# published_repeaters_polarization

R. Mckinven *  — Department of Physics, McGill University, 3600 rue
University, Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill
University, 3550 rue University, Montréal, QC H3A 2A7, Canada  Dunlap
Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George
Street, Toronto, ON M5S 3H4, Canada  David A. Dunlap Department of Astronomy &
Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S
3H4, Canada  B.M. Gaensler *  — Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto,
50 St. George Street, Toronto, ON M5S 3H4, Canada  D. Michilli *  — Department
of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  MIT Kavli Institute for Astrophysics and Space
Research, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  K. Masui *  — MIT Kavli Institute for Astrophysics
and Space Research, Massachusetts Institute of Technology, 77 Massachusetts
Ave, Cambridge, MA 02139, USA  Department of Physics, Massachusetts Institute
of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  V.M. Kaspi *  —
Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada  McGill Space Institute, McGill University, 3550 rue
University, Montréal, QC H3A 2A7, Canada  J. Su *  — Department of Physics,
McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada  M.
Bhardwaj *  — Department of Physics, McGill University, 3600 rue University,
Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill University, 3550
rue University, Montréal, QC H3A 2A7, Canada  T. Cassanelli *  — David A.
Dunlap Department of Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada  Dunlap Institute for Astronomy &
Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S
3H4, Canada  P. Chawla *  — Anton Pannekoek Institute for Astronomy,
University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
F. (Adam) Dong *  — Dept. of Physics and Astronomy, 6224 Agricultural Road,
Vancouver, BC V6T 1Z1 Canada  E. Fonseca *  — Lane Department of Computer
Science and Electrical Engineering, 1220 Evansdale Drive, PO Box 6109
Morgantown, WV 26506, USA  Center for Gravitational Waves and Cosmology, West
Virginia University, Chestnut Ridge Research Building, Morgantown, WV 26505,
USA  Department of Physics and Astronomy, West Virginia University, P.O. Box
6315, Morgantown, WV 26506, USA  C. Leung *  — MIT Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology, 77
Massachusetts Ave, Cambridge, MA 02139, USA  Department of Physics,
Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA
02139, USA  D.Z. Li *  — Cahill Center for Astronomy and Astrophysics,
California Institute of Technology, 1216 E California Boulevard, Pasadena, CA
91125, USA  C. Ng *  — Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  C.
Patel *  — Department of Physics, McGill University, 3600 rue University,
Montréal, QC H3A 2T8, Canada  Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  A.B.
Pearlman *  — Department of Physics, McGill University, 3600 rue University,
Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill University, 3550
rue University, Montréal, QC H3A 2A7, Canada  E. Petroff *  — Department of
Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
McGill Space Institute, McGill University, 3550 rue University, Montréal, QC
H3A 2A7, Canada  Anton Pannekoek Institute for Astronomy, University of
Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands  Z. Pleunis, *
— Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada  M. Rafiei-Ravandi *  — Department
of Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8,
Canada  McGill Space Institute, McGill University, 3550 rue University,
Montréal, QC H3A 2A7, Canada  M. Rahman *  — Sidrat Research, PO Box 73527 RPO
Wychwood, Toronto, Ontario, M6C 4A7, Canada  K.R. Sand *  — Department of
Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
McGill Space Institute, McGill University, 3550 rue University, Montréal, QC
H3A 2A7, Canada  K. Shin *  — MIT Kavli Institute for Astrophysics and Space
Research, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  Department of Physics, Massachusetts Institute of
Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  I.H. Stairs *  —
Dept. of Physics and Astronomy, 6224 Agricultural Road, Vancouver, BC V6T 1Z1
Canada  S. Tendulkar *  — Department of Astronomy and Astrophysics, Tata
Institute of Fundamental Research, Mumbai, 400005, India  National Centre for
Radio Astrophysics, Post Bag 3, Ganeshkhind, Pune, 411007, India R. Mckinven
<EMAIL_ADDRESS>
# Revealing the Dynamic Magneto-ionic Environments of Repeating Fast Radio
Burst Sources through Multi-year Polarimetric Monitoring with CHIME/FRB

R. Mckinven *  — Department of Physics, McGill University, 3600 rue
University, Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill
University, 3550 rue University, Montréal, QC H3A 2A7, Canada  Dunlap
Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George
Street, Toronto, ON M5S 3H4, Canada  David A. Dunlap Department of Astronomy &
Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S
3H4, Canada  B.M. Gaensler *  — Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto,
50 St. George Street, Toronto, ON M5S 3H4, Canada  D. Michilli *  — Department
of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  MIT Kavli Institute for Astrophysics and Space
Research, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  K. Masui *  — MIT Kavli Institute for Astrophysics
and Space Research, Massachusetts Institute of Technology, 77 Massachusetts
Ave, Cambridge, MA 02139, USA  Department of Physics, Massachusetts Institute
of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  V.M. Kaspi *  —
Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada  McGill Space Institute, McGill University, 3550 rue
University, Montréal, QC H3A 2A7, Canada  J. Su *  — Department of Physics,
McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada  M.
Bhardwaj *  — Department of Physics, McGill University, 3600 rue University,
Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill University, 3550
rue University, Montréal, QC H3A 2A7, Canada  T. Cassanelli *  — David A.
Dunlap Department of Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada  Dunlap Institute for Astronomy &
Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S
3H4, Canada  P. Chawla *  — Anton Pannekoek Institute for Astronomy,
University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
F. (Adam) Dong *  — Dept. of Physics and Astronomy, 6224 Agricultural Road,
Vancouver, BC V6T 1Z1 Canada  E. Fonseca *  — Lane Department of Computer
Science and Electrical Engineering, 1220 Evansdale Drive, PO Box 6109
Morgantown, WV 26506, USA  Center for Gravitational Waves and Cosmology, West
Virginia University, Chestnut Ridge Research Building, Morgantown, WV 26505,
USA  Department of Physics and Astronomy, West Virginia University, P.O. Box
6315, Morgantown, WV 26506, USA  C. Leung *  — MIT Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology, 77
Massachusetts Ave, Cambridge, MA 02139, USA  Department of Physics,
Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA
02139, USA  D.Z. Li *  — Cahill Center for Astronomy and Astrophysics,
California Institute of Technology, 1216 E California Boulevard, Pasadena, CA
91125, USA  C. Ng *  — Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  C.
Patel *  — Department of Physics, McGill University, 3600 rue University,
Montréal, QC H3A 2T8, Canada  Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  A.B.
Pearlman *  — Department of Physics, McGill University, 3600 rue University,
Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill University, 3550
rue University, Montréal, QC H3A 2A7, Canada  E. Petroff *  — Department of
Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
McGill Space Institute, McGill University, 3550 rue University, Montréal, QC
H3A 2A7, Canada  Anton Pannekoek Institute for Astronomy, University of
Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands  Z. Pleunis, *
— Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada  M. Rafiei-Ravandi *  — Department
of Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8,
Canada  McGill Space Institute, McGill University, 3550 rue University,
Montréal, QC H3A 2A7, Canada  M. Rahman *  — Sidrat Research, PO Box 73527 RPO
Wychwood, Toronto, Ontario, M6C 4A7, Canada  K.R. Sand *  — Department of
Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
McGill Space Institute, McGill University, 3550 rue University, Montréal, QC
H3A 2A7, Canada  K. Shin *  — MIT Kavli Institute for Astrophysics and Space
Research, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  Department of Physics, Massachusetts Institute of
Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  I.H. Stairs *  —
Dept. of Physics and Astronomy, 6224 Agricultural Road, Vancouver, BC V6T 1Z1
Canada  S. Tendulkar *  — Department of Astronomy and Astrophysics, Tata
Institute of Fundamental Research, Mumbai, 400005, India  National Centre for
Radio Astrophysics, Post Bag 3, Ganeshkhind, Pune, 411007, India R. Mckinven
<EMAIL_ADDRESS>
###### Abstract

Fast radio bursts (FRBs) display a confounding variety of burst properties and
host galaxy associations. Repeating FRBs offer insight into the FRB population
by enabling spectral, temporal and polarimetric properties to be tracked over
time. Here, we report on the polarized observations of 12 repeating sources
using multi-year monitoring with the Canadian Hydrogen Intensity Mapping
Experiment (CHIME) over 400-800 MHz. We observe significant RM variations from
many sources in our sample, including RM changes of several hundred
$\rm{rad\,m^{-2}}$ over month timescales from FRBs 20181119A, 20190303A and
20190417A, and more modest RM variability ($\rm{\Delta RM\lesssim}$ few tens
rad m-2) from FRBs 20181030A, 20190208A, 20190213B and 20190117A over
equivalent timescales. Several repeaters display a frequency dependent degree
of linear polarization that is consistent with depolarization via scattering.
Combining our measurements of RM variations with equivalent constraints on DM
variability, we estimate the average line-of-sight magnetic field strength in
the local environment of each repeater. In general, repeating FRBs display RM
variations that are more prevalent/extreme than those seen from radio pulsars
in the Milky Way and the Magellanic Clouds, suggesting repeating FRBs and
pulsars occupy distinct magneto-ionic environments.

##  1 Introduction

Fast radio bursts (FRBs; Lorimer et al., 2007; Petroff et al., 2022) are short
(microsecond to millisecond) bursts of radio emission with uncertain origins.
FRB polarization measurements can characterize several properties that contain
information on the emission physics of the source and/or its environment.
These properties can be summarized as a handful of quantities: the position
angle of the linear polarization vector (PA), the linear/circular polarized
fractions ($L/I$, $V/I$), and the Faraday rotation (quantified through the
rotation measure, RM).

Evolution in the PA can be tracked both within a burst and, for a repeating
source, between bursts. Such information can greatly improve our understanding
of the geometry of the FRB emission mechanism in a manner similar to the
rotating vector model (RVM; Radhakrishnan & Cooke, 1969) of pulsar radio
emission. To date, a wide variety of PA behavior has been observed from FRBs.
Large PA swings have been observed from repeating source FRB 20180301A (Luo et
al., 2020). Meanwhile, other sources displaying apparent flat PA curves have
since been shown to exhibit subtle intraburst PA variability when observed at
high temporal resolution (FRB 20180916B; Nimmo et al., 2021). Some repeating
sources also display significant PA variations across bursts. A recent example
is FRB 20201124A (Hilmarsson et al., 2021a; Kumar et al., 2022a; Xu et al.,
2021), which also exhibits significant circular polarization (Hilmarsson et
al., 2021a; Xu et al., 2021) that in many cases exceeds what can be produced
from Faraday conversion between linear and circular polarized modes (Vedantham
& Ravi, 2019; Levin et al., 2020).

Recently, Wang et al. (2021) have demonstrated that other mechanisms may
produce anomalous circular polarization seen from FRB 20201124A, including
mechanisms such as inverse Compton scattering or cyclotron resonance
absorption. Polarized observations are, therefore, tremendously valuable for
both constraining FRB emission models and possibly the magneto-ionic
properties of the local environment. For example, both the PA evolution and
substantial $V/I$ fractions observed in some FRB sources are features that are
naturally favorable to models invoking magnetospheric origins (e.g., Zhang,
2020). However, synchrotron maser emission models (Metzger et al., 2019) may
also be capable of explaining such features under certain conditions. Indeed,
recent simulations of a flaring magnetar (Yuan et al., 2020) have demonstrated
the existence of strong variations in the orientation of the magnetar wind’s
magnetic field that would be required to explain the PA variability observed
in some FRBs.

Meanwhile, the $\rm{RM}$ probes the intervening magnetized plasma between the
source and the observer. As such, this quantity can be decomposed in terms of
the $\rm{RM}$ contributions of the various media encountered along the line-
of-sight (LoS)111For simplicity, we have absorbed the diluting effect of
cosmological expansion on $\rm{RM}$ by representing each $\rm{RM}$ component
in the observer’s frame. As such, both the $\rm{RM_{IGM}}$ and
$\rm{RM_{host}}$ contributions are diluted by a factor of $(1+z)^{2}$, $z$
being the redshift of the Faraday rotating medium.,

$\rm{RM=RM_{MW}+RM_{IGM}+RM_{host}}.$ (1)

Here, $\rm{RM_{MW}}$ represents the $\rm{RM}$ contribution of the Milky Way
and $\rm{RM_{IGM}}$ is the modest contribution ($\rm{|RM_{IGM}|\ll
10\;rad\,m^{-2}}$) expected from the intergalactic medium (IGM; Akahori et
al., 2016). $\rm{RM_{host}}$ is the RM contribution of the FRB host galaxy,
which represents the shared contribution from its interstellar medium (ISM)
and the local magneto-ionic environment of the FRB source. FRB RMs often
significantly exceed $\rm{RM_{MW}}$ estimates from Galactic RM maps (see
Section 2.1). In such cases, FRB RMs offer a window into the magneto-ionic
properties of the local environments and hosts galaxies of FRB sources (Masui
et al., 2015; Petroff et al., 2017; Michilli et al., 2018).

When applying this analysis to repeaters, any temporal changes in the RM can
be used to constrain the magnetization, configuration and dynamics of the
medium producing those changes. If the changes are substantial, then these
variations are a direct probe of a changing magneto-ionic environment that is,
very likely, in the vicinity of the FRB source. This analysis was recently
done for FRB 20121102A, whose non-monotonically decreasing RM evolution was
found to be consistent with theoretical models describing it in terms of an
evolving supernova remnant (SNR; Hilmarsson et al., 2021b). A similar
interpretation has been put forth to describe observations of the repeater,
FRB 20190520B (Niu et al., 2021), which along with displaying an association
with a compact persistent radio source (PRS), also shares a number of other
similarities with FRB 20121102A. Based on these similarities, Zhao & Wang
(2021) argue for a young ($\sim 14-22$ years) magnetar embedded in a wind
nebula and SNR. While young SNR systems remain a popular model for explaining
these observations, other possibilities exist. Indeed, interesting
similarities have been drawn with the RM behavior of the radio-loud Galactic
center magnetar, whose substantial and evolving RM is very likely related to
its shared environment with the nearby supermassive black hole, Sagittarius A∗
(Desvignes et al., 2018). Meanwhile, recent observations by the FAST telescope
of nearly two thousand polarized bursts from FRB 20201124A (Xu et al., 2021)
have shown a number of interesting properties that include significant and
irregular RM variations on week-long timescales. Such behavior is discrepant
with the secular decrease expected if the RM is dominated by a shocked,
uniform medium (e.g. Piro & Gaensler, 2018) and instead suggests a high degree
of non-uniformity in the local environment of the source. These observations,
however, are insufficient to rule out the existence of an associated SNR since
the observed non-monotonic RM evolution could be produced by the SNR’s small-
scale turbulent magnetic field (Dickel & Milne, 1976; Milne, 1987). In such a
scenario, the observed RM behavior would manifest either through the relative
motion between the FRB source and the small-scale field or through the dynamic
evolution of turbulences in the SNR itself.

