# The High Time Resolution Universe Pulsar Survey – XVIII. The reprocessing of
the HTRU-S Low Lat survey around the Galactic centre using a Fast Folding
Algorithm pipeline for accelerated pulsars

J. Wongphechauxsorn ,1 D. J. Champion,1 M. Bailes,2,3 V. Balakrishnan,1 E. D.
Barr,1 M. C. i Bernadich,1 N. D. R. Bhat,4 M. Burgay,5 A. D. Cameron,2,3 W.
Chen,1 C. M. L. Flynn,2,3 A. Jameson,2,3 S. Johnston,6 M. J. Keith,7 M.
Kramer,1,7 C. Ng,8 A. Possenti,5,9 R. Sengar,10,2,3 R. M. Shannon,2,3 B.
Stappers,7 W. van Straten10
1Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany
2ARC Center of Excellence for Gravitational Wave Discovery (OzGrav), Swinburne
University of Technology, Mail H11, PO Box 218, VIC 3122.
3Centre for Astrophysics and Supercomputer, Swinburne University of
Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
4International Centre for Radio Astronomy Research, Curtin University,
Bentley, WA 6102, Australia.
5 INAF - Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047
Selargius (CA), Italy.
6CSIRO Astronomy $\&$ Space Science, Australia Telescope National Facility,
P.O. Box 76, Epping, NSW 1710, Australia.
7Jodrell Bank Center for Astrophysics, University of Manchester, Alan Turing
Building, Oxford Road, Manchester M13 9PL, United Kingdom.
8Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada.
9Universit´a di Cagliari, Dept of Physics, S.P. Monserrato-Sestu Km 0,700 -
09042 Monserrato, Italy.
10Center for Gravitation, Cosmology, and Astrophysics, Department of Physics,
University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA.
11Institute for Radio Astronomy $\&$ Space Research, Auckland University of
Technology, Private Bag 92006, Auckland 1142, New Zealand E-mail:
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The HTRU-S Low Latitude survey data within 1∘of the Galactic Centre (GC) were
searched for pulsars using the Fast Folding Algorithm (FFA). Unlike
traditional Fast Fourier Transform (FFT) pipelines, the FFA optimally folds
the data for all possible periods over a given range, which is particularly
advantageous for pulsars with low-duty cycle. For the first time, a search
over acceleration was included in the FFA to improve its sensitivity to binary
pulsars. The steps in dispersion measure (DM) and acceleration were optimised,
resulting in a reduction of the number of trials by 86 per cent. This was
achieved over a search period range from 0.6-s to 432-s, i.e. 10 per cent of
the observation time (4320s), with a maximum DM of 4000 pc cm-3 and an
acceleration range of $\pm 128$m s-2. The search resulted in the re-detections
of four known pulsars, including a pulsar which was missed in previous FFT
processing of this survey. This result indicates that the FFA pipeline is more
sensitive than the FFT pipeline used in the previous processing of the survey
within our parameter range. Additionally, we discovered a 1.89-s pulsar, PSR
J1746-2829, with a large DM, located 0.5 from the GC. Follow-up observations
revealed that this pulsar has a relatively flat spectrum($\alpha=-0.9\pm 0.1$)
and has a period derivative of $\sim 1.3\times 10^{-12}$ s s-1, implying a
surface magnetic field of $\sim 5.2\times 10^{13}$ G and a characteristic age
of $\sim 23000$ yr. While the period, spectral index, and surface magnetic
field strength are similar to many radio magnetars, other characteristics such
as high linear polarization are absent.

###### keywords:

surveys – stars: neutron – pulsars: general

††pubyear: 2021††pagerange: The High Time Resolution Universe Pulsar Survey –
XVIII. The reprocessing of the HTRU-S Low Lat survey around the Galactic
centre using a Fast Folding Algorithm pipeline for accelerated pulsars –The
High Time Resolution Universe Pulsar Survey – XVIII. The reprocessing of the
HTRU-S Low Lat survey around the Galactic centre using a Fast Folding
Algorithm pipeline for accelerated pulsars

##  1 Introduction

The Galactic Centre (GC) is regarded as one of the most interesting regions in
our Galaxy due to the dense environment of matter and relatively large
magnetic field around the supermassive black hole, Sgr A* (Eckart & Genzel,
1996). Discovering radio pulsars, a subclass of neutron stars whose rotation
is visible in pulses of radio emission detectable at Earth, located in the GC
can lead to many applications, including studying stellar evolution and the
magneto-ionised environment around the GC (e.g. Desvignes et al., 2018; Abbate
et al., 2023). Moreover, the discovery of a typical pulsar orbiting Sgr A*
with an orbital period of approximately one year would be sufficient to test
two predictions of General Relativity Theory (Wex & Kopeikin, 1999; Kramer et
al., 2004; Liu et al., 2012; Liu & Eatough, 2017): the No-Hair-Theorem (e.g.
Israel, 1967, 1968) and the Cosmic Censorship Conjecture (e.g. Penrose, 1979).
The No-Hair-Theorem predicts that all stationary black holes can be described
by their mass, spin, and electric charge alone, while the Cosmic Censorship
Conjecture predicts that all black holes must be surrounded by event horizons.

The environment around the GC favours the formation of massive stars (see e.g.
Figer, 2003, for a review). It is predicted that there will be
$10^{7}$-$10^{8}$ neutron stars, with 102 to 106 of them being pulsars at the
central 100 pc (Cordes & Lazio, 1997). Wharton et al. (2012) estimated that
the inner 150 pc of the Galaxy could harbour as many as 1000 active radio
pulsars that beam towards Earth, further motivating ongoing searches for
pulsars around the GC. However, only six pulsars have thus far been detected
within half a degree of angular separation from the GC (Johnston et al., 2006;
Deneva et al., 2009; Eatough et al., 2013).

One reason for the disparity between the predicted and observed number of
pulsars is that the GC environment diminishes pulsar detectability. The dense
environment in the GC affects the pulsar’s detectability in two main ways.
Firstly, the arrival times of the radio pulses are delayed towards lower
observational frequency as $\Delta t\propto f^{-2}$. This effect, known as
‘dispersion’, originates from the ionised interstellar medium (ISM), and can
be entirely mitigated by performing de-dispersion (see Section 2.3.2.
Secondly, multi-path propagation caused by scattering in the ISM broadens the
pulse width with a timescale that scales as $\tau_{\rm ts}\propto f^{-4}$ for
a thin screen scenario (see Rickett, 1977, for a review). Critically, this
effect can only be reduced by observing at higher frequencies. If the
broadened pulse width is larger than the pulse period, it is impossible to
detect periodicity from the pulsar as the pulses are completely smeared out.
At the GC, the scatter broadening time of radio pulses at 1.4 GHz is expected
to be as large as 2300 s (e.g. Cordes & Lazio, 2002), longer than known
periods of pulsars (e.g. PSRcat, Manchester et al.,
2005)111https://www.atnf.csiro.au/research/pulsar/psrcat/. This is one
possible explanation for the lack of pulsar discoveries around the GC from the
numerous pulsar surveys to date (e.g. Kramer et al., 1996; Klein et al., 2004;
Suresh et al., 2022; Torne et al., 2021; Wharton, 2017; Liu et al., 2021;
Eatough et al., 2021). By comparison, real data shows that the scattering
broadening of the GC magnetar PSR J1745$-$2900, the closest pulsar to Sgr A*
with a projected distance of 0.1 pc from the GC (Eatough et al., 2013; Kennea
et al., 2013), is only on the order of seconds (Spitler et al., 2014). This is
in stark contrast to the previous prediction. However, even this lower
scattering time may still be responsible for the scarcity of pulsars detected,
given that this scattering time at the typical pulsar search frequency, 1.4
GHz, is longer the period of approximately 30 per cent of the known pulsars
(e.g. PSRcat, Manchester et al., 2005)1.

Conducted over the last 25 years, most pulsar surveys have used an observing
frequency around 1.4 GHz. This balances the reduction in sensitivity due to
scatter broadening at low frequencies with the steep pulsar spectrum (see e.g.
Bates et al., 2013; Jankowski et al., 2018). The anomalously low number of
pulsars in this region suggests more substantial chromatic effects (see
Rajwade et al., 2017, for example), prompting surveys at higher frequencies.
High frequency pulsar surveys at the GC range from 4.0-8.0 GHz using the 100-m
Effelsberg, 100-m Green bank, and 64-m Parkes (Murriyang) telescopes (Kramer
et al., 1996; Klein et al., 2004; Macquart et al., 2010a; Suresh et al., 2022)
to 84 and 156 GHz (Torne et al., 2021) using the 30-m IRAM telescope. To
reduce the effect of red-noise caused by fluctuations in the telescope’s
receiver electronics during long integration observations, GC surveys have
also been conducted using interferometers e.g., the Atacama Large
Millimeter/submillimeter Array (ALMA) and Very Large Array (VLA) (Wharton,
2017; Liu et al., 2021). In order to increase the sensitivity of the surveys
as the pulsars become weaker at high frequencies, Eatough et al. (2021) made
repeated high frequency observations (4.85, 8.35, 14.6, and 18.95 GHz) on a
time scale of years. The long duration of the observations meant that the
apparent period changes of a potential pulsar due to orbital motion needed to
be accounted for not only by including the searches for acceleration (period
derivative) but also jerk (the second derivative) (see Section 2.3.3). Despite
these numerous higher-frequency pulsar surveys with various observation
techniques, no new pulsars have been found.

