# Discovery of radio eclipses from 4FGL J1646.5$-$4406: a new candidate
redback pulsar binary

Andrew Zic,1 Ziteng Wang,2,3 Emil Lenc,1 David L. Kaplan,4 Tara Murphy,2,5 A.
Ridolfi,6,7 Rahul Sengar,4 Natasha Hurley-Walker,3 Dougal Dobie,8,5 James K.
Leung,2,1,5 Joshua Pritchard,2,1,5 and Yuanming Wang8,5
1Australia Telescope National Facility, CSIRO, Space and Astronomy, PO Box 76,
Epping, NSW 1710, Australia
2Sydney Institute for Astronomy, School of Physics, University of Sydney,
Sydney, NSW 2006, Australa
3International Centre for Radio Astronomy Research, Curtin University,
Bentley, WA 6102, Australia
4Center for Gravitation, Cosmology, and Astrophysics, Department of Physics,
University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA
5ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav), Hawthorn,
Victoria, Australia
6INAF – Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047
Selargius (CA), Italy
7Max-Planck Institut fur Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany
8Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, Victoria, Australia
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Large widefield surveys make possible the serendipitous discovery of rare sub-
classes of pulsars. One such class are “spider”-type pulsar binaries,
comprised of a pulsar in a compact orbit with a low-mass (sub)stellar
companion. In a search for circularly-polarized radio sources in ASKAP Pilot
Survey observations, we discovered highly variable and circularly polarized
emission from a radio source within the error region of the $\gamma$-ray
source 4FGL J1646.5$-$4406\. The variability is consistent with the eclipse of
a compact, steep-spectrum source behind ablated material from a companion in a
$\sim 5.3$ h binary orbit. Based on the eclipse properties and spatial
coincidence with 4FGL J1646.5$-$4406, we argue that the source is likely a
recycled pulsar in a “redback” binary system. Using properties of the eclipses
from ASKAP and Murchison Widefield Array observations, we provide broad
constraints on the properties of the eclipse medium. We identified a potential
optical/infra-red counterpart in archival data consistent with a variable low-
mass star. Using the Parkes Radio Telescope “Murriyang” and MeerKAT, we
searched extensively for radio pulsations but yielded no viable detections of
pulsed emission. We suggest that the non-detection of pulses is due to
scattering in the intra-binary material, but scattering from the ISM can also
plausibly explain the pulse non-detections if the interstellar dispersion
measure exceeds $\sim$600 pc cm-3. Orbital constraints derived from optical
observations of the counterpart would be highly valuable for future
$\gamma$-ray pulsation searches, which may confirm the source nature as a
pulsar.

###### keywords:

pulsars: general – binaries: eclipsing – radio continuum: transients

††pubyear: 2023††pagerange: Discovery of radio eclipses from 4FGL
J1646.5$-$4406: a new candidate redback pulsar binary–Discovery of radio
eclipses from 4FGL J1646.5$-$4406: a new candidate redback pulsar binary

##  1 Introduction

Millisecond pulsars (MSPs; periods $<30$ ms), are excellent tools for a range
of astrophysical applications, including stringent tests of general relativity
(Kramer et al., 2021), studying the equation-of-state for neutron degenerate
matter (Miller et al., 2019), searches for nanohertz-frequency gravitational
waves (Xu et al., 2023; Reardon et al., 2023; EPTA Collaboration et al., 2023;
Agazie et al., 2023), and studying binary evolution (Benvenuto et al., 2012;
Smedley et al., 2015; Chen et al., 2013). They are formed after accreting
matter from a companion star and spinning up to millisecond spin periods
(Alpar et al., 1982), after which they are typically found in binary orbits
with periods $P_{b}\gtrsim 0.5$ d with their donor companions (Tauris & van
den Heuvel, 2006), though several isolated millisecond pulsars also exist.

“Spiders" are a rare class of MSP binary systems in which material from a low-
mass companion in a compact orbit ($P_{b}<1$ d) is ablated by the relativistic
pulsar wind (Roberts, 2013). Spiders are comprised of two sub-classes, known
as “black widows” with degenerate companions with masses $\sim
0.01-0.05\,M_{\odot}$, and “redbacks” with main sequence companions with
masses $>0.1\,M_{\odot}$ (Roberts, 2013). The ablated companion material often
causes radio eclipses, which occur due to enhanced dispersion, scattering, or
absorption (Fruchter et al., 1988; Stappers et al., 1996; Polzin et al., 2020;
Wang et al., 2021b; Bai et al., 2022).

Spiders likely represent very early stages in the life-cycle of recycled
pulsars (Benvenuto et al., 2014), after the neutron star has completed
accretion from the donor star. This is supported by the observation of
multiple “transitional” MSPs, which switch between a radio-pulsar mode and a
Low-mass X-ray binary (LMXB) mode, where mass transfer occurs (e.g. Archibald
et al., 2009; Roy et al., 2015). There is both theoretical (Benvenuto et al.,
2014) and observational (Strader et al., 2019; Clark et al., 2023a) support
for the mass of spider pulsars being systematically higher than normal pulsar
masses, due to the recent completion of accretion from the donor star, making
these systems particularly useful for studies of the neutron star equation of
state (Özel & Freire, 2016). It also seems apparent that there is an
evolutionary link between LMXBs, redbacks, black widows, and field MSPs, but
multiple formation mechanisms for redback and black widow systems have been
proposed (Chen et al., 2013; Smedley et al., 2015; De Vito et al., 2020;
Ginzburg & Quataert, 2021). Discovery of new and unusual spiders may provide
useful insights into the demographics and formation pathways of these systems
(Pan et al., 2023).

The Large-Area Telescope on the Fermi Space Telescope (Fermi-LAT; Atwood et
al., 2009) has enabled a wealth of pulsar discoveries via follow-up of
unassociated $\gamma$-ray sources. This has included the majority of spider-
type systems (e.g., Barr et al., 2013; Bhattacharyya et al., 2013; Camilo et
al., 2015; Cromartie et al., 2016; Clark et al., 2023b; Au et al., 2023).
There is also growing population of convincing spider candidates (lacking
detections of pulses at radio or $\gamma$-ray wavelengths) identified by
follow-up of Fermi sources at X-ray and optical wavelengths (e.g. Strader et
al., 2014, 2015; Romani, 2015; Braglia et al., 2020; Corbet et al., 2022;
Burdge et al., 2022). Searches for pulsar candidates in radio continuum
imaging datasets is also an increasingly successful approach. These include
identification of radio sources exhibiting a steep radio spectrum (Backer et
al., 1982; Frail et al., 2018; Ray et al., 2022), scintillation (Dai et al.,
2016, 2017), variability (Wang et al., 2022), high degrees of polarization
(Kaplan et al., 2019; Sobey et al., 2022), globular cluster association
(Heywood, 2023), and association with Fermi sources (Frail et al., 2018).

In this paper, we report our analysis and multi-wavelength follow up following
new detections of the putative radio counterpart to the $\gamma$-ray source
4FGL J1646.5$-$4406 (hereafter 4FGL J1646). The source was previously
investigated by Frail et al. (2018) owing to its positional correspondence
with the unassociated Fermi source 4FGL J1646, its apparent angular
compactness, and its steep radio spectrum – properties consistent with a
pulsar origin. However, Frail et al. (2018) determined it was unlikely to be a
pulsar due to a high ratio of its integrated to peak radio flux density, which
they proposed to be due to the source being partially resolved. In this work,
we revisit the nature of this source after we detected highly polarized
emission and periodic radio variability, which we ascribe to the eclipse of a
pulsar behind material from a companion. We summarise our unsuccessful search
for pulsed emission from this source, but argue that the source is nonetheless
most likely a radio pulsar in a redback binary system. We discuss possible
reasons for the non-detection of pulses and place initial constraints on the
eclipse mechanism and properties of the eclipsing medium.