This paper reports on polarimetric observations of a sample of 12 previously
published repeating FRB sources (CHIME/FRB Collaboration et al., 2019a, b;
Fonseca et al., 2020). This sample greatly expands the number of repeaters
with corresponding polarization information, revealing interesting behavior in
individual sources as well as enabling the aggregate properties of this sample
to be compared to the (apparently) non-repeating FRB sample and other sources.
The paper is organized as follows: Section 2 reviews the observations and
analysis methods, Section 3 summarizes results and is followed by Section 4,
which explores the implications of these results for different sources and how
these results may be used in aggregate to characterize the local environments
of repeaters.

##  2 Observations, Data Reduction & Analysis

Observations reported in this paper correspond to bursts from previously
published repeating FRB sources (CHIME/FRB Collaboration et al., 2019b;
Fonseca et al., 2020) that successfully triggered baseband callback data
(Michilli et al., 2021) over a three year period between 2018 December and
2021 December. Figure 1 summarizes the number of bursts from each repeater of
this sample along with the number of significant RM detections (hatched). A
significant fraction of these bursts are associated with the periodically
active source, FRB 20180916B (44 bursts). Results of the polarization analysis
of this repeater can be found in a companion paper (Mckinven et al., 2022) to
which we refer the reader for a summary of the baseband data format and a
description of the methods used to determine relevant quantities like the RM,
polarized fraction ($L/I$) and polarization position angle (PA) curve (see
also; Mckinven et al., 2021). This paper studies the polarized properties of
the remaining 12 repeaters of this sample, which, with the exception of FRB
20190303A and FRB 20190604A (FRB 190303.J1353+48 & FRB 190604.J1435+53,
respectively; Fonseca et al., 2020), are the first polarization measurements
for these sources. Due to resource limitations and the threat posed by false
positives, a higher S/N threshold has been historically set for callbacks of
baseband versus intensity data (CHIME/FRB Collaboration et al., 2018). Hence,
the detections reported here are not entirely reflective of the total number
of detections from each source, which will be reported elsewhere.

Figure 1: The number of bursts observed in polarization from each repeating
source in our sample and the number of RM detections (hatched). The 44-burst
sample from FRB 20180916B is highlighted in blue and is reported on in a
companion paper (Mckinven et al., 2022).

###  2.1 Galactic Dispersion and Rotation Measure Estimates

Galactic RM contributions and associated uncertainties are estimated from the
updated all-sky Faraday Sky map of Hutschenreuter et al. (2022). This map
reconstructs the Galactic RM contribution, $\rm{RM_{MW}}$, using RM
measurements of polarized extragalactic sources. Galactic DM contributions are
estimated using the PyGEDM package222https://github.com/FRBs/pygedm, a Python
interface to the YMW16 (Yao et al., 2017) and NE2001 (Cordes & Lazio, 2002,
2003) electron density models. Table 1 summarizes estimates of the Galactic
dispersion and rotation measure contributions for the sample of repeating FRB
sources studied here. Sources are referred to by their transient name server
(TNS)333https://www.wis-tns.org/ names. Previous names along with the
discovery paper of each source are indicated here as a reference.

Table 1: Galactic DMa and RM estimates for our target sources

Source | $\rm{DM_{MW}}\;\rm{[pc\,cm^{-3}]}$ | $\rm{RM_{MW}}\;\rm{[rad\,m^{-2}]}$
---|---|---
TNS Name | Previous Name | NE2001 | YMW16 |
FRB 20180814A | FRB 180814.J0422+73b | $\sim 88$ | $\sim 108$ | $-45(18)$
FRB 20181030A | FRB 181030.J1054+73c | $\sim 41$ | $\sim 33$ | $-19(9)$
FRB 20181119A | FRB 181119.J12+65c | $\sim 34$ | $\sim 26$ | $+22(5)$
FRB 20190222A | FRB 190222.J2052+69c | $\sim 87$ | $\sim 101$ | $+10(7)$
FRB 20190208A | FRB 190208.J1855+46d | $\sim 65$ | $\sim 71$ | $+8(13)$
FRB 20190604A | FRB 190604.J1435+53d | $\sim 32$ | $\sim 24$ | $+12(2)$
FRB 20190213B | FRB 190212.J18+81d | $\sim 53$ | $\sim 49$ | $+9(13)$
FRB 20180908B | FRB 180908.J1232+74d | $\sim 38$ | $\sim 31$ | $-7(7)$
FRB 20190117A | FRB 190117.J2207+17d | $\sim 48$ | $\sim 40$ | $-26(8)$
FRB 20190303A | FRB 190303.J1353+48d | $\sim 30$ | $\sim 22$ | $+21(5)$
FRB 20190417A | FRB 190417.J1939+59d | $\sim 80$ | $\sim 83$ | $+36(13)$
FRB 20190907A | FRB 190907.J08+46d | $\sim 53$ | $\sim 50$ | $+7(4)$

a These estimates do not include the DM contribution of the Galactic halo,
which is expected to contribute an average value of $\sim
30-50\;\rm{rad\,m^{-2}}$, depending on the halo model assumed (e.g., Dolag et
al., 2015; Yamasaki & Totani, 2020).
b CHIME/FRB Collaboration et al. (2019a)
c CHIME/FRB Collaboration et al. (2019b)
d Fonseca et al. (2020)

###  2.2 Ionospheric Rotation Measure Estimates

Earth’s ionosphere imparts a small but measurable contribution to the observed
Faraday rotation of any linear polarized source. This contribution,
$\rm{RM_{iono}}$, must be corrected to determine the significance of any RM
variations. $\rm{RM_{iono}}$ can vary significantly depending on time of day,
solar cycle and pointing (Mevius, 2018a). However, as described in Mckinven et
al. (2022), most FRB detections with CHIME occur very near (a few degrees) of
zenith, limiting the variation in $\rm{RM_{iono}}$ that would otherwise be
introduced from extreme changes in pointings through the ionosphere. As was
the case for our observations of FRB 20180916B, $\rm{RM_{iono}}$ estimates are
obtained from the RMextract package444https://github.com/lofar-
astron/RMextract (Mevius, 2018b) whose values are provided in Table
LABEL:ta:bursts.

##  3 Results

Table LABEL:ta:bursts reports the results of our polarimetric analysis of our
sample of known repeating FRB sources (CHIME/FRB Collaboration et al., 2019a,
b; Fonseca et al., 2020). The sample contains several sources with burst
separations of multiple years. Bursts from the prolific CHIME/FRB source, FRB
20190303A, are summarized in Figure 2 in the form of dynamic spectra (referred
to as ‘waterfall plots’), displaying each burst as a function of frequency and
time. Here, data have been rebinned to highlight substructure of individual
bursts. Bursts have been dedispersed by their individual structure optimizing
DM ($\rm{DM_{struct}}$; Seymour et al., 2019) which was determined by applying
the DM_phase package555https://github.com/danielemichilli/DM_phase on rebinned
data. Waterfall plots of bursts from other repeaters can be found in Appendix
A (see Figure set 1 for waterfall plots of remaining sample).

Burst profiles are shown directly above waterfall plots and display the
subband averaged signal in total (black), linear polarized (red) and circular
polarized intensities (blue) as a function of time. Each burst’s subband has
been determined by eye and is indicated by an orange line along the left
vertical axis and reported in Table LABEL:ta:bursts under the “Emitting Band”
column. This quantity is not corrected for the non-uniform bandpass of the
CHIME, including the well-known bias for detecting bursts in the lower part of
the band where FFT beams of the realtime detection pipeline are wider
(CHIME/FRB Collaboration et al., 2018). Adjoining the burst profiles in Figure
2 (see also Figure set 1) is an additional panel showing PA behavior as a
function of time. CHIME/FRB observations cannot robustly calibrate for the PA
value (Mckinven et al., 2021); thus, PA profiles shown are only informative
for the evolution over the burst duration and have been determined from
Equation 3 of Mckinven et al. (2022) which centers PA values relative to $\sim
0$ degrees. 666The handful of events with PA curves that are significantly
offset from PA$\sim 0$ degrees is an imprint of instrumental polarization,
namely, a differential response between the primary beam of CHIME for the two
X, Y polarizations. Linear polarization, $L=\sqrt{Q^{2}+U^{2}}$, has been de-
biased by applying Equation 11 of Everett & Weisberg (2001) (see Mckinven et
al. (2022) for further details). We do not display corresponding
linear/circular/PA profiles for bursts without a significant RM detection
since these events are disproportionately affected by residual instrumental
polarization, which is more problematic when the polarized astrophysical
signal is marginal or non-existent. These events are not so much unpolarized
as polarized below the sensitivity threshold of CHIME, and are indicated in
Figure 2 and elsewhere as events where only total intensity profiles are
shown.

The remainder of this section studies burst properties as a function of time
of one of the more prolific repeating CHME/FRB sources, FRB 20190303A (§3.1).
This is followed by a summary of equivalent analysis for the other repeaters
that are more sparsely sampled in time (§3.2).

Bursts whose intensity data were previously reported by CHIME/FRB
Collaboration et al. (2019b).

Bursts whose intensity data were previously reported by CHIME/FRB
Collaboration et al. (2020).

Unconstrained parameters are listed as “$-$”. Uncertainties are reported at
the $1\sigma$ confidence level.

Topocentric TOAs provided here are in Modified Julian Date (MJD) format,
referenced at 400 MHz with $\sim 1$ second precision.

From structure-optimization (see Section 2.2.1 of Mckinven et al. (2022).

The downsampling factor that determines the time resolution (i.e.
$n_{\rm{down}}\times 2.56\,\mu s$) of the waterfalls plots displayed in Figure
2 and Figure set 1.

The linear polarization fraction determined from integrating $L$ over the
burst profile. Upper limits of unpolarized bursts are indicated by a ‘$<$’
prefix.

The portion of the 400$-$800 MHz CHIME band over which emission is observed,
uncorrected for the non-uniform bandpass of the instrument and corresponding
to vertical orange lines in burst waterfalls.

Quoted uncertainties refer to the statistical error, $\sigma_{\rm{stat}}$, and
do not account for additional systematic errors, which we estimate as
$\sigma_{\rm{sys}}=0.85$ rad m-2 based on multi-epoch polarimertic monitoring
of giant pulse data from the Crab pulsar (see Mckinven et al., 2022, for
details).

