# TRAPUM upper limits on pulsed radio emission for SMC X-ray pulsar
J0058$-$7218

E. Carli,1 L. Levin,1 B. W. Stappers,1 E. D. Barr,2 R. P. Breton,1 S.
Buchner,3 M. Burgay,4 M. Kramer,2 P. V. Padmanabh,2,5 A. Possenti,4 V.
Venkatraman Krishnan,2 J. Behrend,2 D. J. Champion,2 W. Chen,2 Y. P. Men2

1Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy,
The University of Manchester, Manchester M13 9PL, UK
2 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany
3 South African Radio Astronomy Observatory (SARAO), 2 Fir Street, Black River
Park, Observatory, Cape Town, 7925
4INAF-Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047,
Selargius, Italy
5Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),
D-30167 Hannover, Germany
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The TRAPUM collaboration has used the MeerKAT telescope to conduct a search
for pulsed radio emission from the young Small Magellanic Cloud pulsar
J0058$-$7218 located in the supernova remnant IKT 16, following its discovery
in X-rays with XMM-Newton. We report no significant detection of dispersed,
pulsed radio emission from this source in three 2-hour L-band observations
using the core dishes of MeerKAT, setting an upper limit of 7.0 $\upmu$Jy on
its mean flux density at 1284 MHz. This is nearly 7 times deeper than previous
radio searches for this pulsar in Parkes L-band observations. This suggests
that the radio emission of PSR J0058$-$7218 is not beamed towards Earth or
that PSR J0058$-$7218 is similar to a handful of Pulsar Wind Nebulae systems
that have a very low radio efficiency, such as PSR B0540$-$6919, the Large
Magellanic Cloud Crab pulsar analogue. We have also searched for bright,
dispersed, single radio pulses and found no candidates above a fluence of 93
mJy ms at 1284 MHz.

###### keywords:

Pulsars: individual: PSR J0058$-$7218

††pubyear: 2022††pagerange: TRAPUM upper limits on pulsed radio emission for
SMC X-ray pulsar J0058$-$7218–References

##  1 Introduction

The Magellanic Clouds are the only galaxies outside our own in which radio
pulsars have been discovered to date. They are nearby galaxies that are
unobstructed by the galactic plane, therefore they are a good target for
extragalactic pulsar searches. Indeed, the Small Magellanic Cloud (SMC) is
just 60 kpc away (Karachentsev et al., 2004), and the expected Milky Way
Dispersion Measure (DM) contribution in its direction is low: about $30$ pc
cm-3 according to the YMW2016 electron density model (Yao et al., 2017), and
$42$ pc cm-3 according to the NE2001 model (Cordes & Lazio, 2002). There was a
recent episode of stellar formation in the SMC about 40 Myr ago (Harris &
Zaritsky, 2004), which led to an abundance of young systems per unit mass
compared to the Milky Way. In particular, the SMC hosts many supernova
remnants (18 confirmed SNRs in Maggi et al. 2019), which can contain young
neutron stars. Due to their rarity in the Milky Way’s older population111In
the Australia Telescope National Facility (ATNF) pulsar catalogue (Manchester
et al., 2005), only about $\simeq$180 pulsars out of $\simeq$2500 with a
catalogued characteristic age are younger than 120 kyr., the discovery of
young pulsars is scientifically interesting. Among them, magnetars (which have
the highest known stellar magnetic fields) are prized for a variety of
fundamental physics and astrophysics investigations (Esposito et al., 2021),
including as one of the progenitors of Fast Radio Bursts (Bochenek et al.,
2020; Caleb & Keane, 2021). Each Magellanic Cloud hosts one known magnetar
(Helfand & Long, 1979; Lamb et al., 2002). Additionally, extragalactic pulsars
are sought after for insights on the impact of different galactic properties
on neutron star formation, such as the impact of metallicity and star
formation history on stellar mass and supernova physics (Heger et al., 2003;
Titus et al., 2020).

There are seven published radio pulsars in the SMC and all have been
discovered with the Parkes 64-m single dish radio telescope in Australia, by
McConnell et al. (1991) (one pulsar), Crawford et al. (2001) (1), Manchester
et al. (2006) (3), and Titus et al. (2019) (2). Their median DM is around 115
pc cm-3. The radio emission from these pulsars is powered by their rapid
rotation. This can also power hard X-ray emission when the pulsar is young and
most rapidly rotating. The X-ray emission has a characteristic hard power-law
spectrum (Becker & Trümper, 1997, and references therein). Only two
young222All other published non-magnetar pulsars in the SMC are over 1 Myr in
characteristic age (Manchester et al., 2005). pulsars have been discovered in
the SMC, both in the X-ray band only: CXOU J010043.1$-$721134 (Lamb et al.,
2002, a magnetar), and most recently, PSR J0058$-$7218 (Maitra et al., 2021).
In this paper, we describe the follow-up radio observations of the latter with
MeerKAT.

