# Spectrum and polarization of the Galactic center radio transient ASKAP
J173608.2$-$321635
from THOR-GC and VLITE

Kierra J. Weatherhead Department of Physics and Astronomy, The University of
Calgary, 2500 University Drive NW, Calgary AB T2N 1N4, Canada  Jeroen M. Stil
Department of Physics and Astronomy, The University of Calgary, 2500
University Drive NW, Calgary AB T2N 1N4, Canada  Michael Rugel Center for
Astrophysics, Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
National Radio Astronomy Observatory, 1003 Lopezville Rd, Socorro, NM 87801,
USA  Wendy M. Peters U.S. Naval Research Laboratory, 4555 Overlook Ave SW,
Washington, DC 20375, USA  Loren Anderson Department of Physics and Astronomy,
West Virginia University, Morgantown, WV 26506, USA  Adjunct Astronomer at the
Green Bank Observatory, P.O. Box 2, Green Bank, WV 24944, USA  Center for
Gravitational Waves and Cosmology, West Virginia University,
Chestnut Ridge Research Building, Morgantown, WV 26505, USA  Ashley Barnes
European Southern Observatory (ESO), Karl-Schwarzschild-Straße 2, 85748
Garching, Germany  Henrik Beuther Max Planck Institute for Astronomy,
Königstuhl 17, D-69117 Heidelberg, Germany  Tracy E. Clarke U.S. Naval
Research Laboratory, 4555 Overlook Ave SW, Washington, DC 20375, USA  Sergio
A. Dzib Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121
Bonn, Germany  Paul Goldsmith Jet Propulsion Laboratory, California Institute
of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA  Karl M. Menten
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany  Kristina E. Nyland U.S. Naval Research Laboratory, 4555 Overlook Ave
SW, Washington, DC 20375, USA  Mattia C. Sormani Department of Physics,
University of Surrey, Guildford GU2 7XH, UK  Università dell’Insubira, via
Valleggio 11, 22100 Como, Italy  James Urquhart Centre for Astrophysics and
Planetary Science, University of Kent, Canterbury CT2 7NH, UK

###### Abstract

The radio transient ASKAP J173608.2$-$321635, at the position
$(\ell,b)=(356.0872\degree,-0.0390\degree)$, was serendipitously observed by
The HI/OH/Recombination Line Survey of the Galactic Center (THOR-GC) at three
epochs in March 2020, April 2020 and February 2021. The source was detected
only on 2020 April 11 with flux density $20.6\pm 1.1$ mJy at 1.23 GHz and in-
band spectral index $\alpha=-3.1\pm 0.2$. The commensal VLA Low-band
Ionsophere and Transient Experiment (VLITE) simultaneously detected the source
at 339 MHz with a flux density $122.6\pm 20.4\ \rm mJy$, indicating a spectral
break below 1 GHz. The rotation measure in April 2020 was $63.9\pm 0.3\ \rm
rad\ m^{-2}$, which almost triples the range of the variable rotation measure
observed by Wang et al. (2021) to $\sim 130\ \rm rad\ m^{-2}$. The
polarization angle, corrected for Faraday rotation, was $97\arcdeg\pm
6\arcdeg$. The 1.23 GHz linear polarization was $76.7\pm 3.9\%$ with
wavelength-dependent depolarization indicating Faraday depth dispersion
$\sigma_{\phi}=4.8^{+0.5}_{-0.7}\ \rm rad\ m^{-2}$. We find an upper limit to
circular polarization $|V|/I<10.1\%$. Interpretation of the data in terms of
diffractive scattering of radio waves by a plasma near the source indicates
electron density and line-of-sight magnetic field strength within a factor 3
of $n_{e}\sim 2\ \rm cm^{-3}$ and $B_{\|}\sim 2\times 10^{5}\ \rm\mu G$.
Combined with causality limits to the size of the source, these parameters are
consistent with the low-frequency spectral break resulting from synchrotron
self-absorption, not free-free absorption. A possible interpretation of the
source is a highly supersonic neutron star interacting with a changing
environment.