Rather than competing with the spectral index of the pulsars in the GC,
another way to reduce the deleterious effect of scattering is to look for
longer period pulsars. Previous searches were biased toward the fast-spinning
pulsars over the slow-spinning ones through their use of the Fast Fourier
Transform (FFT) algorithm to detect the repeating signal. Cameron et al.
(2017); Parent et al. (2018); Morello et al. (2020b) suggested that the
reduction in the FFT sensitivity to long-period pulsars with harmonic
components in the Fourier domain (e.g. a narrow pulse profile) is
significantly more severe than anticipated, primarily due to factors such as
the impact of red instrumental noise at the low-frequency end of the Fourier
power spectrum and incoherence harmonic summing. Another reason to search for
long-period pulsars in the GC is also driven by the hypothesis is Dexter &
O’Leary (2014) that the GC may exhibit a higher efficiency of magnetar
formation (see Section 4.1). In this work, we searched for long-period pulsars
that would not be as strongly affected by a significant scattering of the GC
using the Fast Folding Algorithm (FFA, Staelin, 1969) which is more sensitive
to long-period pulsars.

The organisation of this paper is as follows. Section 2 describes the methods
used in this work, including data selection and the algorithm. The
optimisations, the pipeline, and the search parameters are further elaborated.
Section 3 reports the re-detection of the known pulsars and a new pulsar
discovered in this survey. The discussion of the possible radio image
counterpart of the newly found pulsar and the type of newly discovered pulsar
is shown in Section 4. Finally, we present our conclusion in Section 5.

##  2 Methods

###  2.1 Data selection

The 64-m Parkes radio telescope (Murriyang), located in New South Wales,
Australia, was used for the Southern High Time Resolution Universe Survey
(HTRU-S). Observations started in 2008 and ended in 2014 and made use of the
Parkes Multibeam receiver which consists of 13 feeds, producing 13 telescope
beams (Staveley-Smith et al., 1996). The HTRU-S survey was divided into three
regions based on Galactic latitude. We used only the data set that formed the
low Galactic latitude survey (LowLat) in this work because it has the longest
observation time (4320 s for each pointing) with a sampling time
($t_{\rm{samp},0}$) of 64 $\mu$s, containing $2^{26}$ samples per observation
and covered the GC (Ng et al., 2015). The central observing frequency
$f_{\rm{c}}$ is at 1352 MHz with a bandwidth ($\Delta f$) of 340 MHz,
separated into effective 870 channels (Keith et al., 2010). The long
observation time of LowLat also favours the discovery of slow pulsars as it
records more pulses because the signal-to-noise ratio (S/N) is proportional to
the observation time ($t_{\rm obs}$) as $\rm{S/N}\propto\sqrt{T_{\rm obs}}$.
Additional information regarding other HTRU surveys can be found in Keith et
al. (2010); Ng et al. (2015) and Cameron et al. (2020).

Because this work is focused on the GC, observation beams within one degree of
the GC were selected. The data were processed at the Max-Planck Computing and
Data Facility in Garching, Germany, using the MPIfR’s Hercules cluster.

###  2.2 The search algorithm

As mentioned in the previous section, the vast majority of pulsars have thus
far been discovered by performing an FFT on a time-series and searching for
signals in the Fourier spectrum; this is due to its computational efficiency.
However, narrow duty-cycle signals become more difficult to detect as more
power is distributed to the higher harmonics in the Fourier domain. A fraction
of the Fourier power can be recovered by performing an “Incoherent harmonic
summing” technique (Taylor & Huguenin, 1969). This method adds the power of
each harmonic to the fundamental frequency, recovering the missing Fourier
power. However, it is impossible to recover all of Fourier power if the pulse
is sufficiently narrow. Furthermore, as a result, the FFT has some limitations
when applied to the detection of long-period (P>1 s) and narrow pulse pulsars
(pulse width smaller than 20 per cent of the period for 32 harmonic sums) (see
Morello et al., 2020b).

The FFA is an alternative method used to search for periodicity by brute-force
folding every possible trial period. These folded pulse profiles must then be
evaluated statistically, e.g. using matched-filtering techniques. Although the
FFA was first implemented in 1969 (Staelin, 1969), the algorithm has only been
applied to a few pulsar surveys (e.g., Faulkner et al., 2004; Kondratiev et
al., 2009) as it is computationally expensive. Recently, Morello et al.
(2020b) presented a new FFA implementation (hereafter the Riptide
FFA)222https://github.com/v-morello/riptide. This implementation of the FFA
has been demonstrated to be faster than the previous implementations and can
be used in conjunction with a blind pulsar survey. It has already resulted in
several discoveries, including PSR J0043$-$73 (Titus et al., 2019), a new
pulsar in the Small Magellanic Cloud, and PSR J2251$-$3711, a pulsar from the
SUPERB survey (Keane et al., 2018) with a spin period of 12.1s (Morello et
al., 2020a). Recently, (Singh et al., 2022; Singh et al., 2023) discovered six
new pulsars with the Riptide FFA, one of which has a period of 140-ms, using
data from the GMRT High Resolution Southern Sky (Bhattacharyya et al., 2016)
pulsar survey.

In this work, we searched for periodicity in the selected data using the
Riptide FFA implementation. To avoid confusion between a general FFA
implementation, the Riptide FFA, and the acceleration search pipeline
implemented in this work, we will refer to them as FFA, RFFA, and AFFA,
respectively, for the remainder of this paper. We also present a new method to
optimise the dispersion and acceleration trials when searching for pulsars in
binary systems. Those optimisations could be done due to the fact that the
search step size is proportional to the minimum search period, as the period
searches in the FFA are independent (unlike the FFT) so that they can be
individually tailored.

###  2.3 Optimisation of dispersion measure and acceleration trials

To improve the sensitivity of a survey to highly dispersed pulsars, the effect
of dispersion must first be corrected for. While the FFT searches for all
possible pulse frequencies simultaneously, the FFA only folds a small period
range at a time. Since the acceleration and dispersion step sizes are directly
proportional to the profile bin width, represented as $t_{\text{samp}}$ in
this study, and in turn, $t_{\text{samp}}$ is proportional to the minimum
search period, it is thus possible to optimise the search step size for each
period range.

####  2.3.1 Searched period

First, we define the number of bins we want in each profile ($N_{\rm bins}$).
Then we can determine the minimum search period ($P_{\rm{min}}$) for a time-
series with sampling time $t_{\rm{samp}}$:

$P_{\rm{min}}<=N_{\rm{bins}}\times t_{\rm{samp}}.$ (1)

As we search for longer periods with the same $N_{\rm bins}$ the time-series
can be downsampled. Keeping the same $N_{\rm bins}$ also reduces the required
computational resources. In this work, the RFFA was used to downsample the
time-series by the factor of 2 whenever the search period doubles (see Morello
et al., 2020b, for more details).

####  2.3.2 Searched dispersion measure

The dispersive time delay between two observing frequencies is proportional to
the dispersion measure (DM), and is given by:

$\Delta t=4.15\times 10^{6}{\rm ms}\times(\frac{f_{1}^{-2}}{\rm
MHz}-\frac{f_{2}^{-2}}{\rm MHz})\times\rm{\frac{DM}{pc\ cm^{-3}}}.$ (2)

Dispersion can be mitigated by spitting the bandwidth into channels and
progressively shifting each channel in time, before summing them to create a
time-series. This method is called the de-dispersion. As the DM is initially
unknown, a range of DM must be searched. The $i^{\rm{th}}$ dispersion step at
central frequency ($f_{\rm c}$) at bandwidth ($\Delta f$) and sampling time
($t_{\rm{samp}}$) in ms is calculated using

${\rm DM}_{i}=1.205\times 10^{-7}\times(i-1)\times
t_{\rm{samp}}\left(\frac{f_{c}^{3}}{\rm MHz}\frac{{\Delta f}^{-1}}{\rm
MHz}\right)\,\rm{pc}\,\rm{cm}^{-3},$ (3)

For more information, see Lorimer & Kramer (2004) and references therein. As
the FFA continuously downsamples the data to maintain the same number of
profile bins, the size of the DM steps increases, reducing the total number of
trials.

####  2.3.3 Acceleration search

Any orbital motion will cause an apparent period change in the pulsar during
the observation, depending on the relative size of the orbital period and
observation length. This will smear and reduce S/N of the profile and may make
the pulsar undetectable. Ideally, a search over all five Keplerian parameters
would be performed (e.g. Balakrishnan et al., 2022), however for a large
survey this is too computationally expensive. A simpler approach is to assume
that the pulsar is moving with constant acceleration along the line of sight,
$a$, at a reference time $t$. Johnston & Kulkarni (1991) demonstrated that the
modulated pulse arrival time ($\Delta t$) is

$\Delta t=\frac{at^{2}}{2c}$ (4)

where $c$ is speed of the light. Ransom et al. (2003) and Ng et al. (2015)
demonstrated that this approximation is true only if the observation time is
less than $10$ per cent of the orbital period due to the fact that the
observation time is short enough to consider the acceleration to be constant.