Table 2: Individual burst properties from a sample of repeating CHIME/FRB sourcesa. Burst # |  Arrival Timeb | S/N | $\rm{DM_{struct}}^{c}$ | $\rm{n_{down}}^{d}$ | $\rm{\langle L/I\rangle}^{e}$ |  Emitting Bandf | $\rm{RM_{FDF}}$ | $\rm{RM_{QU}}$ | $\rm{RM_{iono}}$
---|---|---|---|---|---|---|---|---|---
| (MJD) |  |  (pc cm-3) |  |  | (MHz) |  (rad m-2) |  (rad m-2) |  (rad m-2)
FRB20180814A
1 | 58645.78660 | 43.8 | $190.13(84)$ | 128 | $<0.11$ | 600-730 | $-$ | $-$ | +0.94
2 | 58659.73874 | 22.4 | $188.743(70)$ | 256 | $<0.22$ | 400-470 | $-$ | $-$ | +0.89
3 | 58660.77631 | 26.8 | $191.62(73)$ | 512 | $<0.19$ | 400-470 | $-$ | $-$ | +0.73
4 | 58785.40415 | 46.3 | $189.02(35)$ | 128 | $0.691(21)$ | 670-800 | $+699.8(1.0)$ | $+700.1(1.3)$ | +0.17
5 | 58798.37171 | 33.0 | $188.552(35)$ | 256 | $<0.15$ | 520-650 | $-$ | $-$ | +0.21
FRB 20181030A
1 | 58870.43093 | 43.9 | $103.500(13)$ | 32 | $0.728(23)$ | 400-560 | $+36.39(29)$ | $+36.52(30)$ | +0.24
2 | 58870.43542 | 31.3 | $103.504(11)$ | 32 | $0.601(27)$ | 400-500 | $+37.67(54)$ | $+38.53(64)$ | +0.23
3 | 58870.92327 | 22.5 | $103.586(55)$ | 32 | $<0.22$ | 400-520 | $-$ | $-$ | +0.53
4 | 58870.92352 | 26.8 | $103.473(35)$ | 128 | $<0.19$ | 400-550 | $-$ | $-$ | +0.53
5 | 58870.93287 | 30.6 | $103.493(83)$ | 256 | $0.928(43)$ | 400-600 | $+37.08(51)$ | $+36.60(58)$ | +0.51
FRB 20181119A
1 | 59021.11044 | 22.3 | $364.03(16)$ | 128 | $1.024(65)$ | 660-790 | $+606.2(1.2)$ | $+608.8(1.6)$ | +0.77
2 | 59187.65926 | 18.1 | $364.33(15)$ | 256 | $0.473(37)$ | 630-730 | $+1343.7(2.0)$ | $+1339.3(2.7)$ | +0.53
3 | 59379.13757 | 12.7 | $364.009(29)$ | 512 | $<0.39$ | 420-550 | $-$ | $-$ | +0.88
4 | 59389.10515 | 36.9 | $363.59(33)$ | 64 | $0.679(26)$ | 590-720 | $+480.95(59)$ | $+479.20(81)$ | +0.98
5 | 59529.72050 | 28.5 | $364.78(67)$ | 256 | $<0.18$ | 580-700 | $-$ | $-$ | +0.96
FRB 20190222A
1∗ | 58543.75211 | 59.8 | $459.58(10)$ | 16 | $0.2461(58)$ | 530-660 | $+571.2(1.7)$ | $+567.7(2.3)$ | +0.65
FRB 20190208A
1 | 58872.77984 | 32.6 | $579.889(55)$ | 64 | $0.885(38)$ | 410-670 | $+32.99(36)$ | $+31.81(53)$ | +0.74
2 | 58982.47538 | 23.0 | $579.33(16)$ | 128 | $0.884(54)$ | 650-800 | $+17.5(1.0)$ | $+17.4(1.1)$ | +0.43
3 | 59248.74874 | 113.6 | $579.858(19)$ | 8 | $0.903(11)$ | 630-800 | $+13.19(25)$ | $+13.09(38)$ | +0.86
4 | 59377.39380 | 19.7 | $579.836(25)$ | 128 | $0.965(69)$ | 485-605 | $+10.9(1.1)$ | $+10.1(1.5)$ | +0.32
5 | 59496.07040 | 42.1 | $579.859(11)$ | 32 | $0.860(29)$ | 400-490 | $+24.28(34)$ | $+25.75(18)$ | +0.77
6 | 59576.85105 | 43.1 | $579.718(41)$ | 64 | $0.913(30)$ | 400-570 | $+27.90(23)$ | $+29.00(19)$ | +1.70
7 | 59577.84674 | 39.6 | $579.97(11)$ | 64 | $0.686(25)$ | 440-800 | $+36.29(74)$ | $+32.13(81)$ | +1.66
FRB 20190604A
1† | 58640.23231 | 21.7 | $552.53(24)$ | 128 | $0.912(81)$ | 500-625 | $-17.8(8)$ | $-17.8(1.2)$ | +0.59
FRB 20190213B
1 | 58834.36037 | 21.3 | $301.64(12)$ | 256 | $0.742(49)$ | 400-670 | $-3.63(41)$ | $-5.28(63)$ | +0.11
2 | 59055.23537 | 18.1 | $301.38(22)$ | 256 | $0.951(74)$ | 400-500 | $+1.04(42)$ | $-0.41(56)$ | +0.34
3 | 59261.71552 | 35.8 | $301.400(48)$ | 128 | $0.921(36)$ | 420-500 | $+1.06(52)$ | $-0.2(1.0)$ | +0.69
4 | 59314.04279 | 26.2 | $301.720(64)$ | 256 | $0.934(50)$ | 510-620 | $+0.97(52)$ | $-0.25(66)$ | +0.54
5 | 59431.25656 | 22.6 | $301.430(19)$ | 128 | $1.009(63)$ | 400-510 | $-0.28(42)$ | $-0.05(64)$ | +0.38
FRB 20180908B
1 | 58655.09819 | 28.0 | $195.33(38)$ | 256 | $-$ | 400-450 | $<0.18$ | $-$ | +0.80
FRB 20190117A
1 | 58500.92954 | 118.9 | $393.062(74)$ | 8 | $0.1945(23)$ | 460-570 | $+74.30(68)$ | $+70.97(80)$ | +0.84
2 | 58840.00494 | 23.2 | $392.1123(19)$ | 256 | $<0.22$ | 460-590 | $-$ | $-$ | +0.57
3 | 59532.10691 | 222.5 | $395.804(36)$ | 8 | $0.14333(91)$ | 420-590 | $+76.31(40)$ | $+79.57(58)$ | +0.44
FRB 20190303A
1† | 58666.13522 | 76.8 | $221.43(21)$ | 8 | $0.3248(60)$ | 640-800 | $-489.3(6.3)$ | $-499.5(3.4)$ | +0.95
2 | 58769.85517 | 45.0 | $221.233(11)$ | 256 | $<0.11$ | 425-550 | $-$ | $-$ | +0.86
3 | 58776.82559 | 82.1 | $221.579(97)$ | 4 | $0.5413(93)$ | 580-730 | $-498.52(75)$ | $-501.14(73)$ | +0.90
4 | 58797.77293 | 113.7 | $221.354(59)$ | 32 | $0.1861(23)$ | 475-620 | $-601.2(4.5)$ | $-594.8(1.7)$ | +0.80
5 | 58800.75865 | 54.8 | $221.353(82)$ | 32 | $<0.09$ | 510-610 | $-$ | $-$ | +0.68
6 | 58803.75684 | 208.9 | $221.473(62)$ | 1 | $0.1810(12)$ | 575-715 | $-701.31(43)$ | $-703.40(58)$ | +0.93
7 | 58804.76286 | 33.5 | $221.264(61)$ | 256 | $<0.15$ | 400-480 | $-$ | $-$ | +0.80
8 | 58832.67612 | 46.8 | $221.55(16)$ | 32 | $<0.11$ | 450-610 | $-$ | $-$ | +0.44
9 | 58848.63738 | 27.2 | $221.64(57)$ | 64 | $0.487(25)$ | 580-690 | $-556.7(2.4)$ | $-563.9(3.5)$ | +0.36
10 | 58860.60178 | 38.8 | $221.70(25)$ | 128 | $<0.13$ | 425-505 | $-$ | $-$ | +0.27
11 | 59022.16102 | 36.8 | $222.04(29)$ | 128 | $0.716(27)$ | 700-800 | $-559.3(3.9)$ | $-560.1(4.3)$ | +0.91
12 | 59070.02806 | 57.8 | $221.39(38)$ | 4 | $0.723(18)$ | 550-685 | $-483.72(74)$ | $-485.57(83)$ | +0.96
13 | 59101.93754 | 68.7 | $221.71(15)$ | 128 | $<0.07$ | 410-460 | $-$ | $-$ | +0.82
14 | 59248.53543 | 57.7 | $221.333(43)$ | 16 | $0.768(19)$ | 660-800 | $-362.65(73)$ | $-363.74(83)$ | +0.26
15 | 59252.52666 | 80.2 | $221.78(24)$ | 8 | $0.841(15)$ | 635-800 | $-408.76(33)$ | $-409.11(34)$ | +0.23
16 | 59254.52323 | 102.2 | $221.72(12)$ | 8 | $0.4339(60)$ | 600-800 | $-421.33(37)$ | $-421.54(45)$ | +0.18
17 | 59275.46633 | 31.3 | $221.387(90)$ | 128 | $<0.16$ | 480-615 | $-$ | $-$ | +0.23
18 | 59501.84489 | 29.9 | $221.36(50)$ | 128 | $0.611(29)$ | 520-690 | $-270.2(1.2)$ | $-269.0(1.7)$ | +1.40
19 | 59525.77798 | 60.1 | $221.49(48)$ | 16 | $0.555(13)$ | 400-560 | $-200.34(30)$ | $-205.41(42)$ | +1.26
20 | 59543.73255 | 37.5 | $221.91(31)$ | 128 | $<0.13$ | 400-500 | $-$ | $-$ | +0.93
FRB 20190417A
1 | 59056.30674 | 56.2 | $1378.58(13)$ | 16 | $0.1466(37)$ | 620-710 | $+4429.8(3.5)$ | $+4429.3(4.1)$ | +0.26
2 | 59277.69667 | 36.0 | $1378.58(22)$ | 64 | $<0.14$ | 500-620 | $-$ | $-$ | +0.70
FRB 20190907A
1 | 59059.82090 | 18.1 | $309.30(31)$ | 512 | $<0.28$ | 400-535 | $-$ | $-$ | +0.90
|  |  |  |  |  |  |  |  |

###  3.1 FRB 20190303A

Figure 2: Waterfall plots in Stokes I of bursts from repeating source FRB
20190303A in chronological order and dedispersed to their structure optimized
DMs ($\rm{DM_{struct}}$; listed in Table LABEL:ta:bursts). Data have been
rebinned to a fixed frequency resolution of $\nu_{\rm{res}}=1.5625$ MHz. Time
has been rebinned according to $n_{down}$ of each burst, such that
$t_{\rm{res}}=n_{down}\times 2.56\;\rm{\mu s}$. Panels above the spectra
display burst profiles of total intensity (black). Bursts with significant RM
detections are also accompanied by linear polarized (red), and circularly
polarized (blue) intensity profiles (peak normalized), as well as polarization
angle (PA) curves. Burst profiles are obtained by adding signal over the
spectral limits of the burst, indicated by orange lines along the frequency
axis. Masked frequency channels are indicated by red lines along the vertical
axis. Each panel is labeled with the corresponding burst number from Table
LABEL:ta:bursts. Waterfall plots of bursts from other repeating sources in our
sample are available in the online journal.

The CHIME/FRB baseband system captured $20$ bursts from FRB 20190303A between
2019 July and 2021 November. These bursts, displayed in Figure 2, show a wide
range of linear polarization fractions and regularly exhibit complex burst
morphology, with several displaying clear downward drifting (“sad trombone”)
structure commonly seen in other repeating sources. Seven bursts from this
sample are seemingly unpolarized while the remaining 10 have polarization
fractions between $20\%$ and $100\%$.

Bandwidth depolarization only becomes significant for CHIME/FRB at
$\rm{|RM|}\gtrsim 2000\;\rm{rad\,m^{-2}}$ ($\sim 50\%$ loss in linear
polarization at 400 MHz) and therefore cannot explain the range of $L/I$ seen
from the polarized sample. Meanwhile, for the unpolarized sample we apply a
semi-coherent RM search routine (Mckinven et al., 2021) to overcome bandwidth
depolarization. We find no significant RM detection ($S/N>5$) by searching
over a range $-10^{6}\leq\rm{RM}\leq 10^{6}\;rad\,m^{-2}$. While this does not
rule out polarized events with extreme RMs, we consider this an unlikely
scenario given the $L/I$ variability and RM range seen in the polarized
subsample. The most likely scenario is that the bursts observed as unpolarized
are not extreme RM events but simply unpolarized to the limits of our
sensitivity. As such, for each unpolarized burst we use the the total
intensity burst S/N to calculate the $L/I$ that would be required to produce a
polarization detection at a level of $\rm{S/N=5}$. This value is used as a
conservative upper-limit on $L/I$ for unpolarized bursts in Table
LABEL:ta:bursts. A low level of circular polarization can be seen from
inspecting the polarized burst profiles of this source. This seems to
disfavour the observed $L/I$ variability being produced by Faraday conversion,
where linear polarization is converted to circular under special conditions of
a magneto-ionic environment (Gruzinov & Levin, 2019; Vedantham & Ravi, 2019).
An alternate scenario for producing variable $L/I$ via transmission through a
magnetized scattering screen (Melrose & Macquart, 1998; Beniamini et al.,
2021) is discussed in Section 3.1.2. Here, we conservatively estimate an upper
limit of $<10\%$ on the astrophysical circular polarization and note the
strong possibility that most of the observed Stokes $V$ is contamination of
cross-polarization leakage from imperfect feed alignment.

PA behavior displayed from this source is more diverse than that seen from FRB
20180916B. Several bursts (e.g., bursts 6, 14, 15) display PA evolution over
the burst duration, similar to the diverse PA behavior seen from FRB 20180301A
(Luo et al., 2020). Subtle PA variations of $\lesssim 20^{\circ}$ on short
($\ll 1\;\rm{ms}$) timescales also appear in many bursts. For some bursts
(e.g., bursts 4, 6, 11), these variations are in excess of 40∘, suggesting a
possible relation between variability in PA and the changing linear polarized
fraction. Given the limited sample size, it is unclear whether this PA
behavior may be related to the burst morphology.

####  3.1.1 Burst Properties vs. Time

Figure 3 displays the individual burst properties of our $20$-burst sample
from FRB 20190303A. Panel A summarizes the RM evolution, where individual RM
values range over $\sim-700\lesssim\rm{RM}\lesssim-200\;\rm{rad\,m^{-2}}$. The
arrival times of unpolarized bursts are indicated by red lines on the top
horizontal axis. There is no indication of a greater number of unpolarized
bursts (relative to polarized) at any point in the RM evolution. RM variations
exhibit intervals of secular evolution that are interspersed with non-
monotonic behavior, with substantial RM changes occurring over short
timescales. Figure B.1 provides a summary of the RM measurements, showing the
Faraday Dispersion Functions (FDFs) of both the polarized and unpolarized
bursts and highlighting the general agreement between the RMs obatined from
the FDFs, $\rm{RM_{FDF}}$, and those obtained from QU-fitting, $\rm{RM_{QU}}$
(green lines).

Over a six-day period from 2019 November 10 to 2019 November 16, the
$|\rm{RM}|$ increased by more than $\sim 100\;\rm{rad\,m^{-2}}$, implying a
temporal RM gradient of $|\rm{\partial RM/\partial t}|\gtrsim
17\;\rm{rad\,m^{-2}\,day^{-1}}$. This period is followed by an interval of
over a year where $|\rm{RM}|$ steadily decreased to its minimum near
$\rm{RM\sim-200\;rad\,m^{-2}}$, implying an average gradient of $|\rm{\partial
RM/\partial t}|\gtrsim 0.7\;\rm{rad\,m^{-2}\,day^{-1}}$. Subtracting the
Galactic $\rm{RM_{MW}}$ estimate obtained from Table 1 implies an
$\rm{RM_{excess}}=-227\pm 5\;\rm{rad\,m^{-2}}$ for the most recent
observation.

Panel B of Figure 3 displays $\rm{DM_{struct}}$ for the $20$-burst sample. We
do not find strong evidence for significant DM variations relative to the
formal measurements errors. Weighting by the inverse square of these errors,
we determine the average DM to be $\rm{DM_{struct}=221.27\pm
0.01}\;\rm{pc\,cm^{-3}}$, which is slightly lower than the value
($\rm{222.4\pm 0.7\;pc\,cm^{-3}}$) previously determined from CHIME/FRB
intensity data (Fonseca et al., 2020). Such a discrepancy is consistent with
well-known biases introduced from unresolved complex structure in FRBs.

Limiting our analysis to the polarized subsample, we do not find significant
correlation between $\rm{DM_{struct}}$ and $\rm{RM}$. This result is similar
to the equivalent analysis recently applied to CHIME/FRB observations of FRB
20180916B (Mckinven et al., 2022). The lack of correlated variability between
$\rm{RM}$ and $\rm{DM_{struct}}$ suggests that the observed RM variations may
be produced by local variations in $B_{\parallel}$. However, we cannot exclude
the alternate scenario in which $B_{\parallel}$ remains fixed and the observed
$\rm{RM}$ variations are produced from subtle fluctuations in $n_{e}$ or path
length, which are not detectable with our DM measurement precision. In either
scenario, a substantial magnetic field is required to produce the observed
variability in RM, with the estimated strength directly dependent on the
assumed DM contribution of the local Faraday-active medium. We estimate the
average strength of this magnetic field by applying the equation,

$\displaystyle\langle B^{local}_{\parallel}\rangle$
$\displaystyle=1.23\frac{\rm{RM_{local}}}{\rm{DM_{local}}}(1+z)$ (2)
$\displaystyle\sim 1.23\frac{\Delta\rm{RM}}{\rm{DM_{\Delta RM}}}(1+z)$
$\displaystyle\gtrsim 3.6\;\mu\rm{G}.$

Here, $\Delta\rm{RM}$ is the maximum variation in the observed RM, which we
take to be $\Delta\rm{RM}\sim 500\;\rm{rad\,m^{-2}}$ and is a reasonable proxy
for $\rm{RM_{local}}$ given the timescale of the RM evolution. $\rm{DM_{\Delta
RM}}$ is the unknown DM contribution of the local Faraday-active medium, which
is unconstrained by our observations since observed variations in DM and RM do
not appear to be correlated. We arrive at a conservative lower limit for
$\langle B^{local}_{\parallel}\rangle$ by setting $\rm{DM_{\Delta
RM}}=\rm{DM_{excess}}=\rm{DM}-\rm{DM_{MW}}-\rm{DM_{halo}}\lesssim
170\;\rm{pc\,cm^{-3}}$ (see Table 1). The $(1+z)$ term that accounts for the
differential dilution of cosmological expansion on DM and RM is safely ignored
in our estimate given the low redshift of the source777This source has yet to
be localized to a host galaxy. as inferred from its modest $\rm{DM_{excess}}$.