Radio transient sources, Interstellar magnetic fields, Sky surveys

##  1 Introduction

Increases in survey speed, wide-field capability and capabilities for
commensal surveys have increased the chance of detection of transient radio
continuum sources with a variety of origins such as Fast Radio Bursts (FRBs;
Petroff et al., 2022), Rotating Radio Transients (RRATS; McLaughlin et al.,
2006), radio afterglows of gamma ray bursts (Frail et al., 1997), tidal
disruption events (Anderson et al., 2020), stellar flares (Roy et al., 2010a),
and intermittent pulsars (Kramer et al., 2006). Establishing basic
observational parameters is important to uncover the underlying physical
phenomena, but it can be challenging when sources change in an unpredictable
way on short time scales. Some radio interferometers are capable of
simultaneous wide-field, high time resolution, high angular resolution
observations. Examples are the Australian Square Kilometre Array Pathfinder
(ASKAP; Hotan et al., 2021), the South African Square Kilometre Array
precursor MeerKAT (Jonas & MeerKAT Team, 2016), the Low-Frequency Array
(LOFAR; van Haarlem et al., 2013), the Murchison Widefield Array (MWA; Tingay
et al., 2013), the Allen Telescope Array (ATA; Croft et al., 2010), and the
Canadian HI Intensity Mapping Experiment (CHIME; CHIME Collaboration et al.,
2022) with its outrigger stations. Sometimes, surveys that are not designed to
observe transients make significant serendipitous observations of transient
sources, as in the case of this paper.

The unresolved, erratic radio transient ASKAP J173608.2$-$321635 was first
discovered in January 2020 when data from the Variables and Slow Transients
Phase 1 Pilot Survey (VAST-P1; Murphy et al., 2013) were searched for
transient sources. This source had not been detected in ASKAP observations
prior to this, between April 2019 and October 2019. ASKAP measurements between
January 2020 and August 2020 found J173608.2$-$321635 to be variable and also
highly circularly polarized. Later measurements by MeerKAT in February 2021
also found the source to be highly linearly polarized. The nature of ASKAP
J173608.2$-$321635 is unclear. ASKAP J173608.2$-$321635 has similar parameters
to other transient sources near the Galactic center, including its steep
spectral index that varies from $\alpha=-2.7$ to $\alpha=-5.6$, where
$S_{\nu}\sim\nu^{\alpha}$ (Wang et al., 2021). Some Galactic Center Radio
Transients (GCRTs) have also been reported with very steep spectral indices.
GCRT J1742$-$3001 was found to have a spectral index $\lesssim-2$ between 235
MHz and 610 MHz by Hyman et al. (2009). GCRT J1745$-$3009 has a variable in-
band spectral index at 325 MHz ranging from $-4$ to $-13.5$ (Hyman et al.,
2007; Roy et al., 2010b).

Wang et al. (2021) and Wang et al. (2022) found ASKAP J173608.2$-$321635 to
have a high degree of linear polarization, nearly 100% at 1.6 GHz, and
variable circular polarization up to $\sim 40\%$ at 0.9 GHz in two separate
observations in 2020 and 2021. Roy et al. (2010b) reported variable circular
polarization up to 100% for the GCRT J1745$-$3009.

The outburst of ASKAP J173608.2$-$321635 that led to its discovery by ASKAP
was serendipitously observed with the Karl G. Jansky Very Large Array (VLA)
during observations for the extension towards the Galactic center of The
HI/OH/Recombination line survey of the inner Milky Way (THOR; Beuther et al.,
2016).

