/0000-0001-8749-1436
Alec J. M. Thomson https://orcid.org/0000-0001-
9472-041X
Tristan Pinsonneault-Marotte https://orcid.org/0000-0002-
9516-3245
Haochen Wang https://orcid.org/0000-0002-1491-3738
Jennifer L. West https://orcid.org/0000-0001-7722-8458
Maik Wolleben https://orcid.org/0009-0006-9479-7509
Dallas Wulf https://orcid.org/0000-0001-7314-9496
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