# Deep Synoptic Array Science: Polarimetry of 25 New Fast Radio Bursts
Provides Insights into their Origins

Myles B. Sherman  Cahill Center for Astronomy and Astrophysics, MC 249-17
California Institute of Technology, Pasadena CA 91125, USA.  Liam Connor
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Vikram Ravi  Cahill Center for
Astronomy and Astrophysics, MC 249-17 California Institute of Technology,
Pasadena CA 91125, USA.  Owens Valley Radio Observatory, California Institute
of Technology, Big Pine CA 93513, USA.  Casey Law  Cahill Center for Astronomy
and Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA
91125, USA.  Owens Valley Radio Observatory, California Institute of
Technology, Big Pine CA 93513, USA.  Ge Chen  Cahill Center for Astronomy and
Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA 91125,
USA.  Morgan Catha  Owens Valley Radio Observatory, California Institute of
Technology, Big Pine CA 93513, USA.  Jakob T. Faber  Cahill Center for
Astronomy and Astrophysics, MC 249-17 California Institute of Technology,
Pasadena CA 91125, USA.  Gregg Hallinan  Cahill Center for Astronomy and
Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA 91125,
USA.  Owens Valley Radio Observatory, California Institute of Technology, Big
Pine CA 93513, USA.  Charlie Harnach  Owens Valley Radio Observatory,
California Institute of Technology, Big Pine CA 93513, USA.  Greg Hellbourg
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Owens Valley Radio Observatory,
California Institute of Technology, Big Pine CA 93513, USA.  Rick Hobbs  Owens
Valley Radio Observatory, California Institute of Technology, Big Pine CA
93513, USA.  David Hodge  Cahill Center for Astronomy and Astrophysics, MC
249-17 California Institute of Technology, Pasadena CA 91125, USA.  Mark
Hodges  Owens Valley Radio Observatory, California Institute of Technology,
Big Pine CA 93513, USA.  James W. Lamb  Owens Valley Radio Observatory,
California Institute of Technology, Big Pine CA 93513, USA.  Paul Rasmussen
Owens Valley Radio Observatory, California Institute of Technology, Big Pine
CA 93513, USA.  Kritti Sharma  Cahill Center for Astronomy and Astrophysics,
MC 249-17 California Institute of Technology, Pasadena CA 91125, USA.  Jun Shi
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.  Dana Simard  Cahill Center for
Astronomy and Astrophysics, MC 249-17 California Institute of Technology,
Pasadena CA 91125, USA.  Jean Somalwar  Cahill Center for Astronomy and
Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA 91125,
USA.  Reynier Squillace  Department of Astronomy, University of Virginia, 530
McCormick Rd, Charlottesville, VA 22904, USA.  Sander Weinreb  Cahill Center
for Astronomy and Astrophysics, MC 249-17 California Institute of Technology,
Pasadena CA 91125, USA.  David P. Woody  Owens Valley Radio Observatory,
California Institute of Technology, Big Pine CA 93513, USA.  Nitika Yadlapalli
Cahill Center for Astronomy and Astrophysics, MC 249-17 California Institute
of Technology, Pasadena CA 91125, USA.

###### Abstract

We report on a full-polarization analysis of the first 25 as yet non-repeating
FRBs detected at 1.4 GHz by the 110-antenna Deep Synoptic Array (DSA-110)
during commissioning observations. We present details of the data-reduction,
calibration, and analysis procedures developed for this novel instrument.
Faraday rotation measures (RMs) are searched between $\pm 10^{6}$ rad m-2 and
detected for 20 FRBs with magnitudes ranging from $4-4670$ rad m-2. $15/25$
FRBs are consistent with 100% polarization, 10 of which have high ($\geq
70\%$) linear-polarization fractions and 2 of which have high ($\geq 30\%$)
circular-polarization fractions. Our results disfavor multipath RM scattering
as a dominant depolarization mechanism. Polarization-state and possible RM
variations are observed in the four FRBs with multiple sub-components. We
combine the DSA-110 sample with polarimetry of previously published FRBs, and
compare the polarization properties of FRB sub-populations and FRBs with
Galactic pulsars. Although FRB polarization fractions are typically higher
than those of Galactic pulsars, and cover a wider range than those of pulsar
single pulses, they resemble those of the youngest (characteristic ages
$<10^{5}$ yr) pulsars. Our results support a scenario wherein FRB emission is
intrinsically highly linearly polarized, and propagation effects can result in
conversion to circular polarization and depolarization. Young pulsar emission
and magnetospheric-propagation geometries may form a useful analogy for the
origin of FRB polarization.

Cosmic electrodynamics (318), Extragalactic magnetic fields (507), Radio
transient sources (2008), Neutron stars (1108), Polarimetry (1278), Radio
pulsars (1353), Pulsars (1306)

††journal: AJ

##  1 Introduction

Fast Radio Bursts (FRBs) are energetic, millisecond-duration radio transients
of extragalactic origin. There are now over 500 confirmed FRBs recorded in the
Transient Name Server111https://www.wis-tns.org/ (TNS) catalog (Petroff &
Yaron, 2020). Several lines of evidence point to neutron-star progenitors for
FRBs, although models with, e.g., black-hole engines remain viable (e.g.,
Zhang, 2022a). Their exact emission mechanism is unknown, though multiple
theories have been proposed. Some models predict emission from maser processes
within the immediate plasma environments of neutron stars (Lyubarsky, 2014;
Metzger et al., 2019). Others associate them with magnetospheric processes
nearer to neutron-star surfaces, for example driven by crustal oscillations or
magnetic reconnection (Beloborodov, 2021; Beniamini et al., 2020; Gu et al.,
2016). Although both repeating and as yet one-off bursts can be described by
these, other cataclysmic theories imply triggering in compact-object mergers
and/or collapse that only produce one-off events (Falcke & Rezzolla, 2014;
Totani, 2013). It is possible that multiple mechanisms are responsible for the
FRB phenomenon, possibly even from the same source (e.g. Petroff, 2017;
Mckinven, 2022; Kirsten et al., 2023; Hewitt et al., 2023). Perhaps relatedly,
a remarkable diversity of progenitor host-galaxy systems is observed,
including globular clusters (Kirsten et al., 2022), dwarf galaxies (Chatterjee
et al., 2017; Bhandari et al., 2023), a variety of locations within galaxies
on the star forming main sequence of galaxies (Mannings et al., 2021; Gordon
et al., 2023), and massive quiescent galaxies (Sharma et al., 2023; Law et
al., 2023).

The polarization of FRBs can be used to identify viable emission theories.
Coupled with the observed high brightness temperatures $T_{B}\gg 10^{12}\,$K,
high linear polarization implies a coherent emission process such as curvature
radiation, inverse-Compton scattering, or synchrotron-maser emission (e.g., Li
et al., 2021; Wang et al., 2022a; Qu & Zhang, 2023). Smooth variations in the
polarization position angle (PPA) over the burst durations can be associated
with moving emission sites, in analogy with the rotating vector model applied
to pulsar emission, or with propagation effects within or immediately outside
the source magnetosphere (Radhakrishnan & Cooke, 1969; Ravi & Lasky, 2016; Luo
et al., 2020; Cho et al., 2020; Oswald et al., 2023). Rapid jumps in PPA,
observed in several pulsars, can indicate emission in different modes or from
different locations within magnetospheres (e.g., Manchester et al., 1975;
Stinebring et al., 1984). Circular polarization and depolarization from 100%
linearly polarized bursts typically require mode conversion or absorption
during propagation, multiple emission sites, or Faraday depolarization in a
strongly magnetized, possibly inhomogeneous medium (Beniamini et al., 2022; Qu
& Zhang, 2023). Faraday rotation measure (RM) variations observed in some FRBs
also hint toward dynamic local environments of FRB progenitors (e.g. Anna-
Thomas et al., 2023a; Mckinven et al., 2023; Li et al., 2022). Each mechanism
places stringent physical constraints on the sources and near-source
environments.

38 FRB sources have published polarization and/or RM data (see Appendix A for
a detailed compilation). This small sample has limited the characterization of
standard properties, although a few traits appear commonplace. Specifically,
most repeating and non-repeating FRBs possess high linear polarization
fractions ($\geq 70\%$) (e.g., Mckinven et al., 2023; Hilmarsson et al.,
2021b; Nimmo et al., 2021). Some FRBs have exhibited non-negligible circular
polarization ($\geq 30\%$, e.g., FRB 20190611B Day et al., 2020). Repeaters
appear non-uniform in their properties: some have stable polarization states
like FRB 20190208A while others vary from burst to burst, like FRB 20121102A
or FRB 20190520B (Mckinven et al., 2023; Feng et al., 2022a; Anna-Thomas et
al., 2023a). One-off bursts, for example FRB 20181112A, can have complex time-
domain morphologies and polarization properties that evolve over the burst
duration (Cho et al., 2020). Polarization properties so far do not appear to
be a viable means of distinguishing repeaters from non-repeaters (e.g., Zhang,
2022a). Some repeaters exhibit smoothly time-varying RMs on week to month
timescales, including FRB 20121102A, FRB 20190520B, and FRB 20180301
(Hilmarsson et al., 2021a; Kumar et al., 2023; Anna-Thomas et al., 2023a).
Strong burst to burst variability in linear- and circular-polarization
fractions, as well as frequency-dependent oscillations in these quantities,
were observed from the repeating source FRB 20201124A (Xu et al., 2022). These
were interpreted as originating during propagation through a strongly
magnetized, evolving plasma environment within an AU of the FRB source.
Frequency-dependent depolarization has also been observed in multiple FRBs
(Feng et al., 2022b; Mckinven et al., 2023). This may be described by the
stochastic RM model, in which spatial RM variations within a scattering screen
depolarize FRB emission as it propagates along multiple pathways (Melrose &
Macquart, 1998; Beniamini et al., 2022; Yang et al., 2022). No systematic
studies of the polarization properties of as yet non-repeating FRBs have been
published.

During the commissioning phase of the 110-antenna Deep Synoptic Array
(DSA-110), an FRB survey at declination $\delta=71^{\circ}$ at 1.4 GHz
observing frequency was conducted. This paper reports on polarimetry of the
first 25 FRBs detected with the DSA-110. The remainder of the paper will
proceed as follows. Section 2 will describe the DSA-110 observations,
polarization pipeline and methods for RM synthesis. We present linear- and
circular-polarization fractions for 25 FRBs and RMs for 20 FRBs. Section 3
presents and discusses the physical implications of polarization subgroups
based on the DSA-110 sample. In Section 4 we combine the DSA-110 sample with
previously published FRBs to compare the polarization properties of repeaters
and non-repeaters, and of FRBs with Galactic pulsars. The latter two sections
include significant interpretation and discussion. We conclude in Section 5.
We encourage the reader to peruse the extensive appendices for a detailed
description of methodology in data reduction, analysis and interpretation, as
well as a compilation of our data and literature data on FRB and pulsar
polarization. We use a selection of symbols and common abbreviations
summarized in Table 1. Calibrated full-polarization filterbank data and
derived parameters in RMTable format222https://github.com/CIRADA-Tools/RMTable
are made available on the CaltechDATA public
repository333https://data.caltech.edu/. These can be accessed through the
DSA-110 archive (Morrell & Law,
2022).444https://code.deepsynoptic.org/dsa110-archive/ Additional data will be
made available upon request to the corresponding author.

Table 1: Table of Frequently Used Symbols and Abbreviations | Symbol/
---
Abbreviation
Units | Definition
PA, $\chi$ | ∘ | Observed linear-polarization position angle without correcting Faraday rotation
PPA, $\chi_{0}$ | ∘ | Intrinsic linear polarization position angle after correcting for all Faraday rotation
$L/I$ | $\%$ | Frequency- and time-averaged debiased fractional linear polarization
$|V|/I$ | $\%$ | Frequency- and time-averaged fractional absolute value circular polarization
$V/I$ | $\%$ | Frequency and time-averaged fractional signed circular polarization
RVM |  | Rotating vector model
AP |  | Average profiles of Galactic pulsars
SP |  | Single pulses from Galactic pulsars
S/N |  | Signal to noise ratio

##  2 Observations and data analysis

Figure 1: Comparison of the pulse profile of PSR J$1935+1616$ observed with
the DSA-110 (left) to an archival profile from the European Pulsar Network
(right). The observed profile was formed by centroiding and stacking 26
single-pulse detections automatically triggered and processed identically to
DSA-110 FRBs. The top panels show the PA of the average profile (blue), and
for the DSA-110 bursts, the PA of single pulses (grey). The bottom panels show
the Stokes parameters and linear-polarization fraction ($L/I$) as labeled.
Besides a PA offset of unknown origin, the profiles are otherwise similar.

The DSA-110 array is currently in its commissioning phase. During the
observations reported here, spanning January–November 2022, the array
consisted of 48 core antennas for FRB searching, and 15 outrigger antennas to
assist in FRB localization. Each 4.65-m antenna is equipped with dual
orthogonal linearly polarized receivers, operating between 1280–1530 MHz. A
linear basis using the IAU/IEEE handedness convention555The IAU/IEEE
convention assumes that $V>0$ is right-hand polarization, while $V<0$ is left-
hand polarization (Van Straten et al., 2010). is used for all polarimetry
analysis discussed herein. The antennas are movable in elevation only, and are
always pointed at the meridian. All FRBs we present here were detected during
a survey at a declination of $71.6^{\circ}$. Ravi et al. in prep. will
describe the instrument in detail, and some details have been included in
previous publications on DSA-110 FRBs (e.g., Ravi et al., 2022; Law et al.,
2023). None of the FRBs presented here have been observed to repeat by the
DSA-110 in 150 hours of observing time during 2022 (Law et al., 2023), and we
consider them as non-repeaters for the purposes of our analysis. Of the sample
of 25 FRBs presented here, arcsecond-scale localizations, and secure host-
galaxy association and characterization have been summarized for 11 events by
Law et al. (2023). As this paper is focused on the intrinsic polarization
properties of the DSA-110 and other FRBs, we do not utilize information (e.g.,
redshifts) derived from host-galaxy data. A discussion of the RMs of the
localized DSA-110 and other FRBs are presented in the companion paper, Sherman
et al. (2023).