PSR J0058$-$7218 is situated in the supernova remnant (SNR) IKT 16 (Inoue et
al., 1983), also known as DEM S 103 (Davies et al., 1976). The remnant was
first identified as an $\rm{H_{\upalpha}}$ emission nebula LHA 115-N 66 in
Henize (1956). The first radio observations of the nebula were made by Mills &
Aller (1971), and it was tentatively suggested to be a nonthermal radio source
by Clarke et al. (1976). It was catalogued as 1E0057.6$-$7228 with the first
X-ray detection of the system by Seward & Mitchell (1981). Mills et al. (1982)
conducted further radio observations which led to the proposition that DEM S
103 was a tentative SNR candidate. It was officially declared a candidate SNR
based on soft X-ray observations by Inoue et al. (1983), and subsequently
named IKT 16. A radio and $\rm{H_{\upalpha}}$ study by Mathewson et al. (1984)
confirmed that IKT 16 is a SNR, which they found is in the Sedov evolutionary
phase. Further insights as to the nature of the system were made possible by
the launch of the XMM-Newton and Chandra X-ray observatories. Van Der Heyden
et al. (2004) identified a hard X-ray source within the SNR in a single XMM
exposure, but it was too faint to be further characterised. After 8 additional
XMM-Newton observations, Owen et al. (2011) identified the hard X-ray source
as a tentative Pulsar Wind Nebula (PWN), within a larger, extended radio
source from ATCA and MOST radio images (inside the SNR, see Figure 1). As the
PWN is offset from the centre of the SNR, they suggested the existence of a
pulsar in motion, with a transverse kick velocity of 580 km s-1. Using
adiabatic Sedov modelling, they estimated the age of the SNR to be 14.7 kyr.
The putative pulsar emission could not be resolved from the PWN at the time.

Maitra et al. (2015) confirmed the existence of the PWN with Chandra
observations, resolving a putative pulsar at its centre in hard X-rays. IKT 16
was thus defined as a ‘composite SNR’, where there is non-thermal emission
from both the SNR shell in radio and the hard X-ray point source within the
PWN. The latter’s measured X-ray spectral index implied a young, rotation-
powered pulsar with non-thermal radiation from the pulsar magnetosphere (e.g.
Becker & Trümper, 1997; Wang & Zhao, 2004). Using a similar method as
Kargaltsev et al. (2008) using the X-ray luminosities of the PWN and point
source, Maitra et al. (2015) estimated the period of the putative pulsar to be
of the order of 100 ms with a period derivative $\simeq 10^{-13}$. Maitra et
al. (2015) characterised the morphology of the system: the PWN is a 5.2
arcsecond elongated X-ray feature at RA(J2000) $=$
00h58m16$\aas@@fstack{s}$824 $\pm$ 0$\aas@@fstack{\prime\prime}$1 Dec(J2000)
$=$ $-$72°18′05$\aas@@fstack{\prime\prime}$32 $\pm$
0$\aas@@fstack{\prime\prime}$2 (Chandra position). The putative pulsar (hard
X-ray point source) is consistent with the PWN centre, at RA(J2000) $=$
00h58m16$\aas@@fstack{s}$85 Dec(J2000) $=$
$-$72°18′05$\aas@@fstack{\prime\prime}$60 $\pm$ 0$\aas@@fstack{\prime\prime}$6
(Chandra position). The PWN is located within a larger radio feature, which
Maitra et al. (2015) described as two lobes about the PWN each 20$\pm$5
arcseconds in extent (see Figure 1), from a high resolution ATCA 2.1 GHz
image. They concluded that the PWN is in expansion in the cold SNR ejecta. No
radio point source was detected near the X-ray point source.

The first dedicated search for a radio pulsar in IKT 16 was conducted by Titus
et al. (2019) with the Parkes radio telescope, in two four-hour observations
with a beam of the Parkes Multi-Beam receiver (Staveley-Smith et al., 1996)
placed 1.4 arcminutes from the position of the putative pulsar (see Figure 1).
The observations had a 400 MHz bandwidth centred on 1382 MHz
(Berkeley–Parkes–Swinburne data recorder: McMahon 2011; Keith et al. 2010).
They carried out a Fourier domain search with presto (Ransom, 2011; Ransom et
al., 2002) for DMs up to 660 pc cm-3 and a fast-folding search with riptide
for DMs up to 400 pc cm-3 (Morello et al., 2020). PSR J0058$-$7218 was not
detected down to S/N$=$8, corresponding to a 1400 MHz flux density limit of 36
$\upmu$Jy. This limit takes into account the sensitivity loss from the
putative pulsar being off-centre in the beam and assumes a 5 per cent duty
cycle. With a 7 K sky temperature contribution included (Zheng et al., 2017),
the flux density limit is 47 $\upmu$Jy.