To correct for $\Delta t$, the time-series was resampled by shifting each data
point in the time-series to match the expected arrival times for a range of
trial accelerations. The acceleration step size is defined as the value that
changes the arrival time by a bin over half the length of the observation
$T_{\rm obs}$ (by resampling the data from the middle of the observation),
which is written as

$\delta a=\frac{8t_{\rm{samp}}c}{T_{\rm{obs}}^{2}}.$ (5)

Consequently, the $j^{\rm th}$ acceleration step is written as

$\delta a_{j}=(j-1)\frac{8t_{\rm{samp}}c}{T^{2}_{\rm{obs}}}.$ (6)

From the above equation, $\delta a\propto t_{\rm{samp}}$. As a result, the
number of steps can be reduced (similarly to dispersion) as the data are
downsampled. The relation between the downsampling factor, $n$, and the
acceleration step is

$\delta a_{nj}=n\times\delta a_{j}.$ (7)

The key advantage of this optimisation is when the data are dedispersed at
$\rm{DM}_{i}$ and resampled it at $a_{j}$, these data can be reused when the
FFA reaches a fold at twice the period, as shown in Figure 1. As both of the
DM and acceleration step are proportional to the minimum period searched, when
the searched period range changes by a factor of two, the total number of
acceleration and DM trials decreases by a factor of four. As a result, this
optimisation reduces the number of trials by approximately 86 per cent for the
LowLat survey, as shown in Table 1.

Table 1: The comparison of processing steps for a search with and without the
optimisation demonstrated in this work. $N_{r}$ is the total number of trials
for each range. This optimisation reduced the number of trials for
approximately 86 per cent for the selected period range.

$P_{\rm min}$ | Without optimisation | With optimisation
---|---|---
(s) | $N_{\rm DM}$ | $N_{\rm acc}$ | $N_{\rm r}$ | $N_{\rm DM}$ | $N_{\rm acc}$ | $N_{\rm r}$
0.6 | 1,000 | 43 | 43,000 | 1,000 | 43 | 43,000
1.2 | 1,000 | 43 | 43,000 | 500 | 22 | 11,000
2.4 | 1,000 | 43 | 43,000 | 250 | 11 | 2,750
4.8 | 1,000 | 43 | 43,000 | 125 | 6 | 750
9.6 | 1,000 | 43 | 43,000 | 63 | 3 | 189
19.2 | 1,000 | 43 | 43,000 | 32 | 2 | 64
38.4 | 1,000 | 43 | 43,000 | 16 | 1 | 16
76.8 | 1,000 | 43 | 43,000 | 8 | 1 | 8
153.6 | 1,000 | 43 | 43,000 | 4 | 1 | 4
307.2 | 1,000 | 43 | 43,000 | 2 | 1 | 2
$N_{\rm total}$ |  |  | 430,000 |  |  | 57,783

Figure 1: An example of the optimisation of the number of the dispersion and
acceleration steps in the pipeline to search in the period range of $P_{\rm
min}$ to $4P_{\rm min}$, dispersion measure range of 0 to $5\rm{DM}_{i}$, and
the acceleration range of 0 to $5\delta a_{j}$. This pipeline is separated
into two period ranges. The first part of this pipeline is to search for the
period range of $P_{\rm min}$ to $2P_{\rm min}$ and to use the dispersion step
of ${\rm DM}_{i}$ and the acceleration step of $\delta a_{j}$. In the second
part, the period range is $2P_{\rm min}$ to $4P_{\rm min}$ with the dispersion
step and the acceleration step being $2{\rm DM}_{i}$ and $2\delta a_{j}$,
respectively. The existing time-series from the first part is reused in the
second part of the pipeline.

###  2.4 The search pipeline

The initial stage of the search pipeline involves cleaning radio frequency
interference (RFI) from the data. RFIFIND from
PRESTO333https://github.com/scottransom/presto was used to remove the
brightest RFI bursts. The data were then dedispersed using the PREPSUBBAND
routine to generate time-series at the specified DMs. The dedispersed time-
series were resampled at each acceleration step using the resample routine in
SIGPYPROC444https://github.com/ewanbarr/sigpyproc. Afterwards, the RFFA was
used to search in the shortest period range. For the next period range, the
acceleration and dispersion steps doubled and half of the time-series
generated previously were reused. This process was repeated to cover the whole
period range.

Candidates with a S/N lower than a cut-off S/N were filtered out. The cut-off
S/N was determined by calculating the false alarm rate (FAR) for the
$N_{\rm{total}}$ number of trials. The FAR was calculated as follows:

$\rm FAR=\rm
Prob(>S/N)=\frac{1}{2}\left[1-erf\left(\frac{S/N}{\sqrt[]{2}}\right)\right].$
(8)

The error function,
$\rm{erf}(x)=\frac{2}{\sqrt{\pi}}\int_{0}^{x}e^{-x^{2}}dx$, can be solved
numerically (e.g. Press et al., 1992). Where the number of false detection for
the search is calculated from FAR$\times N_{\rm total}$ where $N_{\rm{total}}$
was evaluated from

$N_{\rm total}=N_{\rm FFA}\times N_{\rm acc}\times N_{\rm DM}.$ (9)

$N_{\rm DM}$ and $N_{\rm acc}$ are shown in Table 1, and $N_{\rm FFA}$ was
demonstrated by Morello et al. (2020b) as

$N_{\rm FFA}=\frac{T_{\rm obs}}{P_{\rm min}}N_{\rm bin}^{2}\log{\frac{T_{\rm
obs}}{P_{\rm min}}N_{\rm bin}^{2}}.$ (10)

Applying a limiting S/N to the data reduced the number of candidates greatly.
However, the number of candidates observed per observation typically remains
in the thousands which is impossible to inspect visually for a blind survey.
In this work, we reduce the number of candidates using the kurtosis of the
pulse profile’s power distribution. Kurtosis is a property that quantifies the
“tailiness” of a distribution; for a normal distribution, the kurtosis is 0.
The kurtosis filtering has been typically used to detect bright RFI pulses in
raw data (for example Nita et al., 2007; Nita & Gary, 2010; Purver et al.,
2022). However, here we use the kurtosis score as a way to detect a pulsar-
like signal but filtering out the low kurtosis profiles which were typically
noise or weak RFI. This technique has a negative effect on the survey
sensitivity to very broad pulse profiles. However, it is expected that such
broad pulse profiles would have been identified in previous FFT based
searches, as both FFT and FFA based pipelines should yield similar results for
these types of profile, i.e. converging to predicted value from the radiometer
equation (Morello et al., 2020b). The kurtosis limit was determined by
comparing the kurtosis from a random noise profile to a profile containing a
Gaussian. The comparison was conducted by simulating 2000 pulse profiles with
pure noise and another 2000 Gaussian profiles with noise to represent pulsar
pulse profiles. The duty cycle of these Gaussian profiles ranged from 1 per
cent to 20 per cent. The kurtosis distribution from the simulation showed that
the lowest kurtosis for the pulsar signal was approximately $-$0.5. We doubled
this value to cover some extreme cases. As a result, only the candidates with
kurtosis higher than $-$1.0 were inspected. Such criteria can reduce the
number of candidates by 90 per cent.

###  2.5 Search parameters

The data were searched with the aforementioned pipeline for a total period
range of 0.6-s to 432-s. The longest searched period was chosen based on the
assumption that the FFA requires at least 10 pulses to obtain more S/N than
the single pulse searches (see Keane, 2010, for example ). The shortest period
search was limited by computational resources. As the number of search trials
($N_{\rm FFA}$) is proportional to $N_{\rm{samp}}^{3}$ for FFA searches
(Morello et al., 2020b), processing time increases quickly as the period
reduces. We also chose the minimum search period to be 0.6-s, as this period
covers a large portion of the known pulsars and still achievable with a
reasonable processing time of order 72 h per beam with the available computing
facility. The $N_{\rm{bins}}$ for folded profile was set to be 128 bins based
on a duty cycle of $\sim 1\%$, resulting in a $4.6875$-ms $t_{\rm{samp,1}}$
for the first period range according to Equation 1.

For the maximum search DM, we used the YMW16 free electron distribution model
(Yao et al., 2017) to estimate the dispersion measure on a line-of-sight
directly through the GC to the edge of the Galaxy. This extreme scenario gave
a maximum DM of 3946 $\rm{pc}\,\rm{cm}^{-3}$. Thus, the DM range (DMr) for
this search555Note that NE2001 predicts a maximum DM for this line-of-sight to
be 3396 $\rm{pc}\,\rm{cm}^{-3}$.  was set to be 4000 $\rm{pc}\,\rm{cm}^{-3}$.
The dispersion step size was calculated from Equation 3 with the HTRU-S
LowLat’s bandwidth (340 MHz) and central frequency (1352 MHz) with $i$ of 1
and $t_{\rm{samp,1}}$ of 4.6875 ms at 4.023 $\rm{pc}\,\rm{cm}^{-3}$.

Because the GC is a dense environment, it is necessary for our acceleration
range to be sufficiently wide to cover various kinds of binary companions. The
acceleration range was chosen to be $\pm$ 128 m s-2, which corresponds to a
pulsar (of mass 1.4 M⊙) with a companion up to the mass of a 37$M_{\odot}$, as
e.g. black hole in a 12-hour orbital period (see Ng et al., 2015, for
calculations).

To improve clarity, the text was changed to: For the S/N limit, we used a S/N
of 8.0. With this S/N, the number of false candidates is approximately 0.04
candidates per beam under the assumption that the data contains only white
noise, which is exceptionally low.

