# Pulsar polarization: a broad-band population view with the Parkes Ultra-
Wideband receiver

L. S. Oswald1,2, S. Johnston3, A. Karastergiou1, S. Dai4, M. Kerr5, M. E.
Lower3, R. N. Manchester3, R. M. Shannon6,7, C. Sobey8, P. Weltevrede9
1Department of Astrophysics, University of Oxford, Denys Wilkinson Building,
Keble Road, Oxford OX1 3RH, UK
2Magdalen College, University of Oxford, Oxford OX1 4AU, UK
3Australia Telescope National Facility, CSIRO, Space and Astronomy, PO Box 76,
Epping, NSW 1710, Australia
4School of Science, Western Sydney University, Locked Bag 1797, Penrith, NSW
2751, Australia
5 Space Science Division, Naval Research Laboratory, Washington, DC 20375, USA
6 Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, PO Box 218, Hawthorn, VIC 3122, Australia
7 The ARC Centre for Excellence for Gravitational-wave Discovery (OzGrav)
8 CSIRO Space and Astronomy, PO Box 1130 Bentley, WA 6102, Australia
9Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy,
University of Manchester, Manchester M13 9PL, UK
E-mail<EMAIL_ADDRESS>(LSO)

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The radio polarization properties of the pulsar population are only
superficially captured by the conventional picture of pulsar radio emission.
We study the broadband polarization of 271 young radio pulsars, focusing
particularly on circular polarization, using high quality observations made
with the Ultra-Wideband Low receiver on Murriyang, the Parkes radio telescope.
We seek to encapsulate polarization behaviour on a population scale by
defining broad categories for frequency- and phase-dependent polarization
evolution, studying the co-occurrences of these categorizations and comparing
them with average polarization measurements and spin-down energy ($\dot{E}$).
This work shows that deviations of the linear polarization position angle (PA)
from the rotating vector model (RVM) are linked to the presence of circular
polarization features and to frequency evolution of the polarization.
Polarization fraction, circular polarization contribution and profile
complexity all evolve with $\dot{E}$ across the population, with the profiles
of high-$\dot{E}$ pulsars being simple and highly linearly polarized. The
relationship between polarization fraction and circular contribution is also
seen to evolve such that highly polarized profiles show less variation in
circular contribution with frequency than less strongly polarized profiles.
This evolution is seen both across the population and across frequency for
individual sources. Understanding pulsar radio polarization requires detailed
study of individual sources and collective understanding of population-level
trends. For the former, we provide visualizations of their phase- and
frequency-resolved polarization parameters. For the latter, we have
highlighted the importance of including the impact of circular polarization
and of $\dot{E}$.

###### keywords:

pulsars: general – polarization.

††pubyear: 2023††pagerange: Pulsar polarization: a broad-band population view
with the Parkes Ultra-Wideband receiver–3

##  1 Introduction

When considering the origins and behaviour of pulsar radio polarization, the
results from an observational approach are dependent on the capacities of
radio telescope technology. The Ultra-Wideband Low receiver (UWL) on
Murriyang, the 64-m Parkes radio telescope, has opened up a new broad-band
perspective on pulsar radio emission. With the capacity to observe radio
pulsars across a continuous bandwidth from 704–4032 MHz (Hobbs et al., 2020),
we can now answer questions on a large scale about the frequency-dependent
nature of pulsar radio polarization and what behaviour is seen across the
pulsar population.

The classic, and simplistic, picture of radio pulsar polarization is generally
summarized as follows (Lorimer & Kramer, 2012): pulsars can be anything from
strongly to weakly polarized, that polarization is predominantly linear
(average linear polarization fraction of approximately 20%, but pulsars may be
up to 100% linearly polarized) but most pulse profiles also exhibit a small
amount of circular polarization (average absolute circular polarization
fraction of approximately 10%). The observed angle of the linear polarization
(position angle or PA) evolves smoothly across the pulse profile following an
S-shaped curve, which can be described as a geometrical effect of the magnetic
field according to the rotating vector model (RVM, Radhakrishnan & Cooke,
1969). Fits of the RVM to PA profiles are often used to determine pulsar
geometries—the inclination of the magnetic field from the spin axis and the
impact parameter of the line of sight (see for example Johnston & Kramer,
2019).

A further dimension to observable pulsar polarization is that of observing
frequency. According to the RVM, the PA profile results purely from the
geometry of the pulsar and the observer’s viewing angle, factors which are
independent of frequency. However, it has long been known that this does not
fully account for the observational picture of pulsar polarization, since
individual pulsars show a wide variety of other effects that need to be
considered. For example, pulsars are generally seen to depolarize at high
frequencies (e.g. Sobey et al., 2021) and some pulsars show a frequency-
dependent transition from linear to circular polarization (Von Hoensbroech &
Lesch, 1999). The observation that many pulsar intensity profile shapes are
observed to evolve with frequency could be explained as originating from
refractive effects in the magnetosphere (Lyubarskii & Petrova, 1998). The idea
of radius-to-frequency mapping (RFM, Ruderman & Sutherland, 1975)—that there
is a relationship between radio frequency and the height of emission above the
pulsar surface—is also commonly invoked as an explanation.

An additional level of complexity to consider is the presence of two
orthogonally polarized modes of emission in pulse profiles. These are most
clearly identifiable by the presence of orthogonal jumps in the PA of
90$\degree$, at a phase bin at which the total polarization drops to zero
(e.g. Manchester et al., 1975). These orthogonal jumps are identified as being
the pulse phase at which mode dominance is exchanged, such that the stronger
mode and the weaker mode contributing to the observed profile swap.
Karastergiou et al. (2005) studied the frequency-dependence of linear
polarization for 48 pulsars and demonstrated that the observed frequency
evolution could be explained by the pulse profiles being composed of
orthogonally polarized modes that had different spectral indices for their
intensities. Smits et al. (2006) showed that pulse profile components
dominated by a single orthogonal mode tended to increase in intensity relative
to the rest of the profile with increasing frequency. Regardless of the
precise mechanisms behind emission heights and propagation paths of pulsar
radio emission, interactions between orthogonal modes are by definition path-
dependent and may therefore be the cause of phase- and frequency-dependent
evolution of polarization fractions and non-RVM features in the PA.

The orthogonally polarized modes of emission are explained as originating from
birefringence in the magnetospheric plasma. It is theorised that the ordinary
(O) and extraordinary (X) modes propagate along different paths through the
magnetosphere, and the observed polarization is set at the polarization
limiting radius, the point at which the radiation is decoupled from the
magnetosphere (e.g. Barnard & Arons, 1986). This theory goes some way towards
explaining the diversity of polarization behaviour of pulse profiles across
the pulsar population. But there remain two key aspects of pulsar polarization
that need to be addressed: namely that most pulsars exhibit at least a small
amount of circular polarization, and that many pulsars display polarization
properties, such as features in the PA profiles, that are not adequately
explained by the RVM plus orthogonal jumps. The wide variety of features seen
in the population—and the difficulty of studying more than a few pulsars in
detail at a given time—means that the more in-depth studies of radio pulsar
polarization have generally been limited to a small number of pulsars, or even
a single pulsar, as for the example of PSR B1451$-$68 (Dyks et al., 2021).
Another recent case of interest is that of PSR B1919$+$21, for which Primak et
al. (2022) studied the polarization of its drifting sub-pulses. They found
that some phase regions of the pulse profile appeared to result from
incoherently superposed orthogonally polarized modes, and other regions
resulted from superposition that is partially coherent. Further, the
coherently superposed regions exhibited rotation of the polarization vectors
about the Poincaré sphere at the same rate as the drifting subpulse intensity
modulation.

A coherent or partially-coherent model of orthogonal mode superposition
explains polarization behaviour well in these individual cases, but the
population-wide ramifications of such a model have not previously been
addressed observationally. Nevertheless, there is growing evidence in large
scale pulsar studies of the need to address the magnetospheric origins of more
complex polarization behaviour (e.g. Ilie et al., 2019). Broad-band radio
observations, made with new and upgraded instruments, mean that it is now
possible to measure the continuous evolution of polarization across a large
fractional bandwidth for a large number of pulsars: see for example the
observations below 200 MHz made with LOFAR (Noutsos et al., 2015). This large
increase in the parameter space of polarization measurements means we can
clearly identify how polarization behaviour varies across both the pulsar
population and across frequency for each pulsar, giving new insight into the
question of how it is generated.

In this paper we present full polarization observations of a large sample of
non-recycled pulsars observed with the UWL receiver on Murriyang, the Parkes
radio telescope, with the goal of updating our understanding of the behaviour
of pulsar polarization in broad-band observations. Johnston et al. (2021)
introduced the initial results of two years of such observations and Sobey et
al. (2021) presented a polarization census for 40 bright pulsars from this
dataset. The work presented here is that previewed and promised by Oswald et
al. (2020), where we presented plans for extending our broad-band polarization
study to a population-level scale, with particular focus on the frequency
dependence of circular polarization and the relationships between polarization
behaviour and pulsar parameters including spin-down energy $\dot{E}$.

We describe our observations and data analysis methods in Sections 2 and 3
respectively. In Section 4, we present visualizations of how each pulsar’s
phase-resolved polarization properties evolve with frequency. We also
categorize the key qualitative polarization behaviours of the pulsar
population, and investigate co-occurrences of these features and their
evolution with frequency across the population, with particular focus on
circular polarization and on $\dot{E}$. A summary of the results is presented
in Section 5 and the full collection of broad-band visualizations of the
dataset are presented as supplementary material online.

##  2 Observations

Polarization data were obtained under the P574 observing programme, ongoing
since 2007 at the Parkes radio telescope, Murriyang. Prior to 2018 November,
observations were predominantly carried out monthly at 1369 MHz with a
bandwidth limited to 256 MHz with occasional observations at 3100 MHz and 700
MHz (see Johnston & Kerr, 2018; Petroff et al., 2013). For this paper we use
observations from 2018 November onwards which used the UWL receiver (Hobbs et
al., 2020). The observational band runs from 704 MHz to 4032 MHz, with 3328
channels each of width 1 MHz. The data are coherently dedispersed in each
channel, folded at the topocentric pulsar period and collated into sub-
integrations of length 30 s with 1024 phase bins per period for the duration
of the observation (typically 200 s). Full Stokes information is recorded and
the data is recorded to disk in psrfits format (Hotan et al., 2004; van
Straten et al., 2010).

Data processing is carried out within psrchive (Hotan et al., 2004). A key
element of the analysis is the removal of radio-frequency interference (RFI)
from the data which is carried out using a median filtering process in both
frequency and time. Typically, approximately 1200 channels (out of 3328) are
discarded from the observations. Polarization and flux calibration is carried
out via the routine pac using observations of a pulsed calibration signal and
observations of PKS B1934–68. Corrections due to impurities in the receiver
are computed via observations of the pulsar PSR J0437–4715 and also applied
(van Straten, 2013). Further details of the observing programme with the UWL
can be found in Johnston et al. (2021).

Individual observations are short so in order to improve the signal-to-noise
ratio (S/N) in the pulsar profile we summed together all observations taken
over a three year interval (approximately 35 epochs per pulsar) so that the
typical total observation time is some 7000 s. The frequency resolution of the
UWL is 3328 channels across the band. To increase S/N, and for consistency
across the sample, we split the whole band into eight sub-bands and generated
a single pulse profile per sub-band. For this study we use a dataset of
profiles from 271 pulsars observed regularly as part of the observing
programme.

Figure 1: Positions on the $P$–$\dot{P}$ diagram of the 271 pulsars presented
in this dataset. Blue crosses: 101 high-S/N, non-scattered pulsars used in
categorization analysis. Black points: remaining 170 pulsars of the dataset.
Contours: Gaussian kernel density estimation of the pulsar population as taken
from psrcat. Also plotted are diagonal lines of constant $\dot{E}$, from
$10^{26}$ erg s-1 (bottom right) to $10^{42}$ erg s-1 (top left) in increments
of $10^{2}$ erg s-1.

Fig. 1 shows the positions of our pulsar sample on the $P$–$\dot{P}$ diagram
in relation to the population distribution given by the ATNF catalogue psrcat
(Manchester et al., 2005), version
1.68111https://www.atnf.csiro.au/research/pulsar/psrcat, accessed via queries
with psrqpy (Pitkin, 2018). The pulsars in our sample are marked as points and
crosses and the ATNF population is indicated by contour lines obtained by
fitting a Gaussian kernel density estimate to the distribution of pulsars. As
can be seen, our sample covers most of the area of $P$–$\dot{P}$ space
occupied by the non-recycled population, but with a distribution that favours
higher $\dot{E}$ values than that of the catalogue population and no pulsars
with $\dot{E}\leq 10^{30}$erg s-1.

##  3 Data analysis methods

###  3.1 Visualization

We present the results of our observations and data processing as frequency-
and phase-resolved waterfall plots for each of our 271 pulsars. These are
presented in the online supplementary material (file name: “Appendix B
Polarization visualizations for pulsar sample”, pulsars presented in numerical
order from PSR J0034$-$0721 to J2346$-$0609). An example for PSR J1900$-$2600
is shown in Fig. 2. For the 15 pulsars that have an interpulse—a second pulse
at half the pulse period, inferred to originate from the other magnetic pole
of the neutron star—we present the same information for the interpulse as for
the main pulse. We selected the waterfall plot presentation to display the
maximum possible information about the key observables of each pulsar, and in
particular, the smooth frequency evolution of many features in the pulsar
polarization.

In each visualization, we show a standard pulse profile plot, with linear and
circular polarization and PA profile at 1400 MHz, in the top left corner.
Below it, we show a series of these pulse profiles across the eight sub-bands.
Finally, we display a series of six waterfall plots showing, from top left to
bottom right, total intensity $I$, PA, circular polarization $V$, fractional
polarization $V/I$, linear polarization $L$ and fractional linear polarization
$L/I$. For all of these visualizations the linear polarization $L$ has been
bias-corrected according to the prescription of Everett & Weisberg (2002). The
purpose of having both polarized flux and fractional polarization plots for
linear/circular polarization is that, whereas the polarized flux plots show
the evolution of polarization structures with frequency and phase, the
fractional polarizations show the extent to which these structures are tied to
total intensity.