The 21.7 ms pulsar J0058$-$7218 was finally discovered in X-rays by Maitra et
al. (2021) in 2020 XMM-Newton EPIC camera observations. They measured a hard
X-ray spectral index of 1.4$\pm 0.1$ and a single peak pulse shape. They
determined an ephemeris using the pulsar position from Maitra et al. (2015).
The pulsar has a high period derivative of $\simeq 3\times 10^{-14}$, giving a
young characteristic age of about 12 kyr (in line with the SNR Sedov age from
Owen et al. 2011), and a high spin-down luminosity $\dot{E}=1.1\times 10^{38}$
erg s-1. The inferred surface magnetic field of $B_{\text{surf}}=8\times
10^{11}$ G excludes that PSR J0058$-$7218 is a magnetar (Esposito et al.,
2021). Maitra et al. (2021) conducted multiwavelength searches of PSR
J0058$-$7218: they reported no gamma-ray pulsations in the most recent Fermi
LAT data set, and no radio pulsations in a reprocessing of the Titus et al.
(2019) Parkes data. They folded the data at the predicted topocentric period
of the pulsar using dspsr and searched the folded data for the highest S/N
profile over DMs 0-1000 pc cm-3 with psrchive’s pdmp tool (Van Straten &
Bailes, 2011; Hotan et al., 2004). They quote a better flux density limit than
Titus et al. (2019), 15 $\upmu$Jy at 1400 MHz, as they use a lower signal-to-
noise ratio (S/N) limit of 5 in their folding search, and do not take into
account the sensitivity loss from the pulsar being off-centre in the Parkes
beam (M. Pilia, private communication). Adding this sensitivity loss, a sky
temperature contribution of 7 K, and a S/N cut of 7 to compare with our own
searches, this limit becomes 41 $\upmu$Jy at 1400 MHz. They also did not find
any single pulses in this dataset with heimdall over DMs 0-1000 pc cm-3
(Barsdell et al., 2012). Using the survey parameters from Titus et al. (2019),
and taking into account the sensitivity loss from the pulsar being off-centre
in the Parkes beam, a sky temperature contribution of 7 K, and a S/N cut of 8
to compare with our own searches, we find their single pulse search has a
limiting fluence of 821 mJy ms333In Maitra et al. (2021), a fluence limit of
160 mJy ms down to S/N$=$5 is quoted. The beam correction and sky temperature
are again not taken into account. Additionally, the correction factor
accounting for data acquisition system imperfections is not used (M. Pilia,
private communication). for a 1 ms pulse width at 1400 MHz (with a 1 ms
integration time).

TRAPUM (TRAnsients and PUlsars with MeerKAT) is a Large Survey Project of the
MeerKAT telescope (trapum.org, Stappers & Kramer 2016). One of TRAPUM’s
science goals is to find new extragalactic pulsars. Thus, the collaboration is
currently conducting a survey of the SMC with the MeerKAT telescope. PSR
J0058$-$7218 and its Pulsar Wind Nebula are located within several of the
survey’s pointings. The X-ray pulsar discovery in Maitra et al. (2021) was
published during our survey, after one observation of the PWN was made.

##  2 Observations and data reduction

Figure 1: Regions of interest are overlaid on a 1320 MHz ASKAP image of the
SMC (Joseph et al., 2019). The morphology of the composite SNR is delineated
by purple circles. The largest purple circle delimits the SNR shell as
catalogued by Maggi et al. (2019). It contains a comparatively bright feature
around the 5.2 arcsecond diameter PWN (smallest purple circle, Maitra et al.
2015). Our observed MeerKAT beams are shown at 50 per cent sensitivity as blue
ellipses, simulated with mosaic (Chen et al., 2021). The innermost beam is
OBS1 and the outermost beam is OBS3 (cf. Table 1). They are centred on the PWN
position. The centre of the Parkes telescope beam from the Titus et al. (2019)
survey is shown as a pink cross. The 14 arcminute Parkes half-power beam width
lies outside the figure. This figure was generated with the aplpy Python
package. Table 1: Characteristics of the MeerKAT coherent beam observations of
PSR J0058$-$7218\. For each observation, one coherent beam is placed at the
centre of the PWN as defined by Maitra et al. (2015), RA(J2000) $=$
00h58m16$\aas@@fstack{s}$824 Dec(J2000) $=$
$-$72°18′05$\aas@@fstack{\prime\prime}$32. The coherent beam is placed within
the MeerKAT primary incoherent beam, which pointing location is given in Right
Ascension and Declination (J2000). The coherent beam major axes are given in
arcseconds in the Right Ascension and Declination directions, with the ellipse
position angle.

Observation Number and Date | Primary incoherent beam location | Number of dishes | Coherent beam size (50 per cent sensitivity) | Sampling time | Processing
---|---|---|---|---|---
| OBS1
---
14 Jan 2021
| 0h55m14$\aas@@fstack{s}$6910
---
-72°26′06$\aas@@fstack{\prime\prime}$899
40 |  | 40$\aas@@fstack{\prime\prime}$0, 21$\aas@@fstack{\prime\prime}$3
---
9$\aas@@fstack{\circ}$2
76 $\upmu$s |  | Pulsar search
---
Fold on downsampled data
| OBS2
---
24 Apr 2021
| 0h55m14$\aas@@fstack{s}$6910
---
-72°26′06$\aas@@fstack{\prime\prime}$899
44 |  | 46$\aas@@fstack{\prime\prime}$2, 22$\aas@@fstack{\prime\prime}$9
---
6$\aas@@fstack{\circ}$6
153 $\upmu$s |  | Pulsar search
---
Fold
Single pulse search
| OBS3
---
27 Oct 2021
| 0h57m21$\aas@@fstack{s}$2370
---
-71°52′35$\aas@@fstack{\prime\prime}$195
44 |  | 48$\aas@@fstack{\prime\prime}$9, 24$\aas@@fstack{\prime\prime}$9
---
9$\aas@@fstack{\circ}$0
153 $\upmu$s |  | Pulsar search
---
Fold
Single pulse search