The THOR Galactic Center extension (THOR-GC) covers $-6\degree<l<15\degree$
with $|b|<1.25\degree$. Fortuitously, the VLA Low-Band Ionosphere and
Transient Experiment (VLITE; Clarke et al. 2016)111https://vlite.nrao.edu
system was operational at the time, providing us with simultaneous low-
frequency data at 339 MHz. In this work we present the new observations of
ASKAP J173608.2$-$321635 from the THOR-GC survey and discuss some possible
interpretation in view of the new results.

Table 1:  THOR and VLITE flux density and polarization measurements

Civil Date | Epoch | $\nu$ | $S_{\nu}$ | $\alpha$ | $\Pi_{\nu}$ | $\theta$ | $RM$ | $\sigma_{\phi}$ | $V_{\nu}/I_{\nu}$
---|---|---|---|---|---|---|---|---|---
| (MJD) | (MHz) | (mJy) |  | (%) | $(\degree)$ | $(\rm rad\ m^{-2})$ | $(\rm rad\ m^{-2})$ | (%)
2020 March 17 | 58925a | 339 | $<34.5$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$
1243c,d | $<6.8$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$
2020 April 11 | 58950a | 339 | $122.6\pm 20.4$ |  $-1.0\pm 0.2$f | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$
1233c,d | $20.6\pm 1.1$ |  $-3.1\pm 0.2$d | $76.7\pm 3.9$ | $-46.7\pm 0.3$ | $63.9\pm 0.3$ | $4.8^{+0.5}_{-0.7}$ | $<10.1^{g}$
2021 April 28 | 59332b | 1435c,e | $<11.4$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$ | $\ldots$

aafootnotetext: C-configuration

bbfootnotetext: D-configuration

ccfootnotetext: Frequencies from 2020 March 17 and 2021 April 28 are derived
from multi-frequency synthesis and frequency from 2020 April 11 is derived
from $RM$ synthesis

ddfootnotetext: Includes measurements from subbands centered at 1.051 and
1.435 GHz

eefootnotetext: Includes measurements from subbands centered at 1.435 GHz

fffootnotetext: Spectral index between 339 MHz and 1 GHz

ggfootnotetext: Upper limit for circular polarization at 1.248 GHz

##  2 Observations and data reduction

###  2.1 THOR-GC

The HI/OH/Recombination line Survey of the inner Milky Way (THOR Beuther et
al., 2016) is an L-band (1-2 GHz) survey with the Jansky Very Large Array
(VLA) of the interstellar medium (ISM) in the inner Galaxy, with separate data
products for spectral lines of the HI 21 cm line, four 18 cm OH lines, several
hydrogen recombination lines and the continuum. Details of the observational
setup, calibration and imaging were described by Beuther et al. (2016) and in
particular for the continuum polarization by Shanahan et al. (2022). THOR-GC
(VLA project 20A-160) is an extension of the THOR survey towards and across
the Galactic center region, with the same data products. A notable difference
between THOR and THOR-GC is that THOR was observed in C-configuration only,
using D-configuration data from the VLA Galactic Plane Survey (VGPS, Stil et
al., 2006, HI line and 1.4 GHz continuum only) that were observed before the
upgrade of the VLA. THOR-GC observed ASKAP J173608.2$-$321635 in
C-configuration on 2020 March 17 and 2020 April 11 and with a short snapshot
in D-configuration on 2021 April 28.

Calibration and imaging were performed in the CASA environment 6.5.0 (CASA
Team et al., 2022) following standard procedures. THOR-GC includes 6 of the
continuum subbands used in THOR. In this work, we present observations from
subbands centered at 1.05 and 1.44 GHz, each with a bandwidth of 128 MHz. The
spectrum of the source was so steep that it was not detected in our higher
frequency subbands.