##  2 Observations and analysis

Telescope | Start | $\Delta t$ | $\nu$ | $\Delta\nu$ | Mode | $\phi$
---|---|---|---|---|---|---
| (UT) | (h) | (MHz) | (MHz) |  |
ASKAP | 2021 Jun 26 09:22:55 | 9.9 | 943 | 288 | Imaging | 0 – 1
ASKAP | 2021-Sep 19 19:16:16 | 1.0 | 943 | 288 | Imaging | 0.59 – 0.78
ATCA | 2021 Sep 21 01:12:55 | 3.6 | 2100 | 2048 | Imaging | 0.28 – 0.09
Murriyang | 2021 Sep 21 03:41:40 | 1.0 | 2368 | 3328 | Pulsar search | 0.75 – 0.94
ASKAP | 2021 Sep 20 12:54:53 | 9.8 | 943 | 288 | Imaging | 0 – 1
ASKAP | 2022 Feb 25 22:24:40 | 5.5 | 943 | 288 | Imaging | 0 – 1
MeerKAT | 2022 Mar 07 03:39:39 | 0.67 | 1284 | 856 | Imaging$+$Pulsar search | 0.69 – 0.82
MeerKAT | 2022 Mar 09 03:01:15 | 0.67 | 1284 | 856 | Imaging+Pulsar search | 0.68 – 0.81
MeerKAT | 2022 Mar 19 00:00:29 | 0.67 | 1284 | 856 | Imaging$+$Pulsar search | 0.68 – 0.80
MeerKAT | 2022 Mar 20 23:24:56 | 0.67 | 1284 | 856 | Pulsar search | 0.68 – 0.80
MWA | 2022 June 02 – September 22 | $21\times 1.5$ | 200 | 30 | Imaging | 0 – 1
Table 1: Summary of radio observations. Notes: $\Delta t$ is the integration
time on-source, and $\Delta\nu$ is the total bandwidth around central
frequency $\nu$. $\phi$ is the inferred orbital phase spanned by the
observations. For the MWA, we summarise the twenty-one observations taken from
the Galactic Plane Monitoring program used for this source.

###  2.1 Australian SKA Pathfinder (ASKAP)

Figure 1: ASKAP field image in Stokes $I$ (left) and $V$ (right). Inset on
both axes is a $6\arcmin\times 6\arcmin$ cutout around ASKAP J1646, where the
Fermi 95 per cent positional error ellipse around 4FGL J1646 is shown in
black. Note that direction-dependent leakage calibration has not been applied
to the Stokes $V$ image, so leakage on the order of $\lesssim 1$ per cent is
visible toward bright, extended regions of emission. Figure 2: ASKAP radio
lightcurve for ASKAP J1646, folded to the putative orbital period of
$5.267104$ h. Points are coloured by their observing epoch. For clarity we
repeat the data from phases 1–2 and provide a scale-bar to indicate the time-
span of the orbit. Long-term variability is evident through the differing out-
of-eclipse flux densities across different epochs, ranging from $\sim 4$ – 9
mJy. Figure 3: VVV $JHK_{s}$ (left) and DECaPS $grz$ (right) RGB-coloured
cutouts around the position of ASKAP J1646, with radio contours from ASKAP
(blue, dashed) and ATCA (pink, dot-dashed) and MeerKAT (gold, solid).

We detected circularly-polarized emission from the radio source ASKAP
J164622$-$440540 (hereafter ASKAP J1646) in an observation taken for the ASKAP
EMU Pilot Survey (Norris et al., 2021) (Schedule Block ID 28280, observed 2021
June 26). The observations were taken at a central frequency of 943.41 MHz,
with 36 beams tiled in a close-pack configuration. The central field
coordinates were RA=$16^{\text{h}}50^{\text{m}}46^{\text{s}}$
Dec=$-41^{\circ}52^{\prime}44\arcsec$. The data were calibrated using
ASKAPsoft version 1.2.1 and CASA version 6.2. Further details on processing
and imaging can be found in Norris et al. (2021). We show the observation
field in Stokes $I$ and $V$ in Fig. 1.

We detected ASKAP J1646 as a point source in both Stokes $I$ and $V$, with
flux densities of $5.19\pm 0.06$ mJy and $+0.38\pm 0.03$ mJy
respectively.111In this paper, we use the IAU definition of Stokes $V$, where
positive (negative) Stokes $V$ corresponds to right (left) handed circular
polarization. The resulting polarization fraction $f_{c}=7.3\pm 0.6$ per cent.
This is much higher than the typical circular polarization leakage fraction of
$\sim-0.4$ per cent in the local region around ASKAP J1646, determined by
inspection of nearby bright Stokes $I$ sources.

Following the procedure in Zic et al. (2019), we constructed lightcurves and
dynamic spectra for the source by subtracting the sky model constructed during
the deconvolution process from the calibrated visibilities. We then phase-
rotated the visibilities to the target position and vector-averaged all
baselines, yielding complex visibility amplitudes for each correlator
integration cycle, frequency channel, and instrumental polarization. We
transformed the data from the native instrumental polarization basis ($XX$,
$YY$, $XY$, $YX$) into the Stokes basis ($I$, $Q$, $U$, $V$), and produced
lightcurves by averaging the data across frequency.

We found strong, eclipse-like variability in the initial EMU pilot
observation, with bright ($S_{943}\sim 7.5$ mJy), stable emission present for
approximately 3 hours, followed by a period of no detectable emission lasting
approximately 2 hours. This behaviour was then repeated. In order to confirm
the periodic nature of the variability, we conducted further observations with
ASKAP on 2021 September 20, 2022 February 25, and 2022 February 28, with
identical observing configuration and processing methods to the original EMU
pilot observation. After transforming the lightcurve timestamps to the frame
of the solar system barycenter, we measured the period by fitting a double
Fermi-Dirac function with a freely-inferred period and reference epoch (see
§3.5). This fit yielded a period of $5.267104\pm{3\times 10^{-6}}$ h, with a
reference epoch of MJD $59391.3578\pm 0.0005$. We show the ASKAP time-series
from all observations folded at the measured period in Fig. 2.

The apparent non-eclipsed continuum flux density is comparable to measurements
reported by Frail et al. (2018). In addition, the strong variability
introduces point-spread function (PSF) artefacts in the continuum image around
ASKAP J1646. These effects may be responsible for the inflated integrated-to-
peak flux ratio reported for this radio source in Frail et al. (2018).

###  2.2 Parkes/Murriyang pulsar search

Motivated by the detection of periodic, eclipse-like variability and circular
polarization from ASKAP J1646, along with the spatial coincidence with the
$\gamma$-ray source 4FGL J1646 (Frail et al., 2018), we carried out pulsar
search-mode observations with Parkes 64m Radio Telescope, Murriyang, on 2021
September 21 using Director’s Discretionary Time (project code: PX080). The
observations were carried out with the Ultra-Wideband Low (UWL) receiver
(Hobbs et al., 2020), which provides continuous frequency coverage spanning
704 to 4032 MHz. We coordinated simultaneous observations with the Australia
Telescope Compact Array (ATCA; see §2.3) to ensure that the emission was
present during the pulsar search observations.