We placed one coherent beam at the centre of the PWN444Maitra et al. (2015)
showed that the pulsar position is consistent with the centre of the PWN (see
section 1).  (as defined by Maitra et al. (2015): RA(J2000) $=$
00h58m16$\aas@@fstack{s}$824 Dec(J2000) $=$
$-$72°18′05$\aas@@fstack{\prime\prime}$32), in three multi-beam observations
as part of our SMC survey. The beams were formed using the core dishes of
MeerKAT (40 or 44 dishes out of 64) with a maximum baseline length of 1 km.
This reduction from the full array’s 8 km maximum baseline strikes a good
balance between beam area and sensitivity (Chen et al., 2021). We carried out
the three 2-hour observations at L-band (856-1712 MHz, 856 MHz bandwidth),
with 2048 frequency channels, and a beam area large enough to cover the
Chandra hard X-ray pulsar position error: RA(J2000) $=$
00h58m16$\aas@@fstack{s}$85 Dec(J2000) $=$
$-$72°18′05$\aas@@fstack{\prime\prime}$60 $\pm$ 0$\aas@@fstack{\prime\prime}$6
(Maitra et al., 2015). The characteristics of the individual observations are
given in Table 1 and Figure 1.

We have run a pulsar search on all three observations of the PWN, as part of
the standard processing used in the TRAPUM SMC survey. Radio Frequency
Interference (RFI) cleaning was performed with a combination of iqrm (Morello
et al., 2021), presto’s rfifind, and pulsarX’s
filtool555https://github.com/ypmen/PulsarX by Yunpeng Men. As this was part of
a multi-beam search we also used a multi-beam RFI filter
multiTRAPUM666https://github.com/mcbernadich/multiTRAPUM by Miquel Colom i
Bernadich. The latter is a wrapper of rfifind which removes signals detected
in several beams with sufficient spatial separation. The de-dispersion plan
was computed with presto’s DDplan.py script. We used the dedisp library
(Levin, 2012; Barsdell et al., 2012) for dedispersion over DMs from 50 to 350
pc cm-3 as part of the peasoup777https://github.com/ewanbarr/peasoup by Ewan
Barr suite, a GPU-based time-domain linear acceleration pulsar searching
software. The DM range was chosen based on the median DM of the published
pulsars in the SMC, around 115 pc cm-3. The PWN and SNR material could add a
contribution to the DM. Using peasoup, the 2-hour long data were searched with
no acceleration, while 20-minute segments were searched with accelerations up
to $|50|$ m s-2, to allow for binary systems888We already know from Maitra et
al. (2021) and Ho et al. (2022) that the system is not significantly
accelerated, but acceleration searching is part of standard TRAPUM SMC Survey
processing, and OBS1 was processed before the discovery of PSR J0058$-$7218
was published in Maitra et al. (2021). (assuming constant acceleration). We
chose an acceleration tolerance parameter of 10 per cent (Levin, 2012). This
means the acceleration broadening from one acceleration step to the next
cannot exceed 10 per cent of the combined pulse smearing due to sampling time,
intra-channel frequency dispersion, and de-dispersion step size. The 2-hour
timeseries were zero-padded to the next nearest power of 2, $2^{26}$,
resulting in a better resolved Fourier spectrum. Candidates were harmonically
summed by peasoup up to the eighth harmonic (Taylor & Huguenin, 1969). The
resulting candidates were then sifted, i.e. clustered in DM, period,
acceleration and harmonics. A first round of sifting was performed directly by
peasoup, which returned on average around 10 000 candidates in the beam for
one observation. It was followed by multi-beam spatial
sifting999https://github.com/prajwalvp/candidate_filter by Lars Künkel, which
uses the expected spatial relationship of real sources to identify RFI, after
which about 3000 candidates remained. We decided to only keep candidates with
periods longer than 8 time samples (1.216 ms) for OBS2 and OBS3, which had a
sampling time of 153 $\upmu$s (cf. Table 1). For OBS1, that had a 76 $\upmu$s
sampling time, the shortest period folded was the peasoup default minimum
period searched of 0.91 ms. The longest period searched by peasoup is 10
seconds. We folded about 1000 peasoup candidates in these period ranges with a
spectral S/N above 9 using pulsarX’s psrfold_fil. psrfold_fil cleans the full
resolution data before folding and applies clfd on the folded
data101010https://github.com/v-morello/clfd by Vincent Morello. The folds were
searched for the highest S/N profile over a so-called ‘natural’ range around
the candidate period, period derivative, DM, and acceleration. We then
partially classified the folded candidates with pics (Zhu et al., 2014, a
Pulsar Image-based Classification System based on Machine Learning). We used a
minimum score of 10 per cent pulsar-like for both the original and TRAPUM
training sets (Voraganti Padmanabh, 2021), as well as a minimum folded S/N of
7. This returned a handful of candidates in the beam for each observation, all
of which were consistent with RFI or noise. The original peasoup candidates
files, where the spectral S/N was limited to above 8, were inspected in case
the pulsar candidate had a lower spectral S/N than our folding cut-off of 9,
or was lost in sifting, but no periodic signals were found at PSR
J0058$-$7218’s period. More information about the TRAPUM search pipeline can
be found in Chapter 3 of Voraganti Padmanabh (2021).