The Stokes $I$ visibility data were averaged to 20 MHz channels, while the
Stokes $Q$ and $U$ visibility data were averaged to 4 MHz channels before
imaging to improve the signal to noise ratio per channel for cleaning. The
averaging reduces the maximum observable Faraday rotation to $2.4\times
10^{3}\ \rm rad\ m^{-2}$ at 1 GHz, which is sufficient for the purpose of this
paper. The Stokes $V$ visibility data were averaged over the two subbands in
which ASKAP J173608.2$-$321635 was visible in Stokes $I$. The $Q$, $U$, and
$V$ images were convolved to a common angular resolution of $45\arcsec\times
20\arcsec$ using the CASA task imsmooth, with pixels of size $2.5\arcsec\times
2.5\arcsec$. For each polarization image, a Stokes I image with the same
angular resolution was made.

For the analysis of ASKAP J173608.2$-$321635, the observations of the three
epochs were imaged separately as outlined in Table 1. The final images used in
the analysis were made using the surrounding 25 pointings. Each pointing in
the mosaic was imaged to a radius where the sensitivity dropped to 20%. As
such, 6 to 11 of the 25 imaged pointings, depending on frequency, covered the
location of ASKAP J173608.2$-$321635\. The source was near the center of one
pointing, at a distance of $3\farcm 25$, and the center of the furthest
pointing which covered the source at all frequencies used in the analysis was
at a distance of $17\farcm 96$. The six pointings were each observed on three
scans of the sky over a span of 3.59 hours. The average integration time of
each scan for the 6 pointings was 1.72 minutes, and each pointing had an
average total integration time of 5.17 minutes. We tried to image individual
fields to investigate variability on time scales of minutes, but this proved
inconclusive because the integration time of the individual snap shots was
short and the steep spectrum of the source significantly reduced the effective
bandwidth.

Stokes $Q$ and $U$ spectra were extracted by summation over a box of size
$4\times 4$ pixels centered on ASKAP J173608.2$-$321635\. These $Q$ and $U$
spectra were subsequently analyzed with methods designed for broad-band radio
polarimetry called Faraday Rotation Measure Synthesis ($RM$ synthesis,
Brentjens & de Bruyn, 2005) and $QU$ fitting (Law et al., 2011; O’Sullivan et
al., 2012). For a linearly polarized wave with wavelength $\lambda$, traveling
through a magnetized plasma with electron density $n_{e}$ and magnetic field
with line-of-sight component $B_{\|}$, the polarization angle $\theta$ changes
by an amount $\phi\lambda^{2}$ with the Faraday depth $\phi$ defined as

$\phi={e^{3}\over 2\pi m_{e}^{2}c^{4}}\int n_{e}B_{\|}\rm{d}l$ (1)

with $e$ the elementary charge, $m_{e}$ the mass of an electron, and $c$ the
speed of light. The integral is performed from the source to the observer,
with positive $\phi$ indicating a mean magnetic field directed toward the
observer.

If we encounter a situation in which waves experiencing different amounts of
Faraday rotation are blended, the superposition of the polarization states of
these waves leads to changes in the observed fractional polarization with
wavelength and also deviations from the $\lambda^{2}$ dependence of the
polarization angle that can be observed in polarimetry data with good spectral
resolution over a wide wavelength range.

In $RM$ synthesis222This work uses $RM$-tools (Purcell et al., 2020) for
analysis of polarization data. (Brentjens & de Bruyn, 2005), the Stokes $Q$
and $U$ spectra are divided by the Stokes $I$ spectrum and combined into the
complex polarization $\mathcal{P}=q+iu$, with $q=Q/I$ and $u=U/I$. The
division by Stokes $I$ eliminates the power law spectral dependence of
optically thin synchrotron emission, which has constant fractional
polarization. Introducing a weight function $W(\lambda^{2})$ that is zero for
any wavelength $\lambda$ for which no measurements are available, the Fourier
transform of $P(\lambda^{2})W(\lambda^{2})$ is the observed Faraday dispersion
function $\tilde{\mathcal{F}}$,

$\tilde{\mathcal{F}}={\int
W(\xi)\mathcal{P}(\xi)\,e^{-2i\phi\xi}\rm{d}\xi\over\int W(\xi)\rm{d}\xi},$
(2)

where $\xi=\lambda^{2}$ if $\xi>0$. As no measurements can be made for
$\xi\leq 0$, $W(\xi)=0$ for these values to extend the bounds of the Fourier
transform over the required range (Brentjens & de Bruyn, 2005). In this work
we apply uniform weights for all wavelengths where measurements were made.