Figure 2: Summary of polarization and RM data on FRB 20220207C (Zach).
Identical plots on all FRBs presented herein are shown in Appendix L. Left:
From top, we show the PPA (with $1\sigma$ errorbars) measured after correcting
for RM, and frequency averaged time series of Stokes $I$, $L$, and $V$. The
PPA is highlighted in bins with linear-polarization S/N $>3\sigma$. The
dynamic spectrum is shown at center, to the right of which are shown optimally
summed spectra (Appendix H) and the spectrally resolved PPA with $>3\sigma$
bins highlighted. Right: The top panel shows the RM spectra evaluated over the
full range of sensitivity using two different methods (Appendix I), and the
bottom panel shows a detailed analysis of the S/N of the peak.

The calibration and analysis of the full-polarization properties of the 25
FRBs described herein were carried out using standard techniques. The chief
novelty of the present analysis is that it is developed from the ground up
using a custom implementation on a new telescope. Novel methods were developed
for certain aspects of the analysis, such as the estimation of accurate RMs
and the corresponding uncertainties. A summary of the calibration and analysis
techniques can be found in Appendix B, and Appendices C to I justify them in
detail.

In this section we show a single demonstration of the functioning of the
polarization calibration and analysis pipeline. Figure 1 displays the
calibrated, summed, polarized profile formed from 26 single-pulse detections
of bright pulses from the PSR J1935$+$1616 (B1933). These pulses were detected
and processed in exactly the same way as the DSA-110 FRBs. A comparison is
made to the reported average profile from the European Pulsar Network (EPN)
database of pulsar profiles (Gould & Lyne,
1998).666http://www.epta.eu.org/epndb/ Good agreement between the DSA-110
polarization profile and the EPN profile is found: note particularly the swing
in Stokes V. A time offset in the linear polarization peak is observed, which
is attributed to low signal-to-noise of the DSA-110 profile, and pulse
summation based on simple centroiding and stacking. An offset in PA is evident
between the profiles: our method for deriving PAs is given in Appendix D, and
it is unclear exactly what method was used in calibrating the EPN profile.
Additional details on verification of the polarization pipeline with
J1935+1616 are given in Appendix G.

We present polarization and RM results on all FRBs in Appendix L. Figures 14
to 17 show calibrated and RM-corrected burst temporal profiles and dynamic
spectra. Figures 18 to 20 show RM spectra for all FRBs with detectable RMs.
Table 2 summarizes the various polarization fractions and RMs for each FRB.
Throughout this paper we sometimes refer to DSA-110 FRBs by their internal
natural names (e.g., FRB 20220207C is referred to as Zach). Correspondence
between the natural and formal names is noted in Table 2. Example plots for
FRB 20220207C are shown in Figure 2.

=1mm

Table 2: DSA-110 FRB Sample Polarization Properties

FRB Names | R.A. (∘) | Decl. (∘) | $\mathbf{n_{t}}$ | $\mathbf{n_{f}}$ | S/N | $\mathbf{L/I}$ | $\mathbf{|V|/I}$ | $\mathbf{V/I}$ | RM (rad m-2) | DM (pc cm-3)
---|---|---|---|---|---|---|---|---|---|---
FRB 20220121B / “Clare” | $85.66^{\circ}$ | $64.39^{\circ}$ | 8 | 128 | 13.36 | $70.5\pm 20.6\%$ | $51.0\pm 12.7\%$ | $-51.0\pm 12.7\%$ | $-4.6\pm 15.5$ | $313.5\pm 0.2$
FRB 20220204A / “Fen” | $278.27^{\circ}$ | $72.58^{\circ}$ | 6 | 32 | 17.68 | $62.8\pm 15.3\%$ | $7.5\pm 7.7\%$ | $-6.7\pm 7.7\%$ | $-11.0\pm 11.7$ | $612.2^{+0.005}_{-0.049}$
FRB 20220207C / “Zach” | $310.2^{\circ}$ | $72.88^{\circ}$ | 1 | 16 | 72.57 | $74.9\pm 4.5\%$ | $14.8\pm 1.7\%$ | $11.1\pm 1.7\%$ | $162.48\pm 0.04$ | $262.3\pm 0.01$
FRB 20220208A / “Ishita” | $322.58^{\circ}$ | $70.04^{\circ}$ | 32 | 256 | 10.70 | $114.3\pm 29.1\%$ | $11.4\pm 15.5\%$ | $-11.2\pm 15.5\%$ | $-23.3\pm 9.7$ | $437.0^{\pm}0.6$
FRB 20220307B / “Alex” | $350.88^{\circ}$ | $72.19^{\circ}$ | 1 | 128 | 15.72 | $69.8\pm 16.0\%$ | $18.9\pm 8.0\%$ | $-10.3\pm 8.0\%$ | $-947.2\pm 12.3$ | $499.15\pm 0.03$
FRB 20220310F / “Whitney” | $134.72^{\circ}$ | $73.49^{\circ}$ | 1 | 32 | 98.32 | $60.6\pm 4.7\%$ | $16.6\pm 1.6\%$ | $-7.4\pm 1.6\%$ | $11.4\pm 0.2$ | $462.15\pm 0.004$
FRB 20220319D / “Mark” | $32.18^{\circ}$ | $71.04^{\circ}$ | 1 | 32 | 56.37 | $16.1\pm 4.0\%$ | $4.0\pm 2.0\%$ | $-3.0\pm 2.0\%$ | $59.9\pm 14.3$ | $110.95\pm 0.01$
FRB 20220330D / “Erdos” | $163.75^{\circ}$ | $70.35^{\circ}$ | 40 | 64 | 17.98 | $73.2\pm 17.7\%$ | $15.8\pm 9.0\%$ | $3.1\pm 9.0\%$ | $-122.2\pm 4.5$ | $468.1^{+0.8}_{-0.9}$
FRB 20220418A / “Quincy” | $219.11^{\circ}$ | $70.1^{\circ}$ | 2 | 128 | 16.84 | $64.1\pm 13.3\%$ | $21.4\pm 7.7\%$ | $2.7\pm 7.7\%$ | $6.1\pm 7.5$ | $623.45\pm 0.01$
FRB 20220424E / “Davina” | $19.51^{\circ}$ | $71.8^{\circ}$ | 2 | 64 | 14.60 | $59.9\pm 16.2\%$ | $15.8\pm 7.4\%$ | $15.8\pm 7.4\%$ | $126.9\pm 13.4$ | $863.48^{+0.022}_{-0.036}$
FRB 20220506D / “Oran” | $318.05^{\circ}$ | $72.83^{\circ}$ | 1 | 32 | 24.17 | $95.3\pm 10.9\%$ | $31.4\pm 4.6\%$ | $31.4\pm 4.6\%$ | $-32.4\pm 3.6$ | $396.93\pm 0.01$
FRB 20220509G / “Jackie” | $282.67^{\circ}$ | $70.24^{\circ}$ | 1 | 32 | 40.32 | $98.5\pm 11.1\%$ | $6.0\pm 2.8\%$ | $5.4\pm 2.8\%$ | $-109.0\pm 1.2$ | $269.5\pm 0.007$
FRB 20220726A / “Gertrude” | $73.95^{\circ}$ | $69.93^{\circ}$ | 2 | 64 | 18.25 | $93.5\pm 16.7\%$ | $13.8\pm 6.2\%$ | $-3.7\pm 6.2\%$ | $499.8\pm 7.2$ | $686.55\pm 0.01$
FRB 20220801A / “Augustine” | $54.96^{\circ}$ | $70.18^{\circ}$ | 4 | 64 | 11.77 | $30.1\pm 18.0\%$ | $35.8\pm 13.7\%$ | $-1.3\pm 13.7\%$ | $-$ | $412.6\pm 0.04$
FRB 20220825A / “Ansel” | $311.98^{\circ}$ | $72.59^{\circ}$ | 1 | 32 | 32.80 | $53.7\pm 11.4\%$ | $9.0\pm 5.9\%$ | $-7.4\pm 5.9\%$ | $750.2\pm 6.7$ | $651.2\pm 0.02$
FRB 20220831A / “Ada” | $338.7^{\circ}$ | $70.54^{\circ}$ | 6 | 64 | 21.28 | $84.6\pm 12.8\%$ | $16.8\pm 5.3\%$ | $1.7\pm 5.3\%$ | $772.1\pm 7.2$ | $1146.25\pm 0.2$
FRB 20220914A / “Elektra” | $282.06^{\circ}$ | $73.34^{\circ}$ | 1 | 64 | 17.43 | $16.3\pm 14.0\%$ | $20.5\pm 11.9\%$ | $11.9\pm 11.9\%$ | $-$ | $631.05\pm 0.02$
FRB 20220920A / “Etienne” | $240.26^{\circ}$ | $70.92^{\circ}$ | 2 | 128 | 18.88 | $89.0\pm 16.2\%$ | $19.7\pm 8.1\%$ | $-14.9\pm 8.1\%$ | $-830.3\pm 8.3$ | $315.0\pm 0.06$
FRB 20220926A / “Celeste” | $328.73^{\circ}$ | $72.86^{\circ}$ | 2 | 128 | 18.16 | $17.5\pm 21.0\%$ | $9.5\pm 14.2\%$ | $2.0\pm 14.2\%$ | $-$ | $441.53\pm 0.03$
FRB 20221002A / “Arni” | $281.0^{\circ}$ | $71.6^{\circ}$ | 12 | 256 | 8.08 | $26.8\pm 22.7\%$ | $19.7\pm 18.1\%$ | $-12.5\pm 18.1\%$ | $-$ | $322.5\pm 1.0$
FRB 20221012A / “Juan” † | $280.8^{\circ}$ | $70.52^{\circ}$ | 8 | 32 | 9.33 | $63.0\pm 21.4\%$ | $25.7\pm 11.0\%$ | $0.6\pm 10.9\%$ | $165.7\pm 17.7$ | $441.2\pm 0.26$
FRB 20221027A / “Koyaanisqatsi” | $130.9^{\circ}$ | $71.6^{\circ}$ | 1 | 32 | 21.82 | $8.3\pm 7.0\%$ | $18.4\pm 5.2\%$ | $-2.2\pm 5.2\%$ | $-$ | $452.5^{\ddagger}$
FRB 20221029A / “Mifanshan” | $143.8^{\circ}$ | $71.6^{\circ}$ | 4 | 128 | 17.12 | $85.7\pm 16.1\%$ | $15.6\pm 7.0\%$ | $6.8\pm 7.0\%$ | $-155.8\pm 9.7$ | $1391.05^{\ddagger}$
FRB 20221101B / “Nina” | $342.0^{\circ}$ | $71.5^{\circ}$ | 4 | 32 | 14.21 | $99.3\pm 19.3\%$ | $24.5\pm 8.7\%$ | $-19.4\pm 8.7\%$ | $-32.2\pm 9.1$ | $490.7^{\ddagger}$
FRB 20221101A / “Ayo” | $75.6^{\circ}$ | $71.6^{\circ}$ | 2 | 64 | 19.27 | $55.3\pm 11.3\%$ | $11.6\pm 6.2\%$ | $-5.5\pm 6.2\%$ | $4670.4\pm 10.8$ | $1476.5^{\ddagger}$

Notes: $n_{t}$ and $n_{f}$ are the downsampling factors in time and frequency
from the native DSA-110 resolution (see Appendix B) used to maximize S/N. The
total, linear, absolute value of circular and signed circular polarization are
given in columns 7, 8, 9, and 10. The right ascension and declination given
are the ICRS frame coordinates of the beam in which the FRB was detected.

† FRB 20221012A’s polarization is computed after derotating to the reported
$\rm RM$. This detection was marginal, with low linear-polarization S/N below
the $9\sigma$ threshold. However, this is taken as a reliable measurement
given the clear peak the RM spectrum (Figure 20) and apparent coherence when
compared to the RMSF.

‡Detailed burst structure analysis used to estimate DM errors has not yet been
performed for these FRBs. See G. Chen et al., in preparation for details.

##  3 Discussion of Individual Burst Polarization Properties

###  3.1 Motivation for Polarization-based Classification

The DSA-110 FRB sample spans a wide range of polarimetric and spectro-temporal
properties. This is the largest uniform sample of FRB polarization, and
motivates its use as a basis for a polarization-dependent classification
scheme. The need for such classes stems from the ability of polarimetry to
distinguish FRB emission and propagation models. The high brightness
temperatures observed in FRBs require a coherent, highly polarized emission
process (e.g. Luan & Goldreich, 2014). This could apply to pulsar-like
‘antenna’ mechanisms driven by charged particle bunches within the
magnetosphere or synchrotron ‘maser’ emission via a shocked wind outside the
magnetosphere (e.g. Metzger et al., 2019; Wang et al., 2022b, a; Zhang, 2022a,
b; Qu & Zhang, 2023). ‘Antenna’ mechanisms appear more likely, since the
observed circular polarization and de-polarization in FRBs require propagation
through an extreme local plasma environment. For example. Faraday Conversion
(FC) and cyclotron absorption each result in circular polarization; their
presence would represent evidence of a highly magnetized, dense plasma nearby
the source (e.g. Vedantham & Ravi, 2019; Gruzinov & Levin, 2019; Suresh &
Cordes, 2019; Kumar et al., 2022; Qu & Zhang, 2023). Similarly, depolarization
can indicate either multi-path scattering through a screen with non-uniform RM
(e.g. Melrose & Macquart, 1998), or the superposition of multiple emission
modes (e.g. Mitra et al., 2023); these can be investigated through multi-band,
high time-resolution polarization studies of FRBs (e.g. Hankins et al., 2003;
Feng et al., 2022b; Mckinven et al., 2023). A generalized classification
scheme will help identify the characteristic FRB polarization properties to
narrow the range of likely FRB theories.

To date, the predominant FRB categorization method was offered by Pleunis et
al. (2021) based on observations of FRBs from the Canadian Hydrogen Intensity
Mapping Experiment (CHIME). Their classes were based on the spectro-temporal
morphology of FRBs detected in the 400-800 MHz band. However, we find these
classes insufficient to describe the full DSA-110 sample’s morphological
properties. Furthermore, these classes do not include FRB polarization, for
which we would like a straightforward and replicable classification framework.
The DSA-110, whose polarization calibration scheme is verified in Appendices
E, F, and G, is well-equipped to define polarization sub-classes using the
uniform sample of 25 FRBs presented here. However, we acknowledge that such a
classification scheme would be limited by the DSA-110 sensitivity, and
furthermore cannot be generalized beyond L-band detections. While we hope that
these sub-groups will form the groundwork for a more general, polarization-
and frequency-dependent classification scheme, we make no claims on its
universality in the current iteration. Polarization properties are also
difficult to distinguish from being intrinsic or the result of propagation
effects. Therefore, while we identify classes based on total, linear, and
circular polarization, we use them primarily to motivate a more detailed
discussion of linear and circular polarization in the following section.