We performed a pulsar search using presto, to a maximum dispersion measure of
1800 pc cm-3 (corresponding to a distance $>25$ kpc based on the YMW16
electron-density model (Yao et al., 2017)) and acceleration parameter
$z_{\text{max}}=200$ (corresponding an orbital period of $\sim$5.4 hr assuming
a 3.5 ms spin period and 20 min integration). Since the radio source is quite
bright at low frequencies (5.19 mJy at 943 MHz), we split the UWL band into
six segments ($704$ – $1344$ MHz; $1344$ – $1856$ MHz; $1856$ – $2368$ MHz;
$2368$ – $2880$ MHz; $2880$ – $3520$ MHz; $3520$ – $4032$ MHz) and searched
each segment independently. Searches over the low-frequency segments allowed
us to leverage the steep radio spectrum, while searches over the high-
frequency segments mitigated potential pulse smearing due to high degrees of
scattering (scattering timescale $\tau_{s}\sim\nu^{-4}$).

After manual inspection of all candidates above a S/N ratio of 4, we did not
find any convincing pulsations. We describe further (unsuccessful) pulsar
searches with MeerKAT in §2.5 and discuss implications of non-detections in
Section 3.

###  2.3 Australia Telescope Compact Array

We took observations with the Australia Telescope Compact Array under
Director’s Discretionary Time (project code: CX489) with the 16 cm receiver.
We used the Compact Array Broadband Backend (CABB), which delivers $\sim$2 GHz
bandwidth centered at 2.1 GHz. The observations were recorded with 1 MHz
channels and a correlator integration time of 10 s. We observed PKS
B1934$-$638 for approximately 10 mins for flux density, bandpass, and
polarization leakage calibration. We observed ASKAP J1646 in 20 min scans,
book-ended between 2 min scans on a nearby gain calibrator, J1646$-$50\. Due
to telescope maintenance at the time of observations, antenna CA02 was not
available for observing. We flagged and calibrated the data following standard
procedures with miriad. Owing to the steep spectrum of the source, we split
the 2 GHz band into two 1 GHz segments centered at 1.588 GHz and 2.612 GHz. We
used the miriad task mfclean to image each frequency segment. We used a briggs
weighting with a robustness of 0.5, and deconvolved to a depth of $150$
$\mu$Jy, corresponding to approximately $3\times$ the image rms.

We detect the source with a flux density of $1.35\pm 0.06$ mJy at 1588 MHz and
$0.47\pm 0.06$ mJy at 2612 MHz, yielding a spectral index $\alpha=-2.1\pm
0.25$ ($S_{\nu}\propto\nu^{\alpha}$). We constructed lightcurves by
subtracting the sky model generated through deconvolution and self-calibration
from the calibrated visibilities using uvmodel, and fitted the visibilities
with a point source model at the location of ASKAP J1646 in 5- and 20-minute
time intervals. We detected variability in the 20-minute lightcurves at 1588
MHz consistent with eclipse egress near the beginning of the observation (the
orbital phase spanned 0.28 – 0.09), with the source not detected during the
first 40 minutes. However, the signal-to-noise and time resolution of the
lightcurves was not high enough for further modelling, and the source was too
faint to detect significant variability at 2612 MHz on relevant timescales.

###  2.4 MeerKAT Imaging

We observed ASKAP J1646 (see Table 1) for 40 min on March 7th, 9th, 19th, and
20th 2022 using the MeerKAT radio telescope at L-band, with a central
frequency of 1.28 GHz (856 MHz bandwidth, 4096 channels) and an integration
time of 8s (project code DDT-20220227-TM-01). Continuum imaging data were only
recorded for observations on March 7, 9, and 19, whereas high time-resolution
pulsar search data were recorded in all four observations (see §2.5). Each
observation was scheduled to occur around superior conjunction of the pulsar
using an initial eclipse ephemeris derived from ASKAP observations. The
resulting continuum images had an rms noise of 20 $\mu$Jy beam-1. Both
interferometric imaging data and pulsar search-mode data were recorded
simultaneously in all MeerKAT observations. We used PKS B1934$-$638 for
bandpass, flux density scale calibration, and PKS J1744$-$5144 for phase
calibration. The archived raw visibilities were converted to Measurement Set
format with the KAT Data Access Library (katdal222https://github.com/ska-
sa/katdal) for further continuum imaging. We reduced the data using
Oxkat333https://github.com/IanHeywood/oxkat (v0.3; Heywood, 2020), where the
Common Astronomy Software Applications (CASA; McMullin et al., 2007) package
and Tricolour444https://github.com/ska-sa/tricolour (Hugo et al., 2022) were
used for measurement sets splitting, cross calibration, flagging,
CubiCal555https://github.com/ratt-ru/CubiCal (Kenyon et al., 2018) was used
for self-calibration, and Wsclean (Offringa et al., 2014) was used for
continuum imaging. All processes were executed with Oxkat L-band default
settings.

We measured peak flux densities of $3.42\pm 0.02$ mJy beam-1 (Mar 07), and
$3.49\pm 0.03$ mJy beam-1 (Mar 19) for ASKAP J1646. The best-fit position of
the source based on the MeerKAT observations is: (J2000) $16^{\rm h}46^{\rm
m}22\aas@@fstack{s}75\pm 0\aas@@fstack{s}14~{}-44\degr 05\arcmin
41\aas@@fstack{\prime\prime}00\pm 0\aas@@fstack{\prime\prime}14$.

We measured spectral, temporal, and polarization properties for ASKAP J1646
with further reduction on two observations from March 7 and 19. The source had
a steep radio spectrum within the bandpass in our MeerKAT observations, with
spectral indices $\alpha=-3.1\pm 0.1$ in both observations. The discrepancy
between this measurement and the spectral index reported in $\mathsection$2.3
and Frail et al. (2018) may be explained by variability over timescales of
months – years, but we caution that sub-band calibration has not been properly
evaluated for our MeerKAT observations, so our measurements may be subject to
$\sim 10$ per cent systematic errors.

To check short-timescale variability, we imaged the target with an integration
time of 1 minute which resulted in 40 images for each observation. The
lightcurves showed a relatively low modulation index (flux density standard
deviation divided by the mean) of $\sim 20$ per cent and had a reduced
$\chi^{2}$ of 1.4 for 79 degrees-of-freedom (80 observations minus one
parameter for the mean). There was no evidence for minute-scale variability.
The fractional circular polarisation was $\sim 9$ per cent, which was broadly
consistent with ASKAP measurements. To search for linearly polarized emission
from the source, we split the whole bandwidth in 16 parts (53.5 MHz bandwidth
for each part). No linearly polarized emission was detected above the
detection threshold (with a $5\sigma$ upper limit of 0.1 mJy beam-1) with a
maximum accessible rotation measure $|{\rm RM}|\lesssim 4000$ rad m-2.

We also produced dynamic spectra for MeerKAT observations (with the same
procedure as that for ASKAP observations, see $\mathsection$2.1). There was no
evidence of variability beyond the eclipsing behaviour.

###  2.5 MeerKAT pulsar search

We carried out a periodicity search of ASKAP J1646 using high time-resolution
pulsar search observations with MeerKAT, recorded with the PTUSE backend
simultaneously with the imaging observations described above.