In principle, the Faraday dispersion function is the distribution of polarized
intensity as a function of Faraday depth. In practice, $\tilde{F}$ is the
convolution of the true Faraday dispersion function with the Fourier transform
of $W(\xi)$ and a deconvolution is necessary (Heald, 2009).

$QU$ fitting achieves the same goals as $RM$ synthesis in $\lambda^{2}$ space
by fitting a model to the complex polarization. A useful model for analysis of
the current data is (e.g. Burn, 1966; O’Sullivan et al., 2012; Feng et al.,
2022)

$\mathcal{P}=P_{0}e^{-2\sigma_{\phi}^{2}\lambda^{4}}e^{2i(\theta_{0}+\phi_{0}\lambda^{2})}.$
(3)

In this function, the fitting parameters are $P_{0}$, the (real-valued)
fractional polarization in the absence of any Faraday rotation,
$\sigma_{\phi}$, the Faraday depth dispersion, and $\phi_{0}$, the mean
Faraday depth, also referred to as the rotation measure ($RM$). This model is
useful when fitting modest depolarization over the observed frequency range,
yielding a mean and standard deviation of the Faraday dispersion function. It
has been shown to fit the depolarization of FRBs well (Feng et al., 2022)
although its physical interpretation of a turbulent foreground screen with
many unresolved independent cells covering a source (Burn, 1966) does not
align well with the compact nature of these sources.

The standard THOR-GC data products combine the results of both C- and
D-configuration observations. In this paper, we investigate a continuum
transient source that requires imaging of the individual observing epochs.
After some experimentation, it was decided that removing baselines shorter
than 500 m (14% of the visibilities) did not significantly improve the quality
of the images, and data obtained with all baselines could be used in the
imaging of the L-band data. We note that ASKAP J173608.2$-$321635 is too faint
to detect any absorption in the HI 21-cm line data.

Figure 1: Flux density of ASKAP J173608.2$-$321635 as a function of time
(adapted from Wang et al., 2021). The ASKAP, MeerKAT and ATCA flux densities
are from Wang et al. (2021). The colour of the symbols indicates the same
broad frequency ranges as in Wang et al. (2021). Arrows indicate 3$\sigma$
upper limits. THOR-GC total flux densities and upper limits have been
extrapolated to 900 MHz assuming a spectral index of $\alpha=-3.1$. The THOR-
GC circular polarization upper limits is for $\nu=1.23\ \rm GHz$ (Table 1).
The bottom panel shows fractional circular polarization of the source. Figure
2: Images of ASKAP J173608.2$-$321635 and surroundings at 1029 MHz from THOR-
GC (left) and at 339 MHz from VLITE (right). The red and blue circles are
centered on the best-fit positions of ASKAP J173608.2$-$321635 from THOR-GC
and VLITE, respectively. Green circles mark the locations and approximate
angular size of supernova remnants in the catalog of Green (2019) updated in
2022 and made available at http://www.mrao.cam.ac.uk/surveys/snrs/. Toward the
left border is G356.3$-$0.3 (Gray, 1994; Roy & Rao, 2002), which is very
diffuse and undetected in these narrow-band snap shots. Toward the bottom is
G355.6$-$0.0 (Gray, 1994; Roy & Bhatnagar, 2006). The orange ellipses in the
bottom left corners indicate the beam size in THOR (left) and VLITE (right).
Figure 3: Stokes $I$ flux density of ASKAP J173608.2$-$321635 from THOR-GC and
VLITE observations on 2020 April 11. A power law relation
(S${}_{\nu}\sim\nu^{\alpha}$) is fitted (solid) to the THOR-GC data with
$\alpha=-3.1\pm 0.2$. A power law relation with free-free absorption is fitted
(dashed) to the combined THOR-GC and VLITE data with $\alpha=-3.6\pm 0.3$ and
$\tau=0.4\pm 0.06$ at 1 GHz.