We define four unique polarization sub-groups which are applied in turn to the
total, linear, and circular polarization fractions of each DSA-110 FRB:

  1. 1.

Consistent with 100% Polarized: The polarization fraction falls within
$3\sigma$ of 100% and beyond $3\sigma$ of 0%.

  2. 2.

Consistent with 0% Polarized: The polarization fraction falls within $3\sigma$
of 0% and beyond $3\sigma$ of 100%.

  3. 3.

Intermediate: The polarization fraction falls beyond $3\sigma$ of both 100%
and 0%.

  4. 4.

Unconstrained: The polarization fraction falls within $3\sigma$ of both 100%
and 0%. This is equivalent to stating the polarization is not well-defined.

We then define two orthogonal sub-groups which generalize and place more
quantitative limits on the morphological classes of Pleunis et al. (2021):

  1. 1.

Single Component: Bursts exhibit one component (on approx. millisecond
timescales).

  2. 2.

Multi-Component: Bursts exhibit multiple components separated on millisecond
timescales.

In Table 3, we sort the DSA-110 sample among these sub-classes using total,
linear, and circular polarization fractions. For the remainder of the paper,
the sub-groups Consistent with 100% Polarized, Consistent with 0% Polarized,
Intermediate, and Unconstrained will refer only to the total polarization-
based sub-groups unless otherwise noted. In the next section, we explore the
specific properties of FRBs in each class. Figure 3 shows $L/I$ and $|V|/I$
for the DSA-110 FRBs, grouped by their polarization class.

Table 3: Polarization-based FRB subgroups from DSA-110 data.

| Consistent with 100% | Consistent with 0% | Intermediate | Unconstrained
---|---|---|---|---
| Total Polarization
---
$(\sqrt{(L/I)^{2}+(V/I)^{2}})$
| FRB 20220121B (1)
---
FRB 20220204A (1i)
FRB 20220208A (1a)
FRB 20220307B (1)
FRB 20220330D (1i)
FRB 20220424E (1i)
FRB 20220506D (1ia)
FRB 20220509G (1ia)
FRB 20220726A (1a)
FRB 20220831A (1a)
FRB 20220920A (1)
FRB 20221012A (1)‡
FRB 20221029A (1i)
FRB 20220418A (3a)
FRB 20221101B (2)
| FRB 20220914A (1i)
---
FRB 20220926A (1)
FRB 20221027A (1i)†
| FRB 20220319D (1i)
---
FRB 20220825A (1ia)
FRB 20221101A (1a)
FRB 20220207C (2ia)
FRB 20220310F (2ia)
| FRB 20220801A (1ia)
---
FRB 20221002A (1)
| Linear Polarization
---
$(L/I)$
| FRB 20220121B (1)
---
FRB 20220204A (1i)
FRB 20220208A (1a)
FRB 20220307B (1)
FRB 20220330D (1i)
FRB 20220424E (1i)
FRB 20220506D (1ia)
FRB 20220509G (1ia)
FRB 20220726A (1a)
FRB 20220831A (1a)
FRB 20220920A (1)
FRB 20221029A (1i)
FRB 20220418A (3a)
FRB 20221101B (2)
| FRB 20220914A (1i)
---
FRB 20220926A (1)
FRB 20221027A (1i)†
FRB 20220801A (1ia)
FRB 20221002A (1)
| FRB 20220319D (1i)
---
FRB 20220825A (1ia)
FRB 20221101A (1a)
FRB 20220207C (2ia)
FRB 20220310F (2ia)
FRB 20221012A (1)‡
| Circular Polarization
---
$(|V|/I)$
– |  | FRB 20220121B (1)
---
FRB 20220204A (1i)
FRB 20220208A (1a)
FRB 20220307B (1)
FRB 20220330D (1i)
FRB 20220424E (1i)
FRB 20220509G (1ia)
FRB 20220726A (1a)
FRB 20220920A (1)
FRB 20221012A (1)‡
FRB 20221029A (1i)
FRB 20220801A (1ia)
FRB 20221002A (1)
FRB 20220914A (1i)
FRB 20220926A (1)
FRB 20220319D (1i)
FRB 20220825A (1ia)
FRB 20221101A (1a)
FRB 20220418A (3a)
FRB 20221101B (2)
| FRB 20220121B (1)
---
FRB 20220506D (1ia)
FRB 20221027A (1i)†
FRB 20220207C (2ia)
FRB 20220310F (2ia)
FRB 20220831A (1a)
–

Notes: DSA-110 FRBs sorted into subgroups based on polarization significance
as described in Section 3. Each burst is labeled with the number of resolved
components, an “i” if the burst shows significant spectral striation, and an
“a” if the burst shows significant scattering (G. Chen et al., in prep.).
Multi-Component FRBs are boldfaced, while Single-Component FRBs are in regular
font.

†FRB 20221027A is a unique FRB whose total polarization is Consistent with 0%,
but which has Intermediate circular polarization. This is attributed to its
insignificant linear polarization which adds noise to the total polarization
estimate.

‡FRB 20221012A has a total polarization that is Consistent with 100% and a
circular polarization that is Consistent with 0%, but its linear polarization
is Unconstrained. From RM synthesis, we marginally detect an RM, although the
peak in the RM spectrum has linear S/N below the $9\sigma$ threshold as shown
in Figure 20. This suggests there is significant linear polarization which
contributes to the total, though we cannot make more constraining statements
within our current classification scheme.

Figure 3: Linear and Absolute Value Circular Polarization for DSA-110 FRBs.
Each FRB is color-coded by its polarization class as reported in Table 3.
Single Component FRBs are shown as circles and Multi-Component FRBs are shown
as triangles. The errorbars shown are $1\sigma$ uncertainties. The black line
indicates where the total-polarization fraction
$T/I=\sqrt{(|V|/I)^{2}+(L/I)^{2}}=100\%$. While all Consistent with 100%
(blue) and most Intermediate (green) FRBs have $L/I>50\%$, FRB 20220121B and
FRB 20220506D also show significant circular polarization. FRB 20220319D is
the only FRB in either class with less than 50% total polarization. All
Consistent with 0% FRBs (orange) have $L/I$ and $|V|/I$ below 25%.

###  3.2 Single Component FRBs

A significant majority $21/25$ of the DSA-110 sample are described by a single
component on millisecond timescales, with most (13) of these being Consistent
with 100% polarization. 3 Single Component FRBs fall into each of the
Consistent with 0% and Intermediate classes, while two have Unconstrained
polarization properties. In this section we explore the characteristic
polarization properties of Single Component FRBs.

####  3.2.1 Linear Polarization

As shown in Figure 3, all FRBs that are Consistent with 100% have $L/I>50\%$,
including 13 Single Component bursts; two-thirds of these (10) have
$L/I>70\%$. This is not uncommon among FRBs, as 36% of previously published
repeaters and non-repeaters with L-band (1.4 GHz) polarization measurements
also have $L/I>50\%$ . This large fraction of highly linearly polarized FRBs
supports coherent radiation models such as curvature radiation from coherent
charge bunches (Wang et al., 2022a; Qu & Zhang, 2023). While Feng et al.
(2022b) demonstrate that repeaters become depolarized at lower frequencies,
they associate this with stochastic RM scattering rather than intrinsic
emission. Coherent radiation models are further supported by the relatively
flat PPA’s observed in this group. A $\chi^{2}$ goodness-of-fit test was
conducted to compare the PPA in time bins with linear-polarization S/N
$>3\sigma$ to the weighted average PPA value (see Appendix K). None of the 13
Single Component FRBs consistent with 100% polarization were found with
significant variations ($p<10\%$) in position angle. This may imply that there
is a single dominant polarization mode in most FRBs, and resembles the
behavior of young, high spin-down pulsars (Weltevrede & Johnston, 2008; Ravi
et al., 2010; Mitra et al., 2016). In Section 4.2, we explore possible
connections between FRBs and young pulsars in more detail. Notably, of FRBs in
the Consistent with 100% and Intermediate sub-groups, only FRB 20220319D has a
linear polarization fraction below 20%, a trait shared only by the 3 FRBs that
are Consistent with 0%.

####  3.2.2 Circular Polarization

Circular polarization appears to be less common than linear polarization among
the Single Component sample. Only two FRBs that are Consistent with 100% or
Intermediate have $|V|/I>30\%$: FRB 20220121B and FRB 20220506D. Both are
Consistent with 100% and show no clear splitting of different signs of Stokes
V. This is consistent with circular polarization originating through the
propagation effects discussed above. A third FRB, FRB 20220801A, also has a
high $|V|/I$, but falls into the Unconstrained subgroup, making any evident
polarization difficult to confirm. We do not observe any changes in the sign
of Stokes V within FRB 20220121B and FRB 20220506D, as are often observed at
the centers of the main components in radio-pulsar APs (Radhakrishnan &
Rankin, 1990). Furthermore, while most Single Component FRBs appear to have
negligible circular polarization (evident from both $|V|/I$ fractions and
polarized profiles in Figures 14-17), all four Multi-Component bursts appear
to have significant circular polarization. We will explore this further in the
next section.

The large fraction of FRBs that exhibit high linear polarization, as opposed
to circular polarization, suggests that the intrinsic emission mechanism is
often highly linearly polarized. Circular polarization and depolarization may
then arise primarily from propagation effects. In this scenario,
depolarization from the intrinsic mechanism due to unresolved micro or nano-
second scale structure may be less significant than propagation effects, in
contrast to pulsar radio emission (Mitra et al., 2015; Cordes, 1976; Hankins
et al., 2003). However, this claim cannot be confirmed without higher time
resolution observations of FRBs.

The limited 187 MHz bandwidth and 972 kHz resolution777Here we refer to the
limited resolution of the spectra in Figures 14-17, which were binned by at
least $32\times 30.4$ kHz channels to maximize frequency structure. of the
DSA-110 spectra prevent detailed fits of frequency-dependent FC models.
Instead, by assuming FC is significant in the region of interest, we can
estimate the magnetic-field strength from frequency-averaged quantities as
follows (Gruzinov & Levin, 2019). One can estimate the Faraday Conversion
Measure (CM) from the root mean squared circular polarization of each FRB,
assuming the circular emission arises from FC at a single magnetic field
reversal:

$\sqrt{<V(\lambda^{2})^{2}>}=\sqrt{2(e^{-({\rm
CM}\lambda^{2})^{2}/2}-e^{-({\rm CM}\lambda^{2})^{2}})}$ (1)

The CM can be related to the RM and total magnetic field strength, $B$, by:

${\rm CM}\approx B\sqrt{{\rm
RM}\left(\frac{8\pi^{3}e^{2}}{m_{e}^{3}c^{4}}\right)}\sim
10^{-2}\left(\frac{B}{1\,{\rm G}}\right)\left(\frac{\rm RM}{1\,{\rm
rad\,m^{-2}}}\right)^{1/2},$ (2)

where $e$ is the electron charge, $m_{e}$ is the electron mass, and $c$ is the
vacuum speed of light. For FRB 20220121B and FRB 20220506D, we measure root
mean squared circular polarization $\sqrt{<V(\lambda^{2})^{2}>}\approx 50\%$
and $40\%$, corresponding to conversion measures $\rm CM\approx 10\,$m-2 in
both cases. Given their RMs of $-4.60\pm 15.48\,$rad m-2 and $-32.38\pm
3.60\,$rad m-2, we estimate magnetic field strengths of $B\approx 510\,$G and
$150$ G, respectively. These high field strengths are not consistent with
supernova-remnant and plerionic environments, including those of the FRBs
associated with persistent radio sources (e.g., Vedantham & Ravi, 2019).
However, motivated by the likely FC observed during eclipses of the binary-
system PSR B$1744-24$A (Li et al., 2023), the magnetized wind of a companion
to the FRB progenitors is a reasonable possibility for the conversion site.

####  3.2.3 Depolarization

The DSA-110 sample reported here contains 3 Single Component FRBs that are
Consistent with 0% and 3 that have Intermediate polarization. $9/16$ FRBs in
the published literature that have reported errorbars would also fall in these
subgroups. Considering the circular polarization sub-groups, only FRB
20221027A has an Intermediate $|V|/I$ ($>3\sigma$) among FRBs with
Intermediate total polarization888With $|V|/I=18.4\pm 5.2\%$, FRB 20221027A’s
linear polarization fraction is noise-dominated; therefore, its total
polarization class (Consistent with 0%) is likely erroneous due to small
errors in noise statistics. We will consider it as an Intermediate FRB for
this discussion given its significant circular polarization fraction.. The
lack of circular polarization in bursts with low total polarization implies
that FC effects are less common, which one expects to depolarize the burst
while producing residual circular polarization.