To account for possible variability in the pulse properties (e.g. in the
scattering timescale), we conducted a periodicity search on 20-minute time-
spans taken from observations on the 7th, 9th, 19th, and 20th of March 2022,
using the full array at L-band. We divided the data in to two sub-bands
(856-1284 MHz; 1284-1712 MHz) and searched each sub-band separately using
peasoup666https://github.com/ewanbarr/peasoup which is a GPU implementation of
a dedispersion and time domain resampling acceleration search algorithm. We
used a dispersion measure (DM) range of up to $1500\rm\,pc\,cm^{-3}$ (chosen
to span all plausible Galactic DMs based on the YMW16 model Yao et al., 2017)
and spanned an acceleration search range of $|50|\,\rm m\,s^{-2}$, which is
particularly sensitive for detecting circular binary systems with a maximum
companion of mass 0.5 $M_{\odot}$. The candidates obtained after the search
were folded following the methodology outlined in Sengar et al. (2023) before
undergoing manual scrutiny. No convincing candidates were found above a
signal-to-noise ratio (S/N) of 8. We also repeated the same methodology for
the full frequency band, ranging from 856 MHz to 1217 MHz. However, this
analysis also yielded no convincing candidates.

The four observations were also independently searched, within the same DM
range, with pulsar_miner (Ridolfi et al., 2021), an automated pulsar searching
pipeline based on presto777https://github.com/scottransom/presto (Ransom,
2001). With the latter, we performed acceleration searches in the Fourier
domain using the accelsearch routine, with a maximum allowed Doppler-induced
Fourier bin drift $z_{\rm max}=\pm 200$. Besides being searched in its full 20
minutes, each observation was also split into two segments of 10 minutes, and
searched individually, but no splitting of the observing band was made.
Similarly to peasoup, pulsar_miner returned no convincing pulsar-like
candidates.

###  2.6 Murchison Widefield Array

We obtained observations from the Galactic Plane Monitoring program (GPM;
project code G0080) undertaken at 185–215 MHz with the Murchison Widefield
Array (in “Phase ii extended-configuration” Tingay et al., 2013; Wayth et al.,
2018) in June to September 2022. The survey covered $|b|<15^{\circ}$ and
$284^{\circ}<l<73^{\circ}$ using 10$\times$30-min pointings repeated at a
cadence of approximately $3$ – $4$ d. The survey will be described in full by
Hurley-Walker et al., in prep.. One output of the survey are flux-density and
position-calibrated multi-frequency-synthesis 5-minute snapshot images centred
at 200 MHz. ASKAP J1646 lies in the most sensitive part of the main lobe for
30 min per night, and in adjacent pointings for a further 30 min either side,
at decreased sensitivity. We used the aegean source-finder (Hancock et al.,
2012, 2018) to measure the flux density at the location of ASKAP J1646 in
these images, using the priorised-fit mode, in which the position is fixed and
the flux density is fitted (this obtains unbiased estimates when the source is
off). The time of measurement was set to the middle of the 5-minute
integration888While finer timescale ($\sim 4$ s) data is available, noise
levels of $\sim 60--300$ mJy beam-1 (depending on the pointing) render the
signal-to-noise too low for detailed measurements of the ingress and egress..

In Fig. 4, we show the folded, normalized MWA flux density time-series at the
period of $5.267104$ h derived from ASKAP observations, which shows similar
eclipse-like behaviour as described in $\mathsection$2.1 (see Fig. 2). We
discuss these eclipses further in §3.6.

We also retrieved archival measurements from the MWA Transients Survey (MWATS
Bell et al., 2019), which was carried out using an earlier, more compact
configuration of the MWA. We observed similar eclipse-like variability to that
described above, albeit with lower S/N owing to the lower angular resolution.
Due to the lower quality of data, we do not consider these observations any
further in this paper.

Figure 4: Normalized flux density light-curves over orbital phase from ASKAP
and MWA observations. The top panel shows the inferred spectral index. On the
right-hand axes we show the inferred 200 MHz optical depth $\tau_{200}$ and
200 MHz flux density ($S_{200}$) respectively. The apparent discrepancy in the
eclipse depth between ASKAP and MWA is the result of forced fit for flux
density measurements in ASKAP observations, resulting in small but positive
flux densities during eclipse when the source is not detected.

###  2.7 Archival infra-red, optical, and X-ray observations

We searched for archival optical and infra-red observations coincident at the
source location. The deepest available observations were from the Vista
Variables in the Via Lactea (VVV; Minniti et al., 2010) in infrared and the
Dark Energy Camera Plane Survey (DECaPS; Saydjari et al., 2023) in optical
wavelengths.

Inspection of archival infrared images from VVV and DECaPS shows a $H\sim 21$
infrared source spatially coincident with ASKAP J1646, located at $16^{\rm
h}46^{\rm m}22^{\rm s}.74$, $-44\degr 05\arcmin
41\aas@@fstack{\prime\prime}1$. The separation between the infrared source
position and radio source position is $0\aas@@fstack{\prime\prime}12$ – within
the astrometric uncertainty of the radio position. The source is also detected
in $J$-band ($1.2\,\mu$m), but diffraction spikes from a nearby bright ($J\sim
10$) star make accurate flux measurements challenging. The putative
counterpart is also detected in DECaPS in the $g$, $r$, and $z$ bands. We
provide the detection AB magnitudes in Table 2. For DECaPS, we computed the
false-alarm rates based on the density of sources with $r$-band magnitudes
brighter than the putative counterpart within 0.1 deg, and find rates of
$<10^{-3}$ for each epoch. This suggests that the source identified here is
indeed the counterpart to ASKAP J1646. The non-detection in VVV Z-band but
detection in DECaPS $z$ band is puzzling, but may be due to intrinsic
variability from the companion as seen in other spider-type systems (e.g.,
Draghis et al., 2019). We discuss the nature of the optical/infra-red source
further in §3.2.

We retrieved 4.01 ks of archival X-ray observations from the Swift X-ray
Telescope (XRT) aboard the Neils Gehrels Swift Observatory (Burrows et al.,
2005). We merged the individual observations with the online analysis
tools999https://www.swift.ac.uk/user_objects/. There were 2 counts within
15″of ASKAP J1646, but this is consistent with the background. Using a Monte-
Carlo method by summing counts in independent randomly-placed PSF-sized
regions across the image (excluding positions of catalogued X-ray sources), we
set a 95 per cent upper limit of $7.5\times 10^{-4}$ s-1 in the 0.3–10 keV
band. We estimated the upper limit of H I column density for the position of
ASKAP J1646 based on the HI4PI survey (HI4PI Collaboration et al., 2016) using
the HEASARC web-based nH tool101010https://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3nh/w3nh.pl to be $1.42\times 10^{22}$ cm-2. Assuming a power-law
photon index of $\Gamma=2.0$ (e.g. Lee et al., 2018), we obtain an upper limit
on the unabsorbed flux (0.3–10 keV) of $7.6\times 10^{-14}$ erg cm-2 s using
the HEASARC web-based PIMMS tool111111https://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3pimms/w3pimms.pl.

Filter | $\lambda_{\rm eff}$ |  ${\rm AB}_{\rm mag}$ ${}^{\text{{a}}}$
---|---|---
| ($\mu$m) | (mag)
DECaPS $g$ | $0.480$ | $23.56\pm 0.18$
DECaPS $r$ | 0.638 | $22.09\pm 0.07$
DECaPS $i$ | 0.777 | $>22.24$
DECaPS $z$ | 0.911 | $21.8\pm 0.2$
DECaPS $Y$ | 0.985 | $>21.1$
VVV Z | 0.878 | $>23.20$
VVV Y | 1.021 | $21.13\pm 0.26$
VVV J | 1.254 |  $19.20\pm 0.09$ ${}^{\text{{b}}}$
VVV H | 1.646 | $20.94\pm 0.28$
VVV ${\rm K}_{\rm s}$ | 2.149 | $20.68\pm 0.32$
Table 2: AB magnitudes of the possible counterpart to ASKAP J1646. Notes – a:
we report $5\sigma$ magnitude lower limits for non-detections; b: this
measurement is affected by diffraction spikes from a nearby bright star.