###  2.2 VLITE data processing

Data from the VLA Low-band Ionosphere and Transient Experiment were recorded
simultaneously using 18 antennae during the THOR-GC observations described
above in the VLA’s C-configuration on 2020 March 17 and 2020 April 11. The
VLITE 2021 D-configuration data did not have sufficient angular resolution to
reliably separate the transient source from surrounding structures, and those
data are not included here. All VLITE data are processed within a few days of
observation by a dedicated calibration and imaging pipeline which combines
Python with standard processing tasks found in AIPS (Greisen, 2003) and Obit
(Cotton, 2008). Full details of the VLITE calibration pipeline are described
in Polisensky et al. (2016). For both of the 2020 observing sessions, 3C286
was used for primary calibration, and an NVSS image (Condon et al., 1998) was
used as a sky model to correct for ionospheric phase contribution in the
target direction. The data have a final bandwidth of 34 MHz centered at 339
MHz on both days, and an angular resolution of 86$\arcsec\times 22\arcsec$ at
$0.63\arcdeg$ and $60\arcsec\times 26\arcsec$ at $16.9\arcdeg$ on 17 March and
11 April respectively.

In order to match the higher frequency analysis, we used the same 25
surrounding THOR-GC pointings within a radius of 0.72$\arcdeg$ of the target,
observed over a span of 3.95 hours. The uv-data for each of these were shifted
to a common reference center at the position of the source of interest using
the AIPS task ‘UVFIX’, and then combined for each of the two dates. The
combined data were manually flagged to remove any remaining radio frequency
interference (RFI), and then imaged using the Obit task ‘MFImage’, with a
single phase-only self-calibration loop, using a 6-second solution step, to
ensure all the data were well-aligned. In order to minimize the contribution
of large-scale Galactic structures, during the imaging step we removed the
shortest baselines ($<0.4$ k$\lambda$), and used a slightly uniform weighting
scheme (robust factor $-1.5$). The images were corrected using VLITE-specific
beam models that were averaged to properly account for the original telescope
positions.

The final images have rms noise levels at the position of the source of
$\sigma=11.5$, and $10.2$ mJy beam-1 on 17 March and 11 April respectively.
The source is not seen on the first day, but is detected at a signal-to-noise
ratio of 12 with a flux of $122.6\pm 20.4\ \rm mJy$ on 11 April.

##  3 Results

###  3.1 Variability

ASKAP J173608.2$-$321635 was not detected in two epochs of THOR-GC on 2020
March 17 and 2021 April 28. Averaging over a single spectral window, 3$\sigma$
upper limits of 13.5 mJy and 4.3 mJy were found for the epoch on 2020 March 17
at 1.051 and 1.435 GHz, respectively, and 11.4 mJy for the epoch on 2021 April
28 at 1.435 GHz. Averaging over two spectral windows for the 2020 March 17
observation, a 3$\sigma$ upper limit of 6.8 mJy was found at 1.243 GHz. The
source was strongly detected in our observation on 2020 April 11 with a flux
density of $20.6\pm 1.1$ mJy at a centroid frequency of 1.233 GHz. Figure 1
shows the flux density of the ASKAP J173608.2$-$321635 detection and upper
limits in THOR-GC with measurements made by Wang et al. (2021).