The discovery of PSR J0058$-$7218 was published in Maitra et al. (2021) after
the full resolution data for OBS1 were deleted111111As the raw data are too
voluminous to keep, we stored a RFI-cleaned downsampled (512 channels each de-
dispersed at a DM of 115 pc cm-3 and 1.225 ms sampling time) version of OBS1..
We used the ephemeris provided121212Even if the ephemeris did not extend to
our observations, the pulsar search could detect the source within our survey
pipeline limits. to fold a downsampled OBS1 and the full resolution OBS2 and
OBS3 with dspsr (which calls on tempo2 (Hobbs et al., 2006) to predict the
pulsar period). The folded data were cleaned with presto’s rfifind frequency
channel mask from the full resolution data, clfd, and psrchive. We then
searched for the highest S/N profile in the folded data with psrchive’s pdmp
tool up to a DM of 500 pc cm-3, with a period range of $\pm$1 $\upmu$s, which
is three orders of magnitude greater than the period error determined by
Maitra et al. (2021). This should also cover any period derivative
inaccuracies. We also ran folding searches up to a DM of 1000 pc cm-3 with
pulsarX’s psrfold_fil on the downsampled data from OBS1 and the full
resolution OBS2 and OBS3 data. We applied a rfifind frequency channel mask
from the full resolution data. psrfold_fil cleans the full resolution data
before folding and applies clfd on the folded data. The folds were searched
for the highest S/N profile over a so-called ‘natural’ range around the
ephemeris-predicted topocentric spin frequency
$\left(\pm\frac{1}{\text{T}_{\text{obs}}}\right)$ and spin-down rate
$\left(\pm\frac{2}{\text{T}_{\text{obs}}^{2}}\right)$, where
$\text{T}_{\text{obs}}$ is the observation length in seconds. This is 3 and 4
orders of magnitudes larger than the error bounds from Maitra et al. (2021)
respectively. Both folding procedures were split into several searches, each
centred on a DM, with a range of $\pm 5$ pc cm-3 for pdmp, and a DM range so
that the maximum dispersion delay is 1 pulse period over the whole observation
for psrfold_fil. The DMs were spaced by 10 pc cm-3 over the entire DM range,
and returned no significant pulsations at the appropriate parameters.

A new ephemeris for PSR J0058$-$7218 was published in Ho et al. (2022) from
NICER X-ray observations (Gendreau et al., 2016). This ephemeris has smaller
error ranges on its parameters as it covers an 8-month X-ray timing period,
while the ephemeris from Maitra et al. (2021) used data from 2020 XMM-Newton
EPIC camera observations that only spanned 1.4 days. This consolidated the
proposed age and $\dot{E}$ of PSR J0058$-$7218\. Ho et al. (2022) noted that
this is the fourth highest $\dot{E}$ known. The new ephemeris also contains a
second period derivative. We repeated the same folding search procedure as
before with this new ephemeris, except for the rfifind frequency channel mask
which was not applied (pulsarX’s filtool was run directly on the data instead)
and the period derivative plane was not searched (only DM and period). We also
used higher resolution folded data. Again, there were no significant
pulsations at the appropriate parameters.

Young pulsars like PSR J0058$-$7218 can emit giant narrow pulses (e.g. the LMC
Crab pulsar twin, Johnston & Romani, 2003). If PSR J0058$-$7218 is too faint
to be detected by MeerKAT in 2-hour observations, single pulses that are
orders of magnitude stronger than average may still be detected. We thus
searched for single pulses with
transientX131313https://github.com/ypmen/TransientX by Yunpeng Men on the full
resolution data from OBS2 and OBS3, cleaned by rfifind and pulsarX’s filtool.
We used a 100 ms maximum search width over DMs 0 to 5000 pc cm-3. No pulses
were returned down to S/N$=$8\. Similarly, we ran a heimdall search on the
same data, cleaned by iqrm and rfifind. We chose a maximum boxcar width of 157
ms over DMs 25 to 5000 pc cm-3. We discarded any pulses with widths wider than
50 per cent of PSR J0058$-$7218’s period, as giant pulses are typically narrow
(e.g. Crawford et al., 2009). We used dspsr and psrchive to extract single
pulses, search in DM for the highest S/N profile and plot the candidates.
Inspection of all the candidates above S/N$=$8 indicated they were consistent
with RFI or noise.

##  3 Upper limits and discussion

We calculate a radio L-band flux density upper limit for PSR J0058$-$7218 with
the folds performed on the data from OBS2, in which the pointing location of
MeerKAT’s primary incoherent beam was closest to the pulsar and 44 dishes were
used (see Table 1). Owing to the separation between the coherent beam placed
on PSR J0058$-$7218 and the centre of the primary beam, the gain was decreased
to $\simeq$85 per cent of its full value (using a primary beam model based on
Asad et al. 2021). Taking this into account, the radiometer equation applied
to pulsar observations (Lorimer & Kramer, 2005) yields a flux density upper
limit of $S_{\text{1284\,MHz}}=$ 7.0 $\upmu$Jy. We assume a 5 per cent pulsar
duty cycle and a minimum folded S/N of 7 to be able to distinguish the signal
by eye. We use the MeerKAT system temperature ($\simeq$18 K), a sky
temperature of 7 K (Zheng et al., 2017), and a gain of $\simeq$1.925 K Jy-1
for the 44 core dishes (Bailes et al., 2020) at the centre of the pointing
(primary beam location). We assume that a correction factor accounting for any
data acquisition system imperfections is not needed. Using the flux density
from the ASKAP image shown in Figure 1, we take the faint remnant’s
contribution to the system temperature as negligible. Assuming a power law
radio spectral index of -1.60$\pm$0.54 (Jankowski et al., 2018), the radio
flux density upper limits at 1400 MHz are $S_{\text{1400\,MHz}}=$ 6.1$\pm$0.3
$\upmu$Jy141414Titus et al. (2020) calculated the TRAPUM search limiting flux
density to be 12 $\upmu$Jy at 1400 MHz with different assumptions, notably a
smaller bandwidth, higher S/N cut and lower sensitivity (N. Titus, private
communication).. Our 1400 MHz flux density limit is $\simeq$6.7 times deeper
than the 41 $\upmu$Jy limit from Maitra et al. (2021).