We emphasize that the $\rm{DM_{\Delta RM}}$ value assumed here very likely
overestimates the DM contribution of the Faraday-active medium, such that
$\rm{DM_{\Delta RM}}<<\rm{DM_{excess}}$. For instance, $\langle
B^{local}_{\parallel}\rangle\sim 3000\;\mu\rm{G}$ is required if we assume
that only the variable component of the DM inferred from the root-mean-square
of our $\rm{DM_{struct}}$ measurements (i.e.,
$\Delta\rm{DM}=0.2\;pc\,cm^{-3}$), contributes to the observed RM evolution of
this source. This revised $\langle B^{local}_{\parallel}\rangle$ value is
larger than the equivalent estimate of $\sim 100\;\rm{\mu G}$ obtained from
recent observations of FRB 20180916B (Mckinven et al., 2022) and approaches
the $3-17\;\rm{mG}$ constraint arrived at by Katz (2021) from polarimetric
observations of FRB 20121102A (Hilmarsson et al., 2021b). Further discussion
on the implication of these measurements can be found in Section 4.4. Panel C
and D display the linear polarized fraction and emitting band, which again
appear to be uncorrelated with the RM evolution of this source.

Figure 3:  Burst properties as a function of time for baseband data recorded
from FRB 20190303A, displaying the ionospheric corrected RM (panel A; black
diamonds), $\rm{DM_{struct}}$ (panel B), linear polarized fraction ($L/I$;
panel C) and emitting band (panel D; uncorrected for the non-uniform bandpass
of CHIME). Times are in Coordinated Universal Time (UTC) format with vertical
dotted lines indicating the start of each calendar year. The RMs of Panel A
(black points) are determined from QU-fitting ($\mathrm{RM_{QU}}$) applied to
the $20$-burst sample and are displayed alongside previously published RMs
obtained from FAST observations (magenta points; Feng et al., 2022). The
extent of the error bars in Panel A appear invisible for some data points due
to the the large RM variations displayed from this source. Red data points in
panels B, C and D correspond to the unpolarized sample where the inverted red
triangles of panel C indicate upper limits on $L/I$. The times of arrival
(TOA) of the unpolarized bursts are indicated as lines along the top
horizontal axis (panel A).

####  3.1.2 A Frequency Dependence in $L/I$

(a) FRB 20190303A

(b) FRB 20190417A

Figure 4: Degree of linear polarization as a function of frequency for
multiband observations of FRB 20190303A (panel a) and FRB 20190417A (panel b).
The best-fit depolarization models determined by Feng et al. (2022) are
indicated by magenta lines and were calculated from previous measurements
(magenta data points) of these sources (see Feng et al., 2022, for details).
These measurements include a single lower limit measurement for FRB 20190303A
(magenta point with upward arrow) obtained from a previously published
CHIME/FRB observation (Fonseca et al., 2020). The linear polarization
measurements of our sample are represented as black diamonds with the upper
limits of our unpolarized subsample indicated by red downward arrows.
Depolarization curves for different values of $\sigma_{\rm{RM}}$ (1, 2, 4, 8
$\&$ 16 rad m-2) are indicated by grey lines. The excursions of $L/I$
measurements from values predicted by best-fit models is further discussed in
Section 4.2.

Our $20$-burst sample from FRB 20190303A shows $L/I$ to be clearly correlated
with frequency, with all the unpolarized events located in the bottom half
($400-600$ MHz) of the CHIME band (see Figure 3). Figure 4(a) summarizes this
result by displaying $L/I$ measurements as a function of the central frequency
of the emitting band of each burst from both CHIME ($400-800$ MHz; diamonds)
and FAST ($1.0-1.5$ GHz; circles) observations. From this combined sample we
calculate a significant Spearman correlation coefficient of 0.80 (p-value
$<0.001$) between $L/I$ and frequency. Such a dependence is consistent with
expectations for scattering screen models (e.g. Melrose & Macquart, 1998;
Beniamini et al., 2021; Yang et al., 2022) whereby multi-path propagation
through a turbulent magneto-ionic medium produces stochastic Faraday rotation
and partial depolarization that is more significant at lower frequencies and
has several compelling pulsar analogues (Xue et al., 2019; Sobey et al., 2019,
2021). Within this framework, the amount of depolarization is determined by a
single parameter, $\sigma_{\rm{RM}}$, such that
$f_{depol}=1-\exp(-\rm{2\lambda^{4}\sigma_{RM}^{2}})$. Recently, Feng et al.
(2022) fit this model to a small subset of $L/I$ measurements shown in Figure
4 (magenta data points) and arrived at a best-fit
$\sigma_{\rm{RM}}=3.6\;\rm{rad\,m^{-2}}$ for this source.

The additional $L/I$ measurements reported here (black diamonds), although
generally consistent with a depolarization imprint, exhibit significant
excursions from the predicted trend of the best-fit depolarization model. This
suggests that either the intrinsic variability in $L/I$ is significant or that
the observed excursions are produced by variations in $\sigma_{RM}$. Given the
magnitude of the RM variations observed from this source, it would not be
surprising if $\sigma_{RM}$ displayed a similar level of instability in time.
Indeed, only a modest range of
$1.5\;\rm{rad\,m^{-2}}\lesssim\sigma_{\rm{RM}}\lesssim 4.5\;\rm{rad\,m^{-2}}$
value is required to explain the observed excursions in $L/I$ from the
benchmark model of Feng et al. (2022). This range of $\sigma_{\rm{RM}}$ values
is well within the day-to-day RM variations observed from this source and
suggests the possibility that the medium producing the quasi-secular RM
evolution may also generate sufficient scattering to partially depolarize
emission through stochastic Faraday rotation. This scenario assumes that the
observed day-to-day RM variations are due to the relative motion between a
depolarizing/inhomogeneous plasma screen and the FRB source. Another
possibility is that these variations are produced by a plasma screen with a
uniform but evolving magnetic field and/or electron density in which case the
screen would still produce RM variations but not depolarize the signal. In
this latter scenario, any fluctuations in $L/I$ would have to be intrinsic to
the source, reminiscent of the unstable polarized fractions (and PAs) reported
from radio emitting magnetars (e.g. Camilo et al., 2007; Levin et al., 2012;
Dai et al., 2018, 2019).

Studying a larger sample of bursts from this source over a wider range of
frequencies and incorporating information from other burst properties will
illuminate the origins of variability in $L/I$. In particular, correlating
$L/I$ or $\sigma_{\rm{RM}}$ with temporal scattering measurements of bursts
will test the extent to which variations in $L/I$ are an imprint of a
foreground structure or intrinsic to the source.

###  3.2 Other Repeating FRB Sources

(a) FRB 20180814A

(b) FRB 20181030A

(c) FRB 20181119A

(d) FRB 20190208A

(e) FRB 20190213B

(f) FRB 20190117A

(g) FRB 20190417A

Figure 5: Similar to Figure 3, summary plots displaying burst properties as a
function of time for other repeating sources of our sample with two or more
baseband events. Red data points in panels B, C and D correspond to the
unpolarized sample where the inverted red triangles of panel C indicate upper
limits on $L/I$. The times of arrival (TOA) of the unpolarized bursts are
indicated as lines along the top horizontal axis (panel A). The magenta points
of panel (g) indicate additional measurements of FRB 20190417A, recently
reported by FAST (Feng et al., 2022). For sources where $\rm{RM_{excess}}\sim
0\;\rm{rad\,m^{-2}}$ (panels (c) & (e)), blue shaded regions are displayed to
indicate the uncertainty in these measurements as determined from
$\rm{RM_{MW}}$ estimates (see Table 1).

This section summarizes observations of the remaining bursts of our repeating
CHIME/FRB sample. Waterfall plots for each burst can be found in Appendix A.
Similar to Figure 3 for FRB 20190303A, Figure 5 summarizes burst properties
($\rm{RM}$, $\rm{DM}$, $L/I$, emitting band) as a function of time for the
subsample of repeaters with two or more baseband events. In all cases a semi-
coherent RM search was applied to bursts that were observed to be unpolarized,
ruling out $\rm{|RM|}$ values as large as $10^{6}\;\rm{rad\,m^{-2}}$ at our
sensitivity.888This does not rule out the possibility of a marginally
polarized signal (S/N$<5$) at large $\rm{|RM|}$ values.

FRB 20180814A: Five baseband events were recorded from this source over a 5
month period between 2019 June 11 and 2019 November 11. The complex burst
morphology previously reported for this source (CHIME/FRB Collaboration et
al., 2019b, a) is replicated here with baseband data (see Figure set 1).
Bursts are detected over the entire $400-800$ MHz band and several bursts
display downward drifting subbursts. A systematic study of this time-frequency
structure is beyond the scope of this paper and is deferred to a future
analysis of repeater morphology at high time-resolution. We calculate an
average $\mathrm{DM_{struct}}$ value of $188.60\pm 0.03\;\rm{pc\,cm^{-3}}$
that is consistent with previous constraints determined from CHIME/FRB
intensity data and not too dissimilar from a representative value
($188.8\;\mathrm{pc\,cm^{-3}}$) recently determined from analysis of
individual subbursts of this source (Chamma et al., 2021). Only a single burst
(burst 3) appears significantly linearly polarized and produces an RM
detection at $\mathrm{RM}\sim+700\;\mathrm{rad\,m^{-2}}$, implying
$\mathrm{RM_{excess}}\sim+745\pm 18\;\mathrm{rad\,m^{-2}}$. The remaining
bursts appear to be unpolarized. Figure 5(a) summarizes the bursts’ properties
as a function of time for this source.

FRB 20181030A: Five baseband events were captured from this source in a single
day. This source is located at a sufficiently high declination
($>+70^{\circ}$) such that it enters CHIME’s field-of-view (FoV) twice in a
sidereal day, at both upper and lower transit (CHIME/FRB Collaboration et al.,
2019b). As such, two bursts were detected in the lower transit and three were
detected approximately 12 hours later in upper transit. Bursts preferentially
occupy the bottom half of the CHIME bandpass. Significant RM detections are
made in three bursts (bursts 1,2 & 5), all of which are observed to be $\sim
100\%$ polarized. The remaining bursts appear unpolarized. Several events
(bursts 1, 2 & 4; see Figure set 1) display multiple subbursts with
substantial ($\gtrsim 30\;\rm{ms}$) separation in time. Interestingly, bursts
1 and 2 show evidence of PA evolution between these separated subbursts. There
is no evidence for substantial RM variations relative to an average $\rm{RM}$
of $+36.6\pm 0.2\;\rm{rad\,m^{-2}}$. Figure 5(b) summarizes the bursts’
properties as a function of time for this source.

FRB 20181119A: Five baseband events were detected from this source over 2020
June - 2021 December. Three of these bursts are significantly polarized with
the remaining two observed as unpolarized. The most recent unpolarized burst
is sufficiently bright to put an upper limit of $L/I<0.18$. The remaining
unpolarized burst is much less bright and, therefore, the corresponding upper
limit on $L/I$ is significantly higher. The RM from this source appears to be
highly variable, increasing by over $700\;\rm{rad\,m^{-2}}$ to a maximum value
of $\rm{RM}=+1339.3\pm 2.7\;\rm{rad\,m^{-2}}$ over six months and decreasing
by an approximately equal amount over a similar time interval. Such large
variations imply temporal RM gradients of at least $|\rm{\partial RM/\partial
t}|\gtrsim 4\;\rm{rad\,m^{-2}\,day^{-1}}$ and are not accompanied by any
significant DM changes. Figure 5(c) summarizes this source’s burst properties
as a function of time.

FRB 20190222A: A single baseband event was detected from this source on 2019
March 1. The burst was observed to be partially linearly polarized ($\gtrsim
30\%$); however, the significant circular polarization seen from this burst
(see Figure set 1) suggests that the linear polarization could be higher if
instrumental leakage is present. An RM of $+567.7\pm 2.3\;\rm{rad\,m^{-2}}$
was detected for this source.

FRB 20190208A: Seven baseband events were captured from this source between
2020 January and 2021 December. Bursts occured across the CHIME band (see
Figure set 1) and are highly linearly polarized ($L/I\lesssim 0.7$). There is
slight evidence for small variations in the PA of several bursts; however, the
PA excursions are undersampled and tend to occur at the edges of the burst
where the S/N is lower. Figure 5(d) summarizes this source’s burst properties
as a function of time. The RM of this source appears as a “U” shaped evolution
over a two year interval where the evolution “bottoms-out” near
$RM_{\rm{excess}}\sim 0\;\rm{rad\,m^{-2}}$ and is followed by a recovery to
previous RM levels. This RM evolution implies a modest temporal RM gradient of
$|\rm{\partial RM/\partial t}|\sim 0.1-0.2\;\rm{rad\,m^{-2}\,day^{-1}}$ and
there is no evidence for correlated changes in $\rm{DM_{struct}}$ over this
period.

FRB 20190604A: A single baseband event was detected from this source on 2019
June 6. The polarized properties of this burst were originally reported by
Fonseca et al. (their source 2; 2020). Refined analysis applied here
demonstrates this burst to be $100\%$ linearly polarized with a flat PA curve
(see Figure set 1). We detect an RM of $-17.8\pm 1.2\;\rm{rad\,m^{-2}}$ that
is not significantly different from the previous reported value.

FRB 20190213B: Five baseband events were detected from this source between
2019 December and 2021 August. This source (see Figure set 1) exhibits fairly
complex morphology, with several bursts displaying strong frequency drifting
in the emission (e.g. Burst 1). Bursts with more complex morphology appear to
be accompanied by evolution of their PA, however; this may also be a
coincidence given the small size of our sample. Significant circular
polarization is also observed in several sources (bursts 1, 2 & 4). This may
be a real signal from the source but is at odds with our simultaneous $L/I\sim
100\%$ measurement and suggests the presence of cross polarization. Figure
5(e) summarizes this source’s burst properties as a function of time. RMs from
this source are fairly modest ($\sim 0\;\rm{rad\,m^{-2}}$) and would possibly
be regarded as false detections from instrumental polarization were it not for
the high linear polarized fractions observed. Furthermore, the RM of the first
observation is significantly ($>6\sigma$) different from the remaining
observations, which is further evidence that these RM detections are
astrophysical. For the most recent observation, we determine
$\rm{RM_{excess}}=-10\pm 13\;\rm{rad\,m^{-2}}$.

FRB 20180908B: A single baseband event was captured from this source on 2019
June 21. The burst occupies the bottom 50 MHz of the CHIME band and is
observed to be unpolarized. The $\rm{DM_{struct}}=195.3\pm
0.4\;\rm{pc\,cm^{-3}}$ for this source is consistent with previous
measurements determined with CHIME/FRB intensity data (Fonseca et al., 2020).

FRB 20190117A: We captured three baseband events from this source between 2019
January and 2021 November. Bursts appear to be marginally polarized
($L/I\lesssim 30\%$), leading to significant RM detection in only two events.
The remaining event is significantly fainter and a similar level of
polarization as seen from the other two bursts would not be detectable. PA
evolution within the two polarized bursts is unclear given the low S/N of the
linear polarized signal. Figure 5(f) summarizes this source’s burst properties
as a function of time. The RM is observed to increase by $\sim
9\;\rm{rad\,m^{-2}}$ and is accompanied by a significant increase in the DM of
$\sim 2.75\;\rm{pc\,cm^{-3}}$. After correcting for DM and RM contributions
from the Milky Way this amounts to an approximately $9\%$ change in the RM and
$0.7\%$ in the DM.