To test the acceleration part of the pipeline, we generated 5600 artificial
pulsars in various binary systems, using SIGPROC’s FAKE package (Lorimer,
2011). The simulated pulsars were selected to have spin periods randomly
chosen between 1.0 to 6.0-s, with pulse duty cycles ranging from 1 to 25 per
cent.666We chose this period range rather than the full period range (0.6-s to
430-s) because the RFFA downsamples the time-series to the optimal time
resolution, making the period range arbitrary. The companion mass was randomly
selected between 0 and 37 $M_{\odot}$ with a fixed orbital period of 12 h at
an orbital phase of 0.25, making it the easiest orbital phase to detect for an
acceleration search. We then also generated the same pulsars without the
binary companions as an isolated realisation. We compared the S/N values
resulting from the pipeline from the isolated and accelerated realisations to
determine the loss S/N. Our simulations showed that 90 per cent of the
acceleration search FFA results have S/N greater than 95 per cent of the S/N
detected from identical isolated pulsars.

##  3 Results

###  3.1 Redetection of known pulsars

Of the ten previously known pulsars in the targeted region, two of them are
millisecond pulsars, which are outside of our searched period range (PSR
J1747$-$2809 and PSR J1745$-$2912). Three of them (PSR J1745$-$2758, PSR
J1747$-$2802, and PSR J1750$-$28) were detected with previous FFT based
processing (Ng et al., 2015; Cameron et al., 2020). We also detected PSR
J1746$-$2856 that was not reported in the previous FFT based survey
processing. The GC magnetar PSR J1745$-$2900, and three other long period
pulsars (PSR J1746$-$2850, PSR J1746$-$2849, and PSR J1746$-$2856) were not
detected with the FFT or FFA pipelines, while PSR J1745$-$2910 had never been
detected at this observational frequency before. The details about eight
pulsars inside our search period range are shown in Table 2.

The reasons for the non-detections are as follows: PSR J1745$-$2900 and PSR
J1746$-$2850 are known to be transient pulsars and it is possible that these
pulsars were not active during our observations. We further folded those
observations containing these pulsars using the ephemeris from psrcat and
found no pulsations. PSR J1745$-$2910 has never been detected afterward (see
e.g. Macquart et al., 2010b; Eatough et al., 2021), suggesting that it could
also be a transient pulsar. Meanwhile, PSR J1746$-$2849 exhibits a substantial
scattering tail at the L-band (266 ms Deneva, 2010) and has a faint average
flux, leading to an anticipated low S/N. When we folded this pulsar at the
closest pointing using the current ephemeris reported in PSRcat, we did not
find any pulsations with an S/N greater than 5.

The re-detection of PSR J1746$-$2856 with a relatively high S/N suggests that
it was overlooked due to book keeping error in the earlier FFT-based
processing. This assumption is reinforced by the detection of this pulsar
during the reprocessing of the HTRU-S low-lat using an FFT-based GPU-
accelerated pipeline (Sengar et. al., In prep.).

Comparing the S/N from both the FFA and FFT-based pipelines demonstrates that
the S/N from the FFA is consistently higher than that from the FFT, as
predicted by Morello et al. (2020b).

Table 2: Known slow pulsars in the HTRU-S LowLat using the FFA pipeline. Note
that PSR J1745$-$2758 was detected at the 2nd harmonic of the period (0.975s).

NAME | P0 | Flux density at 1400 MHz | duty cycle ♢ | $S/N_{\rm FFA}$ | $S/N_{\rm FFT}$
---|---|---|---|---|---
| (s) | (mJy) | (%) |  |
J1745$-$2758 | 0.487528 | 0.15 | 6.1 | 8.8 | 8.4
J1745$-$2900 ♠ ♡ | 3.763733 | 0.9♣ | 8.3 | - | -
J1745$-$2910 ♠ | 0.982 | - | 8.0 | - | -
J1746$-$2849 ♠ | 1.47848 | 0.4 | 8.2 | - | -
J1746$-$2850 ♠ ♡ | 1.077101 | 0.8 | 5.6 | - | -
J1746$-$2856 ♠ | 0.945224 | 0.4 | 4.8 | 14 | -
J1747$-$2802 | 2.780079 | 0.5 | 1.0 | 15.6 | 14.6
J1750$-$28 | 1.300513 | 0.09 | 1.3 | 12.8 | 8.7

♠Pulsars that are not detected in Ng et al. (2015).
♡Pulsars that shows high flux variation.
♢ The duty cycles were calculated from $\frac{W50}{P0}$, using data from
PSRcat (Manchester et al.,
2005)777https://www.atnf.csiro.au/research/pulsar/psrcat/.
♣ For this work, we estimate the L-band flux density from extrapolating the
flux and spectral index reported in Torne et al. (2017).

###  3.2 PSR J1746$-$2829: A new discovery

A new pulsar, PSR J1746$-$2829 was found during the reprocessing of LowLat
data with an FFA S/N (S/NFFA) of 11.2. Although it is not directly in the
central parsec of the GC, its proximity ($\sim$ 0.5∘) makes it an interesting
source for comparison with the known pulsars in this region. We found that the
pulsar has a high DM ($1309~{}{\rm pc~{}cm}^{-3}$) and a long period
($1.89$s), full parameters of the parameters for this pulsar can be found in
Table 3. This pulsar was also found in the later reprocessing of the HTRU-S
low-lat using FFT based GPU-accelerated pipeline (Sengar et. al., In prep.)
with S/NFFT of 8.6, $\sim$20 per cent less than S/NFFA.

The reason this pulsar was overlooked in the previous FFT survey is due to the
use of 2-bit digitisation in the decimation code. A bug was found in the code
that effectively sampled the data at 1-bit, leading to a approximately 25 per
cent loss in sensitivity. This pushed the pulsar below the 8 sigma threshold
for folding in the older FFT pipeline. This part was removed in the recent FFT
reprocessing (Sengar et. al., In prep.) then the pulsar became detectable by
the FFT (see Sengar, 2023, for more details).

Table 3: Timing parameters for newly discovered pulsar with 1-$\sigma$
uncertainty represented in parentheses.

Parameter |
---|---
Name | J1746-2829
Right ascension (J2000)♡ | 17h46m15s(14)
Declination (J2000)♡ | -28° 29′ 32″(38)
Galactic latitude, b (∘) | 0.117(60)
Galactic longitude, l (∘) | 0.445(56)
Spin period (s) | 1.888928609337(9)
Period derivative (s s-1)♢ | 1300(30) $\times 10^{-15}$
Epoch of period | 58564.0
Dispersion measure (cm-3 pc) | 1309(2)
Estimated distance♠ (kpc) | 8.2
Rotation measure (rad m-2) |  $-$743(14)
Scattering time (ms) | 67(3)
Average flux density at 1400 MHz (mJy) | 0.55(6)
Inferred $B_{\rm field}$ (G) | 5.0 $\times 10^{13}$
Inferred characteristic age (yr) | 23 $\times 10^{3}$
Spin-down luminosity (erg s-1) | 8.4 $\times 10^{33}$
Flux density spectral index |  $-$0.9(1)
Start MJD | 58564
Finish MJD | 59838

♠ Estimated with Yao et al. (2017)
♡ Position obtained from the MeerKAT’s detections.
♢ This uncertainty considers a contribution from positional uncertainty.

####  3.2.1 Follow-up observations

After its discovery, PSR J1746$-$2829 was observed with the Parkes telescope
using the 21-cm Multibeam receiver for seven epochs from April to July 2018.
However, even the 72-min observations at Parkes were yielding S/N of only
approximately 8-9, so observations were also made with the 100-m Effelsberg
telescope. While the larger diameter of the Effelsberg telescope leads to
higher sensitivity, the beam size ($\theta_{\rm b}$) is smaller at the same
frequency. Hence, the Effelsberg’s 21-cm receiver888This receiver has an
effective bandwidth of 250 MHz see https://eff100mwiki.mpifr-bonn.mpg.de was
used to make 1800-s ‘gridding’ observations (see Cruces et al., 2021, for more
details). This technique is performed by observing the pulsar multiple times
with a small offset from the central beam to improve the position, narrowing
down the uncertainty to within the width of the Effelsberg beam at 21-cm
(0.163∘). The pulsar was subsequently observed for seven epochs with the same
receiver and observation time using the Effelsberg telescope.

The installation of the Ultra-Wide Band (UWL) (Hobbs et al., 2020) receiver at
the Parkes telescope provided a substantially larger bandwidth of $\sim$ 3
GHz. The pulsar was therefore also observed for 14 epochs from March 2019 to
October 2022 and was detected at the upper frequency range of the UWL receiver
at $\sim$ 4 GHz, implying that this pulsar might have a flat spectrum (see
Section 3.2.2 for details).

In order to reduce the positional uncertainty of the pulsar further,
observations were scheduled with the MeerKAT interferometer (Jonas & MeerKAT
Team, 2016). The long baselines between individual dishes reduce the size of
the synthesised beam, thus giving an improved localisation of the source of
interest. The FBFUSE (Barr, 2018) system offers the capability of beamforming
(Chen et al., 2021) and recording up to 864 tied array beams and producing
SIGPROC format filterbank data. Using the UWL position of PSR J1746$-$2829 as
a reference, 480 beams were tiled around the position with an integration time
of 9 min at 1.28 GHz. This covered roughly a 25 arcmin radius. Beams within
the UWL positional uncertainty were folded/searched with the pulsar
parameters. The only detection was obtained in a beam centred at RA
17h46m15s.04 and DEC -28$\degr$29$\arcmin$32$\arcsec$.40. Since the
synthesised beams were elliptical, the positional uncertainties in the major
and minor axis were 50 and 80 arcsec respectively.

To estimate the spin-down rate of the pulsar and derive an initial timing
ephemeris, we modeled the measured spin period in each observation as a first-
order polynomial,

as shown in Figure 2. Consequently, the pulsar’s spin period evolution is
dominated by a period derivative ($\dot{P}$) which corresponds to
1229(49)$\times 10^{-15}$s s-1. This initial timing solution was then used to
fold all of the observations of this pulsar.