For the waterfall plots, we only show the pulse profile where the S/N of
Stokes $I$ is greater than 5. This is also the case for the PA in the standard
pulse profile plot in the top left. This means that PA values are still being
calculated at phases with strong intensity but little to no linear
polarization. However, the goal of data visualization is different from that
of data analysis. We choose to maintain the same S/N cut-off for all
variables: partly for consistency and partly because we find that this
provides the maximum visual information about frequency-dependent evolution
even at very low linear polarization.

Figure 2: Broad-band visualization of PSR J1900$-$2600 observed in fold with
the UWL on Murriyang, the Parkes Radio Telescope. Top left: Pulse profile at
1414 MHz, with total intensity (black), linear polarization (red dashes),
circular polarization (blue dots) and position angle (PA, black points). Left:
Pulse profiles at eight frequencies from 812–3780 MHz, colour scheme as
before. Right: Waterfall plots of phase- and frequency-resolved polarization
showing, from top left to bottom right, total intensity, PA, circular
polarization, fractional circular polarization, linear polarization,
fractional linear polarization. The PA colour scheme is chosen to be cyclical
around 180$\degree$ to account for PA wrapping. The circular polarization
colour scheme is chosen so that purple is positive and orange is negative, and
the fractional circular polarization colour scheme is chosen so that red is
positive and blue is negative. Colour scale units for $I$, $V$ and $L$ are in
mJy. The waterfall plot polarizations are only shown where the S/N of the
total intensity exceeds 5; the same is true for the PA profile in the top left
subplot.

In order to define the S/N of the intensity profile, $I/\sigma$, we use an
iterative approach to remove outlier points (on-pulse region and any residual
impulsive RFI) to converge onto a standard deviation measurement of the off-
pulse region. We use this method to calculate $\sigma$ for all pulsars other
than PSRs J0820$-$4114 and J1834$-$0426\. These pulsars have very wide
profiles, causing the iterative outlier-removal method to fail. In those cases
we define the off-pulse region by eye. We split the off-pulse region into four
sections, calculate the standard deviation of each section and select the
smallest as the least likely to include the effect of impulsive RFI and
therefore the most representative value of $\sigma$.

We also present a second piece of online supplementary material visualizing
two additional polarization parameters. The first of these is the total
polarization $P$ as a fraction of the total intensity, Stokes $I$: $p=P/I$.
The second is the “circular contribution”, $\theta$. We introduce the concept
of circular contribution as a helpful metric for investigating the relative
levels of linear and circular polarization in a pulse profile. We define
$\theta$ relative to the ellipticity angle $\chi$ as
$\theta=2\lvert\chi\rvert$. It is the magnitude of the angle of latitude on
the Poincaré sphere, given by the equation $\theta=\arctan{(\lvert
V\rvert/L)}$. It is helpful to define the parameter in this way, rather than
using ellipticity directly, because it gives a more clearly comparable link
between absolute levels of linear and circular polarization, and their
visualization on the Poincaré sphere. Fully linearly polarized radiation will
have a circular contribution of $\theta=0\degree$, whilst fully circularly
polarized radiation has the maximum circular contribution of
$\theta=90\degree$.

This second set of figures in the online supplementary material (file name:
“Appendix C Visualizations of p and theta for pulsar sample”) show waterfall
plots of $P/I$ and $\theta$, following the same S/N and bias correction steps
as described for the waterfall plots in Fig. 2 and in the first piece of
supplementary material (“Appendix B Polarization visualizations for pulsar
sample”).

###  3.2 Polarization measurements

In order to make inferences about the polarization behaviour of the pulsar
population we need to reduce the dimensionality of this observational
information. We take two approaches to address this: polarization measurements
and categorization of polarization behaviour. For the first of these, we sum
the Stokes and polarization parameters across phase to obtain a single
characteristic value per pulse profile, per frequency. To avoid off-pulse RFI
biasing these values, we sum only the bins for which the intensity S/N $>3$
that lie within our visually-defined on-pulse region.

We calculate two sets of average polarization fractions for each pulsar. For
the first set, we calculate total, linear and absolute circular polarizations
from the Stokes parameters for each pulse profile and then sum these across
phase. We label polarization fractions with lower case letters $p$, $l$ and
$\lvert v\rvert$, and for this first set, we indicate that these are averages
by marking them with bars: $\overline{p}$ etc. For the second set, we sum
Stokes parameters across phase first and then convert these into polarization
fractions. We label this second set of average polarization fractions with
asterisks. This gives the following formulae:

$\displaystyle\overline{p}$
$\displaystyle=\frac{\Sigma\left(\sqrt{Q^{2}+U^{2}+V^{2}}^{BC}\right)}{\Sigma
I}$ $\displaystyle\overline{l}$
$\displaystyle=\frac{\Sigma\left(\sqrt{Q^{2}+U^{2}}^{BC}\right)}{\Sigma I}$
$\displaystyle\overline{\lvert v\rvert}$
$\displaystyle=\frac{\Sigma\left(\lvert V\rvert^{BC}\right)}{\Sigma I}$
$\displaystyle p^{\ast}$ $\displaystyle=\frac{\sqrt{(\Sigma Q)^{2}+(\Sigma
U)^{2}+(\Sigma V)^{2}}}{\Sigma I}$ $\displaystyle l^{\ast}$
$\displaystyle=\frac{\sqrt{(\Sigma Q)^{2}+(\Sigma U)^{2}}}{\Sigma I}$
$\displaystyle\lvert v\rvert^{\ast}$ $\displaystyle=\left\lvert\frac{\Sigma
V}{\Sigma I}\right\rvert$

where $\Sigma$ indicates summing across phase and the superscript BC indicates
that bias correction is applied to the polarizations before summing. We also
use the same bar/asterisk labelling for $\theta$ when describing variables
summed over pulse phase. Uncertainties are inferred using the previously
described measurements of $\sigma$ and standard error propagation. We bias-
correct the linear polarization as described in Everett & Weisberg (2002) and
use the same method for the total polarization as well. To bias correct the
absolute circular polarization $\lvert V\rvert$ we follow the method of
Karastergiou et al. (2003) and Posselt et al. (2022) and subtract the
expectation value of the distribution. Being a half-normal distribution, this
is done as follows:

$\lvert V\rvert^{BC}=\left\\{\begin{array}[]{ll}\lvert
V\rvert-\sigma\sqrt{\frac{2}{\uppi}}&\mbox{if $\lvert
V\rvert>\sigma\sqrt{\frac{2}{\uppi}}$}\\\
0&\mbox{otherwise,}\end{array}\right.$ (1)

where $\sigma$ is the standard deviation of the intensity off-pulse region as
described above.

The polarization measurements $\overline{l}$, $\overline{\lvert v\rvert}$,
$\overline{p}$ and $\overline{\theta}$, along with their uncertainties, are
listed for each pulsar in Table LABEL:tab:all_ave_psr_results. For pulsars
with interpulses, we calculate the interpulse polarization fractions in the
same way and list them separately in Table LABEL:tab:all_ave_psr_results.

###  3.3 Categorization of profile polarization features

We seek to present a summary of key features and trends related to
polarization structure observable in the pulsar population. In addition to the
average numerical values, we also categorize certain polarization and profile
features of a high-S/N subset of 101 pulsars. We apply a S/N cut to identify
which pulsars to take forward for this further analysis: we keep those pulsars
for which the peak intensity S/N $>10$ for all eight frequency sub-bands. We
define the peak intensity S/N by taking the maximum intensity value in the on-
pulse region, subtracting the median of the off-pulse region to correct any
zero-offset of the baseline, and then dividing by $\sigma$. We also identify
any strongly scattered pulsars by eye and remove them from the high-S/N sample
(all scattered pulsars are marked with an asterisk in Table
LABEL:tab:all_ave_psr_results). The reasoning for this is that if scattering
is strong enough to be clearly visible by eye, then the effect of scattering
is likely to impact the features of the polarization profile observed
(Karastergiou, 2009).

We identify polarization features by eye from the broad-band waterfall plots
generated for this dataset. The objective is not to state absolute numerical
results for these categorizations, many of which are by definition difficult
to define unequivocally for every pulsar, and in any case such precise
quantification would not provide much additional information based on what we
wish to describe. Instead, we seek to obtain a general understanding of the
existences of these features and the ways in which they co-occur. For
simplicity, we define all but one of the categories as Boolean yes-no cases:
either a pulsar exhibits a particular feature or it does not. The categories
are defined as follows.

  1. 1.

Visible frequency evolution of…

    1. (a)

…intensity profile shape

    2. (b)

…PA profile shape

    3. (c)

…linear polarization fraction

    4. (d)

…linear polarization profile shape

    5. (e)

…circular polarization fraction

    6. (f)

…circular polarization profile shape

  2. 2.

Phase variation of polarization:

    1. (a)

“True” orthogonal jump (Orthogonal jump in PA at the phase at which total
polarization drops to zero)

    2. (b)

Orthogonal jump in PA with non-zero circular polarization

    3. (c)

PA deviation from RVM not otherwise accounted for by the two previous
categories

    4. (d)

$V$ changes hand with phase

Our only non-Boolean category is Profile Complexity. Integrated pulse profiles
are observed to have a wide range of shapes, with multiple components that may
be blended together. We choose to investigate the scaling of polarization
complexity by assigning each pulsar to one of three categories. We number
these in order of increasing complexity: category 0 describes profiles with a
single component. Profiles with a small number of components (two to four)
that are well separated and/or symmetric, or a strongly asymmetric single
component, are assigned to category 1. Category 2 comprises complex profiles
with multiple components or blended components. The categorization of any
individual pulsar is on some level subjective, but we find that the three-
category set-up enables clearer distinctions to be drawn between the pulsars
in categories 0 and 2.

It is worth making clear the difference between categories (i)c/e and (i)d/f,
that is to say the difference between polarization fraction and polarization
profile shape. For the former, we looked for a change across frequency of the
fraction of the linear/circular polarization relative to total intensity in at
least part of the pulse profile. For the latter, we looked not at the
polarization fraction, but at the shapes of any distinct features in the
polarized part of the pulse profile and whether these evolved with frequency.
PSR J1900$-$2600, shown in Fig. 2, has frequency evolution of both the
polarization fraction and profile shape of its linear polarization. The former
can be seen in the stacked pulse profiles: the linear polarization fraction
decreases significantly at high frequencies. The latter is best identified in
the $L/I$ plot, where the shifting positions of light and dark regions of the
profile indicate a change in shape of the linear polarization profile across
frequency.

It is important that the frequency evolution of polarization profile shape is
defined with respect to the fractional polarization plot (e.g. $L/I$) rather
than the absolute polarization (e.g. $L$) because this separates polarization
evolution as distinct from evolution of the total intensity profile. A
relevant example to consider is PSR J1048$-$5832, the visualizations for which
can be found in the online supplementary material. This is a pulsar for which
the linear polarization profile is distinctly different from the intensity
profile, as can be seen from the waterfall plots of $I$ and $L$, yet the
polarization fraction $L/I$ does not evolve with frequency. We also note that,
since pulsars tend to have weaker circular polarization than linear
polarization, this may impact the relative count of visible features in
circular polarization, however, since we apply this analysis only to high-S/N
pulsars, we expect this effect to be small.

The reason for separating PA non-RVM behaviour into three categories is as
follows. Following the theoretical expectation that an orthogonal jump takes
place when there is a change in dominance between the two orthogonal modes of
emission, we would expect “true” orthogonal jumps to be accompanied by a drop
of the polarization to zero. As described by Dyks (2020), apparent orthogonal
jumps in PA will also result from the polarization state transitioning across
the Poincaré sphere and passing close to the Stokes $V$ pole. In these cases,
the polarization does not drop to zero, instead it is rotated from $L$ into
$V$. This means that there will be significant measured circular polarization
accompanying the PA jump. Cases where the PA deviates from an expected RVM
track but do not show a clear jump are the hardest to define: is this
behaviour similar to either of the jump behaviours or is it fundamentally
different? We seek to categorize the different observational manifestations so
that we can compare their co-occurrences with other categories. and so
determine whether the apparent separation between categories is indeed
meaningful.

The full categorization for each pulsar is given in Table
LABEL:tab:all_ave_psr_results, where each category is labelled as in this
list. Note that for pulsars with interpulses we only categorize the main
pulse. As an example, PSR J1900$-$2600 in Fig. 2 is classified as having the
following polarization features: (i)abcdf;(ii)bcd;2. This means it displays
frequency evolution of intensity profile, PA profile, linear polarization
fraction, linear polarization profile shape and circular polarization profile
shape - ‘(i)abcdf’. It also exhibits a PA jump with non-zero circular
polarization at the jump phase, deviation from a classic RVM swing and a
change in hand of the circular polarization - ‘(ii)bcd’. Finally, it has been
categorized as having Profile Complexity ‘2’ - multiple components or blended
components.

##  4 Polarization properties of the dataset

Fig. 2 shows PSR J1900$-$2600 as an example of how we visualize the
polarization properties of each pulsar in the dataset, as described in Section
3. Unlike the majority of past publications of pulse profiles, which show only
the standard profile with PA, this visualization follows the techniques set
out in Oswald et al. (2020) to display the phase- and frequency-evolution of
pulse profiles simultaneously, in order to capture the full capability of the
UWL. Here, we extend those techniques beyond total intensity and PA profile to
encompass polarization fractions, and particularly circular polarization.