Similarly, the limiting fluence for the single pulse search on OBS2 down to
S/N$=$8 is $S_{\text{pulse,1284\,MHz}}=$ 93 mJy ms, for a 1 ms pulse width
(and a 1 ms integration time). This takes into account the primary beam
sensitivity loss and the sky temperature contribution. Again, this greatly
improves the previous upper limit from Maitra et al. (2021) of 821 mJy ms,
resulting from a transient search on Titus et al. (2019) Parkes data with a
central frequency of 1382 MHz.

If PSR J0058$-$7218’s radio beam is sweeping across our line of sight, the
pulsar could be too faint to be detected in 2 hours with the core dishes of
MeerKAT. The upper limit on the flux density of the pulsar at 1400 MHz
translates to a radio pseudo-luminosity upper limit of
$L_{\text{pseudo,1400\,MHz}}=S_{\text{1400\,MHz}}\times D^{2}=$ 22 mJy kpc2,
assuming an approximate distance to the pulsar of $D=$ 60 kpc (Karachentsev et
al., 2004), and a power law radio spectral index of -1.6. According to the
ATNF pulsar database, for pulsars with a catalogued pseudo-luminosity,
approximately 75 per cent of all pulsars and more than 50 per cent of young
pulsars with a characteristic age lower than 120 kyr have a lower pseudo-
luminosity than this upper limit for PSR J0058$-$7218 (Manchester et al.,
2005). Since we did not detect any giant single pulses either, PSR
J0058$-$7218 was either not emitting giant pulses during our observations or
its radio beam is not sweeping our line of sight.

Maitra et al. (2021) measured a pulsed, non-thermal151515The pulsed X-rays are
from the pulsar’s emission beam, not from any heating processes from the
pulsar surface or nebula. X-ray luminosity for PSR J0058$-$7218 of
$1.6(1)\times 10^{35}$ erg s-1 in the energy band 0.2-12 keV, assuming a
distance of 60 kpc (Karachentsev et al., 2004). Furthermore, they determined
the pulsar spin-down luminosity $\dot{E}=1.1\times 10^{38}$ erg s-1. Thus,
they state that the X-ray radiation efficiency of the pulsar,
$\eta_{\text{x}}=\frac{L_{\text{x}}}{\dot{E}}$ is of the order of $10^{-3}$.
This fits well with the expected relationship between $L_{\text{x}}$ and
$\dot{E}$ (Shibata et al., 2016). The ratio of PSR J0058$-$7218’s X-ray
luminosity to its radio luminosity upper limit,
$\frac{L_{\text{x}}}{L_{\text{radio}}}$, is of the order of $10^{5}$. Maitra
et al. (2021) and Ho et al. (2022) did not detect any statistically
significant pulsed gamma-ray flux from PSR J0058$-$7218\. They could not
provide a pulsed gamma-ray luminosity upper limit, so it is not possible to
constrain the gamma-ray efficiency.

Using a general formula for pulsar luminosity derived in Lorimer & Kramer
(2005) and used in Szary et al. (2014) to broadly compare the radio emission
efficiencies of pulsars, we find that the radio luminosity upper limit for PSR
J0058$-$7218 is $L_{\text{radio}}=7.4\times 10^{27}\times
L_{\text{pseudo,1400\,MHz}}=1.6\pm 0.1\times 10^{29}$ erg s-1. Thus the radio
radiation efficiency of the pulsar is lower than
$\eta_{\text{radio}}=\frac{L_{\text{radio}}}{\dot{E}}=1.5\pm 0.1\times
10^{-9}$. The ranges are due to the assumed radio spectral index,
-1.60$\pm$0.54 (Jankowski et al., 2018). According to the ATNF pulsar
database, only eight pulsars out of $\simeq$ 2000 with catalogued radio and
spin-down luminosities have a lower radio radiation efficiency than this upper
limit, although we note that it is speculative to use this general pulsar
luminosity formula to compare individual pulsars, especially with uncertain
distance estimates. They are all young161616The largest characteristic age of
the eight pulsars is 42 kyr. Milky Way pulsars with pulsed high-energy
emission (gamma-ray and/or X-ray), high $\dot{E}$ ($>10^{36}$ erg s-1) and
most have associated Pulsar Wind Nebulae and/or supernova remnants. Notably,
the Crab pulsar is among these systems. It is the only pulsar out of the 8
with known giant pulses. Those detected in X-ray pulsations all have an X-ray
efficiency $\eta_{\text{x}}$ that fits well with the expected relationship
between $L_{\text{x}}$ and $\dot{E}$ (Shibata et al., 2016). PSR J0058$-$7218
could thus be a similar system with a very low radio emission efficiency.
Szary et al. (2014) show that radio efficiency generally increases with pulsar
age, due to the constancy of their radio luminosity and decline in spin-down
luminosity, which is a important insight into the radio emission mechanism.