The phase-connected timing solution (where every rotation of the pulsar is
modelled from the first observation to the last) was only possible with the
UWL observations from MJD 58564 to 59838 due to the combination of a large
timing gap and highly RFI contaminated observations. This timing solution is
shown in Table 3. Although the timing solution was not fully phase-connected
to the other data sets, it confirms the high $\dot{P}$ of this pulsar. The
position was not fitted because it yielded a location outside the MeerKAT
beamwidth, suggesting that the current timing position uncertainty is still
larger than the position uncertainty derived from the MeerKAT pulsar search
observation. Assuming this pulsar to be a magnetic dipole radiator with
canonical neutron star mass ($1.4M_{\odot}$) and radius ($10$ km), the surface
magnetic field ($B_{\rm field}$) can be estimated: $B_{\rm field}\sim 5\times
10^{13}$ G with a characteristic age of $\sim$ 23000 yr. The second-period
derivative was found to be highly correlated with the position uncertainty,
which makes it less likely to be intrinsic to the pulsar.

To further constrain the position, we modelled the MeerKAT beam as a Gaussian
function (see Equation 12). Since this pulsar was detected with an S/N of 12
in only one of the tile-array beams of MeerKAT, and considering that the S/N
limit for the MeerKAT searches was 7, we used the beam to determine how far
the pulsar could be located without being detected in the neighbouring beam
with an S/N < 7 (see e.g. Jankowski et al., 2023). The beam and the current
position uncertainty are shown in Figure 6.

Figure 2: Barycentric spin period evolution of PSR J1746$-$2829\. The spin
period of this pulsar can be described by a simple linear function
($P(t)=\dot{P}t+P_{0}$).The different colours represent the different
instruments used.

####  3.2.2 Polarisation, spectral distribution, pulse profile evolution, and
scattering time

The synthesised beam width of the MeerKAT telescope ($\sim$ 1 arcmin) is
approximately six times smaller than that of the upper band at UWL receiver
($\sim$ 6.6 arcmin) (Hobbs et al., 2020). As a result, we used the beam
position from the MeerKAT observations as this pulsar’s position, minimising
the impact of a potential position offset on the measured flux density. Now
that the angular offset had less effect on the flux of the pulsar, the
intrinsic spectrum could be measured. We carried out an observation with UWL
receiver to measure the polarization properties, the spectral index, the
profile evolution, and the scattering time. Polarisation calibration was done
by observing a noise diode at 45∘ to the receiver dipoles for 90–120s prior to
the observation of the pulsar. The data were calibrated for flux using on- and
off-source scans of radio sources with known, stable flux densities, e.g. the
radio galaxy Hydra A(obtained from, Kerr et al., 2020).

We used the RMcalc code (Porayko et al., 2019) to measure the rotation measure
(RM). This approach was based on Brentjens & de Bruyn (2005) RM synthesis
method and presented the estimates using the Bayesian Generalized Lomb-Scargle
Periodogram (BGLSP) technique. For consistency, we also used the RMFIT routine
from PSRCHIVE (van Straten et al., 2012), which is based on an optimisation of
the linear polarization fraction. The searched RM range was set according to
the analysis by Schnitzeler & Lee (2015), resulting in the RM range of
$\pm$78481 rad m-2. RMcalc gave a rotation measure of -743 $\pm$ 14 rad m-2
while RMFIT gave $-$797 $\pm$ 39 rad m-2. As the results are consistent, the
RM from RMcalc with a lower uncertainty has been used. After applying this RM
we detected linear polarisation of $\sim$ 20 per cent without significant
circular polarisation. The RM of this pulsar, which is notably high i.e.
$\geq$ 500 rad m-2, is consistent with the other known pulsars the direction
of the GC (Schnitzeler et al., 2016; Abbate et al., 2023). The pulse profile
with polarisation is shown in Figure 4.

Subsequently, the observation was split into eight subbands to study the pulse
profile evolution over frequency. The pulse profile at the uppermost band
(3.84 GHz) showed a profile that could be described by a simple Gaussian
function999Due to its low significance, we did not consider the additional
structure near phase 0.44 in the pulse profile, as it origin, whether
intrinsic to the pulsar or residual RFI, remains unclear. with the full width
at half maximum (FWHM) of 10.15$\pm$0.07 ms, resulting in a small duty cycle
for this pulsar of 0.537 $\pm$ 0.04 per cent. The pulse profile shows an
increasingly broader tail towards lower frequencies, as shown in Figure 3.

Figure 3: Frequency vs pulse-phase plot for PSR J1746$-$2829 from an 82-min
observation with the UWL receiver, containing 6 cleaned channels and 1024
pulse phase bins.

Assuming no pulse profile evolution over frequencies, the broadening time is
measured by fitting for an exponential decay101010$e^{-\frac{t}{t_{ts,f}}}$
with a characteristic time defined as:

$\tau_{\rm{ts,f}}=\tau_{\rm{ts}}(\frac{f}{1000\,\rm{MHz}})^{\alpha_{\rm{sc}}}$
(11)

where the reference frequency is 1000 MHz. The frequency-phase pulse profile
was modelled as a Gaussian pulse convolved with exponential decay using Pulse
Portraiture (Pennucci et al., 2014; Pennucci, 2019), $\tau_{\rm ts}$ was
determined through least square minimisation, with $\alpha_{\rm sc}$ at
$-$4.0.111111Depending on the screen and DM. The resulting scattering time for
this pulsar at 1000 MHz as 67 $\pm$ 3 ms.

The scattering time for this pulsar is notably lower than that of other
pulsars in the GC, with $\tau_{\rm sc}\geq 200$ ms at 1.4 GHz (Johnston et
al., 2006; Deneva et al., 2009). This is expected given its 0.5∘ offset from
the GC. However, the $\tau_{\rm sc}$ for this pulsar is approximately 4 ms at
2.0 GHz. Such a scattering time could potentially smear out the pulsations
from some fast recycled pulsars, even at a 0.5∘ separation.

Figure 4: Folded pulse profile of PSR J1746-2829 at 3.2GHz showing a narrow
pulse profile with a low linear (Red) polarization fraction and no significant
circular (Blue) polarisation after correcting for RM.

####  3.2.3 Radio flux density and spectrum

To study the spectrum, we choose observations with $T_{\rm obs}$ longer than
one hour with the UWL receiver, resulting in two observations at MJD 59022 and
MJD 59491. The observation at MJD 59091 was made at the current best position.
However, the observation from MJD 59022 was made before the current position
was determined. It has a position offset ($\theta$) of $\sim$ 2 arcmin. An
offset $\theta$ is causing the observed flux density to be reduced as

$S_{\rm obs}=S_{\rm f}e^{\frac{-\theta^{2}}{2\sigma^{2}}},$ (12)

where $S_{\rm obs}$ is the observed flux density. This equation assumes that
the telescope response pattern is a Gaussian, where $\sigma$ is a Gaussian rms
width calculated from

$\sigma=\frac{\theta_{\rm b}}{2\sqrt{2\ln{2}}},$ (13)

using $\theta_{\rm b}$ in each frequency band as published in Hobbs et al.
(2020).

The $S_{\rm obs}$ was determined using the PSRFLUX routine from PSRCHIVE (van
Straten et al., 2012) with the 2D pulse profile template derived from the
profile discussed in the previous section. After we compensated for the flux
density reduction due to the offset using Equation 12 and Equation 13, the
spectrum was modeled as a power law with a spectral index ($\alpha$),

$S_{\rm f}=S_{f_{\rm{ref}}}(\frac{f}{f_{\rm{ref}}})^{\alpha},$ (14)

where $f_{\rm{ref}}$ is the reference frequency which is 1400 MHz. We measure
the spectral index to be $-$0.8 $\pm$ 0.1 and $-$0.9 $\pm$ 0.2 with a flux
density at 1400 MHz of 0.48 $\pm$ 0.01 mJy and 0.35 $\pm$ 0.01 mJy for MJD
59022 and MJD 59491 respectively, confirming that this pulsar has a relatively
flat spectrum compared to the typical pulsar population, which is in range of
$-$1.4 to $-$1.6 (Bates et al., 2013; Jankowski et al., 2018) and showing no
sign of spectral index variation overtime, which has been found in two radio
loud magnetars (Torne et al., 2021; Champion et al., 2020).

To explore radio flux distribution and evolution in time, the radio light
curve was calculated using two methods. First, all L-band flux densities were
estimated from the radiometer equation using the effective bandwidth,
observation time and system equivalent flux density for Parkes (Keith et al.,
2010), Effelsberg121212https://eff100mwiki.mpifr-bonn.mpg.de and MeerKAT
(Bailes et al., 2020). In addition, all of the observations before the MeerKAT
observation at MJD 59381 had a positional offset which decreases the flux
density which can be corrected using Equation 12. The flux density from the
MeerKAT observation is still affected by the position offset, which is
representing as a large asymmetric uncertainty, where the upper limit
represents the scenario where the pulsar is located at the edge of the
uncertainty. Moreover, we also search for a point source in the GC image
mosaic from MeerKAT (Heywood et al., 2022) (see Section 4). Only one point
source was found within the positional uncertainty, hence the flux density of
this source (0.36 $\pm$ 0.04 mJy) was used as an upper limit for epochs that
covered this source (MJD 58281,58286 and 58287).