The full collection of data visualizations of 271 pulsars is presented in the
online supplementary material. In the remainder of this section we focus on
the results of our measurements and categorizations taken collectively. We aim
to reduce the number of degrees of freedom required to encapsulate the dataset
so that clear and simple statements may be made about its polarization
behaviour.

###  4.1 Average polarization values

Using the standard measurements for fractional polarizations at 1400 MHz, we
find that, on average (median), the pulsars in our sample are 28% linearly
polarized, 5% circularly polarized and 32% polarized in total (see Table 1).
This is comparable to general expectations from the literature: Gould & Lyne
(1998) quote 20% linear and 10% absolute circular polarization fractions.

However, careful consideration should be made about the meaning of these
values.

A median does not capture range of polarization fractions observed, or the
relationship between polarization fraction and $\dot{E}$ (e.g. Weltevrede &
Johnston, 2008), which we discuss further in Section 4.3. We should also
consider the choice of measurement technique. The numbers quoted above are
summed polarizations divided by summed intensity ($\overline{p}$,
$\overline{l}$ and $\overline{\lvert v\rvert}$). Summing Stokes parameters
before converting to polarization ($p^{\ast}$ etc.) results in much smaller
polarization fractions. This is expected, since the PA varies across the pulse
profile, so that summing Stokes $Q$ and $U$ will have an averaging effect.
Similarly, summing Stokes $V$ across phase will generate a smaller measurement
if the direction of circular polarization changes hand.

It is usual in the literature to quote the barred values ($\overline{p}$
etc.), which are a more accurate representation of pulsar polarization
fraction. However, it is worth stressing the difference in results for these
two sets of parameters for two reasons. First, the starred polarization
fractions are the more relevant when searching for pulsars as polarized
sources in the image plane (e.g. Sobey et al., 2022). Secondly, the difference
between $\overline{p}$ and $p^{\ast}$ is an indicator of phase evolution of
polarization in a pulse profile. We note that there is a bigger difference
between $\overline{p}$ and $p^{\ast}$ for more complex pulse profiles
(category 2 vs. category 0), implying that the presence of additional profile
components leads to increased polarization complexity, and/or that pulsars
with simpler pulse profiles tend to have flatter PA profiles.

Table 1: Distributions of the measured polarization fractions and circular contribution at 1400 MHz, summarized with the 25th, 50th and 75th quantiles read from left to right. The parameters $l$, $\lvert v\rvert$, $p$ and $\theta$ are as described in Section 3, and the measurements are shown for phase-averaged polarizations (barred) and polarizations calculated with phase-averaged Stokes parameters (starred). The 50th quantile is indicated in bold. | Barred | Starred
---|---|---
$l$ | 0.17, 0.28, 0.52 | 0.10, 0.19, 0.43
$\lvert v\rvert$ | 0.03, 0.05, 0.09 | 0.02, 0.05, 0.10
$p$ | 0.21, 0.32, 0.56 | 0.11, 0.21, 0.46
$\theta$ ($\degree$) | 6.4, 11.6, 18.9 | 6.9, 13.4, 28.5

###  4.2 Categorization results

Table 2: Table of percentage counts of how many pulsars fit into each of the categories defined in Section 3.3. The categorization was applied to the 101 pulsars that exceeded the S/N cut defined in Section 3 and were identified as not being visibly scattered. A horizontal line separates the frequency-dependent and phase-dependent categorizations.  Polarization category | Occurrence
---|---
(i)a: $I$ shape frequency evolution | 74%
(i)b: PA frequency evolution | 51%
(i)c: $L$ fraction frequency evolution | 40%
(i)d: $L$ shape frequency evolution | 31%
(i)e: $V$ fraction frequency evolution | 32%
(i)f: $V$ shape frequency evolution | 32%
(ii)a: PA orthogonal jump | 37%
(ii)b: PA jump, $\lvert V\rvert>0$ | 20%
(ii)c: PA RVM departure | 45%
(ii)d: $V$ change of hand | 71%

Table 2 shows percentages of the high-S/N sample of 101 pulsars that exhibit
each of the characteristics defined in Section 3.3. Most pulsars show clearly
visible frequency evolution of profile shape in Stokes $I$ and about half of
the sample show frequency evolution of the PA. Frequency evolution of linear
and circular polarization is also commonly observed. By far the most common
phase-dependent feature identified was there being at least one change of
handedness in circular polarization. A sizable fraction of pulsars show
orthogonal jumps in their PA profiles, but at least 45% of pulsars show some
sort of departure from RVM behaviour in their PA profiles across phase that
cannot be explained as being due to orthogonal jumps.

Having identified these categorizations, the next question to consider is how
the occurrences of these profile features relate to each other. For example,
we might expect that the pulsars exhibiting non-RVM behaviour are also likely
to show frequency-evolution of the PA. From Table 2, we see that roughly half
of pulsars show frequency evolution of the PA, and just under half show
departures from the RVM. If these two behaviours are independent, then we
would expect around a quarter of the sample to exhibit both behaviours.
Instead, we find that the two categories co-occur in over a third of the
pulsars: an excess of around 10%. We calculate these co-occurrence excesses
for every pair of parameters, round the values to the nearest 5% and plot them
in a heatmap in Fig. 3.

Figure 3: Heat map of the co-occurrence excesses of the categories assigned to
the 101 high-S/N pulsar subset, as described in the text and introduced in
Table 2. These are defined as the percentage excesses of categories appearing
together in the sample, relative to the expected co-occurrence for independent
categories, rounded to the nearest 5%. The diagonal line indicates the
symmetry of the heatmap. Further details are given in the text.

####  4.2.1 Positive and negative associations

The heatmap in Fig. 3 is divided into sections with black lines indicating the
frequency-dependent and phase-dependent categories. The top right and bottom
left sections both show a large number of co-occurrences, indicating that
there is a link between phase-dependent and frequency-dependent polarization
behaviour.

The strongest positive associations between pairs of parameters, marked dark
red on Fig. 3, are:

  * •

PA frequency evolution with PA RVM departures

  * •

PA frequency evolution with PA jumps where $\lvert V\rvert>0$

  * •

$V$ change of hand with frequency evolution of total intensity

  * •

$V$ change of hand with PA RVM departures.

The only negative association, implying that these two characteristics are
found together less often than expected for independent variables, is that
between PA orthogonal jumps and $V$ shape frequency evolution. Conversely, $V$
shape frequency evolution does show a link with PA jumps where the circular
polarization is non-zero.

####  4.2.2 Most and fewest associations

The two characteristics with the most associations are $I$ shape frequency
evolution and $V$ change of hand. These characteristics display some
association with all of the categories other than $L$ fraction frequency
evolution, which itself is the characteristic with the fewest associations. It
only shows a notable link to $L$ shape frequency evolution and to $V$ fraction
frequency evolution.

####  4.2.3 PA behaviour and circular polarization

Non-RVM behaviour of the PA is associated more with circular polarization than
with linear polarization: PA RVM departures are associated with $V$ fraction
frequency evolution and $V$ change of hand, but not with any frequency
evolution of linear polarization. Similarly, PA jumps with non-zero circular
polarization are associated with $V$ shape frequency evolution and also with
$V$ change of hand. Both these associations are weak, but present, whereas
there is no association with linear polarization frequency evolution. Taken
collectively, the various associations with categories related to circular
polarization indicate a strong link between polarization behaviour not
explained by the rotating vector model and the presence of circular
polarization in the pulse profile. A similar link is noted by Johnston et al.
(2022), who find that, when fitting the RVM to the PA, a large fraction of the
pulsars for which this fails have a circular polarization fraction greater
than the linear polarization fraction. This can be explained as resulting from
the coherent addition of orthogonal modes, a concept we will discuss further
in Section 5.

###  4.3 Average polarizations, profile complexity and $\dot{E}$

Next, we investigate the relationships between polarization measurements and
spin-down energy $\dot{E}$ (measured in erg s-1). The association of high
$\dot{E}$ pulsars with strong linear polarization has been shown before (e.g.
Weltevrede & Johnston, 2008), and it has been noted that high $\dot{E}$
pulsars tend to have simple profiles (Johnston & Weisberg, 2006). In addition,
pulsars with more complex intensity profile shapes tend to have more complex
PA profiles as well: this has been shown for young pulsars (Karastergiou &
Johnston, 2006) and is particularly well demonstrated by millisecond pulsars
(Dai et al., 2015). We investigate these factors together. Fig. 4 shows the
distributions of $\dot{E}$, average polarization fraction $\overline{p}$ and
circular contribution $\overline{\theta}$ at 1400 MHz, divided into three
colours by profile complexity category. Simpler profiles correspond to higher
$\dot{E}$, a more uniform distribution of polarization fraction and lower
circular contribution, whilst more complex profiles are linked to lower
$\dot{E}$, lower polarization fractions and a wider range of
$\overline{\theta}$. This work not only replicates the previous results
relating high $\dot{E}$ to high linear polarization and simple profile shapes,
but demonstrates the associations of all of these factors across $\dot{E}$,
and in particular shows that more complex pulsars tend to have a larger
proportion of circular polarization (higher $\overline{\theta}$) than simpler
profiles.

We also consider these relations for the whole sample of pulsars, including
all of the lower S/N pulsars for which we do not categorize profile
complexity. Applying principal component analysis (PCA) to the 3D parameter
space of $\log_{10}(\dot{E})$, $\overline{p}$ and $\overline{\theta}$, we find
that the principal component vector in this parameter space can be described
by the following parametrization of deviations with respect to the mean
values:

$\begin{pmatrix}\log_{10}(\dot{E_{0}})\\\ \overline{p}_{0}\\\
\overline{\theta}_{0}\end{pmatrix}+t\begin{pmatrix}\Delta\log_{10}(\dot{E})\\\
\Delta\overline{p}\\\
\Delta\overline{\theta}\end{pmatrix}=\begin{pmatrix}33.7\\\ 0.4\\\
13.7$\lx<EMAIL_ADDRESS>0.2\\\
-5.1$\lx<EMAIL_ADDRESS>(2)

This means that an increase in $\dot{E}$ by a factor of 10 corresponds roughly
to an increase in polarization fraction of 20% and a decrease of circular
contribution of around 5$\degree$ (i.e. 6% of 90$\degree$). We note that this
is a simplified description which does not encompass the distribution of
results around that principle component vector: Weltevrede & Johnston (2008)
described the relationship between $L$ and $\dot{E}$ as showing an arctangent
relationship rather than a linear evolution. Our work indicates that it is
possible to infer a smoother evolution, though does not confirm absolutely one
way or the other. The results of the Thousand-Pulsar-Array census on the
MeerKAT telescope will provide a larger population of measurements for
investigating this relationship (Posselt et al., 2022).

Figure 4: Corner plot of spin-down energy $\dot{E}$, phase-averaged
polarization fraction $\overline{p}$ and circular contribution
$\overline{\theta}$ (see definitions in Section 3) for the 101 high-S/N pulsar
subset, split in colour by Profile Complexity category (see definition in
Section 3.3).

###  4.4 Combining categorizations and average polarization measurements

Figure 5: Heat map of the number of counts of pulsars from the high-S/N sample
assigned to each polarization category (y-axis), split by their measurement of
spin-down energy $\dot{E}$ into five quantiles, such that there is the same
number of pulsars in each quantile (x-axis), as shown by the top row which
indicates the total count of pulsars in the quantile. A paler colour indicates
a higher count, and the actual count in each category is written on the heat
map. The polarization categories are defined in Section 3.3. Figure 6: As for
Fig. 5, but now divided by three quantiles for circular contribution
$\overline{\theta}$ (see definition in Section 3).

Having considered polarization categories in Section 4.2 and polarization and
$\dot{E}$ measurements in Section 4.3, we now look to combine the two. Figures
5 and 6 compare the 10 polarization categories against $\dot{E}$ and circular
contribution $\overline{\theta}$ respectively. For each figure we divide the
distribution of $\log_{10}(\dot{E})$ and $\overline{\theta}$ measurements into
quantiles such that each quantile contains the same number of pulsars. We note
that each quantile spans a different range in $\log_{10}(\dot{E})$ space
because the sample is not uniformly distributed across $\log_{10}(\dot{E})$.
The same is true for $\bar{\theta}$. We then count how many pulsars in each
quantile fall into a given category. On the figures, the categories are
divided into frequency-dependent and phase-dependent categories, in a similar
way as for Fig. 3. We also show the total count of pulsars in each quantile,
and define two new categories as absences from the other categories: these are
simply the counts of pulsars that do not exhibit any frequency evolution of
their polarization and do not show departures from the RVM. In Figs 5 and 6,
the count is displayed in each quantile-category box and the colour of the box
also represents the count.

These figures demonstrate three factors: the absolute incidences of each
categorized feature, the rates of incidence relative to each other, and the
relative incidence rates across $\dot{E}$ and $\overline{\theta}$. A general
statement to be drawn from Fig. 5 is the following: there are more occurrences
of frequency- and phase-evolution of polarization at lower spin-down energies,
particularly the three lowest quantiles spanning the $\dot{E}$ range $10^{31}$
to $10^{33.5}$ erg s-1. Similarly, pulsars showing no polarization frequency
evolution and no RVM departures are predominantly found at high spin-down
energies, in the top two quantiles of $\dot{E}$ from $10^{33.5}$ to
$10^{36.9}$ erg s-1. It should be noted that, since the incidences of the
polarization categories are found to be dependent on $\dot{E}$ and our sample
has a different distribution of $\dot{E}$ relative to the population as a
whole, the exact percentages listed in Table 2 are likely to be somewhat
different for the pulsar population as a whole. However, the co-occurrence and
quantile-based analysis would be directly transferable to a different pulsar
sample. In Fig. 6, it can be seen that RVM departures and evolution of the PA
with frequency are both more common for pulsars with higher values of
$\overline{\theta}$, with both of these categories showing increases across
the three quantiles. Conversely, pulsars with no RVM departures are
predominantly found to have lower values of $\overline{\theta}$. From both
figures it can also be seen that the distributions of the “PA orthogonal jump”
category are skewed in different directions to those of the “PA RVM departure”
and “PA jump, $\lvert V\rvert>0$” categories: on a population level, true
orthogonal jumps are identifiably different from other PA behaviours.