RM variations across a scattering screen are also unlikely to be the dominant
depolarization mechanism for the DSA-110 FRBs. The variation in RM is captured
by $\sigma_{\rm RM}$, the standard deviation of RM throughout the screen, and
depolarization would be highly frequency dependent with the linear-
polarization fraction of the form:

$f_{\sigma_{\rm RM}}=1-e^{-2\sigma_{\rm RM}^{2}\lambda^{4}}$ (3)

This model has been found to match observations of 8 repeating FRBs from
0.1–10 GHz, with $\sigma_{\rm RM}$ values from $0.12$ rad m-2 for FRB
20180916B to $218.9$ rad m-2 for FRB 20190520B (Feng et al., 2022b; Mckinven
et al., 2023). However, for $RM<1000$ rad m-2, averaging over the DSA-110
frequency band ($1.3-1.5$ GHz) without RM correction is the dominant
depolarization effect, which we quantify by:

$f_{\rm avg}=1-\sqrt{<{\rm cos}({\rm RM}\lambda^{2})>^{2}+<{\rm sin}({\rm
RM}\lambda^{2})>^{2}}$ (4)

where $<>$ denotes the mean over frequency. Therefore, if we assume an FRB is
intrinsically 100% polarized, we can write the observed polarization fraction
as $L/I\approx f_{\sigma_{\rm RM}}(\rm RM)f_{\rm avg}(\sigma_{\rm RM})$; note
that channel bandwidth depolarization is negligible in this RM range (see
Appendix I). Feng et al. (2022b) (see Figure 4) derives an empirical, linear
relation between $\sigma_{\rm RM}$ and RM, which we adopt to write Equation 4
in terms of $\sigma_{\rm RM}$. We apply this model to the average polarization
of the three bursts with insufficient $L/I$ for RM measurements: FRB
20220914A, FRB 20220926A, and FRB 20221027A. We find that $\sigma_{\rm
RM}\approx 0.3-1.0$ rad m-2 could produce the observed polarization fractions
for FRB 20220914A and FRB 20220926A, while $\sigma_{\rm RM}\approx 0.3-3.0$
rad m-2 could produce the polarization of FRB 20221027A. From Feng et al.
(2022b), these correspond to $RM\approx 200-900$ rad m-2, which should be
detectable with the DSA-110 RM synthesis pipeline; however, no significant RM
was found for these three FRBs. Low $S/N$ could prevent detection, but the low
$\sigma_{\rm RM}$ suggests that RM synthesis would recover nearly 100% linear
polarization, making the maximized linear S/N in each burst $\sim 20\sigma$
which exceeds the $9\sigma$ detection threshold (see Appendix I).

We can perform a similar analysis for Intermediate FRBs, which do have RM
measurements ranging from $10-4670$ rad m2. We find that $\sigma_{\rm RM}$ in
the range of 10–20 rad m-2 would be required for these FRBs. Apart from FRB
20221101A, this is around an order of magnitude higher than expected from Feng
et al. (2022b) for these RM magnitudes, and the $\ll 1$ ms scattering
timescales of the DSA-110 FRBs (G. Chen et al., in prep.). Furthermore,
assuming a common origin for the scattering and depolarization, the implied
magnetic-field variations in the scattering screen are likely to be
uncomfortably high, of order Gauss (Yang et al., 2022; Feng et al., 2022b,
Section S4). A potential exception to these arguments is the event FRB
20220319D, as discussed in Appendix J.

The significant fraction of FRBs in the DSA-110 sample that are Consistent
with 0% or Intermediate poses an interesting challenge to theory (Qu & Zhang,
2023). The fact that depolarization has long been observed and puzzled over in
pulsars, more significantly at high frequencies ($>1$ GHz) than low, (e.g.,
Manchester et al., 1973; Manchester, 1971) should provide some hope that a
common explanation may be found.

###  3.3 Multi-Component FRBs

$4/25$ of the DSA-110 sample exhibit multiple components on millisecond
timescales999We note that sub-microsecond-scale structures have been
previously observed in FRBs (e.g., Majid et al., 2021; Nimmo et al., 2021,
2022), and indeed interesting structure within individual burst components is
observed in some DSA-110 FRBs. We defer a high time resolution analysis of
DSA-110 FRBs to future work.. FRB 20220418A and FRB 20221101B are Consistent
with 100% Polarization, while FRB 20220207C and FRB 20220310F are
Intermediate. In this section we explore the polarization properties of Multi-
Component FRBs.

####  3.3.1 Stable Polarization States

Both FRB 20220207C and FRB 20220310F have two sub-components exhibiting
significant linear polarization with $L/I>50\%$. Significant circular
polarization ($>3\sigma$) is also evident, with $|V|/I\approx 15\%$. In FRB
20220207C, the first component has a flat PPA while the second fluctuates,
although a $\chi^{2}_{\angle}$ test finds this variation is not significant
(see Appendix K for details). In contrast, FRB 20220310F displays a flat PPA
in both components, separated by $\sim 10^{\circ}$. If both components
originate from a fixed region in a rotating magnetosphere, this suggests
negligible rotation over the approximately millisecond burst durations. A
potentially better way to quantify a constraint on the rotation periods of
progenitor objects is by assuming emission from coherent charge bunches, as
motivated by this specific categorization (Wang et al., 2022a; Qu & Zhang,
2023). For this analysis we assume a ‘thin’ bunch of charges, which aligns
with the wide range of polarization properties observed in FRBs101010For
details, see Figures 2, 4, 5, and 6 of Wang et al. (2022a). In this scenario,
the burst duration must be much less than $(\gamma\Omega)^{-1}$, where
$\gamma\sim 100$ is the bunch Lorentz factor111111We assume
$\gamma\mathbf{\sim}100$ based on the DSA-110 observing frequency 1.4 GHz and
the expected curvature radius of magnetic field lines around a neutron star,
$\rho\sim 10^{6-8}$ cm. Using Equation 18 of Qu & Zhang (2023),
$58\lesssim\gamma\lesssim 270$ are reasonable approximations for a coherent
curvature radiation scenario., and $\Omega$ is the rotation angular frequency.
Applying this condition for the $\sim 0.3\,$ms duration of the first FRB
20220207C burst, we find required rotation periods $\gg 30$ ms. Similarly, the
sub-bursts in FRB 20220310F span $\sim 0.2\,$ms each, for which we find
required rotation periods $\gg 20$ ms under the same curvature radiation
assumptions. These estimates are of particular interest since $30\,$ms roughly
demarcates the boundary between millisecond pulsar (MSPs) and slow canonical
pulsar (CPs) rotation periods (e.g. Lorimer, 2008).

####  3.3.2 Polarization Variation

What is most striking about these bursts is that the different components
appear to have different polarization properties, an effect that persists for
non-repeating FRBs from at least the Australian Square Kilometre Array
Pathfinder (ASKAP; Cho et al., 2020; Day et al., 2020). In contrast, none of
the 21 single-component FRBs had statistically significant PPA variability,
suggesting negligible polarization evolution across the burst. The variations
between the polarization properties of the sub-components of FRB 20220207C,
FRB 20220310F, FRB 20220418A, and FRB 20221101B defy a unified description.
FRB 20220418A and FRB 20220207C exhibit multiple components with different
polarization properties. FRB 20220207C’s sub-components have very different
profiles, although a $\chi^{2}_{\angle}$ test finds the PPA variation is not
significant. Beyond this, the first sub-component is Consistent with 100%
linear polarization while the second has $\sim 50\%$ linear polarization and
$\sim 20\%$ circular polarization. FRB 20220418A is less constrained: while
the first sub-component has high linear polarization, the second is
Unconstrained and the third is Consistent with 0% linear and circular
polarization.

FRB 20220310F’s sub-components have more comparable properties, with $L/I$ of
$54.8\pm 6.0\%$ and $67.4\pm 7.2\%$, but while the circular-polarization
fractions have a similar magnitude, the signs are opposite: $V/I$ of $-16.7\pm
1.3\%$ and $10.8\pm 1.8\%$ respectively. Indeed, the polarization states of
the two sub-components are individually well-defined, and the average
locations of the two sub-components on the Poincaré sphere are almost
orthogonal, with an angular separation of $71\pm 2$ degrees (Figure 4). These
are reminiscent of emission in orthogonally polarized modes observed in
several pulsars (Manchester et al., 1975; Stinebring et al., 1984). However,
the change in sign of Stokes V between the two components is rarely if ever
observed in multi-component pulsar APs (Han et al., 1998). Changes in the sign
of Stokes V between components can potentially be interpreted as emission from
different magnetic hemispheres, potentially implying rapid rotation of the
progenitor (Johnston & Kramer, 2019). Alternatively, the opposite signs in
circular polarization may indicate that birefringence could be the cause of
the split sub-components in FRB 20220310F (Suresh & Cordes, 2019; Qu & Zhang,
2023). While birefringent dispersive delay would require $RM\approx 10^{7}$
rad m-2 to produce the observed 0.3 ms split in FRB 20220310F, birefringent
refraction may be more plausible, requiring only $RM\approx 10^{1-2}$ rad m-2.
The closed loop formed on the Poincaré sphere by the polarization vector of
the second component of FRB 20220310F is also reminiscent of the loop observed
in the first component of FRB 20181112A by Cho et al. (2020), which was
potentially ascribed to FC in a relativistic plasma. From equation 2, we
estimate a magnetic field strength $B\approx 150$ G would be required for FC,
which is inconsistent with supernova-remnant and plerionic environments (e.g.
Vedantham & Ravi, 2019).

Figure 4: Projection of the polarization state of FRB 20220310F onto the
Poincaré sphere. The position angle ($\chi$) and longitude ($\psi$) are
related to the Stokes parameters by $Q=\sin(2\psi)\sin(2\chi)$,
$U=\sin(2\psi)\cos(2\chi)$, and $V=\cos(2\psi)$. Note the position angle axis
has been shifted by $90^{\circ}$ for ease of viewing. Data are displayed in
windows of eight and ten 32.768 $\mu$s samples for the first and second
components of the burst.

####  3.3.3 RM Variation

We observe a significant $3.1\sigma$ variation in RM between the sub-
components of FRB 20221101B ($-13.1\pm 10.5\,$rad m-2 and $-75.9\pm 17.5\,$rad
m-2), and marginally significant $1.7\sigma$ and $2.7\sigma$ variations in FRB
20220207C ($161.5\pm 0.4\,$rad m-2 and $173.5\pm 7.2\,$rad m-2) and FRB
20220310F ($10.1\pm 0.6\,$rad m-2 and $13.7\pm 1.2\,$rad m-2), respectively.
Figures 21-24 in Appendix M show the evolution of detected RM across across
all four Multi-Component FRBs. No RM was detected for any but the strongest
sub-component of FRB 20220418A, and intra-component RM variations were not
observed for any other DSA-110 FRB. This effect is commonly observed in the
APs of radio pulsars when sufficient S/N is available (Ilie et al., 2019),
with magnitudes up to several tens of rad m-2, and is attributed to
propagation effects in pulsar magnetospheres (e.g., Yang et al., 2023, Section
4.3). Similar propagation effects, if responsible for the RM variations we
observe, may also be responsible for the multiple emission components as we
only observe these effects (and significant variations in polarization state)
for the FRBs that exhibit sub-components.

##  4 Comparisons

The polarization properties of FRBs provide insight into the nature of FRB
emission and FRB sources, as has been the case for pulsars. We therefore
present comparisons between the polarization properties of FRB sub-samples,
and between FRBs and Galactic pulsars, to search for similarities and
differences. Although emission from FRBs and pulsars is vastly different in
energy scale (e.g., Nimmo et al., 2021), common propagation effects in
magnetospheres and near-source environments may impact the polarization
properties. We augment the DSA-110 FRB sample with a literature sample of 38
FRB sources with polarization data, described in detail in Appendix A. The
literature sample includes 19 repeating sources, for which we use the weighted
mean of polarization measurements for the linear and circular fractions. When
available, we use polarization measurements at L-band (1-2 GHz) for the
literature sample in order to compare with the DSA-110 sample. A minimum
$\rm{S/N}>8\sigma$ is imposed on the literature sample of FRBs. For additional
details, see Appendix A. The DSA-110 sample thus more than doubles the total
number of non-repeating FRBs with polarization measurements. In Section 4.1 we
compare properties of different FRB sub-samples, and assess any frequency
dependent or other selection effects. We then compare FRB polarization
properties with those of various subsets of the Galactic pulsar population in
Section 4.2.

###  4.1 Comparison between FRB sub-samples

Figure 5: Comparison between the linear- and circular-polarization fractions
of various FRB sub-samples. The top and right panels show empirical cumulative
distribution functions (CDFs) for the DSA-110 sample (pink), published non-
repeaters (brown), published repeaters (purple), and FRBs with measurements
only at $<1$ GHz (green). Arrows indicate upper limits in $|V/I|$ estimated
from the measured values of $L/I$. See Appendix A for a summary of the
literature data. In general, no significant differences between sub-samples
are found.

In Figure 5 we compare the distributions of various FRB sub-samples in $L/I$
and $|V|/I$. We consider the DSA-110 sample of 25 so far non-repeating events,
along with published repeaters and non-repeaters, and measurements below 1
GHz. The literature sample contains 17 non-repeaters and 9 repeaters with
polarization measurements at L-band (1 - 2 GHz), while there are 10 repeaters
and 1 non-repeater with measurements only at lower frequencies ($<1$ GHz). 6
repeaters have measurements at multiple frequencies, for which we use the
L-band observations where available. 16 non-repeaters (1 below 1 GHz) and 8
repeaters (1 below 1 GHz) in the literature sample have circular polarization
measurements. Kolmogorov-Smirnov (K-S) and Anderson-Darling (A-D) tests at 90%
confidence (p-values below 10% reject the null hypothesis that the samples are
drawn from the same distribution) reveal no significant differences in the
distributions of DSA-110 and other FRBs in $L/I$. This holds when comparing
with both previously published repeaters and non-repeaters, which themselves
have no evident differences. We acknowledge however that this test is
incomplete, and biases due to the resolution, sky coverage, and bandwidth of
the DSA-110 survey may still exist. Further exploration of this however is
outside the scope of this work, and we proceed on the assumption that such
biases are negligible given the consistency of the DSA-110 sample with the
published sample of FRBs.

A more detailed discussion is required to properly compare circular
polarization. The circular polarization fraction can be defined either by
averaging over the signed Stokes V fraction, $V/I$, or by taking the absolute
value of Stokes V before averaging, $|V|/I$. The former preserves the sign
(handedness) of circular polarization but neglects any significant sign
changes across the burst. The latter accounts for sign changes, but introduces
a bias which is not well-constrained. We provide both values for the DSA-110
bursts in Table 2, but most published FRBs use only $V/I$ (e.g., Hilmarsson et
al., 2021a; Cho et al., 2020). Therefore, we proceed by using $V/I$ so that
the sample is consistent, taking the absolute value ($|V/I|$) so that the
already small sample is not further split by sign. With this definition, we
find no significant difference when comparing the distribution of circular
polarization of DSA-110 FRBs to previously detected non-repeaters. However, it
is encouraged for future polarization surveys to report both $V/I$ and
$|V|/I$, as the latter is a more accurate representation of the magnitude of
circular polarization. Furthermore, $V/I$ and $|V|/I$ cannot be accurately
compared due to the bias in $|V|/I$. For example, using $|V|/I$ for the
DSA-110 sample and $|V/I|$ for the published sample, we find significant
difference between the populations with p-value $1.2\%$. We conclude that the
DSA-110 sample is not biased in its polarization properties with respect to
published FRBs, and that polarization fractions do not appear to be a viable
means of distinguishing repeaters and non-repeaters (see also Qu & Zhang,
2023).