FRB 20190417A: We captured two baseband events from this source between 2020
July and 2021 March with one of these bursts providing a significant RM
detection near $\rm{RM}\sim+4430\;\rm{rad\,m^{-2}}$. This RM is similar to
recent measurements obtained at higher frequencies by FAST (Feng et al.,
2022). However, bursts from this source appear significantly less polarized
when observed at the lower frequencies of CHIME. This result is summarized in
Figure 5(g), which shows burst properties as a function of time and compares
$\rm{RM}$ and $L/I$ of bursts observed by CHIME and FAST. Figure 4(b) displays
the $L/I$ measurements as a function of frequency. The lower degree of linear
polarization of this source when observed in the CHIME band appears to be
generally consistent with predicted behavior from depolarization (Feng et al.,
2022). From this combined sample of FAST and CHIME observations, we calculate
a significant Spearman correlation coefficient of 0.86 (p-value $=0.01$)
between $L/I$ and frequency. If depolarization is indeed responsible for the
observed frequency dependence of $L/I$, future observations of this source
with CHIME will be helpful for constraining the nature of the depolarizing
medium, including the precise value of $\sigma_{\rm{RM}}$ and its stability
over time.

FRB 20190907A: A single baseband event was detected from this source on 2020
July 29. Significant RFI occupies the top half of the CHIME band and is masked
in the corresponding waterfall plot (see Figure set 1). The burst is observed
to be unpolarized. The $\rm{DM_{struct}}$ determined here is found to be in
agreement with previous measurements from CHIME/FRB intensity data (Fonseca et
al., 2020).

##  4 Discussion

We summarize the main results of our analysis below.

  1. 1.

Multi-year polarimetric monitoring of CHIME/FRB repeating sources (CHIME/FRB
Collaboration et al., 2019a, b; Fonseca et al., 2020) has provided a sample of
100 bursts from 13 repeaters. A significant fraction of these bursts originate
from the periodic source FRB 20180916B (44 bursts), which is described in a
companion paper (Mckinven et al., 2022). The remaining sample studied here
include many repeaters for which these are the first reported polarized
measurements (FRB 20180814A, FRB 20181030A, FRB 20181119A, FRB 20190222A, FRB
20190208A, FRB 20190213B, FRB 20180908B, FRB 20190117A & FRB 20190907A) in
addition to a handful with previously reported results (FRB 20190604A, FRB
20190303A & FRB 20190417A; Fonseca et al., 2020; Feng et al., 2022).

  2. 2.

The repeating FRBs studied here exhibit a high degree of variability in their
linear polarized fractions which appears to be intrinsic to the sources.
However, some repeaters also display clear frequency dependence in $L/I$ (see
Figure 4) that is consistent with the general behavior expected from
propagation through a depolarizing medium. Meanwhile, the circular
polarization displayed in some bursts is very likely to be, at least in part,
instrumental.

  3. 3.

Significant burst-to-burst RM variations are observed in the majority of our
repeating sources. These variations often appear to be secular on week-month
timescales rather than stochastic and are, in general, not accompanied by
correlated change in $\rm{DM}$, $L/I$ or emitting band.

  4. 4.

Some repeating sources display extreme RM variations of several hundred
$\rm{rad\,m^{-2}}$. The $20$-burst sample from FRB 20190303A exhibits an RM
that has changed by nearly $500\;\rm{rad\,m^{-2}}$ over a two year period
(Figure 3). FRB 20181119A displays significant RM variations, changing by as
much as $\sim 860\;\rm{rad\,m^{-2}}$ over $\sim 6$ month intervals (Figure
5(c)). FRB 20190208A, meanwhile, displays a “U” shaped RM evolution over the
course of two years, bottoming out near $\rm{RM_{excess}}\sim
0\;\rm{rad\,m^{-2}}$ before recovering to previously measured values
($\rm{RM_{excess}}\sim+30\;\rm{rad\,m^{-2}}$; see Figure 5(d)).

###  4.1 Implications of RM Variations

Burst-to-burst RM variations appear to be a ubiquitous feature of repeating
FRB sources. In many cases these RM changes can be extreme, changing by
several hundred $\rm{rad\,m^{-2}}$ on weeks$-$months timescales and implying a
dynamic local environment, which may or may not be related to the central
engine. Examples of such sources in our sample include FRB 20190303A, FRB
201811119A and FRB 20190417A. These sources join other repeaters FRB 20121102A
(Michilli et al., 2018; Hilmarsson et al., 2021b; Plavin et al., 2022) and FRB
20190520B (Anna-Thomas et al., 2022; Dai et al., 2022) in establishing a
significant subsample of the repeater population that reside in dynamic
magneto-ionic environments. For these sources, negligible (or very little)
change is observed in the DM. This suggests that either the observed RM
evolution is produced mainly from changes in $B_{\parallel}$ or that the small
but significant changes in the electron number density, $n_{e}$, or path
length through the perturbing medium exist but are too small to be detected
with our DM measurement precision. In reality, the observed RM variations
maybe some combination of these two extreme scenarios with changes in
$B_{\parallel}$, $n_{e}$ and path length each imparting individual
contributions to the observed RM variation. If, however, a change in the sign
of the $\rm{RM_{excess}}$ is observed then this necessarily implies a change
in the orientation of $B_{\parallel}$ (field reversal). Indeed, such a
scenario has been observed from FRB 20190520B (Anna-Thomas et al., 2022; Dai
et al., 2022) and several sources in our sample come very close to displaying
this behavior (e.g., FRB 20190208A, FRB 20190213B).999See also recent RM
evolution from FRB 20180916B (Mckinven et al., 2022)

Our best sampled sources commonly display intervals of quasi-secular RM
evolution (e.g., FRB 20190208A, 20190303A) that are similar to the remarkably
linear RM evolution recently observed from FRB 20180916B (Mckinven et al.,
2022). The month$-$year timescales of these secular intervals seem to suggest
the presence of ionized structures permeated by a reasonably ordered, but
changing, magnetic field. Such behavior contrasts the seemingly stochastic RM
variability displayed by repeating sources FRB 20180301A (Luo et al., 2020)
and FRB 20201124A (Hilmarsson et al., 2021b; Kumar et al., 2022a), albeit on
much shorter ($<1$ day) timescales. Whether FRB 20190208A and/or FRB 20190303A
display similar stochasticity on these timescales remains unknown from the
sparse sampling of these sources in time. Subsequent observations by FAST of
FRB 20201124A (Xu et al., 2021) have shown secular intervals of RM evolution
similar to that displayed here for FRB 20190303A, changing by hundreds of
$\rm{rad\,m^{-2}}$ on week$-$month timescales. There are several interesting
similarities between FRB 20201124A and FRB 20190303A that may suggest similar
local environments and/or progenitors. Both sources display large RM
variations on relatively short timescales, variable polarization fractions,
and significant PA evolution across burst durations. There are even
morphological similarities with both sources regularly exhibiting the
frequency drift in subbursts commonly associated with repeaters. However,
unlike FRB 20201124A, FRB 20190303A displays evidence for a secular decrease
in the RM contribution from its local environment. This behavior is
reminiscent of that seen from FRB 20121102A, which displays dramatic RM
evolution that generally follows a decreasing trend but is interspersed by
erratic periods where the RM can change by $\rm{\sim
1000\;\rm{rad\,m^{-2}\,week^{-1}}}$ (Hilmarsson et al., 2021b). Curiously, the
temporal RM gradients, $\rm{\partial RM/\partial t}$, displayed by FRB
20190303A are of comparable amplitude to the erratic RM excursions reported
from FRB 20121102A. The extent to which this is a coincidence or an actual
characteristic feature reflecting spatial scales of magnetized structures in a
similar local environment remains to be seen.

The origins of such strong and varying magnetic fields required to explain the
RM varibility observed here and elsewhere are topics of on-going study.
Popular scenarios commonly involve an FRB-emitting neutron star in which RM
variability is supplied by inhomogeneities in the surrounding circum-burst
medium that may be associated with a supernova remnant, a pulsar wind nebula
or coronal wind from a binary stellar companion (Anna-Thomas et al., 2022).
Alternatively, the RM variations may be an imprint of an intermediate-mass
black hole with strong outflows, as for PSR J1745$-$2900 whose significant RM
variations are believed to be an imprint of magnetized outflows from the
nearby supermassive black hole, Sagittarius A⋆, at the center of the Galaxy
(Pang et al., 2011; Eatough et al., 2013). One important detail for
distinguishing among these competing scenarios is the presence of compact
persistent radio source (PRS) associated with repeaters that display the most
extreme RM behavior101010Whether that be average RM, burst-to-burst RM
variability and/or RM-scatter inferred from frequency-dependent
depolarization.(Feng et al., 2022). Such a result indicates a possible
relation between the luminosity of the PRS and the magnetization of the
source’s local environment. This could be leveraged in the future to
prioritize high sensitivity follow-up observations that seek to identify more
potential FRB-PRS associations (Yang et al., 2020, 2022). In Section 4.4 this
topic is further discussed in the context of $B^{local}_{\parallel}$ estimates
and equivalent estimates gleaned from a limited sample of young pulsars
associated with SNRs.

###  4.2 Depolarization via Stochastic Faraday Rotation

Figure 6: The $\sigma_{\rm{RM}}$, $|\rm{RM}|$ relation of Feng et al. (2022),
updated to include $\sigma_{\rm{RM}}$ upper limits from additional sources
studied here. Measurements of Feng et al. (2022) are indicated by blue circles
with the red line indicating the best-fit linear model (slope$=0.62\pm 0.30$).
Upper limits on $\sigma_{\rm{RM}}$ for six additional sources studied here are
indicated by leftward triangles and are seen to be consistent with the
predicted trend of the linear model. Equivalent measurements for a small
sample of pulsars (PSRs J1721$-$3532, B0531+21, J0742$-$2822, B1946+35) are
indicated by open, black markers. The top horizontal axis indicates the
frequency at which $50\%$ depolarization occurs and is highlighted as a gray
region over the 400-800 MHz bandpass of CHIME. Figure updated and adapted with
permission from Feng et al. (2022).

In Figure 4.2, we showed that $L/I$ measurements of two repeaters (FRB
20190303A, FRB 20190417A) are systematically lower than equivalent
observations at higher frequencies. This feature appears to be replicated in
recent $L/I$ measurements of FRB 20180916B with CHIME/FRB (Mckinven et al.,
2022). These observations support depolarization via multi-path propagation as
a major factor affecting $L/I$ measurements. However, we also find significant
excursions in $L/I$ measurements relative to the best-fit depolarization
trends recently determined for each of these sources (Feng et al., 2022).
These excursions reflect some combination of intrinsic variability and
evolving properties of the depolarizing medium. A changing magneto-ionic
environment was recently proposed by Laha et al. (2022) to explain the
marginal linear polarization ($<10\%$) observed from FRB 20180301A (Laha et
al., 2022), a source that has previously displayed significant linear
polarization at similar frequencies (Luo et al., 2020). Indeed, many of the
$L/I$ measurements reported here cover multi-year timescales. It would not be
surprising therefore if the significant burst-to-burst RM variations observed
from FRB 20190303A, FRB 20190417A and FRB 20180916B translated into similar
variability in the depolarization parameter, $\sigma_{\rm{RM}}$. In the
future, this scenario can be tested by fitting a depolarization model to
discrete epochs of observation and looking for significant changes in
$\sigma_{\rm{RM}}$ and any correlated behavior with the RM evolution of the
source.

Apart from FRB 20190303A, FRB 20190417A and FRB 20180916B, no other repeating
source in our sample contains a sufficient number of observations and/or
bandwidth to sensibly fit a depolarization model. However, we can estimate
upper limits on $\sigma_{\rm{RM}}$ for six additional sources by assuming
$100\%$ intrinsic linear polarization and calculating the $\sigma_{\rm{RM}}$
that would be required to remain consistent with the $L/I$ measurements of
each repeater. The results of this analysis are summarized in Figure 6 where
upper limits on $\sigma_{\rm{RM}}$ for each repeater are indicated as leftward
triangles. These upper limits are all positioned below the best-fit
$\sigma_{\rm{RM}}$, $|\rm{RM}|$ trendline recently established from a small
sample of repeaters with $\sigma_{\rm{RM}}$ measurements (Feng et al., 2022).
Equivalent measurements obtained from a small sample of pulsars (PSRs
J0742-2822, B0531+21, B1946+35, $\&$ J1721-3532 Xue et al., 2019; Sobey et
al., 2019, 2021) are also shown. The large scatter of our upper limits
relative to this trendline does not disprove the existence of a correlation
between $\sigma_{\rm{RM}}$ and $|\rm{RM}|$ but instead likely reflects the
limitations of determining $\rm{\sigma_{RM}}$ for observations with
insufficient bandwidth. In fact, the deficit of CHIME/FRB repeaters with RMs
greater than several thousand $\rm{rad\;m^{-2}}$ supports the notion that
$\sigma_{\rm{RM}}$ is correlated with $|\rm{RM}|$. The gray region in Figure 6
corresponds to the range of $\sigma_{\rm{RM}}$ values at which $50\%$
depolarization occurs over the CHIME band. Sources with $\sigma_{RM}$ to the
right of this region are therefore significantly depolarized at CHIME
frequencies. This implies that unpolarized repeaters in our sample (e.g., FRB
20180908B & FRB 20190907A) may in fact have significant $\sigma_{\rm{RM}}$,
making them good candidates for followup at higher frequencies where the
deleterious effects of depolarization are less substantial. Conversely,
sources with $\sigma_{\rm{RM}}$ to the left of the gray region will likely
need to be observed at frequencies below 400 MHz for a robust measurement of
$\sigma_{\rm{RM}}$. Meanwhile, the absence of correlation between
$\sigma_{\rm{RM}}$ and $|\rm{RM}|$ in the pulsar sample is perhaps not
surprising given their preferential sampling of the Galactic plane where the
RM is dominated by the large scale magnetic field permeating the ISM.