###  4.5 Polarization fraction and circular contribution across the population
and across frequency

Fig. 7 shows the distribution of polarization fraction $\overline{p}$ and
circular contribution $\overline{\theta}$ as in Fig. 4, but now for the full
sample of 271 pulsars, not just the high-S/N subset. It also shows the
measured values at all eight frequency sub-bands, in order to build up a large
scale picture of the distributions of these two parameters with respect to
each other. For a subset of the pulsars, we plot lines to show the frequency
evolution in $\overline{p}$–$\overline{\theta}$ space, and for the rest, we
plot the individual values as grey dots.

####  4.5.1 Population distribution

It can be seen that the distribution is weighted towards the bottom-left of
the plot: low polarization and low circular contribution, and that there exist
no points at all in the top right quadrant. This means that whereas weakly
polarized pulsars have a greater range of circular contribution, strongly
polarized pulsars are linearly polarized. This is the same result as shown for
the high-S/N subset in Fig. 4, now shown to be true across the whole observed
sample and frequency band.

####  4.5.2 Frequency evolution

Since the polarization measurements presented here are averaged across pulse
phase, the values of $\overline{p}$ and $\overline{\theta}$ for a particular
pulsar are not fully representative of its polarization behaviour. However,
taken collectively, they provide useful insights into the population as a
whole. Similarly, for each pulsar, the values for the eight frequency channels
form a track in $\overline{p}$–$\overline{\theta}$ space, but individual
tracks for each pulsar are expected to be noisy and difficult to interpret. We
take an interest therefore in the behaviour of only the straightest tracks in
$\overline{p}$–$\overline{\theta}$ space: does their collective behaviour
reveal anything interesting about the frequency evolution of pulsar
polarization?

To identify these, we define two metrics for line length in
$\overline{p}$–$\overline{\theta}$ space: the full summed length of the line
from one end to the other and its characteristic length, which we define as
the furthest distance between two points in the collection of eight values.
For a noisy track that walks randomly around a tight area of parameter space,
the full summed length of the line will be much longer than the characteristic
length, whereas for a perfectly straight line the ratio of the full and
characteristic lengths will be 1. We calculate these ratios with
$\overline{\theta}$ normalized by 90$\degree$, so that travel through both
$\overline{p}$ and $\overline{\theta}$ space is equally weighted. In Fig. 7,
we plot only those tracks where the ratio of full-length/characteristic-length
< 1.3 (light blue dashed vectors) and full-length/characteristic-length < 1.1
(dark blue vectors). We also plot arrow directions on the vectors to indicate
the direction of increasing frequency.

It can be seen from the figure that at high polarization, the lines plotted
tend to be close to horizontal, or following diagonal tracks with a shallow
negative gradient, whereas at lower polarization, the gradients of these
tracks tend to become steeper. This suggests that the collective
$\overline{p}$–$\overline{\theta}$ spread seen as a population-level effect is
also born out by the frequency-evolution of individual pulsars. The arrows
mainly point in the negative-$\bar{p}$ direction, fitting the general observed
trend that pulsars tend to depolarize with increasing frequency. A more in-
depth investigation of phase-resolved frequency variation of pulsar
polarization would be required to confirm that this effect is truly
representative of the whole population, rather than just the least noisy
measurements extracted here. To aid in such future investigations, we present
waterfall plots of phase- and frequency-resolved polarization fraction $p$ and
circular contribution $\theta$ in the second part of the supplementary
material (file name “Appendix C Visualizations of p and theta for pulsar
sample”).

Figure 7: Plot of circular contribution $\overline{\theta}$ vs polarization
fraction $\overline{p}$ (see definitions in Section 3) for the whole pulsar
sample. Pale grey points: individual measurements for each of eight frequency
channels for all 271 pulsars, including the measurements for 15 interpulses.
Dark and light blue vectors: tracks for individual pulsars showing the
evolution of these parameters with increasing frequency. The subset shown have
been selected as fitting criteria for straightness of line: the method of
selection and justification for this choice are outlined in the text.

##  5 Discussion

###  5.1 Summary of key results

A large fraction of pulsars show frequency and phase evolution not encompassed
by the conventional picture (Lorimer & Kramer, 2012). We find links between
non-RVM behaviour of the PA, frequency evolution of polarization and the
presence of circular polarization features. Non-RVM behaviour of the PA, as
defined by categories (ii)b and (ii)c, is distinct from the behaviour of true
orthogonal jumps.

In general, pulsars with higher $\dot{E}$ also have simpler pulse profiles,
higher polarization fractions and lower values of $\overline{\theta}$. There
exist no high-$\overline{p}$-high-$\overline{\theta}$ pulsars. Frequency
evolution of polarization is seen more in low $\dot{E}$ pulsars. Similarly,
phase evolution of polarization, particularly non-RVM behaviour of the PA, is
observed more frequently in low $\dot{E}$ pulsars, whereas high $\dot{E}$
pulsars demonstrate little to no frequency evolution of polarization, along
with RVM-like PA profiles.

Polarization measurements evolve with frequency on curved tracks from high
$\overline{p}$, low $\overline{\theta}$ to low $\overline{p}$, high
$\overline{\theta}$ for at least some pulsars and for average profile
observations. In addition, lower $\overline{p}$ corresponds to steeper tracks:
more weakly polarized pulsars have stronger frequency evolution of circular
polarization.

###  5.2 Interpretation of results

An explanation previously presented for the links between profile complexity
and $\dot{E}$ is that older and younger pulsars (with lower and higher values
of $\dot{E}$) may have different emission height profiles (Karastergiou &
Johnston, 2007). A narrower range of emission heights for high $\dot{E}$
pulsars could result in simpler profiles, whilst a broader range of emission
heights for low $\dot{E}$ pulsars might introduce more complex profile shapes
and with them the potential for increased frequency evolution, non-RVM
behaviour and reduced polarization fraction.

Under such a scenario, the links between circular polarization features, non-
RVM behaviour in the PA and frequency evolution of polarization could be
explained as originating as propagational effects in the magnetosphere.
Propagational effects discussed in the literature include angular separation
of orthogonal modes due to refraction (Barnard & Arons, 1986), Generalized
Faraday Rotation (Kennett & Melrose, 1998) or coherent mixing of modes (Dyks,
2017). The broad bandwidth of the UWL highlights the relevance of frequency-
dependent effects in the polarization, which in future could be probed further
across even wider bandwidths: current suitable low-frequency instruments
include LOFAR and the MWA, and higher frequency observations will be possible
with future development of the MeerKAT S-band and Parkes Ultra-Wideband High
receivers. In the future, the Square Kilometre Array will increase the
sensitivity of pulsar observations, increasing the available high-S/N sample
size for detailed analysis.

The approach taken in this paper is to consider the collective polarization
behaviour of the pulsar population, reducing the degrees of freedom of the
dataset by calculating average polarizations and defining boolean categories
to describe the features and trends of the dataset. It can immediately be seen
from the online supplementary material that each individual pulsar also
displays its own idiosyncratic and interesting polarization behaviour. This
study focuses on young, non-recycled pulsars, but the polarization
idiosyncrasies of millisecond pulsars (e.g. Dai et al., 2015) and magnetars
(e.g. Dai et al., 2019) are observed to be even more extreme. Descriptions of
radio pulsar polarization must ultimately be able to account for the diversity
of individual polarization behaviours observed in broad-band pulsar data
whilst also explaining the origins of the patterns observed across the pulsar
population, as described here.

We propose a model that can achieve this: the “partially-coherent” model of
orthogonal mode mixing. In a follow-up work, we show how this model can
explain the relationship between polarization fraction and circular
contribution and the link between non-RVM PA behaviour and the presence of
circular polarization. The partially-coherent model can account for the
polarization trends described in this paper and can be used as a mathematical
decomposition of Stokes parameters to account for the idiosyncrasies of
individual pulsars as well.

##  6 Conclusions

The broad-band capabilities of the Parkes UWL observing system, and the long-
term observations of this dataset, provide an opportunity for an updated
picture of the polarization properties of young pulsars. This work presents
broad-band phase-resolved polarization information for 271 pulsars with a new
waterfall plot visualization, to provide a basis for a new description of
radio pulsar polarization. By defining and comparing collective categories for
polarization behaviour for the 101 pulsars passing our S/N criterion, we
demonstrate the relationships between key features of pulsar profiles,
encompassing links between phase- and frequency-dependent polarization
behaviour. We highlight the importance of circular polarization as a key
contributing factor to non-RVM polarization behaviour, and an important
measurable quantity for understanding the origins of pulsar radio
polarization. It is increasingly clear that physical models of pulsar radio
polarization must be able to explain the complexities of broad-band pulse
profile evolution and the key contribution of circular polarization. In
follow-up work, we outline how we can do this using the partially-coherent
model of orthogonal mode interaction.

## Acknowledgements

We would like to thank the reviewer for useful advice on how to improve the
quality of the manuscript. The Parkes radio telescope (Murriyang) is part of
the Australia Telescope National Facility (https://ror.org/05qajvd42) which is
funded by the Australian Government for operation as a National Facility
managed by CSIRO. We acknowledge the Wiradjuri people as the traditional
owners of the Observatory site. LSO acknowledges the support of Magdalen
College, Oxford. SD is the recipient of an Australian Research Council
Discovery Early Career Award (DE210101738) funded by the Australian
Government. Work at NRL is supported by NASA. RMS acknowledges support through
Australian Research Council Future Fellowship FT190100155.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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## Supplementary material

Visualizations of all of the pulsars in this sample are available at MNRAS
online. The two pieces of supplementary material are labelled “Appendix B
Polarization visualizations for pulsar sample” and “Appendix C Visualizations
of p and theta for pulsar sample”.