We compare the sample of FRBs with polarization data at L-band to those
measured at lower frequencies. No significant difference is found. This may
suggest that other effects besides frequency-dependent stochastic RM
depolarization (Feng et al., 2022b; Mckinven et al., 2023) generally determine
the polarization properties of the FRB population at different frequencies.
Alternatively, if stochastic RM depolarization is dominant, this may imply
that FRB progenitors can inhabit a wide variety of turbulent magneto-ionic
environments. However, more robust conclusions would require a careful
dissection of the population, for example into repeaters and non-repeaters;
only two of the literature FRBs with polarization data reported below 1 GHz
are apparent non-repeaters. We further note this method is primarily effective
in characterizing the frequency-dependence of non-repeaters and repeaters
detected in only one frequency band by analyzing the population as a whole.
Feng et al. (2022b) and Mckinven et al. (2023) provide more detailed analyses
of individual repeaters with measurements at multiple frequencies. For the
remainder of the paper, we restrict the sample to the 18 non-repeaters and 9
repeaters with L-band polarization measurements.

###  4.2 Comparison between FRBs and pulsars

Figure 6: Comparison between the linear- and circular- polarization fractions
of FRBs, pulsar APs, and RRATs. Top: FRBs (grey) are observed to have much
higher linear-polarization fractions than MSPs (blue), CPs (orange) and RRATs
(gold). Arrows indicate upper limits in $|V/I|$ estimated from the measured
values of $L/I$. Somewhat higher circular-polarization fractions are also
observed for FRBs. Bottom: We compare FRBs with canonical pulsars ($P>30$ ms)
with various characteristic ages. Young pulsars (blue) have remarkable
similarity to FRBs (grey) in linear polarization, while older pulsars (orange,
green) are more depolarized.

We next compare the linear- and circular-polarization fractions of FRBs with
the Galactic and Magellanic-Cloud pulsar populations. We include RRATs, noting
that no circular polarization data are available for RRATs at the time of
writing. Radio-loud magnetars are also included, and are grouped with
Canonical Pulsars (CPs, $P>30\,$ms) where necessary. We also consider both
average-profile (AP) and single-pulse (SP) polarization fractions of pulsars.

Although the polarization properties of APs across the $P-\dot{P}$ diagram are
well characterized (see Appendix A for a summary of existing observations),
only a few SP polarization studies of substantial pulsar samples exist (e.g.,
Manchester et al., 1975; Stinebring et al., 1984; Mitra et al., 2016, 2023).
Among the non-recycled pulsar population, significant trends in SP and AP
polarization are observed with the spin-down energy loss rate, $\dot{E}$. For
high-$\dot{E}$ pulsars, both SPs and APs typically exhibit high polarization
fractions, and valid rotating vector model (RVM; Radhakrishnan & Cooke, 1969)
fits can sometimes even be made to SPs. For lower-$\dot{E}$ pulsars, while SP
polarization fractions remain high, AP polarization fractions decrease. The
depolarization can have multiple causes: for example, a wider variance of
polarization states of SPs, and SPs clustering into orthogonally polarized
modes. These trends are driven by $L/I$; $|V|/I$ remains consistent with
$\dot{E}$ and between SPs and APs. Here we compare the FRB polarization
fractions to a collation of AP polarization fractions obtained around 1.4 GHz
from the literature, and to the polarization fractions of SPs obtained with
the Meterwavelength Single-pulse Polarimetric Emission Survey (MSPES) at 333
MHz and 618 MHz. The results are shown in Figures 6 and 7.

The distributions of polarization fractions of FRBs are largely dissimilar to
those of pulsars. Pulsar APs and RRATs show characteristically smaller linear
and circular polarization fractions than the FRB sample, both repeaters and
non-repeaters. Of the 9 L-band repeaters we consider, only two have small
($\lesssim 30\%$) $L/I$, and the remainder have large ($\gtrsim 70\%$) $L/I$.
Non-repeating FRBs have similar $L/I$ and somewhat lower $|V/I|$ than
repeaters, though small number statistics may limit concrete statements
regarding repeaters. Although RRATs have slightly higher $L/I$ than pulsar
APs, this difference is marginal in comparison to the FRB-AP difference. A KS
test indicates that repeating FRBs, unlike the non-repeaters, are not
significantly different from CPs in $|V/I|$. Although interpretation of this
is limited by small-number statistics with only 7 repeaters with $|V/I|$
measurements.

Remarkably, FRBs (in particular non-repeating sources) have similar
distributions of $L/I$ and $|V|/I$ to the youngest (characteristic ages
$\tau_{c}<10^{5}$ yr) pulsar APs. The polarization properties of young,
high-$\dot{E}$ pulsars are known to be drastically different to the remainder
of the pulsar population (Weltevrede & Johnston, 2008), with high $L/I$, a
lack of jumps in polarization position-angle and orthogonally polarized modes,
and a close similarity between typical-SP and AP polarization profiles. The
lack of depolarization in young pulsars is attributed to either magnetospheric
propagation effects that cause only one of the modes (likely the $O$-mode) to
be observed, or to the dominance of curvature radiation at high $\dot{E}$
(resulting in $\gamma$-ray emission) that may change the radio emission
mechanism. Young pulsars, with emission likely from high in the magnetosphere
(Ravi et al., 2010), may prove to be useful analogs for the production of FRB
radiation even if the specific radio emission mechanisms differ. As an
example, we refer the reader to recent work by Lin et al. (2023) on the
importance of both extreme emission heights and relativistic motion in giant
pulses emitted by the Crab pulsar.

Finally, we find that the MSPES SP distributions of $L/I$ and $|V/I|$ are not
consistent with the FRB distributions. The SP linear-polarization fractions
are clustered around $\sim 60\%$, whereas the FRBs span a wider range of
$L/I$. The SPs typically exhibit slightly higher values of $|V/I|$ than FRBs.
The MSPES sample only contains seven SP measurements for $\dot{E}>10^{34}$ erg
s-1, a threshold above which significant polarization changes are observed.

Figure 7: Comparison between the linear- and circular- polarization fractions
of FRBs with pulsar single pulses (SPs). Pulsar SPs (red) have similar average
linear polarization fraction ($\sim 60\%$), but cover a narrower range than
FRBs (grey). Arrows indicate upper limits in $|V/I|$ estimated from the
measured values of $L/I$.

##  5 Conclusions

We present a full-polarization analysis of the first 25 as yet non-repeating
FRBs detected at 1.4 GHz with the DSA-110. This analysis includes a detailed
description of data reduction and calibration for full-Stokes high time
resolution data. We detect RMs for 20 FRBs, with magnitudes in the range
$4-4670$ rad m-2. We propose a classification according to polarization, S/N,
and temporal properties. $15/25$ DSA-110 FRBs are labeled as Consistent with
100% Polarization, $3/25$ are labeled Consistent with 0% Polarization, $5/25$
are Intermediate, and $2/25$ have Unconstrained polarization properties due to
their low S/N. Four FRBs that show multiple components on millisecond
timescales are also unique in showing time-variable polarization properties,
including RM.

We combine the DSA-110 sample with polarization measurements of previously
published FRBs, and compare FRB sub-samples and FRBs with Galactic pulsars. We
find no significant differences in the distributions of $L/I$ and $|V/I|$
between the DSA-110 sample and the published samples; neither is there a
significant difference between the repeater and non-repeater samples. We find
that FRBs are typically far more polarized than the average profiles of
pulsars and span a wider range in polarization fractions than pulsar single
pulses, which makes them remarkably similar to young (characteristic ages
$<10^{5}$ yr) pulsars.

We conclude the following.

  1. 1.

The substantial fraction of highly linearly polarized FRBs ($15/25$ in the
DSA-110 sample are Consistent with 100% and have $L/I>50\%$) suggests that the
FRB emission mechanism is often intrinsically linearly polarized. In the full
DSA-110 sample, statistically significant variations in PPA are observed in
$3/25$ events ($2/13$ Consistent with 100% events). This suggests modulation
in some cases caused by a rapidly moving / rotating emission region.

  2. 2.

Bursts with temporally separated components have variable polarization
properties between the components. Of the $4/25$ such DSA-110 events, three
have variable linear-polarization PPAs and fractions, two have variable signs
and magnitudes of Stokes V, and three exhibit evidence for time-variable RMs.
Together this suggests that the emission sites responsible for the different
components originate from different regions of a magnetosphere, and are
potentially viewed along different sightlines through magnetized plasma.

  3. 3.

The origins of circular polarization and depolarization in FRBs remain
mysterious. Faraday conversion in a highly magnetized near-source medium could
explain the observed $|V|/I$ fractions. We disfavor bandwidth depolarization,
RM scattering, and Faraday conversion as dominant depolarization mechanisms.
We therefore have little evidence from polarimetry alone for the generic
presence of dense, highly magnetized, inhomogeneous near-source plasma
environments. Depolarization due to the superposition of multiple short bursts
is possible.

  4. 4.

The strong similarity between the $L/I$ distributions of FRBs and the average
profiles (and likely also single pulses) of the youngest pulsars suggests that
the radio emission from young pulsars may form a useful analog to probe at
least the depolarization mechanisms of FRBs. We note that the abrupt jump in
PA observed in FRB 20220207C and the near-orthogonal positions on the Poincaré
sphere of the two components of FRB 20220310F are uncommon for young pulsars.

Polarization studies have great promise in identifying characteristics of FRB
emission that may prove useful in testing emission-mechanism and progenitor
models. At present, intrinsic emission-mechanism models favor high linear-
polarization fractions, thus ascribing all other properties to propagation
effects. In the future, studying FRB polarization properties in the context of
other diagnostics of near-source environments, e.g., from accurate
localizations, may be used to distinguish between intrinsic and extrinsic
effects. At this point, we urge the further theoretical consideration of the
intrinsic timescale(s) of FRB emission, and the causes of intrinsic
depolarization. First, several of the DSA-110 FRBs are remarkably simple: the
sample is characterized ($21/25$ events) by single emission components that
are several tenths of a millisecond wide, with flat PPAs, and a wide range of
linear-polarization fractions. We suggest that depolarization is likely
intrinsic to the emission rather than a propagation effect; thus, the prospect
of superposing several shorter bursts needs to be considered. At the same
time, the existence of highly linearly polarized FRBs with flat PPAs over
approx. millisecond timescales also requires an explanation. While not
explored in this work, the scattering of FRBs over millisecond durations could
be an alternate cause of flat PPAs. Third, our finding that multiple
temporally separated emission components on approx. millisecond timescales
tend to have different polarization properties poses an interesting additional
challenge.

The authors would like to thank Jim Cordes, Dongzhi Li, Bing Zhang, Yuanhong
Qu, Joel Weisberg, and Alexandra Mannings, for insightful and essential
conversations on polarization theory and direction on the analysis conducted,
as well as Paul Bellan and Yang Zhang for a comprehensive Plasma Physics
course. We also thank Yi Feng, Dipanjan Mitra, Yuan-Pei Yang, Dylan Nelson,
Reshma Anna-Thomas, and an anonymous referee for useful comments and
recommendations on the early draft. This material is based upon work supported
by the National Science Foundation Graduate Research Fellowship under Grant
No. DGE‐1745301. The authors thank staff members of the Owens Valley Radio
Observatory and the Caltech radio group, including Kristen Bernasconi,
Stephanie Cha-Ramos, Sarah Harnach, Tom Klinefelter, Lori McGraw, Corey
Posner, Andres Rizo, Michael Virgin, Scott White, and Thomas Zentmyer. Their
tireless efforts were instrumental to the success of the DSA-110. The DSA-110
is supported by the National Science Foundation Mid-Scale Innovations Program
in Astronomical Sciences (MSIP) under grant AST-1836018.

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##  Appendix A Literature samples of polarization observations of FRBs and
pulsars

Previous analyses have yielded either RM or polarization measurements for at
least 38 FRBs at time of writing; this sample was compiled using the Transient
Name Server121212https://www.wis-tns.org/ (TNS), the FRB
Catalog131313https://www.frbcat.org/ (FRBcat), and the Canadian Hydrogen
Intensity Mapping Experiment (CHIME) FRB Catalog 1141414https://www.chime-
frb.ca/catalog Petroff & Yaron (2020), (Petroff et al., 2016; Amiri et al.,
2021). FRB polarization is often reported without uncertainties due to low
resolution or low S/N that makes constraining the polarization difficult. In
addition there is no standard method of computing the polarization fraction
due to the wide range of morphologies in FRBs, and this should be held in mind
when comparing polarimetry from multiple surveys. The FRBs in the literature
sample compiled here were detected through the Apertif survey with the
Westerbork Synthesis Radio Telescope (WSRT) and the Australian Square
Kilometer Array Pathfinder (ASKAP) survey, as well as observations with the
Parkes Telescope, CHIME, Green Bank Telescope, and Arecibo Observatory. Recent
studies have observed frequency-dependent de-polarization thought to be the
result of stochastic RM variations within a scattering screen (Feng et al.,
2022b; Mckinven et al., 2023). A subset of 11 FRBs in this sample have
polarization measurements at lower ($<1$ GHz) frequencies.

Table 4 summarizes the polarization properties of each burst from the
literature. Of the 38 bursts, 19 are repeaters, 34 have RM measurements, 15
have spectroscopic or photometric redshift measurements (9 repeaters, 6 non-
repeaters), 25 have reported L-band linear polarization measurements, 11 have
linear polarization measurements below 1 GHz, and 26 have reported circular
polarization measurements. Below we describe the selection criteria and
process for the FRB RMs used here:

  1. 1.

Only RM measurements published before a 2023 April 10 cutoff date are
considered for this sample.

  2. 2.

For non-repeaters and repeaters with only 1 RM measurement, we use the
available measurement.

  3. 3.

For FRBs with RM measurements in the TNS or FRBcat databases, we defer to the
catalogued value to maximize sample consistency.