Indeed, when considering the $\eta_{\text{radio}}$-$\dot{E}$ relationship
presented in Szary et al. (2014) with the latest version of the ATNF pulsar
catalogue, as presented in Figure 2, PSR J0058$-$7218’s upper limit on
$\eta_{\text{radio}}$ (and lower values down to $\eta_{\text{radio}}\simeq
10^{-11}$) fits within the large relationship scatter, among young pulsars
with pulsed high-energy radiation and SNR association. This plot was created
with pulsars from the ATNF database with a catalogued distance and 1400 MHz
flux density to calculate $L_{\text{radio}}$; and with a catalogued period
derivative to calculate $\dot{E}=4\pi^{2}\times 10^{45}\times\dot{P}P^{-3}$.
The resulting radio emission efficiencies $0<\eta_{\text{radio}}<1$ were
plotted, removing anomalous values. Note that only so-called ‘normal’ spin-
powered pulsars are shown, excluding millisecond pulsars, pulsars in Globular
Clusters, Rapidly Rotating Radio Transients (RRATs), pulsars in binary
systems, and magnetars.

Figure 2:  The $\eta_{\text{radio}}$-$\dot{E}$ relationship adapted from Szary
et al. (2014). PSR J0058$-$7218 and LMC ‘Crab pulsar twin’ PSR B0540$-$6919
are highlighted. As discussed in the text, it is speculative to use a general
pulsar luminosity formula to compare individual pulsars’ radio efficiencies.

As described in Maitra et al. (2021), the fact that no thermal X-rays are
detected from the pulsar, only non-thermal, could mean that the polar cap
region (where thermal X-rays are emitted due to accelerated ions colliding
with the surface) is not visible. Hence the beam of the radio emission could
be missed (Goldreich, 1969; Cheng et al., 1998), and no pulses or giant pulses
detected. The radio beam could also be intersected at a wide angle where the
emission is faint. Indeed, young, short period pulsars can have wide radio
beaming angles (e.g. Lyne & Manchester, 1988). Since the radio, X-ray and
gamma-ray beams can all have different orientations, the gamma-ray beam could
also be missed (e.g Barnard et al., 2016; Cheng & Zhang, 1999). According to
Smith et al. (2019), PSR J0058$-$7218 is near the putative gamma-ray emission
‘death line’ (with $\dot{E}=1.1\times 10^{38}$ erg s-1 (Maitra et al., 2021)
and a distance of 60 kpc), and thus could have no gamma-ray emission
detectable at all. In the case this ‘death line’ is an artefact of pulsar
distance, the gamma-ray emission could be too faint to be detected with Fermi.

PSR J0058$-$7218 thus joins a growing population of young pulsars with no
radio detection. In the current ATNF pulsar catalogue, only half of the
$\simeq$50 young pulsars with SNR association are detected in both high-energy
and radio pulsations, a quarter are detected only in high-energy pulsations
and a quarter only in radio pulsations, with no particular distribution on the
period-period derivative plane. There are only two other known extragalactic
pulsars in supernova remnants. Both are in Pulsar Wind Nebulae of the Large
Magellanic Cloud. PSR J0537$-$6910, a fast (16 ms) pulsar, is
only171717Unpulsed gamma-rays from the PWN have been detected (Abramowski et
al., 2012). detected in X-rays (Marshall et al., 1998), just like PSR
J0058$-$7218\. PSR B0540$-$6919 is detected in X-rays, radio and gamma-rays
and is considered an analogue of the Crab pulsar (Seward et al., 1984;
Manchester et al., 1993; Marshall et al., 2016). It is a giant pulse emitter
(Johnston & Romani, 2003). It has a very low radio efficiency of
$\eta_{\text{radio}}=2.9\times 10^{-9}$, of the same order as the upper limit
on the radio efficiency of PSR J0058$-$7218\. There is only one other
extragalactic young181818All other published non-magnetar extragalactic
pulsars are over 200 kyr in characteristic age (Manchester et al., 2005). non-
magnetar pulsar known: J0534$-$6703 (Manchester et al., 2006). It is a long
period ($\simeq$1.8 s) radio pulsar with no SNR or PWN association and no
high-energy emission known. There are no confirmed Central Compact Objects
(CCO) in the Magellanic Clouds (e.g. Long et al., 2020). CCOs are soft thermal
X-ray sources near the centre of a supernova remnant, with no hard X-ray
emission, radio emission, or PWN environment (De Luca, 2017).