##  3 Discussion

###  3.1 The nature of the source

We have discovered periodic ($P_{b}=~{}$$5.267104\pm{3\times 10^{-6}}$ h, see
§3.5), eclipse-like radio variability from ASKAP J1646 spatially coincident
with the $\gamma$-ray source 4FGL J1646. The $\gamma$-ray source is offset by
$95\aas@@fstack{\prime\prime}2$ at a position angle of $290^{\circ}$ from the
radio source, well within the Fermi positional error ellipse (see Fig. 1). The
radio source is point-like, exhibits a steep spectral index
($\alpha\sim-2.7$), and has significant circular polarisation ($f_{c}\sim 7$
per cent). Furthermore, we have identified a potential faint ($g\sim 23.5$,
$H\sim 21$) and variable counterpart using archival optical and infra-red
observations.

The only known source class that satisfies this set of characteristics are
spider MSP binary systems. In particular, in §3.6, we infer an eclipse
duration of $0.3994\pm{0.0014}$ orbits at $943$ MHz. The system is therefore
most likely a “redback”, which typically exhibit longer eclipses ($\sim 50$
per cent of the orbit; Deneva et al., 2021; Cromartie et al., 2016) as opposed
to black widows that typically eclipse for $\sim 10$ per cent of the orbit
(e.g. Polzin et al., 2020). This is consistent with the higher mass, main-
sequence (non-degenerate) companions in redback systems, which are capable of
producing larger eclipse regions as the pulsar ablates the companion
atmosphere. Based on these insights, we claim that the radio source ASKAP
J1646 is associated with the $\gamma$-ray source 4FGL J1646, and refer to it
as 4FGL J1646 from hereon. Future detection of pulsations in radio and
$\gamma$-rays would confirm the association.

Multiple spider systems have been previously detected at X-ray wavelengths
with redbacks in particular exhibiting relatively high X-ray luminosities
around $10^{31}$ – $10^{32}$ erg s (Zhao & Heinke, 2022; Lee et al., 2018).
Our unabsorbed X-ray flux upper limit of $<7.6\times 10^{-14}$ erg cm-2 s
implies a luminosity upper limit of $<9\times 10^{30}$ erg s-1
$(d/1\,\text{kpc})^{2}$. The X-ray non-detection could therefore be explained
if the distance is greater than 1 kpc, although this lower limit estimate is
subject to uncertainties around the true hydrogen column density and scatter
in the redback X-ray luminosity distribution.

We compiled integral $\gamma$-ray fluxes above 100 MeV ($E_{100}$), radio flux
densities ($S_{\nu}$), along with DMs (where available) for known spider-type
binaries using the ATNF Pulsar Catalogue (Manchester et al., 2005) and the
Third Fermi-LAT Catalogue of $\gamma$-ray Pulsars (Smith et al., 2023,
hereafter Fermi 3PC).

In Fig. 5 (left panel), we show the ratio of $E_{100}/\nu S_{\nu}$ versus DM.
This quantity, representing the relative flux densities of $\gamma$-ray
emission to radio emission, is independent of distance, and therefore by proxy
is independent of DM. We computed $E_{100}/\nu S_{\nu}$ for 4FGL J1646, and
adopted a lower limit on the DM of 74 pc cm-3 (as estimated in
$\mathsection$3.3) to place 4FGL J1646 in this parameter space. As can be
seen, the properties of 4FGL J1646 are consistent with the population of
radio- and $\gamma$-ray detected spider binaries.

In Fig. 5 (right panel), we show $S_{\nu}$ as a function of $E_{100}$, for
pulsars in Fermi 3PC and for 4FGL J1646. Once again, the parameters of 4FGL
J1646 are consistent with the radio-loud population of $\gamma$-ray pulsars.

Figure 5: Radio and $\gamma$-ray emission properties from the Fermi 3PC and
for 4FGL J1646. Left: Ratio of $E_{100}$ to $\nu S_{\nu}$ as a function of
pulsar DM. Right: $S_{\nu}$ versus $E_{100}$. 4FGL J1646 is marked with a red
star in both panels. The DM lower limit of $\sim 74$ pc cm-3 for 4FGL J1646 is
derived from scattering properties derived from the NE2001 Galactic electron
density model (Cordes & Lazio, 2002), based on the estimated DM at which
diffractive interstellar scintillation becomes undetectable in our
observations. The location of 4FGL J1646 in this parameter space is consistent
with the Fermi $\gamma$-ray pulsar population.

In the following subsections, we discuss further constraints on the nature of
the system with the available observations.

###  3.2 Nature of the optical/infra-red companion

We show the available optical/infrared photometry for the counterpart to 4FGL
J1646 in Fig. 6. Note that while VVV and DECaPS both have multiple epochs (and
so should allow for variability searches), the crowded field and marginal
nature of some of the detections meant that we were limited to a single
average detection for each. As noted above, the data from VVV and DECaPS are
not consistent with each other: the source is detected in DECaPS $z$ band but
not VVV $Z$ band, with contradictory upper limits. However, many spider
systems have significant optical variability from a combination of ellipsoidal
modulation and irradiation (e.g., Strader et al., 2019; Draghis et al., 2019;
Mata Sánchez et al., 2023). While we do not have sufficient data to do a
complete solution of this lightcurve, we can at least see if the available
data are plausibly fit by a variable companion to an energetic pulsar.

We assume that the companion has a radius of 50 per cent of the Roche lobe
radius (on the small end but consistent with those from Mata Sánchez et al.
2023) at a distance of 3 kpc. We take effective temperatures of 4000 K and
10,000 K (again, reasonably consistent with those of the population, although
some non-irradiated faces can be significantly cooler). After accounting for
an extinction $A_{V}=3.4\,$mag, we find that the predicted range in flux
density is consistent with our observed photometry. This is not a unique
solution, but just a plausibility argument: the Roche lobe filling factor and
distance are entirely degenerate, and the effective temperatures can also be
varied by quite a bit. Nonetheless we see that the optical/IR emission from
the counterpart to 4FGL J1646 does not require an emission region larger than
the Roche lobe or an effective temperature much hotter or cooler than other
similar sources. Future time-resolved photometry can help establish a more
unique solution.

Figure 6: Spectral energy distribution of the optical/IR counterpart to 4FGL
J1646. We show the flux densities from VVV and DECaPS (Table 2). We also show
model atmospheres from Castelli & Kurucz (2003). We include atmospheres for
effective temperatures of $10,000$ K (blue dashed line) and 4000 K (cyan dot-
dashed line), roughly bounding the observed range for many spiders. The models
are normalized to a radius 50 per cent of the Roche lobe radius and a distance
of 3 kpc. These models, with an extinction of $A_{V}=3.4$ mag applied are then
shown in the blue shaded region as the observed bounds, which roughly bound
the detections and upper limits of the photometry.

###  3.3 Implications from non-eclipsed radio emission

The lack of significant variability within non-eclipsed time periods in any of
our observations implies the scintillation timescale or bandwidth is lower
than the dynamic spectrum resolution (temporal resolution $\delta_{t}=8\,{\rm
s}$ and frequency resolution $\delta_{\nu}=0.84\,{\rm MHz}$ for MeerKAT).