Based on this detection, the best-fit position of the source is RA(J2000)
$17^{\text{h}}36^{\text{m}}8\fs 25\pm 0\fs 09$, Dec(J2000) $-32\arcdeg
16\arcmin 31\farcs 71\pm 1\farcs 9$, with Galactic coordinates
$(l,b)=(356.0872\arcdeg,-0.0390\arcdeg)$. The best-fit position from the VLITE
measurement on the same day is RA(J2000) $17^{\text{h}}36^{\text{m}}8\fs 21\pm
0\fs 15$, Dec(J2000) $-32\arcdeg 16\arcmin 41\farcs 18\pm 8\farcs 56$,
$(l,b)=(356.0849\arcdeg,-0.0403\arcdeg)$. Figure 2 shows the surroundings of
ASKAP J173608.2$-$321635 in THOR-GC and VLITE. Flux densities and other source
parameters are listed in Table 1.

###  3.2 X-Ray Observations

The extended ROentgen Survey with an Imaging Telescope Array (eROSITA; Predehl
et al., 2021) all-sky survey includes X-ray observations at soft ($0.2-0.6$
keV), medium ($0.6-2.3$ keV), and hard ($2.3-5.0$ keV) energy bands. The hard
energy band is the least susceptible to absorption, and so we use this band in
our analysis. eROSITA (data release 1, 31 January 2024) observed this region
of the sky in the hard energy band between 2020 March 24 and 2020 March 28 for
77 seconds. There were no counts within 4$\arcsec$ of ASKAP
J173608.2$-$321635\. This yields an upper limit on the flux of $1.00\times
10^{-12}$ erg s-1 cm-2 from $2.3-5.0$ keV (Tubín-Arenas et al., 2024; Merloni
et al., 2024). This corresponds to an upper limit of $1.20\times
10^{34}(d/10\text{ kpc})^{2}$ erg s-1 for the X-ray luminosity at a distance
$d$. This upper limit excludes a powerful burst of a magnetar near the
Galactic centre (see discussion in Wang et al., 2021) at the time of the
observation, but the sensitivity of the eROSITA sky survey is much lower than
that of the targeted X-ray observations presented by Wang et al. (2021).

###  3.3 Spectrum

The integrated Stokes $I$ spectrum of ASKAP J173608.2$-$321635 for the 2020
April 11 observation was found to have an in-band spectral index of
$\alpha=-3.1\pm 0.2$, where $S_{\nu}\sim\nu^{\alpha}$. This spectral index is
within the range observed by Wang et al. (2021), which decreased from
$\alpha=-2.7\pm 0.1$ on 2021 February 7 to $\alpha=-5.6\pm 0.3$ on 2021 April
25. We used our in-band spectral index to extrapolate L-band flux densities
and upper limits to 900 MHz for direct comparison with the results of Wang et
al. (2021) (Figure 1). Our detection shows that ASKAP J173608.2$-$321635
reached a peak brightness at least twice during its 2020/2021 period of
activity, and its flux density dropped by a factor $\sim 30$ in between peaks.

The simultaneously measured VLITE flux density at 339 MHz is much lower than
the extrapolated L-band spectrum would predict, as shown in Figure 3. This
indicates a break in the radio spectrum that could be a feature of the
mechanism that produces the radio emission. We will discuss synchrotron self-
absorption in Section 5.2. This break implies that ASKAP J173608.2$-$321635
had an inverted low-frequency spectrum in contrast to the very steep spectrum
of known GCRTs below $\sim 500$ MHz (Hyman et al., 2007, 2009; Roy et al.,
2010b).

For our discussion it will be helpful to know what the opacity would be if the
break were the result of free-free absorption. A power law relation with free-
free absorption ($S_{\nu}\sim\nu_{\rm GHz}^{\alpha}e^{-\tau\nu_{\rm
GHz}^{-2}}$, where $\tau$ is the opacity at 1 GHz), with $\nu_{\rm GHz}=\nu/1\
\rm GHz$, fits the combined THOR-GC and VLITE data with $\alpha=-3.6\pm 0.3$
and $\tau=0.4\pm 0.06$ at 1 GHz. Assuming a temperature of 104 K, this free-
free opacity corresponds to an emission measure of $\sim 1.1\times 10^{6}\ \rm
cm^{-6}\ pc$. This is comparable to the emission measure of the Orion Nebula.