###  4.3 Repeating vs. Non-repeating FRB Samples

Combining the polarized observations from the repeating sources studied here
with previously reported measurements from additional repeaters; FRB 20121102A
(Michilli et al., 2018; Hilmarsson et al., 2021b; Plavin et al., 2022), FRB
20180301A (Luo et al., 2020), FRB 20190520B (Anna-Thomas et al., 2022; Dai et
al., 2022), FRB 20190711A (Day et al., 2020), FRB 20200120E (Bhardwaj et al.,
2021; Nimmo et al., 2022) and FRB 20201124A (Hilmarsson et al., 2021a; Kumar
et al., 2022a; Xu et al., 2021; Kumar et al., 2022b), gives us a sample of 16
sources with unambiguous RM detections that can be compared to a non-repeating
counterpart sample. Such analysis is motivated by the possibility of different
progenitors for the two populations, which could appear as an imprint in the
RM distribution. We investigate this possibility in Figure 7 by displaying the
joint $\rm{DM_{excess}}$, $\rm{RM_{excess}}$ distributions of the repeating
and non-repeating samples. $\rm{DM_{excess}}$ estimates are obtained using the
NE2001 model (Cordes & Lazio, 2002, 2003) with an additional $\rm{DM_{halo}}$
contribution of $30\;\rm{pc\,cm^{-3}}$ while $\rm{RM_{excess}}$ estimates are
obtained from the Galactic Faraday foreground model of Hutschenreuter et al.
(2022) (see Table 1). The resulting joint $\rm{DM_{excess}},\rm{RM_{excess}}$
distribution of the repeating sample is compared to a sample of 18 non-
repeating FRBs that is obtained by combining results from Wang et al. (2020)
with observations of two additional one-off events, FRB 20191219F and FRB
20200917A (Mckinven et al., 2021).

Based on the modest sample shown here, non-repeating FRBs appear to be more
highly represented at larger $\rm{DM_{excess}}$ values. We performed an
Anderson-Darling (AD) test to determine the significance of differences in the
$\rm{DM_{excess}}$ distributions of the repeating and non-repeating samples
and found a marginal p-value of $\sim 0.03$. This simple comparison is
misleading however since it omits differences in the observing
telescopes/surveys of the two samples. For instance, the absence of repeaters
at very large $\rm{DM_{excess}}$ values can easily be explained by the
disproportionate representation (relative to the non-repeating sample) of
CHIME/FRB observations in our repeating sample, which is known to suffer
significant sensitivity loss for higher DM events (CHIME/FRB Collaboration et
al., 2021a). Similarly, we find no obvious difference between the
$|\rm{RM_{excess}}|$ distributions of the repeating and non-repeating samples
($\rm{p-value}>0.13$), with both samples well represented at fairly modest
$|\rm{RM_{excess}}|$ values. RM variations in the repeating sample are denoted
by vertical lines covering the range of observed values. The absence of any
substantial differences between the $|\rm{RM_{excess}}|$ distributions of the
repeating and non-repeating samples suggests that the underlying sources
reside in similar host galaxies and local environments. This result is
consistent with the current localized FRB subsample, which has yet to display
significant differences in the host properties of repeating and apparently
nonrepeating FRBs (e.g., Bhandari et al., 2022).

We calculate the Spearman correlation coefficient between $\rm{RM_{excess}}$
and $\rm{DM_{excess}}$ and find no significant relation in either the
repeating ($\rm{p-value<0.86}$), non-repeating ($\rm{p-value<0.22}$) or
combined samples ($\rm{p-value<0.71}$). This result suggests that, on average,
the media producing $\rm{DM_{excess}}$ and $\rm{RM_{excess}}$ are, at most,
only weakly associated. This agrees nicely with similar conclusions that can
be independently inferred from the relative variability of $\rm{DM}$ and
$\rm{RM}$ of the repeating sample (Section 4.4). This conclusion is perhaps
unsurprising given that in most cases $\rm{DM_{excess}}$ is dominated by the
signal’s transit through the IGM, where accumulated RM contributions should be
well below $10\;\rm{rad\,m^{-2}}$ (Akahori et al., 2016). With a much larger
sample, one might expect to see anti-correlation between $\rm{DM_{excess}}$
and $\rm{RM_{excess}}$ due to the the diluting effect of cosmological
expansion on the RM contribution of the host galaxy / local environment of
FRBs at increasing distances (i.e., $\sim\frac{1}{(1+z)^{2}}$)111111The DM is
less affected by this since: 1) the scaling (i.e., $\sim\frac{1}{(1+z)}$) is
less extreme and 2) the contribution of the host galaxy / local environment to
the total DM is likely substantially smaller than the equivalent contribution
to the total RM.. The strength of such an anti-correlation will depend on how
reliable $\rm{DM_{excess}}$ is as a proxy for distance and the degree to which
$\rm{RM_{excess}}$ dominates the host galaxy / local environment.
Alternatively, such a feature may be investigated with a smaller sample of
localized FRBs that circumvent the need of using $\rm{DM_{excess}}$ as a proxy
for distance.

Figure 7: $\rm{DM_{excess}}$, $|\rm{RM_{excess}}|$ distribution (observer’s
frame) of the current sample of published FRBs showing the non-repeating
(black triangles) and repeating (red stars) subsamples. Empty stars correspond
to repeating sources other than the sample studied here (see text). Red
vertical lines indicate the range of values observed from repeaters displaying
substantial RM variations. $\rm{DM_{MW}}$ estimates are obtained from Table 1
using the NE2001 model of Cordes & Lazio (2002, 2003) and assuming a fixed
$30\;\rm{pc\,cm^{-3}}$ contribution from the Galactic halo. $\rm{RM_{MW}}$
estimates are obtained from the Galactic RM map of Hutschenreuter et al.
(2022).

###  4.4 Implications of $B^{local}_{\parallel}$ Estimates and RM Variability

Table 3: Comparison of $B^{local}_{\parallel}$ estimates for a selection of
repeating FRB sources and pulsarsa

Source | $B^{local}_{\parallel}$ | $|\Delta\rm{RM}|$ | Timescale | RM evolution | Associated Structure | Reference
---|---|---|---|---|---|---
| [$\rm{\mu G}$] | $\rm{[rad\,m^{-2}]}$ | $\%$ |  |  |  |
FRB 20200120Eb | $-$ | $\sim 30$ | $\sim 100$ | weeks$-$months | $-$ | globular cluster | Bhardwaj et al. (2021); Nimmo et al. (2022)
PSR J1825$-$1446 | $\sim 0.2$ | $\sim 20$ | $\sim 9$ |  $\sim 2$ years | Secular | SNR | Johnston et al. (2021)
FRB 20190117A | $\gtrsim 4$ | $\sim 9$ | $\sim 9$ | 1031 days | $-$ | $-$ | this work
FRB 20190213B | $\gtrsim 16$ | $\sim 4.6$ | $\sim 10$ | 220 days | $-$ | $-$ | this work
PSR J0908$-$4913 (B0906$-$49) | $\sim 20$ | $\sim 4$ | $\sim 40$ |  $\sim 3000$ days | Secular | SNR | Johnston & Lower (2021)
PSR B0833$-$45c | $\gtrsim 22$ | $\sim 10$ | $\sim 26$ |  $\sim$15 years | Secular | SNR | Hamilton et al. (1985)
FRB 20180301A | $\gtrsim 50$ | $\sim 43$ | $\sim 8$ |  $<1$ day | Stochastic | – |  Luo et al. (2020) \+ this work
FRB 20180916B | $\gtrsim 55$ | $\sim 50$ | $\sim 40$ |  $\sim 9$ months | Secular & Stochastic | – | (Mckinven et al., 2022)
FRB 20190208A | $\gtrsim 80$ | $\sim 35$ | $\sim 100$ |  $\sim 200$ days | Secular (non-monotonic) | $-$ | this work
FRB 20201124Ad | $\gtrsim 100$ | $\sim 500$ |  $\gtrsim$ 100 |  $\lesssim 0.5$ months | Secular | SF region / PRSe | Hilmarsson et al. (2021b); Kumar et al. (2022a); Xu et al. (2021)
PSR J0540$-$6919 (B0540$-$69) | $115\pm 15$ | $\sim 15$ | $\sim 6$ |  $\sim 5$ months | Secular | SNR | Geyer et al. (2021)
PSR B0531+21f | $150-200$ | 6.6 | $\sim 14$ | 20 months | Secular | SNR | Rankin et al. (1988)
FRB 20181119A | $\gtrsim 2200$ | $\sim 860$ | $\sim 100$ |  $\sim 200$ days | $-$ | $-$ | this work
FRB 20190303A | $\gtrsim 3000$ | $\sim 500$ | $\sim 100$ |  $\sim 2$ years | Secular (non-monotonic) | – | this work
PSR B1259$-$63 | $\sim 500-10,000$ | $\lesssim 15,000$ | $-$ |  $\sim 0.5$ months | $-$ | pulsar-Be star binary | Johnston et al. (2005)
FRB 20190520B | $\gtrsim 4000$ | $\sim 26,000$ | $-$ |  $\sim 7$ months | Secular | PRS | Anna-Thomas et al. (2022); Dai et al. (2022)
PSR J1745$-$2900g | $\gtrsim 10,000$ | $\sim 3500$ | $\sim 5$ |  $\sim 16.5$ months | Secular | Sgr A⋆ | Desvignes et al. (2018); Katz (2021)
FRB 20121102A | $3000-17,000$ | 15,000 / 4000 | 20 / 5 | 160 days / 450 days | Secular | SF region / PRSh | Hilmarsson et al. (2021b); Katz (2021)

a Ordered by increasing $B^{local}_{\parallel}$. Pulsars are indicated by gray
font while CHIME/FRB repeaters are highlighted with boldface font.
b $B^{local}_{\parallel}$ & RM evolution columns are undetermined for FRB
20200120E due to lack of sufficient observations and $\rm{DM_{struct}}$
measurements.
c The ‘Vela pulsar’.
d Hilmarsson et al. (2021a) quote a representative DM for their entire sample
rather than determine a DM for each burst. We therefore estimate the DM
variability as the uncertainty on their DM measurement,
$0.6\;\rm{pc\,cm^{-3}}$.
e Ravi et al. (2021) claim that the spatial extent and luminosity of the
persistent radio source (PRS) associated with FRB 20201124A is consistent with
star-formation activity.
f The ‘Crab pulsar’.
g The Galactic center magnetar.
h FRB 20121102A is associated with a star-forming region within its host
galaxy as well as a persistent radio source (PRS) suggestive of a pulsar wind
nebula or supernova remnant (Bassa et al., 2017; Chatterjee et al., 2017).

The analysis pursued in Section 3.1 leverages $\Delta\rm{DM}$ and
$\Delta\rm{RM}$ measurements of FRB20190303A to constrain the LoS magnetic
field of the medium producing the observed variations. In principle, this
magnetic field could exist at any point along the LoS. Indeed, multi-epoch
observations of Galactic pulsars regularly reveal stochastic RM variations
that are attributed to scattering and some combination of fluctuations in
$B_{\parallel}$ and $n_{e}$ in the Galactic ISM (e.g. Yan et al., 2011; Wahl
et al., 2022). However, these RM variations rarely exceed
$\sim\rm{few}\;\rm{rad\,m^{-2}}$, significantly less than the RM variability
observed from many repeaters reported here. Therefore, given the amplitude of
RM variations and the relatively short timescales seen here for FRBs, it is
highly likely that the magneto-ionic fluctuations producing the RM variability
occur in the immediate environment of the FRB source. $B^{local}_{\parallel}$
estimates reported here are therefore likely a direct probe of the
magnetization of the FRB source environment and can be compared to equivalent
estimates made from observations of other repeating FRB sources and certain
Galactic pulsars.

Table 3 summarizes this analysis, where we have calculated
$B^{local}_{\parallel}$ estimates for all repeating sources with multiple RM
measurements and compared them to equivalent measurements for a sample of
pulsars. Importantly, Equation 2 is undefined when $\rm{DM_{\Delta RM}}$ is
not a priori known. An exception exists when DM and RM variations are
correlated such that $B^{local}_{\parallel}$ can be estimated by substituting
$\rm{DM_{\Delta RM}}=\Delta\rm{DM}$ (e.g., Hamilton et al., 1985; Katz,
2021).121212Such estimates assume that the observed DM, RM variations are an
imprint of a Faraday active medium with a changing $n_{e}$ and a static
magnetic field. However, when DM and RM variations are uncorrelated an
appropriate value for $\rm{DM_{\Delta RM}}$ remains unknown. In such cases, we
make the simplifying assumption that the same medium is responsible for the
observed DM and RM variability and estimate $\rm{DM_{\Delta RM}}$ from the
root-mean-square of the $\rm{DM}$ measurements. Table 3 displays the resulting
$B^{local}_{\parallel}$ estimates in increasing order, and lists additional
quantities such as the RM variation ($\Delta\rm{RM}$), its characteristic
timescale, the nature of the RM evolution (stochastic, secular) and whether an
associated structure has been identified that could possibly produce the
observed variability.

Filamentary structure in SNRs has been invoked to explain the RM variations
observed in most of the pulsars in this sample. These SNRs may either be
associated with the source, as in the case of the Crab (Rankin et al., 1988)
or Vela (Hamilton et al., 1985) pulsars, or be unassociated, as in the case of
the fortuitous alignment of PSR J1825$-$1446 with a foreground SNR,
G16.8$-$1.1 (Moldón et al., 2012).131313See also the putative association of
PSR J0908$-$4913 (B0906$-$49) with the previously unknown SNR G270.4$-$1.0
(Johnston & Lower, 2021). For such systems, $B^{local}_{\parallel}$ estimates
up to several hundred $\mu G$ have been inferred. Such a range is comparable
to equivalent estimates inferred from some repeaters in Table 3. While it
remains plausible that an SNR-like structure may be associated with FRB
sources, a significant subsample of repeaters (FRBs 20121102A, 20190520B,
20190303A, 20181119A) display RM variations that are far more extreme than
what has hitherto been observed from relatively young pulsar-SNR systems.

RM variations from repeaters generally appear to be more significant and
prevalent than that seen from pulsars where stability in RMs from epoch to
epoch is a necessary condition for their application as probes of the large
scale Galactic magnetic field (e.g., Han et al., 2018). Furthermore, pulsars
displaying substantial RM variations remain quite rare. Recent multi-epoch
monitoring of several hundred young, non-recycled pulsars using the Parkes
telescope found only one pulsar (PSR J1825$-$1446) exhibiting significant RM
variability (see Table 3; Johnston et al., 2021). This is difficult to
reconcile with the ubiquity of RM variability displayed from the repeating FRB
sample and suggests a magneto-ionic medium for repeating FRBs distinct from
the environment of young pulsars. These observations may either indicate an
earlier evolutionary stage of FRB–SNR systems, where magneto-ionic
fluctuations are substantially larger, or an entirely different structure
responsible for the strong RM evolution observed in many repeating sources.
This novelty in FRB environments has been independently noted based on a joint
analysis of FRB dispersion and scattering. Most recently, a population
synthesis study of the CHIME/FRB catalog (CHIME/FRB Collaboration et al.,
2021b) found that the ISM of FRB host galaxies alone could not reproduce the
observed scattering timescales of FRBs but instead required a substantial
scattering contribution from the circumgalactic medium (CGM) or an extreme
circum-burst environment dissimilar to that associated with Galactic pulsars
(Chawla et al., 2022).