Using this non-detection of scintillation, we can place an approximate lower
limit on the dispersion measure of $\sim 74\,{\rm pc}\,{\rm cm}^{-3}$, using
the NE2001 Galactic electron density model (Cordes & Lazio, 2002), under the
condition that the scintillation bandwidth $\Delta\nu_{d}<2\delta_{\nu}$.

In addition, we can also rule out putative rotation periods exceeding
$2\delta_{t}=16$ s. While this is not particularly informative under the
spider MSP scenario for 4FGL J1646, it does rule out 4FGL J1646 belonging to
the emerging class of recently-discovered ultra-long period objects (Hurley-
Walker et al., 2022; Caleb et al., 2022; Hurley-Walker et al., 2023) or other
more unusual radio variables such as GCRT-like sources (Wang et al., 2021a;
Hyman et al., 2005).

We also observe long-term variability in the non-eclipsed flux density, as can
be seen in Fig. 2. This is typical of spider systems (Kumari et al., 2023;
Polzin et al., 2020)

###  3.4 Non-detection of radio pulsations

Our search for pulsed radio emission searched from Murriyang and MeerKAT
observations yielded no viable candidates. A likely scenario is that the
pulses are smeared due to high degrees of scattering either from the intra-
binary or interstellar material. In Fig. 7, we show the detectability
thresholds for intrinsic pulse duty cycle lower limits as a function of DM for
a range of spin periods, owing to scattering in the interstellar medium, using
the scattering timescale-DM relationship from Bhat et al. (2004). At the DM
lower limit of 74 pc cm-3, our lack of detected pulsations implies a pulsar-
intrinsic duty cycle close to 1, which we consider unlikely. Instead, an
interstellar DM exceeding $\sim 600$ pc cm-3 would rule out virtually all
millisecond pulsars from detectability. On the other hand, the scattering may
(partially) arise from the intra-binary material, in which case the DM-
scattering relationship is less applicable. We discuss this further in §3.6.

Figure 7: Duty cycle constraints as a function of dispersion measure, for a
range of pulsar periods. Coloured points show pulsars from the ATNF Pulsar
Catalogue (Manchester et al., 2005) within $4^{\circ}$ of 4FGL J1646. These
pulsars all lie below and to the left of the DM-duty cycle locus that defines
the boundary of this parameter space where they are detectable, meaning that
their pulsations are detectable. Solid lines are the limits derived from the
MeerKAT pulsar searches based on the full bandwidth (856–1217 MHz) data, and
dash-dotted lines are the limits derived from the Murriyang UWL pulsar
searches based on the top four subbands (3520–4032 MHz) data (expected flux
density was derived based on the spectral index from MWA and ASKAP
observations $\alpha=-2.7$).

Alternatively, the lack of radio pulsations could arise from an unusual
emission geometry. Typically, spiders are detected with radio and $\gamma$-ray
pulsations, but some are also radio-quiet (Kong et al., 2012; Corbet et al.,
2022). This radio-loud/quiet dichotomy is not fully understood, but it may be
due to eclipse phenomena, or geometry of the radio vs. $\gamma$-ray beam.
Here, we have an intermediate case: radio emission, $\gamma$-ray emission, but
an apparent lack of radio pulsations. While the putative MSP likely produces
$\gamma$-ray pulses, we did not attempt to search for them due to the
excessive computational demands without constrained orbital elements. If the
geometry of the system can be constrained by other means (e.g. through optical
monitoring or through detection and timing of $\gamma$-ray pulsations), this
system may provide key insights into the apparent dichotomy between radio-loud
and quiet spider binaries, and/or the geometry of MSP emission.

###  3.5 Derived eclipse properties

The phenomenology of eclipses carries information on the nature of the system
and the properties of the intra-binary material (Polzin et al., 2020). To
determine the eclipse properties, we fitted the ASKAP and MWA lightcurves with
a double Fermi-Dirac function;

$\begin{split}\frac{S_{\nu}(\phi,t)}{S_{\text{nonecl}}(t)}=\beta\left(\frac{1}{\exp\left({\frac{(\phi-\phi_{i})}{w_{i}}}\right)+1}-\frac{1}{\exp\left({\frac{(\phi-\phi_{e})}{w_{e}}}\right)+1}\right)\\\
+(1-\beta),\end{split}$ (1)

where $\phi\equiv\frac{(t-T_{0})\%P_{b}}{P_{b}}$ is the derived orbital
phase121212The symbol ”$\%$” is the modulo operator., where $t$ is the MJD
time, $P_{b}$ and $T_{0}$ are the binary period and reference MJD
epoch131313Here we define the reference epoch such that the mid-point of the
eclipse, which approximates superior conjunction of the companion, falls at
orbital phase 0.25, following the pulsar convention. Note that because we do
cannot derive a full binary solution, $T_{0}$ in our model is likely only an
approximation to the epoch of ascending node., which we allow to vary. Other
fitted parameters include $S_{\mathrm{nonecl}}(t)$, the non-eclipsed peak flux
density, the ingress/egress phase $\phi_{i}$ and $\phi_{e}$, and the
$1/e$-width of the ingress/egress, $w_{i}$ and $w_{e}$. As can be seen in Fig.
2, the non-eclipsed flux density shows substantial long-term variability at
943 MHz. To account for this, we modelled $S_{\mathrm{nonecl}}$ as a third-
order polynomial in $(t-T_{0})$, allowing the polynomial coefficients to vary
in the fit.

The constraints on $P_{b}$ and $T_{0}$ from MWA measurements were less precise
than ASKAP constraints by about an order of magnitude. To ensure consistency
between the measured eclipse properties between ASKAP and MWA data, we used a
multivariate normal prior on $P_{b}$ and $T_{0}$ for fitting MWA data, with
the mean and covariance of the prior derived from the ASKAP marginal
posteriors. We used uniform priors on all other parameters for both MWA and
ASKAP fits.

Using the broad frequency coverage afforded by ASKAP and MWA, we measured the
frequency dependence of the eclipse properties parametrised with a power-law
spectral index, e.g. $\Delta\phi\propto\nu^{\alpha_{\Delta\phi}}$. We provide
the properties in Table 3, along with the derived eclipse radius $R_{E}=\pi
a\Delta\phi$, where $a$ is the semimajor axis assuming a $1.4\,M_{\odot}$
pulsar and a companion mass of either $0.4\,M_{\odot}$ corresponding to
typical redback companion masses (Strader et al., 2019).

Eclipse parameter | MWA | ASKAP | Spectral index
---|---|---|---
| (200 MHz) | (943 MHz) |
$P_{b}$ (h) | $-$ | $5.267104\pm{3\times 10^{-6}}$ |
$T_{0}$ (MJD) | $-$ | $59391.3567\pm 0.0004$ |
$\phi_{i}$ | $0.047^{+0.003}_{-0.007}$ | $0.0502\pm 0.0016$ | $0.003^{+0.005}_{-0.003}$
$w_{i}$ |  $<0.0064$ ${}^{\text{{a}}}$ | $0.0101\pm 0.0008$ | $1.2^{+1.1}_{-0.8}$
$\phi_{e}$ | $0.491\pm 0.002$ | $0.4497\pm 0.0016$ | $-0.121\pm 0.008$
$w_{e}$ | $0.0118^{+0.0013}_{-0.0014}$ | $0.0089\pm 0.0009$ | $-0.2\pm 0.1$
$\Delta\phi$ | $0.444^{+0.007}_{-0.003}$ | $0.3994\pm 0.0014$ | $-0.069^{+0.005}_{-0.009}$
$R_{E}$ ${}^{\text{{b}}}$ | $2.3\,R_{\odot}$ | $2.6\,R_{\odot}$ |
Table 3: Properties of the radio eclipses derived from fitting a Fermi-Dirac
function as in Equation 1. The spectral index is defined such that the
quantity in each row follows a power-law, e.g.
$\Delta\phi\propto\nu^{\alpha_{\Delta\phi}}$. Notes (a): 90% confidence upper-
limit; (b): assuming a companion mass of $0.4\,M_{\odot}$.