##  Appendix A Table of polarization measurements and categorizations

Table 3: Results of polarization measurements and categorizations for all 271 pulsars (plus 15 interpulses) in the sample. Column labels are defined as follows: ‘PSRJ’ is the pulsar name. Interpulses are indicated with ‘(i)’. $\overline{l}$, $\overline{\lvert v\rvert}$, $\overline{p}$ and $\overline{\theta}$ are polarization fractions and circular contribution as defined in Section 3. ‘Passed S/N cut’ is marked with ‘Y’ if the pulsar is part of the high-S/N subset as defined in Section 3. Column $S$ indicates scattered pulsars with an asterisk. ‘Categories’ lists the polarization categorization applied to the high-S/N pulsar sample as described in Section 3.3. PSRJ | $\overline{l}$ | $\overline{\lvert v\rvert}$ | $\overline{p}$ | $\overline{\theta}$ | Passed | $S$ | Categories
---|---|---|---|---|---|---|---
|  |  |  | ($\degree$) | S/N cut |  |
J0034-0721 | 0.100 $\pm$ 0.002 | 0.044 $\pm$ 0.002 | 0.122 $\pm$ 0.002 | 24 $\pm$ 1 | Y |  | (i)abcd;(ii)a;2
J0108-1431 | 0.768 $\pm$ 0.009 | 0.063 $\pm$ 0.007 | 0.781 $\pm$ 0.009 | 4.7 $\pm$ 0.5 |  |  |
J0134-2937 | 0.454 $\pm$ 0.003 | 0.194 $\pm$ 0.003 | 0.513 $\pm$ 0.003 | 23.1 $\pm$ 0.4 | Y |  | (i)abd;(ii)a;2
J0151-0635 | 0.324 $\pm$ 0.005 | 0.041 $\pm$ 0.005 | 0.338 $\pm$ 0.005 | 7.2 $\pm$ 0.9 |  |  |
J0152-1637 | 0.154 $\pm$ 0.006 | 0.040 $\pm$ 0.006 | 0.172 $\pm$ 0.006 | 15 $\pm$ 2 | Y |  | (i)abd;(ii)cd;2
J0206-4028 | 0.137 $\pm$ 0.006 | 0.070 $\pm$ 0.006 | 0.179 $\pm$ 0.006 | 27 $\pm$ 4 |  |  |
J0255-5304 | 0.088 $\pm$ 0.002 | 0.084 $\pm$ 0.002 | 0.142 $\pm$ 0.002 | 44 $\pm$ 3 | Y |  | (i)b;(ii)cd;1
J0304+1932 | 0.334 $\pm$ 0.003 | 0.111 $\pm$ 0.003 | 0.366 $\pm$ 0.003 | 18.4 $\pm$ 0.6 | Y |  | (i)abcdf;(ii)d;1
J0401-7608 | 0.283 $\pm$ 0.006 | 0.036 $\pm$ 0.005 | 0.296 $\pm$ 0.006 | 7 $\pm$ 1 | Y |  | (i)abd;(ii)abcd;2
J0448-2749 | 0.244 $\pm$ 0.005 | 0.138 $\pm$ 0.005 | 0.295 $\pm$ 0.005 | 30 $\pm$ 2 |  |  |
J0452-1759 | 0.1850 $\pm$ 0.0005 | 0.0216 $\pm$ 0.0004 | 0.1887 $\pm$ 0.0005 | 6.7 $\pm$ 0.1 | Y |  | (i)abdf;(ii)abd;2
J0525+1115 | 0.127 $\pm$ 0.006 | 0.119 $\pm$ 0.006 | 0.209 $\pm$ 0.006 | 43 $\pm$ 7 |  |  |
J0536-7543 | 0.466 $\pm$ 0.002 | 0.148 $\pm$ 0.002 | 0.503 $\pm$ 0.002 | 17.7 $\pm$ 0.3 | Y |  | (i)cdef;(ii);2
J0543+2329 | 0.483 $\pm$ 0.001 | 0.103 $\pm$ 0.001 | 0.501 $\pm$ 0.001 | 12.0 $\pm$ 0.2 | Y |  | (i)c;(ii);1
J0601-0527 | 0.309 $\pm$ 0.004 | 0.108 $\pm$ 0.004 | 0.349 $\pm$ 0.004 | 19.3 $\pm$ 0.9 | Y |  | (i)af;(ii)acd;1
J0614+2229 | 0.723 $\pm$ 0.003 | 0.167 $\pm$ 0.003 | 0.754 $\pm$ 0.003 | 13.0 $\pm$ 0.2 | Y |  | (i);(ii);0
J0624-0424 | 0.219 $\pm$ 0.007 | 0.063 $\pm$ 0.007 | 0.267 $\pm$ 0.007 | 16 $\pm$ 2 |  |  |
J0627+0706 | 0.233 $\pm$ 0.005 | 0.038 $\pm$ 0.005 | 0.244 $\pm$ 0.005 | 9 $\pm$ 1 |  |  |
J0627+0706 (i) | 0.17 $\pm$ 0.01 | 0.05 $\pm$ 0.01 | 0.23 $\pm$ 0.01 | 18 $\pm$ 5 |  |  |
J0630-2834 | 0.4901 $\pm$ 0.0007 | 0.0706 $\pm$ 0.0006 | 0.4971 $\pm$ 0.0007 | 8.19 $\pm$ 0.08 | Y |  | (i)d;(ii);1
J0631+1036 | 0.87 $\pm$ 0.01 | 0.066 $\pm$ 0.009 | 0.89 $\pm$ 0.01 | 4.3 $\pm$ 0.6 | Y |  | (i)a;(ii)d;1
J0659+1414 | 0.797 $\pm$ 0.005 | 0.141 $\pm$ 0.004 | 0.824 $\pm$ 0.005 | 10.0 $\pm$ 0.3 | Y |  | (i)ce;(ii);0
J0729-1448 | 0.89 $\pm$ 0.01 | 0.11 $\pm$ 0.01 | 0.91 $\pm$ 0.01 | 7.0 $\pm$ 0.6 |  |  |
J0729-1836 | 0.266 $\pm$ 0.005 | 0.063 $\pm$ 0.005 | 0.282 $\pm$ 0.005 | 13 $\pm$ 1 |  |  |
J0738-4042 | 0.2743 $\pm$ 0.0001 | 0.0686 $\pm$ 0.0001 | 0.2838 $\pm$ 0.0001 | 14.04 $\pm$ 0.03 | Y |  | (i)abcd;(ii)ad;2
J0742-2822 | 0.8888 $\pm$ 0.0005 | 0.0521 $\pm$ 0.0003 | 0.8909 $\pm$ 0.0005 | 3.35 $\pm$ 0.02 | Y |  | (i)ac;(ii)d;2
J0745-5353 | 0.240 $\pm$ 0.003 | 0.025 $\pm$ 0.003 | 0.248 $\pm$ 0.003 | 5.9 $\pm$ 0.6 | Y |  | (i)d;(ii)d;0
J0758-1528 | 0.168 $\pm$ 0.003 | 0.015 $\pm$ 0.003 | 0.170 $\pm$ 0.003 | 5 $\pm$ 1 | Y |  | (i)ab;(ii)cd;2
J0809-4753 | 0.275 $\pm$ 0.003 | 0.040 $\pm$ 0.003 | 0.286 $\pm$ 0.003 | 8.3 $\pm$ 0.7 |  |  |
J0820-1350 | 0.162 $\pm$ 0.001 | 0.083 $\pm$ 0.001 | 0.190 $\pm$ 0.001 | 27.1 $\pm$ 0.5 | Y |  | (i)abcdef;(ii)cd;2
J0820-3826 | 0.24 $\pm$ 0.02 | 0.04 $\pm$ 0.02 | 0.30 $\pm$ 0.02 | 9 $\pm$ 5 |  |  |
J0820-4114 | 0.279 $\pm$ 0.003 | 0.091 $\pm$ 0.003 | 0.313 $\pm$ 0.003 | 18.0 $\pm$ 0.6 |  |  |
J0834-4159 (i) | 0.2 $\pm$ 0.2 | 0.0 $\pm$ 0.2 | 0.2 $\pm$ 0.2 | 0 $\pm$ 57 |  |  |
J0834-4159 | 0.12 $\pm$ 0.03 | 0.13 $\pm$ 0.03 | 0.31 $\pm$ 0.03 | 47 $\pm$ 49 |  |  |
J0835-4510 | 0.93794 $\pm$ 0.00007 | 0.08339 $\pm$ 0.00005 | 0.94321 $\pm$ 0.00007 | 5.081 $\pm$ 0.003 | Y |  | (i)acde;(ii);1
J0837+0610 | 0.093 $\pm$ 0.002 | 0.051 $\pm$ 0.002 | 0.115 $\pm$ 0.002 | 29 $\pm$ 2 |  |  |
J0837-4135 | 0.1685 $\pm$ 0.0006 | 0.1115 $\pm$ 0.0006 | 0.2166 $\pm$ 0.0006 | 33.5 $\pm$ 0.3 | Y |  | (i)abef;(ii)acd;1
J0842-4851 (i) | 0.07 $\pm$ 0.04 | 0.02 $\pm$ 0.04 | 0.10 $\pm$ 0.04 | 13 $\pm$ 32 |  |  |
J0842-4851 | 0.083 $\pm$ 0.008 | 0.014 $\pm$ 0.008 | 0.100 $\pm$ 0.008 | 10 $\pm$ 6 |  |  |
J0855-4644 | 0.54 $\pm$ 0.03 | 0.05 $\pm$ 0.02 | 0.60 $\pm$ 0.03 | 6 $\pm$ 3 |  |  |
J0857-4424 | 0.08 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.12 $\pm$ 0.01 | 25 $\pm$ 9 |  |  |
J0901-4624 | 0.60 $\pm$ 0.02 | 0.30 $\pm$ 0.02 | 0.75 $\pm$ 0.02 | 27 $\pm$ 3 |  |  |
J0904-7459 | 0.245 $\pm$ 0.009 | 0.013 $\pm$ 0.009 | 0.257 $\pm$ 0.009 | 3 $\pm$ 2 |  |  |
J0905-5127 (i) | 0.2 $\pm$ 0.1 | 0.0 $\pm$ 0.1 | 0.2 $\pm$ 0.1 | 7 $\pm$ 38 |  |  |
J0905-5127 | 0.84 $\pm$ 0.01 | 0.091 $\pm$ 0.009 | 0.86 $\pm$ 0.01 | 6.2 $\pm$ 0.7 |  |  |
J0907-5157 | 0.359 $\pm$ 0.001 | 0.031 $\pm$ 0.001 | 0.367 $\pm$ 0.001 | 5.0 $\pm$ 0.2 | Y |  | (i)abdf;(ii)d;1
J0908-1739 | 0.140 $\pm$ 0.003 | 0.054 $\pm$ 0.003 | 0.166 $\pm$ 0.003 | 21 $\pm$ 1 | Y |  | (i)abd;(ii)cd;2
J0908-4913 (i) | 0.966 $\pm$ 0.005 | 0.035 $\pm$ 0.004 | 0.969 $\pm$ 0.005 | 2.1 $\pm$ 0.2 | Y |  | (i)aef;(ii)d;1
J0908-4913 | 0.982 $\pm$ 0.002 | 0.023 $\pm$ 0.001 | 0.984 $\pm$ 0.002 | 1.35 $\pm$ 0.07 | Y |  | (i)aef;(ii)d;1
J0924-5814 | 0.521 $\pm$ 0.004 | 0.018 $\pm$ 0.003 | 0.525 $\pm$ 0.004 | 2.0 $\pm$ 0.4 | Y |  | (i)c;(ii);0
J0940-5428 | 0.60 $\pm$ 0.02 | 0.04 $\pm$ 0.02 | 0.63 $\pm$ 0.02 | 4 $\pm$ 2 |  |  |
J0942-5552 | 0.372 $\pm$ 0.001 | 0.085 $\pm$ 0.001 | 0.392 $\pm$ 0.001 | 12.9 $\pm$ 0.2 | Y |  | (i)a;(ii)acd;1
J0954-5430 | 0.55 $\pm$ 0.02 | 0.08 $\pm$ 0.01 | 0.57 $\pm$ 0.02 | 9 $\pm$ 2 |  |  |
J0959-4809 | 0.38 $\pm$ 0.01 | 0.030 $\pm$ 0.009 | 0.40 $\pm$ 0.01 | 5 $\pm$ 1 |  |  |
J1001-5507 | 0.100 $\pm$ 0.001 | 0.062 $\pm$ 0.001 | 0.129 $\pm$ 0.001 | 32 $\pm$ 1 | Y |  | (i)abde;(ii)acd;2
J1003-4747 | 0.151 $\pm$ 0.008 | 0.023 $\pm$ 0.008 | 0.177 $\pm$ 0.008 | 9 $\pm$ 3 |  |  |
J1012-5857 | 0.130 $\pm$ 0.005 | 0.032 $\pm$ 0.005 | 0.144 $\pm$ 0.005 | 14 $\pm$ 2 | Y | * |
J1015-5719 | 0.80 $\pm$ 0.01 | 0.108 $\pm$ 0.008 | 0.83 $\pm$ 0.01 | 7.7 $\pm$ 0.6 |  |  |
J1016-5819 | 0.17 $\pm$ 0.02 | 0.05 $\pm$ 0.02 | 0.22 $\pm$ 0.03 | 17 $\pm$ 10 |  |  |
J1016-5857 | 0.50 $\pm$ 0.02 | 0.08 $\pm$ 0.02 | 0.57 $\pm$ 0.03 | 9 $\pm$ 3 |  |  |
J1017-5621 | 0.168 $\pm$ 0.004 | 0.196 $\pm$ 0.004 | 0.282 $\pm$ 0.004 | 49 $\pm$ 5 | Y |  | (i)bce;(ii)cd;1
J1019-5749 | 0.17 $\pm$ 0.01 | 0.01 $\pm$ 0.01 | 0.21 $\pm$ 0.01 | 5 $\pm$ 4 | Y | * |
J1028-5819 | 0.99 $\pm$ 0.02 | 0.01 $\pm$ 0.02 | 0.99 $\pm$ 0.02 | 0.8 $\pm$ 0.9 |  |  |
J1034-3224 | 0.228 $\pm$ 0.004 | 0.039 $\pm$ 0.004 | 0.253 $\pm$ 0.004 | 9.7 $\pm$ 0.9 |  |  |