##  4 Conclusion

We conclude from our unprecedentedly deep radio search that the X-ray pulsar
J0058$-$7218 is either similar to a handful of pulsars in Pulsar Wind Nebulae
with very low radio efficiency or its radio beam does not cross our line of
sight. The latter hypothesis is supported by the non-detection of thermal
X-rays from the polar cap of PSR J0058$-$7218 in Maitra et al. (2021), and the
non-detection of giant pulses in this study. Only about half of young pulsars
with SNR associations have been detected in both high-energy and radio
pulsations. The upper limit set on PSR J0058$-$7218’s radio flux density in
this work is nearly 7 times deeper than previous searches. The MeerKAT full
array, or the future Square Kilometer Array, could carry out a deeper search
on this source. The MeerKAT full array could improve the search sensitivity by
a factor of $\simeq 1.5$ compared to this work with 20 additional dishes. If
PSR J0058$-$7218 was not detected in a deeper search with the full array, this
would not significantly strengthen the case for a non-alignment, as its radio
efficiency upper limit would still be higher than 7 pulsars. There are only
about 20 radio pulsar-PWN systems in the Milky Way. If it was detected, PSR
J0058$-$7218 would be the second extragalactic radio pulsar-PWN system (after
PSR B0540$-$6919 in the Large Magellanic Cloud, Manchester et al. (1993)), and
the first in the SMC.

## Acknowledgements

The MeerKAT telescope is 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. SARAO acknowledges the
ongoing advice and calibration of GPS systems by the National Metrology
Institute of South Africa (NMISA) and the time space reference systems
department of the Paris Observatory.

TRAPUM observations used the FBFUSE and APSUSE computing clusters for data
acquisition, storage and analysis. These clusters were funded and installed by
the Max-Planck-Institut für Radioastronomie and the Max-PlanckGesellschaft.

EC acknowledges funding from the United Kingdom’s Research and Innovation
Science and Technology Facilities Council (STFC) Doctoral Training
Partnership, project reference 2487536. For the purpose of open access, the
author has applied a Creative Commons Attribution (CC BY) licence to any
Author Accepted Manuscript version arising.

EB, MK, PVP and VVK acknowledge continuing support from the Max Planck
society.

RPB acknowledges support from the ERC under the European Union’s Horizon 2020
research and innovation programme (grant agreement No. 715051; Spiders).

We thank Fabian Jankowski and James Turner (Pulsar and Time-Domain
Astrophysics group, Jodrell Bank Centre for Astrophysics, University of
Manchester) for their help with the primary beam model and the sky temperature
estimation respectively.

This paper has made use of the ATNF pulsar catalogue version 1.67.

We thank the anonymous referee for their helpful and constructive comments
which improved this manuscript.

## Data Availability

The data underlying this article will be shared upon reasonable request to the
TRAPUM collaboration.

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internally than to the rest of the network. The larger communities found by
ECoHeN tend to have relatively smaller (albeit large) ratio of densities,
proving at least five times more dense internally than to the rest of the
network.

Figure C.13: Each of the communities found by ECoHeN across the 20 replicates
is particularly dense. Small communities necessitate a higher ratio of
densities to be deemed a community, sometimes twenty times more dense
internally than to the rest of the network. The larger communities found by
ECoHeN tend to have relatively smaller, albeit still large, ratio of
densities, proving to be at least five times more dense internally than to the
rest of the network.

To gauge how unlikely it would be to attain the observed ratio of densities,
we gather 1000 snowball samples for each community, compute the ratio of
densities for each sample, and record the 95% quantile. Any observed ratio of
densities larger than the respective 95% quantile is deemed sufficiently dense
to be considered a community. For computational feasibility, we isolate the
largest community found by ECoHeN at each of the twenty replicates, plotted in
Figure C.14 in relation to the observed ratio of densities. Notice, as the
community size increases, the threshold ratio of densities required decreases
as it becomes increasingly unlikely to observe large communities with a large
ratio of densities than a small community with an equally large ratio of
densities. Each of the largest ECoHeN communities is sufficiently dense
compared to the respective threshold, indicating that while these communities
were attained from an Erdős-Rényi network, they are still sufficiently dense.

To describe the snowball sampling routine, consider an ECoHeN community of
size $n_{C}$. One snowball sample is attained by first picking a node
uniformly at random and recording its neighbors. There are $n_{C}-1$ nodes
left to select. Should there be more neighbors than left to select, the
remaining nodes left to select are chosen from the recorded neighbors
uniformly at random. Otherwise, all of the neighbors are recorded, and the
number of nodes left to select is updated accordingly. The process continues
until $n_{C}$ nodes have been selected. Since the snowball sampling routine
results in dense, well-connected sets of nodes, it is a reasonable (albeit
computationally burdensome) null model when assessing community structure in
an Erdős-Rényi network.

Figure C.14: The largest communities across the twenty replicates are isolated
and plotted with respect to the observed ratio of densities. To gauge how
unlikely it would be to attain the observed ratio of densities, we gather 1000
snowball samples for each community, compute the ratio of densities for each
sample, and record the 95% quantile. Any observed value larger than the 95%
quantile is deemed sufficiently dense and arguably embodies community
structure (even for a random network). Each of the largest ECoHeN communities
maintains a ratio of density that is roughly twice as large as the estimated
respective 95% quantile.

##  Appendix D Extraction Routines

The extraction routines AddWellConnected and RemoveLooselyConnected are
provided in pseudocode in Algorithm 2. For the most up-to-date R
implementation of ECoHeN (with a C++ backend), see the following GitHub url:

https://github.com/ConGibbs10/ECoHeN.

List of palgorithms 2 Pseudocode for the ECoHeN extraction routines
AddWellConnected and RemoveLooselyConnected.