The inferred eclipse radius is $\sim 2.3\,R_{\odot}$, which is $\sim 1.5$
times larger than the Roche lobe radius $R_{L}\sim 1.6\,R_{\odot}$ assuming a
pulsar mass of $1.4\,M_{\odot}$ and companion mass of $0.4\,M_{\odot}$
(computed using the approximation of Eggleton, 1983), confirming that the
eclipses are due to an unbound cloud of material from the companion. The
source of this material could either be the ablated material from the
companion, and/or the wind from the putative pulsar itself.

###  3.6 Nature of the radio eclipses

The phenomenology of radio eclipses in spider systems is very broad,
considering eclipses both in individuals systems and across different systems
(Polzin et al., 2019, 2020). Multiple (possibly overlapping) mechanisms have
been suggested to drive the eclipses – see e.g. Thompson et al. (1994) for
analytic treatment of eclipse mechanisms and Polzin et al. (2020) for an
overview of observational results across multiple systems. The eclipse
mechanisms may influence the pulse properties (e.g., DM or scattering), and
can also absorb the continuum flux density. In the case of 4FGL J1646, we
observe 100 per cent absorption of the continuum flux density, but the lack of
observed pulsations renders other observables (e.g. change in DM)
unattainable.

Nonetheless, our relatively long observational time-span from ASKAP and MWA
observations, and the broad frequency coverage they afford, enable us to
investigate the properties of the eclipse and make some initial estimates of
the physical conditions within the eclipse medium.

Following similar arguments to e.g. Kansabanik et al. (2021), we investigated
eclipse mechanisms proposed by Thompson et al. (1994): cyclotron absorption,
induced Compton scattering, free-free absorption, and synchrotron absorption.
Without strong constraints on the properties of the companion or the binary
orbit, we can only make broad estimates of the properties of the eclipse
medium. Nonetheless, we carry out this exercise to determine if any eclipse
mechanisms can be ruled out and to estimate a plausible range of eclipse
medium properties. For the following calculations we assume a companion mass
of $0.4\,M_{\odot}$, which is typical for redback systems (Strader et al.,
2019), and a pulsar mass of $1.4\,M_{\odot}$. The measured period of
$0.2194594\,$d implies an orbital semi-major axis of $\sim 1.9\,R_{\odot}$ for
the assumed companion mass.

For cyclotron absorption, we estimate the eclipse region magnetic field
assuming equilibrium between the wind energy density $U_{E}=\dot{E}/4\pi
ca^{2}$ and the magnetic pressure $P_{B}=B_{E}^{2}/8\pi$. Assuming
$\dot{E}\sim 10^{34}$ erg s-1, we have $U_{E}\sim 1.6$ erg cm-3, and
$B_{E}\sim 6.3$ G. We find that the required temperature to produce eclipses
at 943 MHz is $>4\times 10^{7}$ K, which exceeds the $1.7\times 10^{6}$ K
upper threshold for cyclotron absorption (Thompson et al., 1994). We therefore
rule it out as the eclipse mechanism.

For induced Compton scattering, we varied the electron column density (between
$10^{4}$ and $10^{30}$ cm-2), temperature (between $10^{2}$ and $10^{9}$ K),
and de-magnification factor (between $0$ and $1$) due to reflection of the
radiation off a curved plasma cloud. The maximum optical depth we calculated
across the parameter space was $\tau\sim 10^{-2}$, so we therefore rule out
induced Compton scattering as the eclipse mechanism.

To determine the viable range of parameters for free-free and synchrotron
absorption, we calculated the optical depth for MWA 200 MHz observations just
after full eclipse egress for at 943 MHz, around orbital phase 0.47 (i.e.,
when the 943 MHz optical depth $\tau$ first returns to 0). The resulting 200
MHz optical depth was $\tau=2.3\pm 0.9$. An important caveat for these
estimates is that the measurements at the relevant orbital phase were taken
several months apart, so long-term variability will introduce a systematic
uncertainty of $\sim 10$ per cent. Any constraints on the physical properties
of the medium should therefore be taken as order-of-magnitude estimates only.
To determine the physical properties, we fit the optical depth for free-free
and synchrotron absorption using Markov Chain Monte Carlo, fitting to the 943
MHz and 200 MHz flux density at the chosen orbital phase $\phi=0.47$ during
partial egress.

For free-free absorption, we varied the electron column density between
$10^{10}\,\mathrm{cm}^{-2}$ to $10^{25}\,\mathrm{cm}^{-2}$ – a very broad
range around typical column densities of $\sim 10^{16}\,\mathrm{cm}^{-2}$
(e.g. Stappers et al., 1996; Bai et al., 2022). We also allowed the
temperature to vary between $10^{0}$ – $10^{10}$ K, and the clumping factor to
vary between $10^{0}$ – $10^{10}$. We held the size of the absorbing medium
fixed at $2R_{E}=4.7\,R_{\odot}$ assuming a $0.4\,M_{\odot}$ companion.

Synchrotron absorption is caused by a population of non-thermal electrons,
often assumed to possess a power-law energy distribution $n(E)=n_{0}E^{-p}$
between minimum and maximum energies $E_{\text{min}}$ and $E_{\text{max}}$
(Thompson et al., 1994). We allowed the reference volume density of non-
thermal electrons $n_{0}$ to vary between $10^{1}\,\text{cm}^{-3}$ to
$10^{8}\,\text{cm}^{-3}$, the eclipse average magnetic field strength between
$10^{-2}$ G to $10^{2}$ G, and the electron energy power-law index $p$ between
0 and 8. We held the viewing angle $\theta$ fixed to $\pi/3$ (corresponding to
the expectation value of $\theta$ assuming a uniform distribution in
$\cos\theta$). As with free-free absorption, we held the size of the absorbing
medium fixed at $2R_{E}=4.7\,R_{\odot}$.

Figs 8 and 9 show the marginal posterior probability densities on each of the
varied parameters in the synchrotron and free-free absorption models. We found
that a broad range of parameters could reproduce the observed optical depths
at the relevant orbital phase, but we are able to rule some regions of
parameter space out. For instance, if free-free absorption is responsible for
the eclipses, then the electron column density must exceed $10^{15}$ cm-2. If
we assume an equipartition magnetic field strength of $\sim 6$ G (as with
cyclotron absorption) in the synchrotron-absorbing plasma, then $n_{0}\lesssim
100$ cm-3. Independent constraints on the eclipse medium density (e.g. from
measurements of DM variations near eclipse) will significantly improve
constraints on the eclipse medium properties.

Figure 8: Marginal posterior probability densities of eclipse medium
properties (non-thermal electron density $n_{0}$, magnetic field strength $B$,
and electron energy power-law index $p$) assuming synchrotron absorption.
Figure 9: As with Fig. 8, but for eclipse medium properties (clumping factor
$f_{\mathrm{cl}}$, temperature $T$, and electron column density $N_{e}$)
assuming free-free absorption.