Secondly, since more than 75 per cent of the UWL observations at approximately
1400 MHz were heavily polluted by RFI, the channels around 1400 MHz were
removed. In this case, the flux density at 1400 MHz is determined by the flux
density from the upper frequency data and the spectral index from all
available UWL observations with polarisation and flux calibrators, using the
average spectral index, $\alpha=-0.9(1)$.

The flux density is plotted against epoch of observation in Figure 5. The
radio light curve shows large flux density variations (more than 50 per cent),
corresponding to a characteristic of the high $B_{\rm field}$ pulsars and
magnetars (see e.g., Dexter et al., 2017). According to NE2001 (Cordes &
Lazio, 2002), the estimated diffractive scintillation time scale ($t_{\rm d}$)
at this location is approximately 1.3 s at 1000 MHz. This is significantly
shorter than the observation time. NE2001 also predicted the scintillation
bandwidth ($\Delta f_{\rm d}$) to be $3\times 10^{-6}$ MHz, Stinebring &
Condon (1990) demonstrated that the reflective scintillation time scale
($t_{\rm r}$) can be estimated from

$t_{\rm r}=\frac{4f_{\rm obs}t_{\rm d}}{\pi\Delta f_{\rm d}}.$ (15)

The $t_{\rm r}$ at $f_{\rm obs}$ of 1000 MHz is $\sim 20$ yr, which is
significantly longer than the flux density variation timescale ($\sim$ months)
as shown in Figure 5. As a result, the observed flux density variation is
unlikely dominated by the interstellar scintillation.

Figure 5: Upper panel: Spectral indexes ($\alpha$) at two epochs showing no
significant $\alpha$ variation, the dashed line represents the average
$\alpha$. Lower panel: Radio light curve of PSR J1746$-$2829\. Red circles
represent the flux densities from Parkes L-band observations while the blue
triangles represent the L-band fluxes densities from the Effelsberg telescope.
The green hexagon represents the flux density calculated using the radiometer
equation based on the MeerKAT follow-up observation of this pulsar. The
uncertainty here also includes the contribution from any position offset. The
magenta square represents the flux density derived from the only source within
the position uncertainty (see Section 4). The red diamonds show the 1400 MHz
flux densities extrapolated from the UWL observations assuming the spectral
index of -0.9.

###  3.3 X-RAY DATA

Given the similarities between PSR J1746-2829 and some magnetars (see Section
4.1), we have considered the possibility of detecting the new pulsar in
X-rays, given that magnetars are often detectable at these energies. We
searched for X-ray emission by cross-referencing with the sources from GC
Chandra X-ray survey. One source was found with an angular separation of 0.441
arcmin from the centre of the MeerKAT radio beam where this pulsar was
detected (Muno et al., 2009). The location of this source at the edge of the
tile array beam makes it unlikely to be the pulsar as it was not detected in
any neighbouring beams.

An upper limit for X-ray emission was estimated from the processed and cleaned
Chandra composite images131313Obs ID:07045,07044,02294,18326,18329 that
covered the whole positional uncertainty. We searched for the X-ray pixel with
the highest count that is not within one pixel from the known X-ray source and
used that as the upper limit for the number of photons, which was then
converted to a count rate by dividing by the exposure time.
WebPIMMS141414https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3pimms/w3pimms.pl
was used to convert from the Chandra telescope count rate to X-ray luminosity
using the spectrum (blackbody with kT = 1 keV) of the GC magnetar PSR
J1745$-$2900 (Rea et al., 2013) and the column density $N_{H}$ at the pulsar’s
position151515https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3nh/w3nh.pl
$N_{H}=9.42\times 10^{21}\rm{cm}^{-2}$. The upper limit for X-ray flux for
each epoch shown in Table 4, is approximately $10^{32}$ to $10^{33}$ erg/s,
which is 100 times less than the spin-down luminosity, $\sim 10^{34}$ erg/s.
In terms of higher-energy emission, specifically gamma-rays, no point source
has been reported within 1 arcmin of this source (Abdollahi et al., 2022).
This absence is expected not only due to the considerable distance of the
pulsar but also because the region exhibits a high gamma-ray background level,
reducing the number of detectable point sources (Smith et al., 2019, see,
e.g.,).

Table 4: Results from X-ray archival images. All of them were observed before the start of the timing campaign and showing the minimum X-ray flux of $10^{32}$ to $10^{33}$ erg s-1 which is approximately 1 to 10 per cent of this pulsar’s spin down luminosity. The count rate uncertainties were calculated from root-mean-square of the count rate in the MeerKAT beam. MJD | Count rate (photons ks-1) |  $L_{x}10^{32}$ (erg s-1) |  $T_{\rm obs}$ (ks)
---|---|---|---
54154.30 | 0.135(14) | 1.05(11) | 37
54040.59 | 0.132(15) | 1.02(12) | 38
52107.89 | 0.258(20) | 2.00(16) | 12
57584.33 | 1.036(69) | 8.04(54) | 1.9
57584.43 | 1.036(65) | 8.05(50) | 1.9

##  4 Discussion

This evidence of increased sensitivity from the FFA based pipeline compared to
the FFT based pipeline can be seen in the S/N of the detected pulsars in Table
2, as the FFA always has a higher S/N than in the FFT. This reflects the
previous results reported in Cameron et al. (2017); Parent et al. (2018).
However, it should be noted that our FFA pipeline has reduced sensitivity to
pulsars with duty cycles of less than $\sim$ 1 per cent, due to the number of
bins used in the fold.

The newly discovered pulsar, PSR J1746$-$2829, has a flat spectrum, long
period, and a relatively high $\dot{P}$. These are characteristics that are
similar to those of magnetars. However, the degree of linear polarisation is
surprisingly low if it is indeed a magnetar (see discussions below). The
parameters of this pulsar are shown in Table 3.

Recently, Heywood et al. (2022) published a deep radio image of the GC made
with the MeerKAT telescope at 1.28 GHz. The mosaic image also covered the
location of PSR J1746$-$2829\. The expected flux density of PSR J1746$-$2829
at the observing frequency of the imaging survey was calculated using Equation
14 with $S_{\rm{1400}}$ and $\alpha$ reported in Section 3.2.3, resulting in
an expected flux density of $0.57^{+0.098}_{-0.070}$ mJy.

As shown in Figure 6, a point source was detected with a peak flux density of
0.3 mJy visible within the position uncertainty of the pulsar. The sensitivity
of the imaging survey (Heywood et al., 2022) implies that the pulsar should be
visible, and the fact that there is only one point source within the
positional uncertainty and the flux density of this pulsar varies between 0.1
mJy to 0.6 mJy suggests that it may indeed be the pulsar. Unfortunately,
neither the spectral index nor the polarisation of this point source is
reported, which would help to further confirm the association.

Using a kick velocity of 380 km s-1 reported by Faucher-Giguère & Kaspi (2006)
and assuming that this pulsar is located 8.2 kpc from Earth, the upper limit
for the angular separation from the birthplace of this pulsar is approximately
4 arcminutes. According to the MeerKAT L-band Mosaic at the GC(Heywood et al.,
2022), there are several sources that could be supernova remnants within 4
arcminutes from this pulsar. Consequently, a further proper motion measurement
is required to determine if this pulsar is associated with any of these
sources.

Figure 6: The L-band observations image mosaic obtained at MeerKAT (Heywood et
al., 2022). Left: The MeerKAT pulsar search beam of PSR J1746$-$2829 (white
dashed ellipse) reveals a point source with 0.36 mJy flux density and 0.04 mJy
rms in the field with a position uncertainty derived from non-detections in
the other beams from the follow-up observation with MeerKAT (white ellipse).
Right: The magnified version of the image on the left, displaying the location
of the point source in the MeerKAT pulsar search beam.

###  4.1 Is PSR J1746$-$2829 a magnetar?

Magnetars are a group of neutron stars characterised by an implied surface
magnetic field strength orders of magnitude larger than that of the normal
pulsar population. They are also found to have relatively long spin periods
($\geq$ 1 s) (e.g., Kaspi & Beloborodov, 2017). Magnetars predominately emit
X-rays and gamma rays, sometimes with a luminosity that exceeds the spin-down
luminosity for a rotating magnetic dipole ($\dot{E}=4\pi^{2}I\dot{P}/P^{3}$).
For this reason, magnetar emission is believed to be powered by the decay of
the magnetic field energy, rather than purely by rotation. Most magnetars are
radio-quiet; out of the 31 magnetars discovered to-date
161616http://www.physics.mcgill.ca/~pulsar/magnetar/main.html (Olausen &
Kaspi, 2014), only six of them are detectable at radio frequencies (Camilo et
al., 2006; Camilo et al., 2007b; Levin et al., 2010; Livingstone et al., 2011;
Levin et al., 2012; Eatough et al., 2013; Shannon & Johnston, 2013;
Karuppusamy et al., 2020; Lower et al., 2020). The radio-loud magnetars are
usually observed to be transient in nature, some magnetars have been known to
be in a quiet state for years before becoming active (e.g. Mori et al., 2013;
Lyne et al., 2018). Most of these radio loud magnetars show flat radio spectra
($\alpha\leq-1.0$) (Kramer et al., 2007; Camilo et al., 2007b; Shannon &
Johnston, 2013; Torne et al., 2017; Camilo et al., 2018) and all of the known
radio magnetars are intrinsically almost 100 per cent linearly polarised
(Camilo et al., 2007a, 2008; Eatough et al., 2013; Camilo et al., 2018; Lower
et al., 2020; Champion et al., 2020). In addition, Agar et al. (2021) showed
that all magnetars have boarder intrinsic pulse profiles (duty cycle more than
4 per cent) compared to most slow pulsars (duty cycle less than 1 per cent).