J1038-5831 | 0.333 $\pm$ 0.008 | 0.080 $\pm$ 0.007 | 0.356 $\pm$ 0.008 | 14 $\pm$ 1 | Y |  | (i)acef;(ii)ad;1
J1043-6116 | 0.130 $\pm$ 0.006 | 0.111 $\pm$ 0.006 | 0.208 $\pm$ 0.006 | 41 $\pm$ 6 | Y | * |
J1046-5813 | 0.145 $\pm$ 0.007 | 0.034 $\pm$ 0.006 | 0.167 $\pm$ 0.007 | 13 $\pm$ 3 |  |  |
J1047-6709 | 0.737 $\pm$ 0.005 | 0.112 $\pm$ 0.004 | 0.753 $\pm$ 0.005 | 8.6 $\pm$ 0.4 | Y |  | (i);(ii);1
J1048-5832 | 0.751 $\pm$ 0.001 | 0.040 $\pm$ 0.001 | 0.755 $\pm$ 0.001 | 3.03 $\pm$ 0.08 | Y |  | (i)ae;(ii)d;2
J1049-5833 | 0.23 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.26 $\pm$ 0.01 | 9 $\pm$ 3 |  |  |
J1055-6028 | 0.26 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.28 $\pm$ 0.01 | 6 $\pm$ 2 |  |  |
J1056-6258 | 0.4021 $\pm$ 0.0006 | 0.0215 $\pm$ 0.0005 | 0.4037 $\pm$ 0.0006 | 3.07 $\pm$ 0.08 | Y |  | (i)ac;(ii);2
J1057-5226 | 0.975 $\pm$ 0.005 | 0.036 $\pm$ 0.003 | 0.978 $\pm$ 0.005 | 2.1 $\pm$ 0.2 | Y |  | (i);(ii)d;1
J1057-5226 (i) | 0.438 $\pm$ 0.004 | 0.023 $\pm$ 0.004 | 0.447 $\pm$ 0.004 | 3.0 $\pm$ 0.5 | Y |  | (i);(ii)d;1
J1105-6107 | 0.89 $\pm$ 0.01 | 0.08 $\pm$ 0.01 | 0.91 $\pm$ 0.01 | 5.4 $\pm$ 0.7 |  |  |
J1110-5637 | 0.264 $\pm$ 0.003 | 0.081 $\pm$ 0.003 | 0.292 $\pm$ 0.003 | 17.0 $\pm$ 0.8 | Y |  | (i)c;(ii)ad;1
J1112-6103 | 0.13 $\pm$ 0.01 | 0.02 $\pm$ 0.01 | 0.16 $\pm$ 0.01 | 7 $\pm$ 5 | Y | * |
J1114-6100 | 0.189 $\pm$ 0.004 | 0.008 $\pm$ 0.004 | 0.193 $\pm$ 0.004 | 3 $\pm$ 1 |  | * |
J1115-6052 | 0.69 $\pm$ 0.02 | 0.05 $\pm$ 0.02 | 0.71 $\pm$ 0.02 | 4 $\pm$ 1 |  |  |
J1119-6127 | 0.94 $\pm$ 0.02 | 0.06 $\pm$ 0.01 | 0.95 $\pm$ 0.02 | 3.4 $\pm$ 0.7 |  |  |
J1123-6259 | 0.55 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.56 $\pm$ 0.01 | 4 $\pm$ 1 |  |  |
J1136-5525 | 0.079 $\pm$ 0.002 | 0.018 $\pm$ 0.002 | 0.090 $\pm$ 0.002 | 13 $\pm$ 2 | Y |  | (i)ac;(ii)a;2
J1146-6030 | 0.242 $\pm$ 0.002 | 0.068 $\pm$ 0.002 | 0.259 $\pm$ 0.002 | 15.6 $\pm$ 0.6 | Y |  | (i)abcd;(ii)ad;2
J1156-5707 | 0.51 $\pm$ 0.02 | 0.04 $\pm$ 0.02 | 0.53 $\pm$ 0.02 | 5 $\pm$ 2 |  |  |
J1157-6224 | 0.312 $\pm$ 0.002 | 0.121 $\pm$ 0.002 | 0.373 $\pm$ 0.002 | 21.3 $\pm$ 0.5 |  |  |
J1210-5559 | 0.226 $\pm$ 0.005 | 0.026 $\pm$ 0.005 | 0.236 $\pm$ 0.005 | 7 $\pm$ 1 | Y |  | (i);(ii)ad;1
J1224-6407 | 0.324 $\pm$ 0.001 | 0.245 $\pm$ 0.001 | 0.435 $\pm$ 0.001 | 37.0 $\pm$ 0.3 | Y |  | (i)abcdef;(ii)bcd;2
J1225-6408 | 0.335 $\pm$ 0.008 | 0.046 $\pm$ 0.008 | 0.348 $\pm$ 0.008 | 8 $\pm$ 1 |  |  |
J1243-6423 | 0.2245 $\pm$ 0.0004 | 0.1394 $\pm$ 0.0004 | 0.2729 $\pm$ 0.0004 | 31.8 $\pm$ 0.2 | Y |  | (i)acdef;(ii)cd;2
J1253-5820 | 0.616 $\pm$ 0.003 | 0.078 $\pm$ 0.003 | 0.625 $\pm$ 0.003 | 7.2 $\pm$ 0.2 | Y |  | (i)a;(ii);1
J1301-6305 | 0.67 $\pm$ 0.04 | 0.05 $\pm$ 0.03 | 0.72 $\pm$ 0.04 | 4 $\pm$ 3 |  |  |
J1302-6350 (i) | 0.83 $\pm$ 0.01 | 0.181 $\pm$ 0.009 | 0.88 $\pm$ 0.01 | 12.3 $\pm$ 0.7 |  |  |
J1302-6350 | 0.916 $\pm$ 0.009 | 0.055 $\pm$ 0.007 | 0.925 $\pm$ 0.009 | 3.5 $\pm$ 0.4 |  |  |
J1305-6203 | 0.44 $\pm$ 0.02 | 0.03 $\pm$ 0.01 | 0.45 $\pm$ 0.02 | 4 $\pm$ 2 |  |  |
J1306-6617 | 0.204 $\pm$ 0.003 | 0.060 $\pm$ 0.003 | 0.227 $\pm$ 0.003 | 16.3 $\pm$ 0.9 | Y | * |
J1317-6302 | 0.114 $\pm$ 0.007 | 0.045 $\pm$ 0.007 | 0.156 $\pm$ 0.007 | 21 $\pm$ 4 |  | * |
J1319-6056 | 0.360 $\pm$ 0.006 | 0.092 $\pm$ 0.006 | 0.387 $\pm$ 0.006 | 14 $\pm$ 1 |  | * |
J1320-5359 | 0.216 $\pm$ 0.005 | 0.066 $\pm$ 0.004 | 0.238 $\pm$ 0.005 | 17 $\pm$ 1 |  |  |
J1326-5859 | 0.3412 $\pm$ 0.0004 | 0.1855 $\pm$ 0.0004 | 0.4061 $\pm$ 0.0004 | 28.53 $\pm$ 0.09 | Y | * |
J1326-6408 | 0.197 $\pm$ 0.005 | 0.085 $\pm$ 0.005 | 0.243 $\pm$ 0.005 | 23 $\pm$ 2 | Y |  | (i)a;(ii)cd;1
J1326-6700 | 0.3524 $\pm$ 0.0008 | 0.0623 $\pm$ 0.0007 | 0.3610 $\pm$ 0.0008 | 10.0 $\pm$ 0.1 | Y |  | (i)acd;(ii)acd;2
J1327-6222 | 0.0990 $\pm$ 0.0005 | 0.0450 $\pm$ 0.0005 | 0.1145 $\pm$ 0.0005 | 24.4 $\pm$ 0.4 | Y | * |
J1327-6301 | 0.291 $\pm$ 0.004 | 0.022 $\pm$ 0.004 | 0.303 $\pm$ 0.004 | 4.4 $\pm$ 0.7 |  |  |
J1328-4357 | 0.316 $\pm$ 0.002 | 0.049 $\pm$ 0.002 | 0.326 $\pm$ 0.002 | 8.8 $\pm$ 0.4 | Y |  | (i)ace;(ii)ad;2
J1338-6204 | 0.270 $\pm$ 0.003 | 0.104 $\pm$ 0.003 | 0.325 $\pm$ 0.003 | 21.0 $\pm$ 0.8 | Y | * |
J1340-6456 | 0.090 $\pm$ 0.008 | 0.037 $\pm$ 0.008 | 0.123 $\pm$ 0.008 | 22 $\pm$ 6 |  |  |
J1341-6220 | 0.643 $\pm$ 0.008 | 0.142 $\pm$ 0.007 | 0.680 $\pm$ 0.008 | 12.4 $\pm$ 0.6 |  | * |
J1349-6130 | 0.28 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.30 $\pm$ 0.01 | 5 $\pm$ 3 |  |  |
J1352-6803 | 0.35 $\pm$ 0.02 | 0.06 $\pm$ 0.02 | 0.38 $\pm$ 0.02 | 10 $\pm$ 3 |  |  |
J1356-5521 | 0.269 $\pm$ 0.006 | 0.023 $\pm$ 0.006 | 0.284 $\pm$ 0.006 | 5 $\pm$ 1 |  |  |
J1357-62 | 0.199 $\pm$ 0.001 | 0.100 $\pm$ 0.001 | 0.236 $\pm$ 0.001 | 26.6 $\pm$ 0.5 | Y | * |
J1357-6429 | 0.82 $\pm$ 0.03 | 0.09 $\pm$ 0.02 | 0.86 $\pm$ 0.03 | 6 $\pm$ 2 |  |  |
J1359-6038 | 0.789 $\pm$ 0.001 | 0.138 $\pm$ 0.001 | 0.810 $\pm$ 0.001 | 9.90 $\pm$ 0.07 | Y | * |
J1401-6357 | 0.258 $\pm$ 0.001 | 0.014 $\pm$ 0.001 | 0.259 $\pm$ 0.001 | 3.0 $\pm$ 0.3 | Y |  | (i)abe;(ii)bd;0
J1410-6132 | 0.15 $\pm$ 0.04 | 0.00 $\pm$ 0.04 | 0.18 $\pm$ 0.04 | 2 $\pm$ 16 | Y | * |
J1412-6145 | 0.58 $\pm$ 0.02 | 0.10 $\pm$ 0.01 | 0.61 $\pm$ 0.02 | 10 $\pm$ 1 |  | * |
J1413-6141 | 0.15 $\pm$ 0.02 | 0.04 $\pm$ 0.02 | 0.22 $\pm$ 0.02 | 16 $\pm$ 9 |  | * |
J1418-3921 | 0.08 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.13 $\pm$ 0.01 | 23 $\pm$ 10 |  |  |
J1420-6048 | 0.81 $\pm$ 0.02 | 0.21 $\pm$ 0.02 | 0.89 $\pm$ 0.02 | 15 $\pm$ 1 |  |  |
J1424-5822 | 0.181 $\pm$ 0.009 | 0.040 $\pm$ 0.009 | 0.221 $\pm$ 0.009 | 12 $\pm$ 3 |  |  |
J1428-5530 | 0.184 $\pm$ 0.001 | 0.015 $\pm$ 0.001 | 0.189 $\pm$ 0.001 | 4.7 $\pm$ 0.4 | Y |  | (i)abcf;(ii)b;2
J1430-6623 | 0.1475 $\pm$ 0.0008 | 0.0391 $\pm$ 0.0007 | 0.1590 $\pm$ 0.0008 | 14.8 $\pm$ 0.3 | Y |  | (i)af;(ii)cd;1
J1435-5954 | 0.101 $\pm$ 0.009 | 0.014 $\pm$ 0.009 | 0.122 $\pm$ 0.009 | 8 $\pm$ 5 |  |  |
J1452-6036 | 0.405 $\pm$ 0.007 | 0.090 $\pm$ 0.007 | 0.429 $\pm$ 0.007 | 13 $\pm$ 1 |  | * |
J1453-6413 | 0.2933 $\pm$ 0.0006 | 0.0675 $\pm$ 0.0006 | 0.3083 $\pm$ 0.0006 | 13.0 $\pm$ 0.1 | Y |  | (i)abdf;(ii)acd;2
J1456-6843 | 0.1238 $\pm$ 0.0002 | 0.0617 $\pm$ 0.0002 | 0.1470 $\pm$ 0.0003 | 26.5 $\pm$ 0.2 | Y |  | (i)abcf;(ii)cd;2
J1509-5850 | 0.30 $\pm$ 0.04 | 0.07 $\pm$ 0.04 | 0.39 $\pm$ 0.04 | 13 $\pm$ 8 |  |  |
J1512-5759 | 0.107 $\pm$ 0.002 | 0.030 $\pm$ 0.002 | 0.121 $\pm$ 0.002 | 16 $\pm$ 1 | Y | * |
J1513-5908 | 0.92 $\pm$ 0.02 | 0.14 $\pm$ 0.02 | 0.96 $\pm$ 0.02 | 8 $\pm$ 1 |  |  |
J1515-5720 | 0.12 $\pm$ 0.03 | 0.07 $\pm$ 0.03 | 0.21 $\pm$ 0.03 | 30 $\pm$ 20 |  |  |
J1522-5829 | 0.295 $\pm$ 0.002 | 0.056 $\pm$ 0.002 | 0.311 $\pm$ 0.002 | 10.7 $\pm$ 0.4 | Y | * |
J1524-5625 | 0.67 $\pm$ 0.02 | 0.05 $\pm$ 0.01 | 0.70 $\pm$ 0.02 | 4 $\pm$ 1 |  |  |
J1524-5706 | 0.49 $\pm$ 0.02 | 0.08 $\pm$ 0.02 | 0.53 $\pm$ 0.02 | 9 $\pm$ 2 |  |  |
J1530-5327 | 0.151 $\pm$ 0.009 | 0.020 $\pm$ 0.009 | 0.17 $\pm$ 0.01 | 7 $\pm$ 4 |  |  |
J1531-5610 | 0.83 $\pm$ 0.02 | 0.07 $\pm$ 0.01 | 0.85 $\pm$ 0.02 | 5 $\pm$ 1 |  |  |
J1534-5334 | 0.091 $\pm$ 0.002 | 0.061 $\pm$ 0.002 | 0.128 $\pm$ 0.002 | 34 $\pm$ 2 | Y |  | (i)ab;(ii)cd;1
J1534-5405 | 0.178 $\pm$ 0.007 | 0.038 $\pm$ 0.007 | 0.206 $\pm$ 0.007 | 12 $\pm$ 3 |  |  |
J1535-4114 | 0.494 $\pm$ 0.005 | 0.026 $\pm$ 0.004 | 0.501 $\pm$ 0.005 | 3.0 $\pm$ 0.5 | Y |  | (i)acdf;(ii);1