Polzin et al. (2020) noted substantial differences in the behaviour of
eclipses in the continuum and pulsed flux in a sample of black widows. These
differences imply that multiple eclipse mechanisms are operating in at least
some spiders – one that absorbs the continuum flux density, and another that
reduces the pulsed flux density via temporal smearing. We now explore whether
a similar scenario may apply to 4FGL J1646, whereby the continuum flux density
is absorbed by e.g. synchrotron absorption, but scattering across a more
extended volume in the intra-binary material destroys the pulsed flux density
across the full orbit.

We consider an extended scattering eclipse medium with radius $R_{E}=2a$, such
that the pulsar is always enveloped, and its pulsed emission therefore
scatter-broadened beyond detectability. Thompson et al. (1994) considered the
density fluctuations required to render pulsed emission undetectable due to
scattering in a turbulent eclipse medium. The fractional density fluctuations
$\Delta n_{e}/n_{e}$ over a length scale $L_{n}$ required to broaden a pulse
for more than a pulsar spin period $P$ is (Thompson et al., 1994)

$\frac{\Delta n_{e}}{n_{e}}\gtrsim 7.6\times
10^{-6}\frac{\nu_{9}^{2}}{n_{e,8}}\frac{P_{-3}^{1/2}}{(R_{E,11}a_{11})^{1/2}}L_{n}^{1/2}\,,$
(2)

where the subscript numerals represent the normalization factor for the
various quantities in cgs units, e.g.
$n_{e,8}=n_{e}/10^{8}\,\mathrm{cm}^{-3}$. We show the constraints on the
density fluctuations in Fig. 10. For typical densities $n_{e}\sim
10^{7}\,\mathrm{cm}^{-3}$ and short fluctuation length scales $L_{n}\sim
10^{3}\,\mathrm{cm}$, fractional density fluctuations of $\sim 10^{-2}$ –
$10^{-1}$ are required to scatter-broaden the pulses out of detectability.
However, the requirements are less stringent at higher mean densities.

Figure 10: Constraints on the fractional electron density variations $\Delta
n_{e}/n_{e}$ required in the eclipse medium to scatter-broaden pulsed emission
beyond detectability in Murriyang observations centred at 3200 MHz, as a
function of the mean electron density $n_{e}$ and the length-scale of density
variations $L_{n}$. For clarity we show contours at each decade of $\Delta
n_{e}/n_{e}$ from $1$ – $10^{-7}$.

Better constraints on the companion and its orbit, along with ultra wide-band
continuum observations will enable more precise measurements of the physical
properties of the eclipse in future. If the scattering is indeed eclipse-
dominated, a dedicated radio observing campaign targeting the period just
before eclipse ingress – where the density of the eclipsing material is likely
to be lowest – may yield a future detection of radio pulses.

##  4 Conclusions

We have presented the discovery of radio eclipses from ASKAP J1646$-$4406,
which we associate with the $\gamma$-ray source 4FGL J1646. The radio-
frequency and multi-wavelength properties strongly suggest that 4FGL J1646 is
a spider-type pulsar, most likely a “redback” with a $\sim 0.4\,M_{\odot}$
companion, owing to the long eclipse ($\sim 40$ per cent of the orbit). We
measure a putative orbital period of $5.267104\pm{3\times 10^{-6}}$, typical
for spider-type systems (Strader et al., 2019). Using the eclipse properties
at 943 and 200 MHz, we place broad constraints on plausible eclipse medium
properties derived from synchrotron or free-free absorption models, and rule
out induced Compton scattering and cyclotron absorption as the eclipse
mechanism. Constraints on the electron density of the medium obtained from DM
enhancements in pulsed radio emission would greatly improve the constraints on
other properties of the eclipse medium.

We searched extensively for radio pulses with Murriyang and MeerKAT, but our
searches yielded no convincing pulsar candidates. The non-detection of radio
pulses can be explained by temporal smearing due to angular scattering of the
emission, either from propagation through the ISM or the eclipse medium. In
the ISM case, the lack of pulses can be explained if the interstellar DM
exceeds $\sim 600\,\mathrm{pc}\,\mathrm{cm}^{-3}$. If the scattering is
dominated by the eclipse medium, a range of turbulent density fluctuations
$\Delta n_{e}/n_{e}$ could smear pulses beyond detectability.

Additional multi-wavelength studies for this source are warranted. As
discussed in §3.2, available optical and infra-red measurements of the
inferred counterpart plausibly agree with the hypothesis of a spider binary,
but available data are not sufficient to sufficiently constrain the properties
of the system. Future photometric and spectroscopic monitoring of the
counterpart across the inferred orbit will be crucial both for confirming the
nature of 4FGL J1646 as a redback, and to derive a full orbital solution
(Nieder et al., 2020). These orbital constraints will enable a $\gamma$-ray
pulsation search toward 4FGL J1646, which is computationally infeasible unless
the orbital elements are well-determined.

## acknowledgments

Corresponding authors AZ and ZW contributed equally to this project. We thank
the anonymous reviewer whose comments improved this manuscript. Thanks to
George Hobbs, Daniel Reardon and Matthew Kerr for helpful discussions. Thanks
to Eddie Schlafly and Andrew Saydjari for help accessing DECaPS data. DK is
supported by NSF grant AST-1816492. RS is supported by NSF grant AST-1816904.
N.H.-W. is the recipient of an Australian Research Council Future Fellowship
(project number FT190100231). Parts of this research were conducted by the
Australian Research Council Centre of Excellence for Gravitational Wave
Discovery (OzGrav), project number CE170100004. AR gratefully acknowledges
financial support by the research grant “iPeska” (P.I. Andrea Possenti) funded
under the INAF national call Prin-SKA/CTA approved with the Presidential
Decree 70/2016, and continuing valuable support from the Max-Planck Society.
ASKAP is part of the Australia Telescope National Facility, which is managed
by the CSIRO. Operation of ASKAP is funded by the Australian Government with
support from the National Collaborative Research Infrastructure Strategy.
ASKAP uses the resources of the Pawsey Supercomputing Centre. Establishment of
ASKAP, Inyarrimanha Ilgari Bundara, the CSIRO Murchison Radio-astronomy
Observatory, and the Pawsey Supercomputing Centre are initiatives of the
Australian Government, with support from the Government of Western Australia
and the Science and Industry Endowment Fund. We acknowledge the Wajarri
Yamatji as the traditional owners of Inyarrimanha Ilgari Bundara, the CSIRO
Murchison Radio-astronomy Observatory site, the Wiradjuri people as the
traditional owners of the CSIRO Parkes Radio Observatory site, and the Gomeroi
people as the traditional owners of the CSIRO Paul Wild Observatory site.
Support for the operation of the Murchison Widefield Array is provided by the
Australian Government (NCRIS), under a contract to Curtin University
administered by Astronomy Australia Limited. Thanks to ATNF and SARAO
Operations staff for supporting our DDT observations.

## Data Availability

ASKAP data used in this paper can be accessed through the CSIRO ASKAP Science
Data Archive
(CASDA141414https://data.csiro.au/dap/public/casda/casdaSearch.zul), using the
project codes and SBIDs provided. Murriyang observations can be obtained
through the CSIRO Data Access Portal
(DAP)151515https://data.csiro.au/domain/atnf, and ATCA observations can be
obtained from the Australia Telescope Online Archive
(ATOA)161616https://atoa.atnf.csiro.au/. MeerKAT continuum observations can be
obtained from the MeerKAT
archive171717https://apps.sarao.ac.za/katpaws/archive-search. Other data can
be provided upon reasonable request.

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