However, some magnetars contradict these common properties at least for a
period of time. For example, PSR J1846$-$0258, a young radio magnetar, has a
rotation period of 0.3 s (Livingstone et al., 2011), Swift J1818.0-1607 has a
steep spectral index of $-$2.8 (Champion et al., 2020), and some magnetars
(PSR J1745$-$2900, XTE J1810$-$197, 1E 1547.0$-$5408, Swift J1818.0$-$1607)
were also reported to have low linear polarisation for some epochs (Camilo et
al., 2007a; Torne et al., 2017; Lower et al., 2021; Lower et al., 2023).

Finally, nine magnetars have been reported with X-ray quiescent luminosities
approximately 20 times lower than the spin-down luminosities, which is unusual
for magnetars (1E 1547.0$-$5408, PSR 1622$-$4950, SGR J1745$-$2900, XTE
J1810$-$197, Swift J1818.0$-$1607, SGR 1833$-$0832, Swift J1834.9$-$0846, SGR
1935+2154, PSR J1846$-$0258) (see Olausen & Kaspi, 2014, for reviews).
Interestingly, six of these are radio loud magnetars, suggesting that radio
emission from radio magnetars may have lower X-ray quiescent luminosity.

PSR J1746$-$2829 has some observational features commonly found in radio loud
magnetars; The spectrum is flatter than most pulsars and two of the radio
magnetars. It has a long rotation period. The measured $\dot{P}$ indicates the
magnetic field near the lower-end of the magnetar $B_{\rm field}$ limit ($\sim
4.4\times 10^{13}$ G) (Rea et al., 2012). This study of the radio flux
distribution shows that this pulsar has highly variable flux. However, it also
shows some properties that are not in common with radio magnetars, but instead
are typical for slow pulsars; a narrow pulse profile and low polarisation
fraction at high frequency as shown in Figure 4. Critically, we have not been
able to conclude whether PSR J1746$-$2829 belongs to the family of magnetars
or not.

A magnetar or not, this pulsar is the third flat spectrum pulsar out of seven
pulsars found around 0.5∘ from the GC. The other objects are the GC magnetar
and a transient flat spectrum pulsar, with a high $B_{\rm{field}}$, named PSR
J1746$-$2850, which is another magnetar-like object (Dexter et al., 2017). If
this pulsar, along with PSR J1746$-$2850, is a magnetar, the proportion of
magnetars to non-recycled pulsars in the observed population (0.4 per cent)
appears to be significantly different to that of the GC (40 per cent). This
could be explained by a larger intrinsic population of magnetars or the
environmental conditions in the GC favour the detection of radio magnetars
rather than non-recycled pulsars. This could be explained by a higher
intrinsic population of magnetars in the GC as predicted by Dexter & O’Leary
(2014), or that the interstellar medium conditions within the GC favour the
detection of radio magnetars.

##  5 Conclusions

We report on the reprocessing of the HTRU-S LowLat around the GC using the
first FFA pipeline with an acceleration search. The survey resulted in the
discovery of a new slow pulsar with a very high period derivative, and a flat
spectrum, indicating that this pulsar might be a magnetar. The observations
showed that this pulsar has a high DM, RM, and $\tau_{\rm ts}$, which is
expected for an object found inside a dense magneto-ionic environment such as
the GC. As this pulsar is a magnetar or a high $B_{\rm field}$ pulsar, is the
third such object out of seven pulsars located less than 0.5∘ from the GC and
may suggest that the GC hosted an anomalously high number of magnetar. All
known pulsars detected by the previous FFT processing were detected, as well
as a missing pulsar from the FFT based processing of the survey. By comparing
the S/N from the FFT to the S/N from the FFA, we found that the FFA pipeline
has shown more sensitivity than the FFT pipeline in the searched parameter
space.

## Acknowledgements

The Parkes (Murriyang) radio telescope is part of the Australia Telescope,
which is funded by the Commonwealth Government for operation as a National
Facility managed by CSIRO. This publication is based on observations with the
100-m telescope of the Max-Planck-Institut fuer Radioastronomie at Effelsberg.
The localisation of the source was completed using the MPIfR FBSUE backend on
the 64-dish MeerKAT radio telescope owned and operated by the South African
Radio Astronomy Observatory, which is a facility of the National Research
Foundation, an agency of the Department of Science and Innovation. We would
like to thank F. Abbate for useful discussions and M. Cruces for providing
help for the Effelsberg observations.

## Data Availability

Pulsar data taken for the P860 and P1050 project are made available through
the CSIRO’s Data Access Portal (https://data.csiro.au) after an 18 month
proprietary period. The rest of the data underlying this article will be
shared on reasonable request to the corresponding author.