J1536-5433 | 0.177 $\pm$ 0.006 | 0.029 $\pm$ 0.006 | 0.197 $\pm$ 0.006 | 9 $\pm$ 2 |  |  |
J1539-5626 | 0.336 $\pm$ 0.003 | 0.059 $\pm$ 0.003 | 0.355 $\pm$ 0.003 | 9.9 $\pm$ 0.5 | Y | * |
J1541-5535 | 0.49 $\pm$ 0.03 | 0.07 $\pm$ 0.03 | 0.54 $\pm$ 0.03 | 8 $\pm$ 3 |  |  |
J1543-5459 | 0.21 $\pm$ 0.01 | 0.21 $\pm$ 0.01 | 0.39 $\pm$ 0.02 | 45 $\pm$ 11 |  | * |
J1544-5308 | 0.171 $\pm$ 0.002 | 0.071 $\pm$ 0.002 | 0.209 $\pm$ 0.002 | 22 $\pm$ 1 | Y |  | (i)adf;(ii)d;2
J1548-5607 | 0.73 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.73 $\pm$ 0.01 | 2.3 $\pm$ 0.8 |  | * |
J1549-4848 | 0.17 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.18 $\pm$ 0.01 | 9 $\pm$ 3 |  |  |
J1549-4848 (i) | 0.30 $\pm$ 0.02 | 0.02 $\pm$ 0.02 | 0.34 $\pm$ 0.02 | 5 $\pm$ 4 |  |  |
J1555-3134 | 0.140 $\pm$ 0.003 | 0.048 $\pm$ 0.003 | 0.163 $\pm$ 0.003 | 19 $\pm$ 1 | Y |  | (i)abdf;(ii)bd;2
J1557-4258 | 0.297 $\pm$ 0.004 | 0.131 $\pm$ 0.004 | 0.352 $\pm$ 0.004 | 23.8 $\pm$ 0.9 |  |  |
J1559-4438 | 0.3705 $\pm$ 0.0004 | 0.0999 $\pm$ 0.0004 | 0.3974 $\pm$ 0.0004 | 15.08 $\pm$ 0.07 | Y |  | (i)abcf;(ii)acd;2
J1600-5044 | 0.1843 $\pm$ 0.0007 | 0.2616 $\pm$ 0.0007 | 0.3349 $\pm$ 0.0007 | 55 $\pm$ 1 | Y | * |
J1600-5751 | 0.148 $\pm$ 0.007 | 0.041 $\pm$ 0.007 | 0.184 $\pm$ 0.007 | 15 $\pm$ 3 |  |  |
J1602-5100 | 0.195 $\pm$ 0.002 | 0.079 $\pm$ 0.002 | 0.230 $\pm$ 0.002 | 22.0 $\pm$ 0.6 | Y |  | (i)abc;(ii)abcd;2
J1603-5657 | 0.399 $\pm$ 0.009 | 0.181 $\pm$ 0.008 | 0.470 $\pm$ 0.009 | 24 $\pm$ 2 |  |  |
J1604-4909 | 0.114 $\pm$ 0.002 | 0.033 $\pm$ 0.002 | 0.126 $\pm$ 0.002 | 16 $\pm$ 1 | Y |  | (i)abf;(ii)cd;2
J1605-5257 | 0.361 $\pm$ 0.001 | 0.041 $\pm$ 0.001 | 0.366 $\pm$ 0.001 | 6.5 $\pm$ 0.2 | Y |  | (i)abce;(ii)a;2
J1611-5209 | 0.182 $\pm$ 0.007 | 0.032 $\pm$ 0.007 | 0.198 $\pm$ 0.007 | 10 $\pm$ 2 | Y |  | (i)abe;(ii)cd;1
J1611-5209 (i) | 0.19 $\pm$ 0.07 | 0.05 $\pm$ 0.07 | 0.30 $\pm$ 0.07 | 16 $\pm$ 23 | Y |  | (i)abe;(ii)cd;1
J1613-4714 | 0.145 $\pm$ 0.006 | 0.031 $\pm$ 0.006 | 0.160 $\pm$ 0.006 | 12 $\pm$ 2 |  |  |
J1614-5048 | 0.725 $\pm$ 0.007 | 0.192 $\pm$ 0.006 | 0.773 $\pm$ 0.007 | 14.8 $\pm$ 0.5 |  | * |
J1623-4256 | 0.258 $\pm$ 0.005 | 0.047 $\pm$ 0.005 | 0.277 $\pm$ 0.005 | 10 $\pm$ 1 |  |  |
J1626-4537 | 0.061 $\pm$ 0.009 | 0.025 $\pm$ 0.009 | 0.100 $\pm$ 0.009 | 23 $\pm$ 11 |  |  |
J1630-4733 | 0.302 $\pm$ 0.005 | 0.157 $\pm$ 0.005 | 0.384 $\pm$ 0.006 | 27 $\pm$ 1 |  | * |
J1632-4621 | 0.27 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.28 $\pm$ 0.01 | 8 $\pm$ 3 |  | * |
J1633-4453 | 0.130 $\pm$ 0.005 | 0.016 $\pm$ 0.005 | 0.142 $\pm$ 0.005 | 7 $\pm$ 2 |  | * |
J1633-5015 | 0.293 $\pm$ 0.002 | 0.121 $\pm$ 0.002 | 0.328 $\pm$ 0.002 | 22.5 $\pm$ 0.4 | Y | * |
J1637-4553 (i) | 0.24 $\pm$ 0.07 | 0.12 $\pm$ 0.07 | 0.40 $\pm$ 0.08 | 27 $\pm$ 24 |  |  |
J1637-4553 | 0.88 $\pm$ 0.01 | 0.021 $\pm$ 0.008 | 0.89 $\pm$ 0.01 | 1.4 $\pm$ 0.6 |  |  |
J1637-4642 | 0.89 $\pm$ 0.03 | 0.08 $\pm$ 0.02 | 0.93 $\pm$ 0.03 | 5 $\pm$ 1 |  |  |
J1638-4417 | 0.75 $\pm$ 0.04 | 0.03 $\pm$ 0.03 | 0.77 $\pm$ 0.04 | 3 $\pm$ 2 |  |  |
J1638-4608 | 0.65 $\pm$ 0.02 | 0.05 $\pm$ 0.02 | 0.67 $\pm$ 0.02 | 4 $\pm$ 2 |  |  |
J1638-4725 | 0.08 $\pm$ 0.02 | 0.03 $\pm$ 0.02 | 0.15 $\pm$ 0.02 | 23 $\pm$ 18 |  | * |
J1640-4715 | 0.18 $\pm$ 0.01 | 0.02 $\pm$ 0.01 | 0.21 $\pm$ 0.01 | 7 $\pm$ 4 |  | * |
J1643-4505 | 0.58 $\pm$ 0.03 | 0.34 $\pm$ 0.02 | 0.76 $\pm$ 0.03 | 30 $\pm$ 4 |  |  |
J1644-4559 | 0.21939 $\pm$ 0.00008 | 0.03564 $\pm$ 0.00008 | 0.22439 $\pm$ 0.00008 | 9.23 $\pm$ 0.02 | Y | * |
J1645-0317 | 0.1324 $\pm$ 0.0005 | 0.0324 $\pm$ 0.0005 | 0.1422 $\pm$ 0.0005 | 13.8 $\pm$ 0.2 | Y |  | (i)abc;(ii)abcd;1
J1646-4346 | 0.43 $\pm$ 0.01 | 0.02 $\pm$ 0.01 | 0.45 $\pm$ 0.01 | 3 $\pm$ 2 |  | * |
J1646-6831 | 0.383 $\pm$ 0.003 | 0.079 $\pm$ 0.003 | 0.410 $\pm$ 0.003 | 11.6 $\pm$ 0.5 |  |  |
J1648-3256 | 0.115 $\pm$ 0.006 | 0.068 $\pm$ 0.006 | 0.167 $\pm$ 0.007 | 30 $\pm$ 5 |  |  |
J1648-4611 | 0.70 $\pm$ 0.02 | 0.15 $\pm$ 0.01 | 0.75 $\pm$ 0.02 | 12 $\pm$ 1 |  |  |
J1649-3805 | 0.16 $\pm$ 0.01 | 0.06 $\pm$ 0.01 | 0.21 $\pm$ 0.01 | 20 $\pm$ 5 |  |  |
J1649-4653 | 0.52 $\pm$ 0.03 | 0.05 $\pm$ 0.03 | 0.56 $\pm$ 0.03 | 6 $\pm$ 3 |  |  |
J1650-4502 | 0.73 $\pm$ 0.01 | 0.05 $\pm$ 0.01 | 0.75 $\pm$ 0.01 | 4.3 $\pm$ 0.8 |  | * |
J1650-4921 | 0.75 $\pm$ 0.02 | 0.26 $\pm$ 0.01 | 0.81 $\pm$ 0.02 | 19 $\pm$ 1 |  |  |
J1651-4246 | 0.444 $\pm$ 0.001 | 0.127 $\pm$ 0.001 | 0.497 $\pm$ 0.001 | 16.0 $\pm$ 0.2 | Y | * |
J1651-5222 | 0.174 $\pm$ 0.002 | 0.075 $\pm$ 0.002 | 0.209 $\pm$ 0.002 | 23 $\pm$ 1 | Y |  | (i)ab;(ii)bcd;2
J1651-5255 | 0.368 $\pm$ 0.004 | 0.079 $\pm$ 0.004 | 0.394 $\pm$ 0.004 | 12.1 $\pm$ 0.7 |  |  |
J1652-2404 | 0.112 $\pm$ 0.006 | 0.053 $\pm$ 0.006 | 0.142 $\pm$ 0.006 | 25 $\pm$ 4 |  |  |
J1653-3838 | 0.360 $\pm$ 0.003 | 0.054 $\pm$ 0.003 | 0.370 $\pm$ 0.003 | 8.5 $\pm$ 0.5 | Y |  | (i);(ii)ad;1
J1653-4249 | 0.161 $\pm$ 0.007 | 0.022 $\pm$ 0.007 | 0.176 $\pm$ 0.007 | 8 $\pm$ 3 |  | * |
J1700-3312 | 0.361 $\pm$ 0.009 | 0.120 $\pm$ 0.008 | 0.407 $\pm$ 0.009 | 18 $\pm$ 2 |  |  |
J1701-3726 | 0.313 $\pm$ 0.003 | 0.187 $\pm$ 0.003 | 0.398 $\pm$ 0.003 | 30.9 $\pm$ 0.9 | Y |  | (i)abcde;(ii)bcd;2
J1701-4533 | 0.268 $\pm$ 0.005 | 0.104 $\pm$ 0.005 | 0.306 $\pm$ 0.005 | 21 $\pm$ 1 |  | * |
J1702-4128 | 0.60 $\pm$ 0.02 | 0.04 $\pm$ 0.01 | 0.62 $\pm$ 0.02 | 4 $\pm$ 1 |  |  |
J1702-4310 | 0.96 $\pm$ 0.02 | 0.11 $\pm$ 0.01 | 0.99 $\pm$ 0.02 | 6.6 $\pm$ 0.8 |  |  |
J1703-3241 | 0.429 $\pm$ 0.001 | 0.089 $\pm$ 0.001 | 0.443 $\pm$ 0.001 | 11.7 $\pm$ 0.2 | Y |  | (i)acde;(ii)cd;2
J1703-4851 | 0.135 $\pm$ 0.008 | 0.062 $\pm$ 0.008 | 0.183 $\pm$ 0.008 | 25 $\pm$ 4 |  |  |
J1705-1906 | 0.473 $\pm$ 0.003 | 0.186 $\pm$ 0.002 | 0.530 $\pm$ 0.003 | 21.5 $\pm$ 0.4 | Y |  | (i)ae;(ii)d;2
J1705-1906 (i) | 0.81 $\pm$ 0.01 | 0.180 $\pm$ 0.009 | 0.84 $\pm$ 0.01 | 12.6 $\pm$ 0.7 | Y |  | (i)ae;(ii)d;2
J1705-3423 | 0.130 $\pm$ 0.002 | 0.031 $\pm$ 0.002 | 0.146 $\pm$ 0.003 | 13 $\pm$ 1 | Y |  | (i)f;(ii)bd;0
J1705-3950 | 0.80 $\pm$ 0.01 | 0.266 $\pm$ 0.009 | 0.90 $\pm$ 0.01 | 18.3 $\pm$ 0.8 |  |  |
J1707-4053 | 0.240 $\pm$ 0.003 | 0.055 $\pm$ 0.003 | 0.257 $\pm$ 0.003 | 13.0 $\pm$ 0.7 |  | * |
J1707-4729 | 0.309 $\pm$ 0.007 | 0.083 $\pm$ 0.007 | 0.349 $\pm$ 0.007 | 15 $\pm$ 1 |  | * |
J1708-3426 | 0.166 $\pm$ 0.005 | 0.088 $\pm$ 0.005 | 0.217 $\pm$ 0.005 | 28 $\pm$ 2 |  |  |
J1709-1640 | 0.104 $\pm$ 0.001 | 0.014 $\pm$ 0.001 | 0.110 $\pm$ 0.001 | 7.7 $\pm$ 0.7 | Y |  | (i)abe;(ii)d;0
J1709-4429 | 0.950 $\pm$ 0.002 | 0.213 $\pm$ 0.002 | 0.980 $\pm$ 0.002 | 12.7 $\pm$ 0.1 | Y |  | (i);(ii);0
J1715-3903 | 0.89 $\pm$ 0.03 | 0.09 $\pm$ 0.02 | 0.92 $\pm$ 0.03 | 6 $\pm$ 1 |  |  |
J1715-4034 | 0.224 $\pm$ 0.007 | 0.033 $\pm$ 0.007 | 0.243 $\pm$ 0.007 | 8 $\pm$ 2 |  |  |
J1716-4005 | 0.08 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.12 $\pm$ 0.01 | 19 $\pm$ 9 |  | * |
J1717-3425 | 0.092 $\pm$ 0.003 | 0.071 $\pm$ 0.003 | 0.140 $\pm$ 0.003 | 38 $\pm$ 4 |  | * |
J1718-3825 | 0.95 $\pm$ 0.02 | 0.14 $\pm$ 0.01 | 0.99 $\pm$ 0.02 | 8.2 $\pm$ 0.7 |  |  |
J1719-4006 | 0.080 $\pm$ 0.009 | 0.042 $\pm$ 0.009 | 0.121 $\pm$ 0.009 | 28 $\pm$ 9 |  |  |
J1720-2933 | 0.152 $\pm$ 0.007 | 0.050 $\pm$ 0.007 | 0.185 $\pm$ 0.007 | 18 $\pm$ 3 |  |  |
J1721-3532 | 0.081 $\pm$ 0.003 | 0.051 $\pm$ 0.003 | 0.130 $\pm$ 0.003 | 32 $\pm$ 4 |  | * |
J1722-3207 | 0.233 $\pm$ 0.002 | 0.031 $\pm$ 0.002 | 0.241 $\pm$ 0.002 | 7.6 $\pm$ 0.5 | Y |  | (i)abcef;(ii)cd;1