  4. 4.

For repeaters with multiple RM measurements, we use the weighted mean, with
the reciprocal of the errors as weights.

We make three exceptions based on the observed RM behavior:

  * •

FRB 20190208A shows a secular evolution in RM which follows a ‘U’ shaped curve
(Mckinven et al., 2023). Therefore, we use the most recent RM value rather
than the weighted mean.

  * •

FRB 20190231B has multiple RM measurements from Mckinven et al. (2023);
however, CHIME reports difficulty in distinguishing RM detections near 0 from
instrumental leakage. Therefore, we use the RM measurement with the lowest
uncertainty to minimize propagation of any leakage errors.

  * •

FRB 20191117A has 2 RM measurements from Mckinven et al. (2023) separated by
$\sim 9\,$rad m-2, but it is unclear with only 2 bursts whether this variation
is stochastic or secular. Therefore, we use the value with the smallest error
to avoid improperly combining secularly evolved RMs.

We make three additional exceptions based on the conventions in the available
literature; in cases where RM measurements are commonly compared to a well-
constrained ‘accepted’ value which has not yet been superceded in accuracy, we
use this accepted value. This affects the following FRBs:

  * •

FRB 20121102A (e.g., Plavin et al., 2022; Michilli et al., 2018; Hilmarsson et
al., 2021b); the value from Plavin et al. (2022) is used as it pre-dates other
RM measurements and has a low relative error. However, since Sherman et al.
(2023) compares the logarithm of the RM, deviations of the RM within an order
of magnitude make little change to the analysis, and do not affect the
analysis in this paper at all.

  * •

FRB 20200120E (e.g., Bhardwaj et al., 2021; Nimmo et al., 2021); we use the
value from the first detected burst in Bhardwaj et al. (2021).

  * •

FRB 20201124A (e.g., Hilmarsson et al., 2021a; Kumar et al., 2022) we use the
weighted mean value from Hilmarsson et al. (2021a)

We acknowledge that these constraints are not complete; secularly time-varying
RMs are not properly represented either by the weighted mean or the value with
the lowest error. In addition, while the weighted mean incorporates the
signal-to-noise of individual bursts via the uncertainties, limitations due to
the intrinsic bandwidth of the FRB are not explicitly accounted for. We
proceed with our analysis, reasonably assuming that the reported RM’s
uncertainty properly quantifies the limitations of the measurement system. We
leave additional revisions for variable RMs to future work.

We furthermore describe the selection criteria and process for the FRB
polarization fractions used here:

  1. 1.

Only polarization measurements published before the 2023 April 10 cutoff date
are considered for this sample.

  2. 2.

For non-repeaters and repeaters with only 1 polarization fraction measurement,
we use the available measurement. If the polarization is reported for
individual sub-components of the same burst, we use the weighted mean of the
sub-components.

  3. 3.

A minimum signal-to-noise $S/N>8\sigma$ is imposed on all non-repeaters and
individual bursts from repeaters included in this sample.

  4. 4.

For FRBs with polarization measurements in the TNS or FRBcat databases, we
defer to the catalogued value to maximize sample consistency.

  5. 5.

For repeaters with multiple polarization measurements, we use the weighted
mean, with the reciprocal of the errors as weights. If measurements are
available at multiple frequencies, we use the L-band (1-2 GHz) if available.
Otherwise, the observation with the nearest frequency below 1 GHz.

  6. 6.

If only the signed circular polarization ($V/I$) is reported, then the
absolute value circular polarization ($|V|/I$) is taken as the absolute value
($|V/I|$) (for further details, see Section 4). We make this condition given
that most FRBs in the literature were reported with no $|V|/I$ measurement. If
both $L/I$ and $V/I$ are reported but the total polarization
$\sqrt{L^{2}+V^{2}}/I$ is not explicitly stated, the total polarization is
calculated as $\sqrt{(L/I)^{2}+(V/I)^{2}}$.

Expanding on criteria 3, the minimum $S/N>8\sigma$ applies both to non-
repeaters and to the individual bursts of repeaters included in the reported
weighted average polarization fractions. Many studies fail to report the S/N
of FRB detections (e.g. Feng et al., 2022b, a). In these cases, we estimate
the S/N as the reported flux density $S$ divided by the radiometer noise RMS
$\sigma_{S}$ of the detector (e.g. Condon & Ransom, 2016). If neither the S/N
nor $S$ are reported, we have chosen to include the FRB in our sample under
the assumption that a reasonable detection threshold was used in the original
survey.

As noted above, these selection criteria are not complete, as the weighted
mean does not fully capture secularly time-varying polarization properties. We
maintain the average FRB polarization fractions are sufficient for the
cumulative distribution analysis presented here, and leave a fully time-
dependent study to future work.

In the main text, we compare FRB properties to a sample of 1445 Galactic (and
Magellanic Cloud) pulsars with published polarimetry of APs: 1305 canonical
pulsars (CPs) with periods $P>30\,$ms, 137 millisecond pulsars (MSPs,) with
periods $P<30\,$ms, and 3 magnetars and 22 RRATs with published polarization
or RM data at L-band. These are compiled from Johnston et al. (2022), Serylak
et al. (2021), Wahl et al. (2022), Spiewak et al. (2022), Cameron et al.
(2020), Olszanski et al. (2019), Weisberg et al. (1999), Weisberg et al.
(1999), Johnston & Kerr (2018), Yan et al. (2011), Gould & Lyne (1998), Kramer
et al. (2007), Camilo et al. (2007), Camilo et al. (2008), Levin et al.
(2012), Levin et al. (2010), Keane et al. (2011), Caleb et al. (2019),
Karastergiou et al. (2009), Xie et al. (2022). We use the following criteria
and process for selecting the pulsar polarimetry and RM data:

  1. 1.

Only polarization measurements published before the 2023 April 10 cutoff date
are considered for this sample.

  2. 2.

For each pulsar, we use the polarization fractions from the average profiles
(APs) (except for the MSPES single-pulse sample discussed in Section 4).

  3. 3.

Most pulsars are published with both $|V|/I$ and $V/I$; we record both values
and use the absolute value of $V/I$ for consistency as discussed in Section 4.

  4. 4.

If multiple RM or polarization fractions are reported, the most recent
measurement is used.

We note here that, as for the FRB literature sample, these criteria are not
complete, as they do not capture time-varying RMs or polarization fractions in
pulsars. A weighted average of measurements is not used for pulsars given the
large amount of available data. Additionally, the most recent average profile
is more well-constrained, and using average profile polarization fractions
consistent the current literature on pulsar polarimetry. The average profile
polarization fractions are sufficient for the analysis presented in this work,
and we leave a fully time-dependent discussion to future work.

Table 4: Previously Published FRB Sample Polarization Properties

FRB Names |  | Polarization
---
Telescope/
Frequency
$\mathbf{L/I}$ | $\mathbf{|V/I|}$ |  | Polarization
---
Reference
| $\rm\mathbf{RM}$
---
$\rm\mathbf{(rad\,m^{-2})}$
| RM
---
Reference
| $\rm\mathbf{DM}^{\ddagger}$
---
$\rm\mathbf{(pc\,cm^{-3})}$
FRB 20201020A | Apertif/1375.0 | – | – | – | $110.0\pm 69.0$ | 1 | $398.59\pm 0.08$
FRB 20191108A | Apertif/1375.0 | $70.0\%$ | $10.0\%$ | 2 | $474.0\pm 3.0$ | 3 | $588.1\pm 0.1$
FRB 20190711A | ASKAP/1297.5 |  $97.48\pm 1.39\%$† |  $0.96\pm 1.15\%$ † | 4 | $9.0\pm 2.0$ | 4 | $593.1\pm 0.4$
FRB 20190611B | ASKAP/1297.5 |  $81.5\pm 2.1\%$† |  $31.8\pm 1.7\%$† | 4 | $20.0\pm 4.0$ | 4 | $321.4\pm 0.2$
FRB 20190608B | ASKAP/1297.5 | $91.0\pm 3.0\%$ | $9.0\pm 2.0\%$ | 4 | $353.0\pm 2.0$ | 4 | $338.7\pm 0.5$
FRB 20181112A | ASKAP/1297.5 | $90.0\%$ | $10.0\%$ | 5 | $10.9\pm 0.9$ | 5 | $589.27\pm 0.03$
FRB 20180924B | ASKAP/1297.5 | $90.2\pm 2.0\%$ | $13.3\pm 1.4\%$ | 4 | $14.0\pm 1.0$ | 6 | $361.42\pm 0.06$
FRB 20180311A | Parkes/1382.0 | $75.0\pm 3.0\%$ | $11.0\pm 2.0\%$ | 7 | $4.8\pm 7.3$ | 7 | $1570.9\pm 0.5$
FRB 20171209A | Parkes/1382.0 | $100.0\pm 1.0\%$ | $0.0\pm 1.0\%$ | 7 | $121.6\pm 4.2$ | 7 | $1457.4\pm 0.03$
FRB 20150807A | Parkes/1382.0 | $80.0\pm 1.0\%$ | – | 8 | $12.0\pm 0.7$ | 8 | $226.5\pm 0.1$
FRB 20150418A | Parkes/1382.0 | $8.5\pm 1.5\%$ | $0.0\pm 4.5\%$ | 9 | $36.0\pm 52.0$ | 9 | $776.2\pm 0.5$
FRB 20150215A | Parkes/1382.0 | $43.0\pm 5.0\%$ | $3.0\pm 1.0\%$ | 10 | $1.5\pm 10.5$ | 10 | $1105.6\pm 0.8$
FRB 20190604A | CHIME/600.0 | $91.2\pm 8.1\%$ | – | 11 | $-20.0\pm 1.0$ | 12 | $553.18\pm 3.23$
FRB 20190303A | FAST/1250.0 |  $88.7\pm 7.7\%$† |  $3.7\pm 5.8\%$† | 13 | $-499.0\pm 0.7$ | 11 | $223.21\pm 3.23$
FRB 20190102C | ASKAP/1297.5 |  $81.14\pm 0.91\%$† |  $5.08\pm 0.66\%$† | 4 | $-110.0\pm 1.0$ | 14 | $363.6\pm 0.3$
FRB 20180916.J0158+65 | Effelsburg/1700.0 |  $102.1\pm 4.5\%$† |  $5.7\pm 4.4\%$† | 15 | $-114.6\pm 0.6$ | 16 | $347.76\pm 1.62$
FRB 20180714A | Parkes/1382.0 | $91.0\pm 3.0\%$ | $5.0\pm 2.0\%$ | 7 | $-25.9\pm 5.9$ | 7 | $1467.92\pm 0.3$
FRB 20160102A | Parkes/1382.0 | $84.0\pm 15.0\%$ | $30.0\pm 11.0\%$ | 17 | $-220.6\pm 6.4$ | 17 | $2596.1\pm 0.3$
FRB 20110523A | GBT/800.0 | $44.0\pm 3.0\%$ | $23.0\pm 30.0\%$ | 18 | $-186.1\pm 1.4$ | 18 | $623.3\pm 0.06$
FRB 20121102A |  | Effelsburg,
---
FAST/1700,1250.0
$13.0\pm 3.0\%$ |  $23.5\pm 0.6\%$ † | 19,20 | $127000.0\pm 800.0$ | 19 | $557\pm 2$
FRB 20191001A | ASKAP/1297.5 | $57.0\pm 1.0\%$ | $5.0\pm 1.0\%$ | 21 | $55.5\pm 9.0$ | 21 | $506.92\pm 0.04$
FRB 20201124A |  | Effelsburg,
---
FAST/1360.0,1250.0
$86.21\pm 0.01\%$† |  $10.23\pm 0.01\%$† | 13,22,23,31 |  $-601.0\pm 11.1$† | 22 | $410.83\pm 3.23$
FRB 20180309A | Parkes/ 1382.0 | $45.56\pm 0.06\%$ | $24.33\pm 0.05\%$ | 7 | – | – | $263.42\pm 0.01$
FRB 20200120E | Effelsburg/1400.0 |  $99.3\pm 1.3\%$† |  $4.5\pm 0.9\%$† | 30 | $-29.8\pm 5.0$ | 24 | $88.96\pm 1.62$
FRB 20151230A | Parkes/1352.0 | $35.0\pm 13.0\%$ | $6.0\pm 11.0\%$ | 25 | – | – | $960.4\pm 0.5$
FRB 20140514A | Parkes/1352.0 | $0.0\%$ | $21.0\pm 7.0\%$ | 26 | – | – | $562.7\pm 0.6$
FRB 20190520B | GBT/1450.0 | $9.0\%$ |  $9.83\pm 0.68\%$ † | 27,20 |  $-11000.0\pm 13100.0$ † | 27 | $1202\pm 10$
FRB 20220912A | FAST/1400.0 |  $80.3\pm 24.3\%$† |  $5.2\pm 0.2\%$† | 28 | $0.6\pm 0.1$ | 29 | $219.46\pm 0.04$
FRB 20180814A | CHIME/600.0 | $69.1\pm 4.7\%$ | – | 11 | $699.8\pm 1.0$ | 11 | $190.86\pm 3.23$
FRB 20181030A | CHIME/600.0 |  $72.75\pm 2.22\%$† | – | 11 |  $36.6\pm 0.2$† | 11 | $101.9\pm 1.62$
FRB 20181119A | CHIME/600.0 |  $67.58\pm 2.76\%$† | – | 11 |  $1340.0\pm 2.0$ † | 11 | $368.79\pm 6.47$
FRB 20190222A | CHIME/600.0 | $24.61\pm 0.58\%$ | – | 11 | $571.0\pm 1.7$ | 11 | $462.6\pm 3.23$
FRB 20190208A | CHIME/600.0 |  $86.52\pm 1.03\%$ † | – | 11 | $36.3\pm 0.7$ | 11 | $579.06\pm 3.23$
FRB 20190213B | CHIME/600.0 |  $90.19\pm 2.68\%$ † | – | 11 | $-3.63\pm 0.41$ | 11 | $302.47\pm 1.62$
FRB 20180908B | CHIME/600.0 | $0.0\%$ | – | 11 | $0.18$ | 11 | $197.33\pm 3.23$
FRB 20190117A | CHIME/600.0 |  $19.44\pm 0.40\%$† | – | 11 | $76.31\pm 0.40$ | 11 | $393.05\pm 1.62$
FRB 20190417A | FAST/1250.0 | $71.5\pm 2.5\%$ | $11.7\pm 2.0\%$ | 13 | $4429.8\pm 3.5$ | 11 | $1378.11\pm 6.47$
FRB 20190907A | CHIME/600.0 | $28.0\%$ | – | 11 | – | – | $307.32\pm 3.23$

Notes: Observation and polarization information for the compiled sample of
previously published FRBs. The telescope and system observing frequency are
those used for the polarization measurements. Names in boldface are repeaters,
while non-boldfaced FRBs are non-repeating as of April 10th, 2023. For FRB
20220912A, the RM is that reported by CHIME while the polarization was
measured from the DSA-110 detections. For repeaters with multiple RM or
polarization measurements, values are the weighted average of observations.
The sample was compiled with the use of the Transient Name Server (TNS), the
FRB Catalog (FRBcat), and the Canadian Hydrogen Intensity Mapping Experiment
(CHIME) FRB Catalog 1 (Petroff & Yaron (2020), Petroff et al. (2016), Amiri et
al. (2021)). FRB 20180301 was excluded from this literature sample due to its
inconsistent RM and L-band polarization properties, which are not accurately
described by average values (Luo et al., 2020; Kumar et al., 2023). While
Zhang et al. (2023) and Anna-Thomas et al. (2023a) (a later version of Anna-
Thomas et al. (2023b)) presented additional polarization data, they were
released after the data cutoff date and are excluded from this sample.