## References

  * Abbate et al. (2023) Abbate F., et al., 2023, MNRAS, 524, 2966
  * Abdollahi et al. (2022) Abdollahi S., et al., 2022, ApJS, 260, 53
  * Agar et al. (2021) Agar C. H., et al., 2021, MNRAS, 508, 1102
  * Bailes et al. (2020) Bailes M., et al., 2020, Publ. Astron. Soc. Australia, 37, e028
  * Balakrishnan et al. (2022) Balakrishnan V., Champion D., Barr E., Kramer M., Venkatraman Krishnan V., Eatough R. P., Sengar R., Bailes M., 2022, MNRAS, 511, 1265
  * Barr (2018) Barr E. D., 2018, in Weltevrede P., Perera B. B. P., Preston L. L., Sanidas S., eds, Pulsar Astrophysics the Next Fifty Years. "". pp 175–178, doi:10.1017/S1743921317009036
  * Bates et al. (2013) Bates S. D., Lorimer D. R., Verbiest J. P. W., 2013, MNRAS, 431, 1352
  * Bhattacharyya et al. (2016) Bhattacharyya B., et al., 2016, ApJ, 817, 130
  * Brentjens & de Bruyn (2005) Brentjens M. A., de Bruyn A. G., 2005, A&A, 441, 1217
  * Cameron et al. (2017) Cameron A. D., Barr E. D., Champion D. J., Kramer M., Zhu W. W., 2017, MNRAS, 468, 1994
  * Cameron et al. (2020) Cameron A. D., et al., 2020, MNRAS, 493, 1063
  * Camilo et al. (2006) Camilo F., Ransom S. M., Halpern J. P., Reynolds J., Helfand D. J., Zimmerman N., Sarkissian J., 2006, Nature, 442, 892
  * Camilo et al. (2007a) Camilo F., Reynolds J., Johnston S., Halpern J. P., Ransom S. M., van Straten W., 2007a, ApJ, 659, L37
  * Camilo et al. (2007b) Camilo F., Ransom S. M., Halpern J. P., Reynolds J., 2007b, ApJ, 666, L93
  * Camilo et al. (2008) Camilo F., Reynolds J., Johnston S., Halpern J. P., Ransom S. M., 2008, ApJ, 679, 681
  * Camilo et al. (2018) Camilo F., et al., 2018, ApJ, 856, 180
  * Champion et al. (2020) Champion D., et al., 2020, MNRAS, 498, 6044
  * Chen et al. (2021) Chen W., Barr E., Karuppusamy R., Kramer M., Stappers B., 2021, Journal of Astronomical Instrumentation, 10, 2150013
  * Cordes & Lazio (1997) Cordes J. M., Lazio T. J. W., 1997, ApJ, 475, 557
  * Cordes & Lazio (2002) Cordes J. M., Lazio T. J. W., 2002, arXiv e-prints, pp astro–ph/0207156
  * Cruces et al. (2021) Cruces M., et al., 2021, MNRAS, 508, 300
  * Deneva (2010) Deneva J. S., 2010, PhD thesis, Cornell University, United States
  * Deneva et al. (2009) Deneva J. S., Cordes J. M., Lazio T. J. W., 2009, ApJ, 702, L177
  * Desvignes et al. (2018) Desvignes G., et al., 2018, ApJ, 852, L12
  * Dexter & O’Leary (2014) Dexter J., O’Leary R. M., 2014, ApJ, 783, L7
  * Dexter et al. (2017) Dexter J., et al., 2017, MNRAS, 468, 1486
  * Eatough et al. (2013) Eatough R. P., et al., 2013, Nature, 501, 391
  * Eatough et al. (2021) Eatough R. P., et al., 2021, MNRAS, 507, 5053
  * Eckart & Genzel (1996) Eckart A., Genzel R., 1996, Nature, 383, 415
  * Faucher-Giguère & Kaspi (2006) Faucher-Giguère C.-A., Kaspi V. M., 2006, ApJ, 643, 332
  * Faulkner et al. (2004) Faulkner A. J., et al., 2004, MNRAS, 355, 147
  * Figer (2003) Figer D. F., 2003, Astronomische Nachrichten Supplement, 324, 255
  * Heywood et al. (2022) Heywood I., et al., 2022, ApJ, 925, 165
  * Hobbs et al. (2020) Hobbs G., et al., 2020, Publ. Astron. Soc. Australia, 37, e012
  * Israel (1967) Israel W., 1967, Physical Review, 164, 1776
  * Israel (1968) Israel W., 1968, Communications in Mathematical Physics, 8, 245
  * Jankowski et al. (2018) Jankowski F., van Straten W., Keane E. F., Bailes M., Barr E. D., Johnston S., Kerr M., 2018, MNRAS, 473, 4436
  * Jankowski et al. (2023) Jankowski F., et al., 2023, arXiv e-prints, p. arXiv:2302.10107
  * Johnston & Kulkarni (1991) Johnston H. M., Kulkarni S. R., 1991, ApJ, 368, 504
  * Johnston et al. (2006) Johnston S., Kramer M., Lorimer D. R., Lyne A. G., McLaughlin M., Klein B., Manchester R. N., 2006, MNRAS, 373, L6
  * Jonas & MeerKAT Team (2016) Jonas J., MeerKAT Team 2016, in MeerKAT Science: On the Pathway to the SKA. p. 1
  * Karuppusamy et al. (2020) Karuppusamy R., et al., 2020, The Astronomer’s Telegram, 13553, 1
  * Kaspi & Beloborodov (2017) Kaspi V. M., Beloborodov A. M., 2017, ARA&A, 55, 261
  * Keane (2010) Keane E. F., 2010, PhD thesis, University of Manchester
  * Keane et al. (2018) Keane E. F., et al., 2018, MNRAS, 473, 116
  * Keith et al. (2010) Keith M. J., et al., 2010, MNRAS, 409, 619
  * Kennea et al. (2013) Kennea J. A., et al., 2013, ApJ, 770, L24
  * Kerr et al. (2020) Kerr M., et al., 2020, Publ. Astron. Soc. Australia, 37, e020
  * Klein et al. (2004) Klein B., Kramer M., Müller P., Wielebinski R., 2004, in Camilo F., Gaensler B. M., eds, "" Vol. 218, Young Neutron Stars and Their Environments. p. 133
  * Kondratiev et al. (2009) Kondratiev V. I., McLaughlin M. A., Lorimer D. R., Burgay M., Possenti A., Turolla R., Popov S. B., Zane S., 2009, ApJ, 702, 692
  * Kramer et al. (1996) Kramer M., Jessner A., Muller P., Wielebinski R., 1996, in Johnston S., Walker M. A., Bailes M., eds, Astronomical Society of the Pacific Conference Series Vol. 105, IAU Colloq. 160: Pulsars: Problems and Progress. p. 13
  * Kramer et al. (2004) Kramer M., Backer D. C., Cordes J. M., Lazio T. J. W., Stappers B. W., Johnston S., 2004, New Astron. Rev., 48, 993
  * Kramer et al. (2007) Kramer M., Stappers B. W., Jessner A., Lyne A. G., Jordan C. A., 2007, MNRAS, 377, 107
  * Levin et al. (2010) Levin L., et al., 2010, ApJ, 721, L33
  * Levin et al. (2012) Levin L., et al., 2012, MNRAS, 422, 2489
  * Liu & Eatough (2017) Liu K., Eatough R., 2017, Nature Astronomy, 1, 812
  * Liu et al. (2012) Liu K., Wex N., Kramer M., Cordes J. M., Lazio T. J. W., 2012, ApJ, 747, 1
  * Liu et al. (2021) Liu K., et al., 2021, ApJ, 914, 30
  * Livingstone et al. (2011) Livingstone M. A., Ng C. Y., Kaspi V. M., Gavriil F. P., Gotthelf E. V., 2011, ApJ, 730, 66
  * Lorimer (2011) Lorimer D. R., 2011, SIGPROC: Pulsar Signal Processing Programs, Astrophysics Source Code Library, record ascl:1107.016 (ascl:1107.016)
  * Lorimer & Kramer (2004) Lorimer D. R., Kramer M., 2004, Handbook of Pulsar Astronomy. Vol. 4
  * Lower et al. (2020) Lower M. E., Shannon R. M., Johnston S., Bailes M., 2020, ApJ, 896, L37
  * Lower et al. (2021) Lower M. E., Johnston S., Shannon R. M., Bailes M., Camilo F., 2021, MNRAS, 502, 127
  * Lower et al. (2023) Lower M. E., et al., 2023, arXiv e-prints, p. arXiv:2302.07397
  * Lyne et al. (2018) Lyne A., Levin L., Stappers B., Mickaliger M., Desvignes G., Kramer M., 2018, The Astronomer’s Telegram, 12284, 1
  * Macquart et al. (2010a) Macquart J. P., Kanekar N., Frail D. A., Ransom S. M., 2010a, ApJ, 715, 939
  * Macquart et al. (2010b) Macquart J. P., Kanekar N., Frail D. A., Ransom S. M., 2010b, ApJ, 715, 939
  * Manchester et al. (2005) Manchester R. N., Hobbs G. B., Teoh A., Hobbs M., 2005, AJ, 129, 1993
  * Morello et al. (2020a) Morello V., et al., 2020a, MNRAS, 493, 1165
  * Morello et al. (2020b) Morello V., Barr E. D., Stappers B. W., Keane E. F., Lyne A. G., 2020b, MNRAS, 497, 4654
  * Mori et al. (2013) Mori K., Gotthelf E. V., Barriere N. M., Hailey C. J., Harrison F. A., Kaspi V. M., Tomsick J. A., Zhang S., 2013, The Astronomer’s Telegram, 5020, 1
  * Muno et al. (2009) Muno M. P., et al., 2009, ApJS, 181, 110
  * Ng et al. (2015) Ng C., et al., 2015, MNRAS, 450, 2922
  * Nita & Gary (2010) Nita G. M., Gary D. E., 2010, MNRAS, 406, L60
  * Nita et al. (2007) Nita G. M., Gary D. E., Liu Z., Hurford G. J., White S. M., 2007, PASP, 119, 805
  * Olausen & Kaspi (2014) Olausen S. A., Kaspi V. M., 2014, ApJS, 212, 6
  * Parent et al. (2018) Parent E., et al., 2018, ApJ, 861, 44
  * Pennucci (2019) Pennucci T. T., 2019, ApJ, 871, 34
  * Pennucci et al. (2014) Pennucci T. T., Demorest P. B., Ransom S. M., 2014, ApJ, 790, 93
  * Penrose (1979) Penrose R., 1979, Singularities and time-asymmetry.. pp 581–638
  * Porayko et al. (2019) Porayko N. K., et al., 2019, MNRAS, 483, 4100
  * Press et al. (1992) Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P., 1992, Numerical recipies in C. Vol. 2, Cambridge university press Cambridge
  * Purver et al. (2022) Purver M., et al., 2022, MNRAS, 510, 1597
  * Rajwade et al. (2017) Rajwade K. M., Lorimer D. R., Anderson L. D., 2017, MNRAS, 471, 730
  * Ransom et al. (2003) Ransom S. M., Cordes J. M., Eikenberry S. S., 2003, ApJ, 589, 911
  * Rea et al. (2012) Rea N., Pons J. A., Torres D. F., Turolla R., 2012, ApJ, 748, L12
  * Rea et al. (2013) Rea N., et al., 2013, ApJ, 775, L34
  * Rickett (1977) Rickett B. J., 1977, ARA&A, 15, 479
  * Schnitzeler & Lee (2015) Schnitzeler D. H. F. M., Lee K. J., 2015, MNRAS, 447, L26
  * Schnitzeler et al. (2016) Schnitzeler D. H. F. M., Eatough R. P., Ferrière K., Kramer M., Lee K. J., Noutsos A., Shannon R. M., 2016, MNRAS, 459, 3005
  * Sengar (2023) Sengar R., 2023, Thesis, Swinburne University of Technology
  * Shannon & Johnston (2013) Shannon R. M., Johnston S., 2013, MNRAS, 435, L29
  * Singh et al. (2022) Singh S., Roy J., Panda U., Bhattacharyya B., Morello V., Stappers B. W., Ray P. S., McLaughlin M. A., 2022, ApJ, 934, 138
  * Singh et al. (2023) Singh S., Roy J., Bhattacharyya B., Panda U., Stappers B. W., McLaughlin M. A., 2023, ApJ, 944, 54
  * Smith et al. (2019) Smith D. A., et al., 2019, ApJ, 871, 78
  * Spitler et al. (2014) Spitler L. G., et al., 2014, ApJ, 780, L3
  * Staelin (1969) Staelin D. H., 1969, IEEE Proceedings, 57, 724
  * Staveley-Smith et al. (1996) Staveley-Smith L., et al., 1996, Publ. Astron. Soc. Australia, 13, 243
  * Stinebring & Condon (1990) Stinebring D. R., Condon J. J., 1990, ApJ, 352, 207
  * Suresh et al. (2022) Suresh A., et al., 2022, ApJ, 933, 121
  * Taylor & Huguenin (1969) Taylor J. H., Huguenin G. R., 1969, Nature, 221, 816
  * Titus et al. (2019) Titus N., et al., 2019, MNRAS, 487, 4332
  * Torne et al. (2017) Torne P., et al., 2017, MNRAS, 465, 242
  * Torne et al. (2021) Torne P., et al., 2021, A&A, 650, A95
  * Wex & Kopeikin (1999) Wex N., Kopeikin S. M., 1999, ApJ, 514, 388
  * Wharton (2017) Wharton R. S., 2017, PhD thesis, Cornell University
  * Wharton et al. (2012) Wharton R. S., Chatterjee S., Cordes J. M., Deneva J. S., Lazio T. J. W., 2012, ApJ, 753, 108
  * Yao et al. (2017) Yao J. M., Manchester R. N., Wang N., 2017, ApJ, 835, 29
  * van Straten et al. (2012) van Straten W., Demorest P., Oslowski S., 2012, Astronomical Research and Technology, 9, 237