The discrepancy in $\rm{RM}$ variability between repeating FRBs and pulsars is
illustrated in Figure 8, which compares the DM and RM variability of the two
samples. $\Delta\rm{RM}$ of the repeater sample regularly exceeds several tens
of $\rm{rad\,m^{-2}}$ while pulsar-SNR systems rarely exceed 10
$\rm{rad\,m^{-2}}$. Two exceptions are the Galactic center magnetar, PSR
J1745$-$2900, and PSR B1259$-$63\. Both these sources display significant
variability in their RMs that can be explained by peculiarities of their
immediate environments. In particular, PSR J1745$-$2900 is located at a
projected distance of 0.12 pc from Sgr A⋆ (Eatough et al., 2013). The
substantial RM variability recently observed from this source (Desvignes et
al., 2018) is expected to be an imprint of inhomogeneities produced by the
accretion flow onto Sgr A⋆ (Pang et al., 2011). PSR B1259$-$63, meanwhile,
displays significant changes in its DM and RM that are produced from its
orbital passage through the dense circumstellar disc of its Be-star companion.
Interestingly, multiple epochs of observations have established differences in
the observed properties from one periastron to the next, indicating
significant changes in disc density and magnetic field structure on its $\sim
1237$ day orbital timescale (Connors et al., 2002; Johnston et al., 2005).
This source is particularly interesting given its relevance to “cosmic comb”
models that have been put forth to explain both the FRB emission mechanism and
periodic bursting cycles observed from some repeaters (Ioka & Zhang, 2020;
Lyutikov et al., 2020; Wada et al., 2021). Indeed, these models predict that
the RM modulation of FRBs will correlate with orbital phase, since the former
is caused by the companion wind. However, as observations of PSR B1259$-$63
have shown, RM variations can be erratic due to substantial inhomogeneities in
the magnetic field strength and free electron density in the ambient medium of
the companion. It may therefore be naive to expect smooth RM evolution tied to
orbital phase as would be assumed for the above FRB models.

Without additional information, several key parameters characterizing the
local environment of repeating FRBs remain degenerate vis-a-vis RM variations
(i.e., $n_{e}$, $B_{\parallel}$, path length / relative velocity). For
prolifically repeating sources, future observations may further constrain
these properties by extending our analysis to include variability in
scattering timescales, as was done for the Crab pulsar (McKee et al., 2018).
This would greatly help our understanding of repeater environments by enabling
correlation of the scattering, RM and DM to be simultaneously probed. Any
significant correlated behavior would indicate a common structure producing
the variability, with scattering/scintillation measurements providing further
information on the structure, namely, its physical size and distance from the
source.

Figure 8: $\rm{\Delta RM}$, $\rm{\Delta DM}$ distribution of repeating FRB
sources (red stars) compared to a sample of pulsars from which significant RM
variations have been observed (black circles). Empty stars correspond to
repeating sources other than the sample studied here. Special pulsars include
the Galactic center magnetar (PSR J1745$-$2900; green diamond), and
measurements from PSR B1259$-$63 (blue points), a pulsar in a close binary
orbit with a Be star companion. Gray diagonal lines indicate different
strength levels of the parallel component of the magnetic field
($B^{local}_{\parallel}$) required to explain $\rm{\Delta RM}$, $\rm{\Delta
DM}$ measurements.

###  4.5 Repeater Burst Morphology

The morphology of bursts (the change in flux as a function of time and
frequency) from our sample of repeating FRBs in the CHIME band has been
discussed before (CHIME/FRB Collaboration et al., 2019b, 2020; Fonseca et al.,
2020; Pleunis et al., 2021). However, similar to our recent analysis of FRB
20180916B, the baseband data presented here have several properties that are
amenable to burst morphology analysis (see Mckinven et al. (2022) for
details). Inspection of Figure 2 and the additional waterfall plots for the
remaining sources (see Figure set 1) reveals that bursts from these repeaters
show similar characteristics in the CHIME band as were identified at coarser
time resolution. The bursts typically show wide burst emission envelopes, of
up to $\sim$40 ms (e.g., burst 1 of FRB 20190213B). Some more narrow subbursts
with widths down to $\lesssim 80\,\mu$s are present, e.g., in bursts 1, 2 and
4 of FRB 20181030A – as have been detected before in bursts from FRBs
20180916B and 20200120E (Nimmo et al., 2021, 2022). We note that these are
three of the closest repeating sources of FRBs, and that the CHIME/FRB
detection pipeline with its $\sim 1-$ ms time resolution may not be sensitive
to similarly narrow emission from more distant sources (see also Connor,
2019). The repeater bursts show narrowband emission ($\sim$50–200 MHz) with
varying central frequency. Downward-drifting subbursts (the “sad trombone
effect”) are ubiquitous, with burst 7 of FRB 20190208A being a prominent
example. Drift rates are consistent with previous measurement in the CHIME
band, with linear drift rates of a few to a few tens of MHz ms-1. We have
detected pre- and post-cursors that are significantly fainter than the main
component of the burst, e.g., burst 1 of FRB20180814A, burst 1 of FRB
20190222A, bursts 3 and 5 of FRB 20190208A and burst 1 of FRB 20190117A, as
has also been detected for other FRB sources by, e.g., Caleb et al. (2020) and
Chawla et al. (2020). As recently noted for FRB 20180916B (Mckinven et al.,
2022), the distinction between multiple subbursts under one burst envelope vs.
multiple separate burst envelopes without a “bridge” in emission remains
ambiguous (e.g., bursts 1, 2 and 4 of FRB 20181030A, all seem to be comprised
of at least two burst envelopes, whereas this is less obvious in the case of
bursts 1 and 3 of FRB 20190208A, and burst 1 of FRB 20190303A; see also
discussion in Pleunis et al., 2021). In general, the interpretation of burst
structure remains dependent on the detection S/N, with fainter bursts
requiring more substantial downsampling that possibly ‘washes-out’ fine scale
but faint substructure. This likely affects our $\rm{DM_{struct}}$
measurements, with downward-drifting subbursts remaining unresolved and
biasing the DM measurement high. Burst-to-burst $\rm{DM_{struct}}$ variations
are therefore very likely over-estimated here due to confusion with unresolved
structure. Regardless, temporal DM variations from the FRB sources studied
here appear to be significantly lower than those observed elsewhere (e.g.,
$\Delta\rm{DM}\sim$ few pc cm-3; Oostrum et al., 2020), a somewhat surprising
result considering the multi-year timescales of these observations and the
ubiquity of substantial RM variations.

##  5 Conclusion

Multi-year polarimetric monitoring of a sample of CHIME/FRB repeaters has
provided a sample of 100 bursts from 13 previously published sources
(CHIME/FRB Collaboration et al., 2019a, b; Fonseca et al., 2020). The
morphology of the bursts from these sources in the CHIME band show
qualitatively similar characteristics at the higher time resolution presented
here to what has been described before by Pleunis et al. (2021) based on data
with coarser time resolution. In general, bursts from our sample are
significantly linearly polarized, with only two sources observed as
(apparently) unpolarized. Significant burst-to-burst variability in $L/I$ is
observed from many sources along with marginal circular polarization
($\lesssim 20\%$), whose origin is likely instrumental. A systematic study of
$L/I$ as a function of frequency for some of our sources (Section 4.2; see
also Section 4.2 of Mckinven et al. (2022)) has provided further support to
the existence of depolarization via multi-path propagation (Feng et al.,
2022). However, significant excursions in individual $L/I$ measurements
relative to the best-fit depolarization models of each source indicate
additional sources of variability.

Significant RM variability appears to be a characteristic feature of repeating
FRB sources, with our sample displaying secular intervals of RM variations on
week to month timescales that are not accompanied by any equivalent DM
evolution. Some repeating sources exhibit extreme RM variations of several
hundred $\rm{rad\,m^{-2}}$ over multi–month timescales. From our constraints
on $\Delta\rm{DM}$ and $\Delta\rm{RM}$, we estimate the strength of the line-
of-sight component of the magnetic field ($B^{local}_{\parallel}$) in the FRB
source’s environment and compare to equivalent estimates from a sample of
pulsars. Although our $B^{local}_{\parallel}$ estimates are similar to
equivalent estimates for pulsars with associated SNRs, there exist a
signifcant subsample of repeating FRBs that display RM variations that are far
more extreme than what has been hitherto been observed from pulsar-SNR
systems. This suggests that repeaters occupy magneto-ionic environments that
are significantly different than those associated with our current sample of
pulsar–SNR systems, an interpretation that is reinforced by the scattering
distribution of FRBs (Chawla et al., 2022). Without additional information,
several key parameters characterizing the local environments of reeating FRBs
remain degenerate vis-a-vis RM variations. Additional measurements such as
those inferred from scattering or frequency-dependent depolarization will be
invaluable for constraining this parameter space. Finally, if the non-uniform
magneto-ionic environments of repeating FRBs extends to the non-repeating
sample then this will be unfavorable to efforts to model the FRB RM
distribution, since a significant contribution to the RM distribution will be
associated with inhomogeneities in the local magneto-ionic environment that
are quasi-random and difficult to model.

The Dunlap Institute is funded through an endowment established by the David
Dunlap family and the University of Toronto. R.M. recognizes support from the
Queen Elizabeth II Graduate Scholarship and the Lachlan Gilchrist Fellowship.
B.M.G. is supported by an NSERC Discovery Grant (RGPIN-2015-05948), and by the
Canada Research Chairs (CRC) program. K.W.M. is supported by an NSF Grant
(2008031). V.M.K. holds the Lorne Trottier Chair in Astrophysics $\&$
Cosmology, a Distinguished James McGill Professorship, and receives support
from an NSERC Discovery grant (RGPIN 228738-13), from an R. Howard Webster
Foundation Fellowship from CIFAR, and from the FRQNT CRAQ. A.B.P. is a McGill
Space Institute (MSI) Fellow and a Fonds de Recherche du Quebec – Nature et
Technologies (FRQNT) postdoctoral fellow. Z.P. is a Dunlap Fellow. C.L. was
supported by the U.S. Department of Defense (DoD) through the National Defense
Science $\&$ Engineering Graduate Fellowship (NDSEG) Program. FQD is supported
by the 4YF. E.P. acknowledges funding from an NWO Veni Fellowship. K.S. is
supported by the NSF Graduate Research Fellowship Program. The polarization
analysis presented here makes use of the RMtools
package141414https://github.com/CIRADA-Tools/RM-Tools(Purcell et al., 2020)
written by Cormac Purcell, and maintained by Cameron Van Eck.