†Weighted mean of multiple bursts; ‡DM values are from the TNS catalog

Citations are listed below: (1)Pastor-Marazuela et al. (2022) (2)Connor et al.
(2020) (3)van Leeuwen et al. (2022) (4)Day et al. (2020) (5)Prochaska et al.
(2019) (6)Bannister et al. (2019) (7)Osłowski et al. (2019) (8)Ravi et al.
(2016) (9)Keane et al. (2016) (10)Petroff et al. (2017) (11)Mckinven et al.
(2023) (12)Fonseca et al. (2020) (13)Feng et al. (2022b) (14)Macquart et al.
(2020) (15)Nimmo et al. (2021) (16)Andersen et al. (2019) (17)Caleb et al.
(2018) (18)Masui et al. (2015) (19)Plavin et al. (2022) (20)Feng et al.
(2022a) (21)Bhandari et al. (2020) (22)Hilmarsson et al. (2021a) (23)Jiang et
al. (2022) (24)Bhardwaj et al. (2021) (25)Bhandari et al. (2018) (26)Petroff
et al. (2015) (27)Anna-Thomas et al. (2023b) (28)Ravi et al. (2023)
(29)McKinven & Chime/Frb Collaboration (2022) (30)Nimmo et al. (2022) (31)Xu
et al. (2022)

##  Appendix B DSA-110 voltage data model and polarization processing

All polarization analysis of DSA-110 FRBs detected during the commissioning
observations reported on herein, and the calibration of these data, are
accomplished using automatically triggered voltage dumps. This refers to the
storage of 61440 contiguous post-channelization complex (i.e., undetected)
spectra for each antenna, with a time-resolution of 32.768 $\mathrm{\mu}$s.
The spectra consist of voltage measurements in two polarization channels for
each of 63 antennas, in 6144 channels of 30.52 kHz width centered on 1405 MHz.
Each complex sample is stored with 4-bit resolution for the real and imaginary
parts. The four most significant bits are chosen using channel-dependent
coefficients determined from the mean bandpass shapes of each
antenna/polarization pair. For FRB data, the triggers are generated such that
the arrival times of the bursts at 1498.75 MHz (the upper limit of the sampled
band) correspond to exactly 0.5 s into the voltage dumps. Each voltage dump is
stored in raw binary format, and is accompanied by a json header that includes
all relevant descriptive information.

The voltage dumps are processed using a custom full-polarization beamforming
pipeline (dsa110-bbproc). Post-correlation beamforming is implemented (Roy et
al., 2018) with the addition of both auto- and cross-correlation terms to
mitigate quantization noise in applying per-antenna beamforming weights. For
FRB data, the weights are determined from visibility data on bright bandpass
calibrators typically within 12 hr of detection. For voltage dumps on the
continuum-source calibrators 3C48 and 3C286, the weights are determined from
visibility data on the calibrators themselves. Ultimately, filterbank-format
files are generated for each Stokes parameter by synthesizing beams in the
directions of interest for each voltage dump. The polarization and Faraday-
rotation definitions adopted here are summarized in Appendix C.

The dsa110-pol module was developed to calculate FRB polarization and RM
parameters offline from the polarized filterbank data. Major processing steps
are as follows:

  1. 1.

Polarimetric calibration is applied using the formalism described in Appendix
D. The stability of the calibration solutions is justified in Appendix E, and
critical assumptions on leakage are justified in Appendix F.

  2. 2.

Full-polarization spectra for each FRB are generated by optimally averaging
over the burst temporal profiles (Appendix H).

  3. 3.

RM estimation then proceeds on these spectra as described in Appendix I. If a
significant RM is detected, the Stokes parameters are corrected for this RM.

  4. 4.

Then, the total ($T$), linear ($L$) and circular ($C$) polarization spectra,
as well as polarization position angle ($\chi$) are computed. The average
polarization fractions, referred to as $L/I$, $|V|/I$ and
$\sqrt{L^{2}+V^{2}}/I$, are calculated as the weighted mean of $L_{\rm
unbias}(t)/I(t)$, $C(t)/I(t)$, and $T(t)/I(t)$ across the FWHM of the burst
using the optimal weights (Appendix H). In addition, the sign-dependent
circular polarization fraction $V/I$ is computed as the weighted mean of
$V(t)/I(t)$ across the burst. The mean position angle $\chi$ is calculated
with a similar weighted mean across the FWHM.

##  Appendix C Polarization and Faraday Rotation Background

The polarization of light is defined by the correlation properties of
components of the propagating electric field. In a linear basis, where $V_{A}$
and $V_{B}$ refer to orthogonal linear components of the electric field, the
Stokes parameters are one representation of the polarization state:

$I=\frac{1}{2}(<V_{A}V^{*}_{A}>+<V_{B}V^{*}_{B}>)$ (C1)

$Q=\frac{1}{2}(<V_{A}V^{*}_{A}>-<V_{B}V^{*}_{B}>)$ (C2)

$U={\rm Re}\\{<V_{A}V^{*}_{B}>\\}$ (C3)

$V=-{\rm Im}\\{<V_{A}V^{*}_{B}>\\}$ (C4)

The DSA-110 uses the IAU/IEEE convention that $V>0$ is right-hand
polarization, while $V<0$ is left-hand polarization (Van Straten et al.,
2010). The linear, circular, and total polarization fractions as a function of
time are computed as:

$\frac{L_{\rm
unbias}(t)}{I(t)}=\begin{cases}\sqrt{L(t)^{2}-\sigma^{2}}/I(t),\text{ for
}\frac{L(t)}{\sigma}>1\\\ 0\text{, o/w}\\\ \end{cases}$ (C5)

$\frac{C(t)}{I(t)}=\sqrt{V(t)^{2}}/I(t)$ (C6) $\frac{T(t)}{I(t)}=\sqrt{L_{\rm
unbias}(t)+V(t)^{2}}/I(t)$ (C7)

where $L_{\rm unbias}(t)$ is the unbiased linear polarization following
Simmons & Stewart (1985) and Everett & Weisberg (2001), and
$L(t)=\sqrt{Q(t)^{2}+U(t)^{2}}$ 151515Note we adopt the convention used in
equations 10 and 16 of Simmons & Stewart (1985) due to ambiguity in the
unbiasing factor reported in Everett & Weisberg (2001).. These are averaged
across a burst to estimate the average polarization fractions. For all
sources, $T\leq I$; in unpolarized sources, $T=0$. In partially polarized
sources, $T=pI<I$, where $p$ is the polarization fraction. Finally, the
position angle $\chi$ defines the phase difference between linearly polarized
components:

$\chi=0.5\tan^{-1}(\frac{U}{Q})=0.5\angle P$ (C8)

where $P=Q+iU$ is the linear polarization vector. Errors in the position angle
are estimated using a Monte Carlo simulation of 100 boxcar pulses with
$\chi=0$ and unity off-pulse standard deviation. The resulting error as a
function of linear-polarization S/N is well-fit by a piecewise exponential
with scale $28\sigma$ for $S/N>19\sigma$, and $10\sigma$ for $S/N\leq
19\sigma$. Figure 8 shows the results of the simulation and best fit piecewise
exponential; note these results imply that the Naghizadeh-Khouei & Clarke
(1993) PA distribution significantly under-estimates the error, particularly
for $S/N>6\sigma$.

Figure 8: Simulated error in the linear polarization position angle (PA), as a
function of linear-polarization S/N. See text for details of the simulation.
The simulated error (blue) is taken as the standard deviation of the PA across
the width of each boxcar pulse. The red lines indicate the piecewise
exponential fit of the simulated error, while the red markers show the
resulting error for each trial when computed using the fit. The error derived
from the PA distribution of Naghizadeh-Khouei & Clarke (1993), shown in
orange, appears to underestimate the error, especially at high S/N.

A different dispersion relation applies to orthogonal circularly polarized
components for propagation through a plasma-filled region with a magnetic
field, resulting in a rotation of the position angle of linearly polarized
radiation. The position angle changes as a function of squared wavelength such
that the RM is defined as:

${\rm RM}=\frac{d\chi}{d\lambda^{2}}$ (C9)

The RM characterizes the integrated line of sight magnetic field
$\bar{B}_{||}$ that induces this rotation, weighted by the plasma electron
number density $n_{e}$:

${\rm RM}=0.81\int\frac{n_{e}B_{||}}{(1+z(l))^{2}}dl$ (C10)

where $z$ is the redshift of the dispersive material. Note that the $\bar{}$
indicates the field is averaged over the line-of-sight. In general, the RM has
contributions from an FRB’s host galaxy, the intergalactic medium (IGM), the
Milky Way’s circumgalactic medium (CGM) and interstellar medium (ISM), and the
Earth’s ionosphere due to the magnetic fields in these regions. This can, in
addition to changing the magnitude of the RM, change the sign due to the
direction dependence of the magnetic field. If the same plasma is assumed to
contribute to both dispersion and RM:

${\rm DM}=\int_{l}^{0}\frac{n_{e}}{1+z(l)}dl$ (C11)

the average line-of-sight magnetic field can be estimated as:

$\bar{B}_{||}[\mu{\rm G}]\approx\frac{\rm RM}{0.81\cdot{\rm DM}}(1+z)$ (C12)

Recent analyses imply a correlation between host RM (RM with contributions
from the ionosphere, ISM, and IGM subtracted) and DM, implying that this
approximation is reasonable (Mannings et al., 2022). We refer to position
angle after correcting for RM is as the polarization position angle (PPA;
$\chi_{0}$), while PA, or $\chi$, refer to the position angle measured without
RM correction.

##  Appendix D Derivation of Jones Matrix and Parallactic Angle Calibration
for DSA-110

An effective Jones matrix for the coherently combined DSA-110 must be used to
calibrate polarized observations, as described by, e.g., Robishaw & Heiles
(2021). Calibration with a fully-defined Jones matrix accounts for cross-
coupling between the orthogonal linearly polarized receptors, as well as gain
and phase differences between the receptors (Heiles et al., 2001). Here we
will choose a Cartesian basis aligned with the linearly polarized receptors.
For the DSA-110, we operate in the ‘ideal feed’ assumption, that is, that
there is zero cross-coupling between receptors. This requires that differences
in gain or phase between the X and Y feeds are the dominant instrumental
effect, which results in mixing among Stokes parameters. A difference between
the X and Y gain will mix Stokes I and Q creating apparent linear
polarization. A difference in phase corresponds to a time delay $\Delta
t\approx\phi(\nu)(2\pi\nu)^{-1}$ between the X and Y feeds. This mixes Stokes
U and V and creates residual circular polarization. Quantitatively, for the
arbitrary Jones matrix below consisting of four complex terms:

$J(\nu)=\begin{bmatrix}g_{xx}(\nu)&g_{xy}(\nu)\\\
g_{yx}(\nu)&g_{yy}(\nu)\end{bmatrix}$ (D1)

we assume $|g_{xy}(\nu)|=|g_{yx}(\nu)|=0$. We further simplify this by
assuming $g_{yy}(\nu)$ is real and parameterize in terms of the absolute gain
in the Y receptor, $|g_{yy}(\nu)|$, the ratio of the magnitudes of X and Y
gains, $r(\nu)=|g_{xx}(\nu)|/|g_{yy}(\nu)|$, and the phase difference between
the X and Y receptors, $\phi(\nu)$. The Jones matrix is then simplified to:

$J(\nu)=\begin{bmatrix}r(\nu)|g_{yy}(\nu)|e^{i\phi(\nu)}&0\\\
0&|g_{yy}(\nu)|\end{bmatrix}$ (D2)

One can estimate $r$ by observing a known unpolarized source and assuming
$Q=U=V=0$. Similarly, one estimates $\phi$ by observing a known linearly
polarized source and assuming $V=0$. For DSA-110 observations, 3C48 was
periodically observed as the unpolarized calibrator to estimate $r(\nu)$,
while 3C286 was observed as the linearly polarized calibrator to estimate
$\phi(\nu)$. Given the fixed declination (71.6∘) of the DSA-110 commissioning
survey, the affect of sky position on polarization calibration is left to
future work. For this work, it is reasonable to assume that a single set of
calibrators, 3C48 and 3C286, is sufficient for a constant pointing. At our 1.4
GHz observing frequency, 3C48 is known to be weakly polarized ($\sim 0.5\%$),
which we assume is acceptable for use as an unpolarized calibrator within the
error of the DSA-110161616In Appendix F we verify this assumption through
leakage polarization tests. For additional information on polarized
calibrators, see documentation for the Very Large Array (VLA) at
https://science.nrao.edu/facilities/vla/docs/manuals/obsguide/modes/pol.
(Perley & Butler, 2013). 3C286 is known to have 9.5% linear polarization at
1.4 GHz, making it suitable as a linearly polarized calibrator (Perley &
Butler, 2013). The absolute gain in the Y receptor, $|g_{yy}(\nu)|$, is
estimated using 3C48 by comparing the observed flux to the polynomial fit
(after correcting for the measured RM171717Note the RM of 3C48 is measured at
higher frequencies ($1.6-30$ GHz, or $1-18$ cm wavelengths) where the
polarization fraction is higher (Perley & Butler, 2013). of $-68$ rad m-2 and
estimated parallactic angle) defined by Perley & Butler (2017). $r(\nu)$,
$\phi(\nu)$, and $|g_{yy}(\nu)|$ were determined after averaging over spurious
peaks in Stokes parameters for each source as function of frequency,
downsampling in frequency, then interpolating back to native resolution. For
FRB observations, we calibrate by applying the inverse Jones matrix to the
observed Stokes parameters, effectively setting the gain and phase of the X
and Y feeds equal and minimizing the mixing of Stokes parameters.