J1722-3632 | 0.193 $\pm$ 0.007 | 0.041 $\pm$ 0.007 | 0.218 $\pm$ 0.007 | 12 $\pm$ 2 |  |  |
J1722-3712 (i) | 0.86 $\pm$ 0.02 | 0.03 $\pm$ 0.02 | 0.87 $\pm$ 0.02 | 2 $\pm$ 1 | Y |  | (i);(ii);0
J1722-3712 | 0.377 $\pm$ 0.002 | 0.122 $\pm$ 0.002 | 0.403 $\pm$ 0.002 | 18.0 $\pm$ 0.4 | Y |  | (i);(ii);0
J1723-3659 | 0.544 $\pm$ 0.008 | 0.175 $\pm$ 0.007 | 0.597 $\pm$ 0.008 | 17.8 $\pm$ 0.9 |  |  |
J1727-2739 | 0.489 $\pm$ 0.004 | 0.045 $\pm$ 0.004 | 0.496 $\pm$ 0.004 | 5.3 $\pm$ 0.5 |  |  |
J1730-3350 | 0.572 $\pm$ 0.007 | 0.023 $\pm$ 0.006 | 0.582 $\pm$ 0.007 | 2.3 $\pm$ 0.6 |  | * |
J1731-4744 | 0.170 $\pm$ 0.002 | 0.018 $\pm$ 0.002 | 0.173 $\pm$ 0.002 | 6.0 $\pm$ 0.8 | Y |  | (i)abce;(ii)cd;2
J1733-2228 | 0.195 $\pm$ 0.004 | 0.090 $\pm$ 0.004 | 0.246 $\pm$ 0.004 | 25 $\pm$ 2 |  |  |
J1733-3716 | 0.791 $\pm$ 0.007 | 0.129 $\pm$ 0.006 | 0.832 $\pm$ 0.007 | 9.3 $\pm$ 0.4 | Y |  | (i);(ii)a;1
J1735-0724 | 0.260 $\pm$ 0.005 | 0.041 $\pm$ 0.005 | 0.277 $\pm$ 0.005 | 9 $\pm$ 1 |  |  |
J1737-3137 | 0.62 $\pm$ 0.02 | 0.21 $\pm$ 0.02 | 0.71 $\pm$ 0.02 | 19 $\pm$ 2 |  |  |
J1738-3211 | 0.177 $\pm$ 0.005 | 0.049 $\pm$ 0.005 | 0.193 $\pm$ 0.005 | 15 $\pm$ 2 |  |  |
J1739-2903 (i) | 0.36 $\pm$ 0.01 | 0.044 $\pm$ 0.009 | 0.37 $\pm$ 0.01 | 7 $\pm$ 2 | Y |  | (i)a;(ii)abcd;2
J1739-2903 | 0.086 $\pm$ 0.004 | 0.031 $\pm$ 0.004 | 0.103 $\pm$ 0.004 | 20 $\pm$ 3 | Y |  | (i)a;(ii)abcd;2
J1739-3023 | 0.80 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.81 $\pm$ 0.01 | 2.8 $\pm$ 0.7 |  |  |
J1739-3131 | 0.123 $\pm$ 0.004 | 0.022 $\pm$ 0.004 | 0.140 $\pm$ 0.004 | 10 $\pm$ 2 |  | * |
J1740-3015 | 0.834 $\pm$ 0.003 | 0.364 $\pm$ 0.002 | 0.945 $\pm$ 0.003 | 23.6 $\pm$ 0.2 | Y |  | (i)aef;(ii);1
J1741-2733 | 0.174 $\pm$ 0.008 | 0.032 $\pm$ 0.008 | 0.199 $\pm$ 0.008 | 10 $\pm$ 3 |  |  |
J1741-3016 | 0.37 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.39 $\pm$ 0.01 | 5 $\pm$ 2 |  |  |
J1741-3927 | 0.237 $\pm$ 0.003 | 0.034 $\pm$ 0.003 | 0.246 $\pm$ 0.003 | 8.3 $\pm$ 0.6 | Y |  | (i)abef;(ii)abd;2
J1743-3150 | 0.20 $\pm$ 0.01 | 0.01 $\pm$ 0.01 | 0.20 $\pm$ 0.01 | 2 $\pm$ 3 |  |  |
J1745-3040 | 0.489 $\pm$ 0.001 | 0.040 $\pm$ 0.001 | 0.493 $\pm$ 0.001 | 4.7 $\pm$ 0.1 | Y |  | (i)ae;(ii)acd;2
J1749-3002 | 0.307 $\pm$ 0.006 | 0.113 $\pm$ 0.005 | 0.372 $\pm$ 0.006 | 20 $\pm$ 1 |  |  |
J1750-3157 | 0.28 $\pm$ 0.02 | 0.07 $\pm$ 0.01 | 0.34 $\pm$ 0.02 | 14 $\pm$ 3 |  |  |
J1751-3323 | 0.30 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.32 $\pm$ 0.01 | 7 $\pm$ 2 |  |  |
J1751-4657 | 0.159 $\pm$ 0.001 | 0.088 $\pm$ 0.001 | 0.199 $\pm$ 0.001 | 28.9 $\pm$ 0.6 | Y |  | (i)bcde;(ii)cd;1
J1752-2806 | 0.0951 $\pm$ 0.0004 | 0.0716 $\pm$ 0.0004 | 0.1266 $\pm$ 0.0004 | 37.0 $\pm$ 0.5 | Y |  | (i)abce;(ii)bcd;2
J1757-2421 | 0.246 $\pm$ 0.002 | 0.035 $\pm$ 0.002 | 0.254 $\pm$ 0.002 | 8.1 $\pm$ 0.6 | Y |  | (i)abd;(ii)ad;1
J1801-2304 | 0.05 $\pm$ 0.01 | 0.01 $\pm$ 0.01 | 0.07 $\pm$ 0.01 | 17 $\pm$ 16 | Y | * |
J1801-2451 | 0.80 $\pm$ 0.01 | 0.181 $\pm$ 0.009 | 0.84 $\pm$ 0.01 | 12.7 $\pm$ 0.7 |  |  |
J1803-2137 | 0.577 $\pm$ 0.004 | 0.258 $\pm$ 0.003 | 0.662 $\pm$ 0.004 | 24.1 $\pm$ 0.5 | Y |  | (i)a;(ii);1
J1807-0847 | 0.2487 $\pm$ 0.0007 | 0.0886 $\pm$ 0.0007 | 0.2752 $\pm$ 0.0007 | 19.6 $\pm$ 0.2 | Y |  | (i)abf;(ii)abcd;2
J1809-1917 | 0.85 $\pm$ 0.01 | 0.27 $\pm$ 0.01 | 0.94 $\pm$ 0.01 | 17.6 $\pm$ 0.9 |  |  |
J1816-2650 | 0.310 $\pm$ 0.006 | 0.085 $\pm$ 0.006 | 0.343 $\pm$ 0.006 | 15 $\pm$ 1 |  |  |
J1817-3618 | 0.171 $\pm$ 0.005 | 0.120 $\pm$ 0.005 | 0.244 $\pm$ 0.005 | 35 $\pm$ 3 |  |  |
J1817-3837 | 0.139 $\pm$ 0.006 | 0.012 $\pm$ 0.006 | 0.155 $\pm$ 0.006 | 5 $\pm$ 2 | Y |  | (i)f;(ii)d;2
J1820-0427 | 0.240 $\pm$ 0.002 | 0.095 $\pm$ 0.002 | 0.272 $\pm$ 0.002 | 21.5 $\pm$ 0.5 | Y |  | (i)abef;(ii)bcd;2
J1822-2256 | 0.210 $\pm$ 0.005 | 0.040 $\pm$ 0.005 | 0.225 $\pm$ 0.005 | 11 $\pm$ 2 |  |  |
J1822-4209 | 0.18 $\pm$ 0.02 | 0.02 $\pm$ 0.02 | 0.22 $\pm$ 0.02 | 7 $\pm$ 5 |  |  |
J1823-3106 | 0.443 $\pm$ 0.002 | 0.049 $\pm$ 0.002 | 0.452 $\pm$ 0.002 | 6.4 $\pm$ 0.3 | Y |  | (i)af;(ii)d;1
J1824-1945 | 0.210 $\pm$ 0.001 | 0.048 $\pm$ 0.001 | 0.223 $\pm$ 0.001 | 12.9 $\pm$ 0.3 | Y |  | (i)ab;(ii)abcd;1
J1825-0935 | 0.279 $\pm$ 0.002 | 0.036 $\pm$ 0.002 | 0.286 $\pm$ 0.002 | 7.3 $\pm$ 0.4 | Y |  | (i)b;(ii);1
J1825-0935 (i) | 0.10 $\pm$ 0.02 | 0.02 $\pm$ 0.02 | 0.12 $\pm$ 0.02 | 9 $\pm$ 11 | Y |  | (i)b;(ii);1
J1825-1446 | 0.633 $\pm$ 0.006 | 0.020 $\pm$ 0.005 | 0.638 $\pm$ 0.006 | 1.9 $\pm$ 0.4 |  | * |
J1826-1334 | 0.863 $\pm$ 0.008 | 0.308 $\pm$ 0.006 | 0.956 $\pm$ 0.008 | 19.7 $\pm$ 0.5 |  |  |
J1828-1101 (i) | 0.27 $\pm$ 0.05 | 0.06 $\pm$ 0.05 | 0.35 $\pm$ 0.05 | 13 $\pm$ 12 |  | * |
J1828-1101 | 0.71 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.73 $\pm$ 0.01 | 2.8 $\pm$ 0.9 |  | * |
J1829-1751 | 0.342 $\pm$ 0.001 | 0.090 $\pm$ 0.001 | 0.380 $\pm$ 0.001 | 14.8 $\pm$ 0.2 | Y |  | (i)abd;(ii)acd;2
J1830-1059 | 0.857 $\pm$ 0.007 | 0.167 $\pm$ 0.005 | 0.880 $\pm$ 0.007 | 11.0 $\pm$ 0.4 | Y |  | (i)b;(ii);1
J1832-0827 | 0.218 $\pm$ 0.003 | 0.028 $\pm$ 0.003 | 0.229 $\pm$ 0.003 | 7.3 $\pm$ 0.9 | Y |  | (i)ade;(ii)ad;1
J1833-0827 | 0.205 $\pm$ 0.003 | 0.036 $\pm$ 0.003 | 0.221 $\pm$ 0.003 | 10 $\pm$ 1 |  | * |
J1834-0426 | 0.268 $\pm$ 0.002 | 0.037 $\pm$ 0.002 | 0.281 $\pm$ 0.002 | 7.8 $\pm$ 0.4 | Y |  | (i)abf;(ii)acd;2
J1835-0643 | 0.10 $\pm$ 0.01 | 0.04 $\pm$ 0.01 | 0.16 $\pm$ 0.01 | 20 $\pm$ 9 |  | * |
J1835-1106 | 0.619 $\pm$ 0.006 | 0.066 $\pm$ 0.005 | 0.629 $\pm$ 0.006 | 6.1 $\pm$ 0.5 | Y |  | (i)c;(ii);0
J1841-0345 | 0.94 $\pm$ 0.01 | 0.033 $\pm$ 0.009 | 0.95 $\pm$ 0.01 | 2.0 $\pm$ 0.6 |  |  |
J1841-0425 | 0.616 $\pm$ 0.005 | 0.035 $\pm$ 0.004 | 0.624 $\pm$ 0.005 | 3.2 $\pm$ 0.4 | Y | * |
J1842-0905 | 0.21 $\pm$ 0.01 | 0.06 $\pm$ 0.01 | 0.26 $\pm$ 0.01 | 17 $\pm$ 3 |  |  |
J1844-0538 | 0.492 $\pm$ 0.005 | 0.068 $\pm$ 0.004 | 0.506 $\pm$ 0.005 | 7.8 $\pm$ 0.5 | Y | * |
J1845-0434 | 0.192 $\pm$ 0.003 | 0.066 $\pm$ 0.003 | 0.226 $\pm$ 0.003 | 19 $\pm$ 1 |  |  |
J1845-0743 | 0.326 $\pm$ 0.004 | 0.028 $\pm$ 0.004 | 0.337 $\pm$ 0.004 | 5.0 $\pm$ 0.7 | Y |  | (i)b;(ii)ac;1
J1847-0402 | 0.194 $\pm$ 0.003 | 0.049 $\pm$ 0.003 | 0.210 $\pm$ 0.003 | 14.3 $\pm$ 0.9 | Y |  | (i)abce;(ii)cd;2
J1848-0123 | 0.170 $\pm$ 0.001 | 0.020 $\pm$ 0.001 | 0.179 $\pm$ 0.001 | 6.6 $\pm$ 0.5 | Y |  | (i)abce;(ii)acd;2
J1852-0635 | 0.618 $\pm$ 0.003 | 0.011 $\pm$ 0.002 | 0.621 $\pm$ 0.003 | 1.0 $\pm$ 0.2 | Y |  | (i)a;(ii)a;1
J1852-2610 | 0.36 $\pm$ 0.01 | 0.03 $\pm$ 0.01 | 0.40 $\pm$ 0.01 | 4 $\pm$ 2 |  |  |
J1853-0004 | 0.86 $\pm$ 0.03 | 0.04 $\pm$ 0.02 | 0.88 $\pm$ 0.03 | 3 $\pm$ 1 |  |  |
J1900-2600 | 0.340 $\pm$ 0.001 | 0.147 $\pm$ 0.001 | 0.402 $\pm$ 0.001 | 23.4 $\pm$ 0.2 | Y |  | (i)abcdf;(ii)bcd;2
J1913-0440 | 0.136 $\pm$ 0.002 | 0.040 $\pm$ 0.002 | 0.147 $\pm$ 0.002 | 16.4 $\pm$ 0.8 | Y |  | (i)abce;(ii)abd;2
J1941-2602 | 0.514 $\pm$ 0.004 | 0.113 $\pm$ 0.004 | 0.544 $\pm$ 0.004 | 12.4 $\pm$ 0.5 | Y |  | (i);(ii)c;2
J2006-0807 | 0.433 $\pm$ 0.009 | 0.062 $\pm$ 0.008 | 0.461 $\pm$ 0.009 | 8 $\pm$ 1 |  |  |
J2048-1616 | 0.3900 $\pm$ 0.0007 | 0.0467 $\pm$ 0.0006 | 0.3949 $\pm$ 0.0007 | 6.83 $\pm$ 0.09 | Y |  | (i)adf;(ii)d;1
J2330-2005 | 0.147 $\pm$ 0.003 | 0.070 $\pm$ 0.003 | 0.188 $\pm$ 0.003 | 25 $\pm$ 1 | Y |  | (i)abc;(ii)c;2
J2346-0609 | 0.451 $\pm$ 0.003 | 0.102 $\pm$ 0.003 | 0.468 $\pm$ 0.003 | 12.8 $\pm$ 0.3 | Y |  | (i)c;(ii)a;1