## References

  * Akahori et al. (2016) Akahori, T., Ryu, D., & Gaensler, B. M. 2016, ApJ, 824, 105, doi: 10.3847/0004-637X/824/2/105
  * Anna-Thomas et al. (2022) Anna-Thomas, R., Connor, L., Burke-Spolaor, S., et al. 2022, arXiv e-prints, arXiv:2202.11112.  https://arxiv.org/abs/2202.11112
  * Bassa et al. (2017) Bassa, C. G., Tendulkar, S. P., Adams, E. A. K., et al. 2017, ApJ, 843, L8, doi: 10.3847/2041-8213/aa7a0c
  * Beniamini et al. (2021) Beniamini, P., Kumar, P., & Narayan, R. 2021, arXiv e-prints, arXiv:2110.00028.  https://arxiv.org/abs/2110.00028
  * Bhandari et al. (2022) Bhandari, S., Heintz, K. E., Aggarwal, K., et al. 2022, AJ, 163, 69, doi: 10.3847/1538-3881/ac3aec
  * Bhardwaj et al. (2021) Bhardwaj, M., Gaensler, B. M., Kaspi, V. M., et al. 2021, ApJ, 910, L18, doi: 10.3847/2041-8213/abeaa6
  * Caleb et al. (2020) Caleb, M., Stappers, B. W., Abbott, T. D., et al. 2020, MNRAS, 496, 4565, doi: 10.1093/mnras/staa1791
  * Camilo et al. (2007) Camilo, F., Ransom, S. M., Peñalver, J., et al. 2007, ApJ, 669, 561, doi: 10.1086/521548
  * Chamma et al. (2021) Chamma, M. A., Rajabi, F., Wyenberg, C. M., Mathews, A., & Houde, M. 2021, MNRAS, 507, 246, doi: 10.1093/mnras/stab2070
  * Chatterjee et al. (2017) Chatterjee, S., Law, C. J., Wharton, R. S., et al. 2017, Nature, 541, 58, doi: 10.1038/nature20797
  * Chawla et al. (2020) Chawla, P., Andersen, B. C., Bhardwaj, M., et al. 2020, ApJ, 896, L41, doi: 10.3847/2041-8213/ab96bf
  * Chawla et al. (2022) Chawla, P., Kaspi, V. M., Ransom, S. M., et al. 2022, ApJ, 927, 35, doi: 10.3847/1538-4357/ac49e1
  * CHIME/FRB Collaboration et al. (2018) CHIME/FRB Collaboration, Amiri, M., Bandura, K., et al. 2018, ApJ, 863, 48, doi: 10.3847/1538-4357/aad188
  * CHIME/FRB Collaboration et al. (2019a) —. 2019a, Nature, 566, 235, doi: 10.1038/s41586-018-0864-x
  * CHIME/FRB Collaboration et al. (2019b) CHIME/FRB Collaboration, Andersen, B. C., Bandura, K., et al. 2019b, ApJ, 885, L24, doi: 10.3847/2041-8213/ab4a80
  * CHIME/FRB Collaboration et al. (2020) CHIME/FRB Collaboration, Amiri, M., Andersen, B. C., et al. 2020, Nature, 582, 351, doi: 10.1038/s41586-020-2398-2
  * CHIME/FRB Collaboration et al. (2021a) —. 2021a, ApJS, 257, 59, doi: 10.3847/1538-4365/ac33ab
  * CHIME/FRB Collaboration et al. (2021b) CHIME/FRB Collaboration, Andersen, B. C., Bandura, K., et al. 2021b, arXiv e-prints, arXiv:2107.08463.  https://arxiv.org/abs/2107.08463
  * Connor (2019) Connor, L. 2019, MNRAS, 487, 5753, doi: 10.1093/mnras/stz1666
  * Connors et al. (2002) Connors, T. W., Johnston, S., Manchester, R. N., & McConnell, D. 2002, MNRAS, 336, 1201, doi: 10.1046/j.1365-8711.2002.05850.x
  * Cordes & Lazio (2002) Cordes, J. M., & Lazio, T. J. W. 2002, arXiv e-prints, astro.  https://arxiv.org/abs/astro-ph/0207156
  * Cordes & Lazio (2003) —. 2003, arXiv e-prints, astro.  https://arxiv.org/abs/astro-ph/0301598
  * Dai et al. (2018) Dai, S., Johnston, S., Weltevrede, P., et al. 2018, MNRAS, 480, 3584, doi: 10.1093/mnras/sty2063
  * Dai et al. (2019) Dai, S., Lower, M. E., Bailes, M., et al. 2019, ApJ, 874, L14, doi: 10.3847/2041-8213/ab0e7a
  * Dai et al. (2022) Dai, S., Feng, Y., Yang, Y. P., et al. 2022, arXiv e-prints, arXiv:2203.08151.  https://arxiv.org/abs/2203.08151
  * Day et al. (2020) Day, C. K., Deller, A. T., Shannon, R. M., et al. 2020, MNRAS, 497, 3335, doi: 10.1093/mnras/staa2138
  * Desvignes et al. (2018) Desvignes, G., Eatough, R. P., Pen, U. L., et al. 2018, ApJ, 852, L12, doi: 10.3847/2041-8213/aaa2f8
  * Dickel & Milne (1976) Dickel, J. R., & Milne, D. K. 1976, Australian Journal of Physics, 29, 435, doi: 10.1071/PH760435
  * Dolag et al. (2015) Dolag, K., Gaensler, B. M., Beck, A. M., & Beck, M. C. 2015, MNRAS, 451, 4277, doi: 10.1093/mnras/stv1190
  * Eatough et al. (2013) Eatough, R. P., Falcke, H., Karuppusamy, R., et al. 2013, Nature, 501, 391, doi: 10.1038/nature12499
  * Everett & Weisberg (2001) Everett, J. E., & Weisberg, J. M. 2001, ApJ, 553, 341, doi: 10.1086/320652
  * Feng et al. (2022) Feng, Y., Li, D., Yang, Y.-P., et al. 2022, Science, 375, 1266, doi: 10.1126/science.abl7759
  * Fonseca et al. (2020) Fonseca, E., Andersen, B. C., Bhardwaj, M., et al. 2020, ApJ, 891, L6, doi: 10.3847/2041-8213/ab7208
  * Geyer et al. (2021) Geyer, M., Serylak, M., Abbate, F., et al. 2021, MNRAS, 505, 4468, doi: 10.1093/mnras/stab1501
  * Gruzinov & Levin (2019) Gruzinov, A., & Levin, Y. 2019, ApJ, 876, 74, doi: 10.3847/1538-4357/ab0fa3
  * Hamilton et al. (1985) Hamilton, P. A., Hall, P. J., & Costa, M. E. 1985, MNRAS, 214, 5P, doi: 10.1093/mnras/214.1.5P
  * Han et al. (2018) Han, J. L., Manchester, R. N., van Straten, W., & Demorest, P. 2018, ApJS, 234, 11, doi: 10.3847/1538-4365/aa9c45
  * Hilmarsson et al. (2021a) Hilmarsson, G. H., Spitler, L. G., Main, R. A., & Li, D. Z. 2021a, arXiv e-prints, arXiv:2107.12892.  https://arxiv.org/abs/2107.12892
  * Hilmarsson et al. (2021b) Hilmarsson, G. H., Michilli, D., Spitler, L. G., et al. 2021b, ApJ, 908, L10, doi: 10.3847/2041-8213/abdec0
  * Hutschenreuter et al. (2022) Hutschenreuter, S., Anderson, C. S., Betti, S., et al. 2022, A&A, 657, A43, doi: 10.1051/0004-6361/202140486
  * Ioka & Zhang (2020) Ioka, K., & Zhang, B. 2020, ApJ, 893, L26, doi: 10.3847/2041-8213/ab83fb
  * Johnston et al. (2005) Johnston, S., Ball, L., Wang, N., & Manchester, R. N. 2005, MNRAS, 358, 1069, doi: 10.1111/j.1365-2966.2005.08854.x
  * Johnston & Lower (2021) Johnston, S., & Lower, M. E. 2021, MNRAS, 507, L41, doi: 10.1093/mnrasl/slab092
  * Johnston et al. (2021) Johnston, S., Sobey, C., Dai, S., et al. 2021, MNRAS, 502, 1253, doi: 10.1093/mnras/stab095
  * Katz (2021) Katz, J. I. 2021, MNRAS, 501, L76, doi: 10.1093/mnrasl/slaa202
  * Kumar et al. (2022a) Kumar, P., Shannon, R. M., Lower, M. E., et al. 2022a, MNRAS, 512, 3400, doi: 10.1093/mnras/stac683
  * Kumar et al. (2022b) —. 2022b, MNRAS, doi: 10.1093/mnras/stac683
  * Laha et al. (2022) Laha, S., Younes, G., Wadiasingh, Z., et al. 2022, arXiv e-prints, arXiv:2203.07465.  https://arxiv.org/abs/2203.07465
  * Levin et al. (2012) Levin, L., Bailes, M., Bates, S. D., et al. 2012, MNRAS, 422, 2489, doi: 10.1111/j.1365-2966.2012.20807.x
  * Levin et al. (2020) Levin, Y., Beloborodov, A. M., & Bransgrove, A. 2020, ApJ, 895, L30, doi: 10.3847/2041-8213/ab8c4c
  * Lorimer et al. (2007) Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic, D. J., & Crawford, F. 2007, Science, 318, 777, doi: 10.1126/science.1147532
  * Luo et al. (2020) Luo, R., Wang, B. J., Men, Y. P., et al. 2020, Nature, 586, 693, doi: 10.1038/s41586-020-2827-2
  * Lyutikov et al. (2020) Lyutikov, M., Barkov, M. V., & Giannios, D. 2020, ApJ, 893, L39, doi: 10.3847/2041-8213/ab87a4
  * Masui et al. (2015) Masui, K., Lin, H.-H., Sievers, J., et al. 2015, Nature, 528, 523, doi: 10.1038/nature15769
  * McKee et al. (2018) McKee, J. W., Lyne, A. G., Stappers, B. W., Bassa, C. G., & Jordan, C. A. 2018, MNRAS, 479, 4216, doi: 10.1093/mnras/sty1727
  * Mckinven et al. (2021) Mckinven, R., Michilli, D., Masui, K. W., et al. 2021, arXiv e-prints, arXiv:2107.03491.  https://arxiv.org/abs/2107.03491
  * Mckinven et al. (2022) Mckinven, R., Gaensler, B. M., Michilli, D., et al. 2022, arXiv e-prints, arXiv:2205.09221, doi: 10.48550/arXiv.2205.09221
  * Melrose & Macquart (1998) Melrose, D. B., & Macquart, J. P. 1998, ApJ, 505, 921, doi: 10.1086/306204
  * Metzger et al. (2019) Metzger, B. D., Margalit, B., & Sironi, L. 2019, MNRAS, 485, 4091, doi: 10.1093/mnras/stz700
  * Mevius (2018a) Mevius, M. 2018a, Ionospheric Effects, Vol. 426, 103, doi: 10.1007/978-3-319-23434-2_7
  * Mevius (2018b) —. 2018b, RMextract: Ionospheric Faraday Rotation calculator.  http://ascl.net/1806.024
  * Michilli et al. (2018) Michilli, D., Seymour, A., Hessels, J. W. T., et al. 2018, Nature, 553, 182, doi: 10.1038/nature25149
  * Michilli et al. (2021) Michilli, D., Masui, K. W., Mckinven, R., et al. 2021, ApJ, 910, 147, doi: 10.3847/1538-4357/abe626
  * Milne (1987) Milne, D. K. 1987, Australian Journal of Physics, 40, 771, doi: 10.1071/PH870771
  * Moldón et al. (2012) Moldón, J., Ribó, M., Paredes, J. M., et al. 2012, A&A, 543, A26, doi: 10.1051/0004-6361/201219205
  * Nimmo et al. (2021) Nimmo, K., Hessels, J. W. T., Keimpema, A., et al. 2021, Nature Astronomy, 5, 594, doi: 10.1038/s41550-021-01321-3
  * Nimmo et al. (2022) Nimmo, K., Hessels, J. W. T., Kirsten, F., et al. 2022, Nature Astronomy, 6, 393, doi: 10.1038/s41550-021-01569-9
  * Niu et al. (2021) Niu, C. H., Aggarwal, K., Li, D., et al. 2021, arXiv e-prints, arXiv:2110.07418.  https://arxiv.org/abs/2110.07418
  * Oostrum et al. (2020) Oostrum, L. C., Maan, Y., van Leeuwen, J., et al. 2020, A&A, 635, A61, doi: 10.1051/0004-6361/201937422
  * Pang et al. (2011) Pang, B., Pen, U.-L., Matzner, C. D., Green, S. R., & Liebendörfer, M. 2011, MNRAS, 415, 1228, doi: 10.1111/j.1365-2966.2011.18748.x
  * Petroff et al. (2022) Petroff, E., Hessels, J. W. T., & Lorimer, D. R. 2022, A&A Rev., 30, 2, doi: 10.1007/s00159-022-00139-w
  * Petroff et al. (2017) Petroff, E., Burke-Spolaor, S., Keane, E. F., et al. 2017, MNRAS, 469, 4465, doi: 10.1093/mnras/stx1098
  * Piro & Gaensler (2018) Piro, A. L., & Gaensler, B. M. 2018, ApJ, 861, 150, doi: 10.3847/1538-4357/aac9bc
  * Plavin et al. (2022) Plavin, A., Paragi, Z., Marcote, B., et al. 2022, MNRAS, doi: 10.1093/mnras/stac500
  * Pleunis et al. (2021) Pleunis, Z., Good, D. C., Kaspi, V. M., et al. 2021, arXiv e-prints, arXiv:2106.04356.  https://arxiv.org/abs/2106.04356
  * Purcell et al. (2020) Purcell, C. R., Van Eck, C. L., West, J., Sun, X. H., & Gaensler, B. M. 2020, RM-Tools: Rotation measure (RM) synthesis and Stokes QU-fitting, Astrophysics Source Code Library, record ascl:2005.003.  http://ascl.net/2005.003
  * Radhakrishnan & Cooke (1969) Radhakrishnan, V., & Cooke, D. J. 1969, Astrophys. Lett., 3, 225
  * Rankin et al. (1988) Rankin, J. M., Campbell, D. B., Isaacman, R. B., & Payne, R. R. 1988, A&A, 202, 166
  * Ravi et al. (2021) Ravi, V., Law, C. J., Li, D., et al. 2021, arXiv e-prints, arXiv:2106.09710.  https://arxiv.org/abs/2106.09710
  * Seymour et al. (2019) Seymour, A., Michilli, D., & Pleunis, Z. 2019, DM_phase: Algorithm for correcting dispersion of radio signals.  http://ascl.net/1910.004
  * Sobey et al. (2019) Sobey, C., Bilous, A. V., Grießmeier, J. M., et al. 2019, MNRAS, 484, 3646, doi: 10.1093/mnras/stz214
  * Sobey et al. (2021) Sobey, C., Johnston, S., Dai, S., et al. 2021, MNRAS, 504, 228, doi: 10.1093/mnras/stab861
  * Vedantham & Ravi (2019) Vedantham, H. K., & Ravi, V. 2019, MNRAS, 485, L78, doi: 10.1093/mnrasl/slz038
  * Wada et al. (2021) Wada, T., Ioka, K., & Zhang, B. 2021, ApJ, 920, 54, doi: 10.3847/1538-4357/ac127a
  * Wahl et al. (2022) Wahl, H. M., McLaughlin, M. A., Gentile, P. A., et al. 2022, ApJ, 926, 168, doi: 10.3847/1538-4357/ac4045
  * Wang et al. (2021) Wang, W.-Y., Jiang, J.-C., Lu, J., et al. 2021, arXiv e-prints, arXiv:2112.06719.  https://arxiv.org/abs/2112.06719
  * Wang et al. (2020) Wang, W.-Y., Zhang, B., Chen, X., & Xu, R. 2020, MNRAS, 499, 355, doi: 10.1093/mnras/staa2693
  * Xu et al. (2021) Xu, H., Niu, J. R., Chen, P., et al. 2021, arXiv e-prints, arXiv:2111.11764.  https://arxiv.org/abs/2111.11764
  * Xue et al. (2019) Xue, M., Ord, S. M., Tremblay, S. E., et al. 2019, PASA, 36, e025, doi: 10.1017/pasa.2019.19
  * Yamasaki & Totani (2020) Yamasaki, S., & Totani, T. 2020, ApJ, 888, 105, doi: 10.3847/1538-4357/ab58c4
  * Yan et al. (2011) Yan, W. M., Manchester, R. N., van Straten, W., et al. 2011, MNRAS, 414, 2087, doi: 10.1111/j.1365-2966.2011.18522.x
  * Yang et al. (2020) Yang, Y.-P., Li, Q.-C., & Zhang, B. 2020, ApJ, 895, 7, doi: 10.3847/1538-4357/ab88ab
  * Yang et al. (2022) Yang, Y.-P., Lu, W., Feng, Y., Zhang, B., & Li, D. 2022, ApJ, 928, L16, doi: 10.3847/2041-8213/ac5f46
  * Yao et al. (2017) Yao, J. M., Manchester, R. N., & Wang, N. 2017, ApJ, 835, 29, doi: 10.3847/1538-4357/835/1/29
  * Yuan et al. (2020) Yuan, Y., Beloborodov, A. M., Chen, A. Y., & Levin, Y. 2020, ApJ, 900, L21, doi: 10.3847/2041-8213/abafa8
  * Zhang (2020) Zhang, B. 2020, Nature, 587, 45, doi: 10.1038/s41586-020-2828-1
  * Zhao & Wang (2021) Zhao, Z.-Y., & Wang, F. Y. 2021, arXiv e-prints, arXiv:2112.00935.  https://arxiv.org/abs/2112.00935

##  Appendix A Additional Waterfall Plots

Fig. Set1. Waterfall plots of individual bursts from our repeating FRB source
sample.

##  Appendix B Supplemental Figures

Figure B.1: Cleaned FDFs (see Section 2.2.2 of Mckinven et al. (2022) for
bursts from FRB 20190303A. Each curve is normalized to a unitary peak and
ordered chronologically by burst number (see Table LABEL:ta:bursts).
$\rm{RM}_{QU}$ measurements are indicated as vertical green lines. Peaks near
$\phi\sim 0\;\rm{rad\,m^{-2}}$ correspond to instrumental polarization. Red
curves correspond to bursts where no significant RM detection was made. Peaks
near $\phi\sim 0\;\rm{rad\,m^{-2}}$ correspond to instrumental polarization.

Figure B.2: Examples of QU-fitting (left) and RM-synthesis (right) results for
individual bursts from repeating source FRB 20190303A after correcting for a
non-zero $\tau$ parameter (see Mckinven et al., 2022). Left panel: The
polarization spectra displaying, from top to bottom, Stokes $I$ (blue points)
and its cubic spline smoothed version (black line), Stokes $Q$ parameter
divided by the total linear polarization ($L$), Stokes $U$ divided by the
total linear polarization, and the uncalibrated polarization angle
($\psi_{0}$). Frequency channels with highly polarized signal are indicated
with darker points. Best-fit models are indicated as black lines (red lines
for $\psi_{0}$). Right panel: The cleaned FDFs displaying linear polarized
intensity as a function of $\phi$ (RM). The upper panel shows the FDFs
confined to $\pm 500\;\rm{rad\,m^{-2}}$ of their peak locations. The complete
figure set, including those of other repeating sources, is available in the
online journal.

Fig. Set2. QU-fitting and RM-synthesis results for individual bursts from our
repeating FRB source sample.