Absolute position angles cannot be estimated with the current DSA-110
pipeline, as it would require tracking a calibrator source over a wide range
of parallactic angles which the DSA-110, as a transit instrument, is not
currently equipped for. In this work, an attempt to derive absolute position
angle estimates by treating the DSA-110 as a single antenna; following
Thompson et al. (2017) (Chapter 4), the elevation and azimuth of the array for
a given FRB are estimated using the RA, $\alpha$, and declination, $\delta$,
of the detected beam and observation time $\rm LST$:

$\sin(\theta)=\sin(b_{\rm DSA})\sin(\delta)+\cos(b_{\rm
DSA})\cos(\delta)\cos({\rm LST}-\alpha)$ (D3)

$\sin(\phi+(b-125)\delta\theta_{b})=-\frac{\cos(\delta)\sin({\rm
LST}-\alpha)}{\cos(\theta)}$ (D4)

where $l_{\rm DSA}$ and $b_{\rm DSA}$ are the longitude and latitude of the
DSA-110 (Owens Valley). $b$ is the detected beam and $\delta\theta_{b}=14"$ is
the synthesized beamwidth. The parallactic angle $\chi_{\rm par}$ is then
estimated as:

$\sin(\chi_{\rm par})=-\frac{\sin(\phi)\cos(b_{\rm DSA})}{\cos(\delta)}$ (D5)

and can be applied as a correction $\chi_{\rm cal}=\chi_{0}+\chi_{\rm par}$.

##  Appendix E Calibration Stability with Time and Primary-Beam Location

Four epochs of calibration observations were taken during the survey to apply
to the sample of FRBs reported in this paper. Table 5 summarizes each
observation. Each observation consists of multiple voltage dumps during the
calibration-source transit. The transits nearest the center of the primary
beam were used to derive Jones matrix parameters at each epoch. Figure 9 shows
the Jones matrix solutions as a function of frequency for each epoch. From
this, it is clear that the solution is stable, with standard deviation across
epoch of 0.2%, 0.1 rad, and 3.6% for $r(\nu),\,\phi(\nu),$ and
$|g_{yy}(\nu)|$, respectively. Given this stability, the solutions were
averaged together over all epochs and filtered in the frequency domain with a
first order Savitsky-Golay filter, and this average solution was then used to
calibrate all FRBs detected. The outlier $|g_{yy}(\nu)|$ solution from the
2022 April 14 observation was investigated and attributed to a software error
which prevented the measurement set from being properly saved. The beamformer
weights for this observation were therefore not gain calibrated resulting in a
vertical offset in the measured Stokes parameters. Following the correction of
this issue, no outliers were identified in subsequent calibration solutions,
as shown in Figure 9. We therefore do not include the $|g_{yy}(\nu)|$ value
from the 2022 April 14 observation in the average $|g_{yy}(\nu)|$ solution or
the standard deviation reported above.

Table 5: Polarization Calibration Observations and Jones Matrix Parameters

| 3C48 observation
---
name (Beam)
MJD |  | 3C286 observation
---
name (Beam)
MJD | $\mathbf{<r(\nu)>}$ | $\mathbf{<\phi(\nu)>}$ | $\mathbf{<|g_{yy}(\nu)|>}$
2022/04/14, 2022/05/24 Observation
kkz (46) | 59683.829 | dnz (18) | 59723.215 | $1.00\pm 0.04$ | $2.09\pm 0.14$ | $1.48\pm 0.06$
ane (197) | 59683.837 | fvn (57) | 59723.217 |  |  |
bzj (110) | 59572.309 |  kus (135) | 59723.221 |  |  |
|  | oxr (174) | 59723.223 |  |  |
2022/09/14 Observation
lck (107) | 59835.417 | mph (44) | 59835.908 | $0.99\pm 0.02$ | $2.11\pm 0.20$ | $1.86\pm 0.02$
bxc (182) | 59835.422 |  tnh (122) | 59835.912 |  |  |
|  | ezb (200) | 59835.916 |  |  |
2022/10/21 Observation
xtu (47) | 59872.313 | gbf (45) | 59872.807 | $1.00\pm 0.03$ | $2.15\pm 0.12$ | $1.78\pm 0.04$
eit (123) | 59872.317 |  lrp (123) | 59872.811 |  |  |
jvp (198) | 59872.321 | fml (201) | 59872.815 |  |  |
2022/11/23 Observation
xxc (22) | 59906.219 | quh (19) | 59906.713 | $1.00\pm 0.03$ | $2.29\pm 0.11$ | $1.80\pm 0.04$
fjr (72) | 59906.222 | xnr (71) | 59906.716 |  |  |
mia (123) | 59906.224 |  wtw (123) | 59906.718 |  |  |
xol (173) | 59906.227 | vxo (175) | 59906.721 |  |  |
wsj (223) | 59906.230 | hwj (227) | 59906.724 |  |  |

Notes: Labels in bold are those nearest the center beam and are used to derive
the Jones parameters in the last three columns. $<>$ indicates the average
value over frequency.

|
---|---
|
|
Figure 9: Jones matrix solutions on four epochs. Left: Frequency dependent
$r(\nu)$, $\phi(\nu)$, and $|g_{yy}(\nu)|$ after removing birdies,
downsampling and interpolating. Right: Solutions averaged over frequency for
each observation. The violin plots show the distribution of the frequency
dependent points while the red line shows the average value over all epochs.

In addition to long-term stability, stability across the primary beam was
estimated by using multiple Jones solutions from each epoch to calibrate the
adjacent voltage dumps during the transits of 3C48 and 3C286. For each epoch,
the gain solutions $r(\nu)$ and $|g_{yy}(\nu)|$ were taken as piecewise
polynomial fits, while the phase solution $\phi(\nu)$ was taken as the median
value across the band in order to reduce the impact of noise. The calibration
is deemed stable if there is no systematic change in the resulting
polarization fraction and position angle as a function of each source’s
location within the primary beam. No significant variations in the recovered
polarization properties, including RM, for 3C48 and 3C286 were observed. We
therefore proceeded to use the beam-center voltage dumps to derive calibration
parameters.

##  Appendix F Calibration Leakage Estimates

In the above method, the off-diagonal terms characterizing leakage between the
orthogonal receptors are assumed negligible, meaning that calibrated data will
be uncertain up to the true magnitude of these terms. The above calibration
corrects leakage between Stokes I and Q and between U and V. The leakage terms
cannot be explicitly solved for without the observation of additional
polarized sources over a wide range of position angles; this is not feasible
with the DSA-110. Leakage between the other pairs of Stokes parameters is
instead estimated by again calibrating adjacent voltage dumps on 3C48 and
3C286 on each observation epoch as described in the previous section. The
remaining Q, U, and V fractions in calibrated 3C48 observations then estimate
the remaining I leakage. Subtracting these leakages and the expected $9.6\%$
linear polarization at position angle of $\chi=33^{\circ}$ from calibrated
3C286 then allows for other leakage terms to be estimated. Specifically, the
residual linear polarization above the expected 9.6% then corresponds to
leakage from V into Q or U; the residual circular polarization is likewise
leakage from Q and U into V. One can visualize this with the Mueller
polarization matrix formalism (Heiles et al., 2001). The I-Q, I-U, I-V
leakages then roughly estimate the first row and first column of the Mueller
matrix, while QU-V and V-QU roughly estimate the other off-diagonal terms, and
the diagonal terms are derived from $r(\nu)$, $\phi(\nu)$, and
$|g_{yy}(\nu)|$. While the matrix cannot be explicitly solved based on the
3C48 and 3C286 observations available, the leakage estimates reported here
offer order of magnitude estimates.

Error bars are estimated by taking the standard error and subtracting the
systematic standard error from beams within each voltage dump in which the
source was not present, which characterizes the thermal noise. Leakage values
for each epoch are summarized in Figure 10; the maximum leakage observed is
$1.6\%$ between I and U. This is within acceptable limits and justifies the
ideal feed assumption above.

|
---|---
|
Figure 10: Violin plots of leakage estimates. The mean values are shown as
markers, while the distributions are values from all calibrated voltage dumps
and all frequency channels in each observation.

##  Appendix G Example of Polarization Calibration with Pulsar J1935+1616

In Section 2, we presented the functioning polarization pipeline using the
stacked profile of J1935+1616 shown in Figure 1. Here we further compute
$L/I$, $|V|/I$, and $V/I$ for each of the 26 pulses and for the folded profile
to compare to the measured values from Gould & Lyne (1998). The linear
polarization of the folded profile is $L/I=14.6\pm 5.6\%$, which is lower than
the expected $18\%$ but agrees within the $1\sigma$ errorbar. The absolute
value circular polarization is $|V|/I=16.9\pm 5.7\%$ which is also within
$1\sigma$ of the expected $15\%$. The signed circular polarization, $-2.5\pm
21.6\%$ agrees with expected $2\%$ within $1\sigma$ despite the opposite sign.
From the pulse profiles in Figure 1 it is clear that this difference in sign
is stochastic rather than a sign error in calibration181818In this paper we
adopt the IAU/IEE convention for Stokes V, in which $V>0$ is right-handed and
$V<0$ is left-handed. Gould & Lyne (1998) use the PSR/IEE convention which has
the opposite definition. Therefore, we have flipped the sign of Stokes V in
both the EPN profile in Figure 1 and the expected $V/I$ so that both are in
the IAU/IEE convention for more accurate comparison.. From this we conclude
that there is good agreement between the DSA-110 polarization measurement of
J1935+16 and expectation and find no significant systematic errors to apply.
Figure 11 shows the polarization fractions of each of the 26 pulses as well as
those of the average profiles. Note the low expected RM, $-2.3\pm 0.5\,$rad
m-2, and the low detected linear-polarization S/N prevent a confident RM
measurement for verification.

---
Figure 11: Linear (top), absolute value circular (middle), and signed circular
polarization (bottom) measurements of J1935+1616. Polarization fractions for
individual pulses are shown in blue, and the weighted mean is shown in purple,
with the shaded area indicating the weighted error. The expected polarization
fractions from Gould & Lyne (1998) ($18\%$, $15\%$, and $2\%$ from top to
bottom) are shown in black. The linear and absolute value circular
polarization fractions measured from the folded profiles, shown in red, are in
good agreement with expectation within the $1\sigma$ errorbar.

##  Appendix H Optimal Spectral Estimation

After calibration of each FRB, full-Stokes spectra are calculated by averaging
over the burst time series. In order to prevent inclusion of noise in the
spectrum, a window around each burst is first manually defined to contain all
apparent emission components, over which the average spectrum is computed.
Ideally, the pulse would then be weighted using the variance at each time
step. These variances are estimated as the inverse of the frequency averaged
S/N at each time step, i.e., the temporal profile of the burst. Previous
studies have used a Gaussian fit and similar functions to estimate pulse
profiles. However, the large variety in burst morphology among FRBs implies a
Gaussian may not offer a reasonable fit. The pulse profile is determined by
first averaging the total-intensity dynamic spectrum over frequency, then
downsampling and linear interpolating to the desired time resolution to
eliminate stochasticity and insignificant mid-pulse structure. Finally, to
remove artifacts in due to the interpolation, the profile is filtered with a
third-order Savitsky-Golay filter, with the filter width chosen specific to
each burst. The profile is set to zero outside of the burst window defined
above. The spectrum can then be computed as a weighted sum of the time series
within the defined window using the profile as weights.

##  Appendix I Detailed RM Synthesis Derivation and S/N Method Error

What follows is a detailed derivation of the RM Synthesis method and its
variation, the S/N Method, utilized in this paper (Heald, 2008; Brentjens & De
Bruyn, 2005; Burn, 1966). In the discrete case, Burn (1966) estimates the
Faraday dispersion function (FDF) as the Fourier transform of the observed
linear polarization vector $P_{\rm obs}(\lambda^{2})=Q_{\rm
obs}(\lambda^{2})+iU_{\rm obs}(\lambda^{2})$ from $\lambda^{2}$ space to RM
space:

$\hat{F}({\rm RM})=\frac{1}{N_{\lambda^{2}}}\sum_{\lambda^{2}}{P_{\rm
obs}(\lambda^{2})W(\lambda^{2})(\lambda^{2})e^{-2i{\rm
RM}(\lambda^{2}-\lambda_{0}^{2}})}$ (I1)

where $\lambda_{0}$ is the mean of the $\lambda^{2}$ axis, and
$W(\lambda^{2})$ are weights applied to the spectra. Note that $Q_{\rm
obs}(\lambda^{2})$ and $U_{\rm obs}(\lambda^{2})$ are the optimally weighted
spectra of Q and U as described above. $\hat{F}({\rm RM})$ is proportional to
the linear polarization for a given RM correction, and this can therefore be
interpreted as a linear polarization maximization method. The most probable
value of the RM then occurs where $\hat{F}({\rm RM})$ peaks; a parabola is fit
to an oversampled RM range around the peak and its maximum taken to be the RM
estimate. An error on this value is estimated as the full-width at half-max
(FWHM) of the RM spread function (RMSF), divided by the linear-polarization
S/N:

$\sigma_{\rm RM1}=\frac{{\rm FWHM}\sigma_{L}}{{\rm max}(\hat{F}({\rm RM}))}$
(I2)

where $\sigma_{L}$ is the off-peak standard deviation in the linear-
polarization signal, $|P(t)|$, after applying the ideal spectral weights