Rubin (1968) models the total flux density of optically thin free-free
emission from regions of varying sizes as

$S_{\nu}=\frac{8.61\times 10^{-76}}{D^{2}\nu^{0.1}}\int
n_{e}n_{i}T^{-0.35}dV,$ (4)

where $D$ is the distance in pc, $\nu$ is the frequency in GHz, $n_{e}$ and
$n_{i}$ are the electron and ion densities in cm-3, $dV$ is a volume element
in cm3, and $S_{\nu}$ is in ergs cm-2 s-1 Hz-1. For an optically thin sphere
with a 10 pc radius at a distance of 8.3 kpc (the distance to the Galactic
center, GRAVITY Collaboration et al., 2021), assuming a uniform density of 2.0
cm-3, which is more normal for the inner Galaxy (Yao et al., 2017), and a
temperature of 104 K, we find $20$ mJy for the flux density of free-free
emission. This flux is high enough that it would have been detected in our
measurements, but we do not see any persistent emission at the location of the
source. If the radius of the sphere were 1 pc, the expected free-free emission
would drop to $2\times 10^{-2}$ mJy, which is below our detection threshold.
As such, the observed spectral break could be due to a small region of plasma
with a density predicted by the modelling, but only if its filling factor in
the synthesized beam is very small. We will discuss the possibility that the
spectral break is due to free-free absorption further in Section 5.

Figure 4: Results of $QU$ fitting and $RM$ clean for ASKAP J173608.2$-$321635
for the detection in THOR-GC on 2020 April 11. The top left panel shows
polarization angle as a function of $\lambda^{2}$ with the model from $QU$
fitting. The top right panel shows Stokes $Q$ (blue) and $U$ (red) as a
function of $\lambda^{2}$ with the result of $QU$ fitting indicated by the
solid lines. The bottom panel shows the dirty Faraday dispersion function
(FDF) in gray, clean FDF and $RM$ in black and clean components from $RM$
clean in red.

##  4 Polarization

The source was highly linearly polarized ($|L|/I\ \sim\ 76.7\pm 3.9\%$, where
$|L|=\sqrt{Q^{2}+U^{2}}$) at 1.233 GHz, which is consistent with MeerKAT
measurements of $|L|/I\sim 80\%$ (Wang et al., 2021). The rotation measure of
the source was determined using two methods: $RM$ synthesis and $QU$ fitting
(Figure 4). $RM$ synthesis found a rotation measure of $+63.9\pm 0.3$ rad m-2.
The $RM$ value determined by $QU$ fitting was consistent within the margin of
error. $QU$ fitting of Equation 3 also found the source to be depolarizing,
with $\sigma_{\phi}=4.8^{+0.5}_{-0.7}$ rad m-2. Wang et al. (2021) found a
similar depolarization, $\sigma_{\phi}=5.7$ rad m-2, on 2021 February 7, but
found the $RM$ to vary from $-11.8\pm 0.8$ rad m-2 on 2021 February 7 to
$-64.0\pm 1.5$ rad m-2 on 2021 February 9. The THOR-GC measurement increases
the $RM$ variability range from $\sim$50 rad m-2 to $\sim$130 rad m-2.

The polarization angle at the reference frequency 1.23 GHz is $-46\fdg 7\pm
0\fdg 3$. Correcting for Faraday rotation, we find an intrinsic polarization
angle $97\fdg 1\pm 1\fdg 9$ from $RM$ synthesis and $96\fdg 8_{-3.1}^{+2.7}$
from $QU$ fitting. The uncertainty in the calibration of the absolute
polarization angle is approximately $5\arcdeg$ related to hour-angle and
baseline dependent effects in the $RL$ phase that are not well understood
(EVLA memo 205333https://library.nrao.edu/public/memos/evla/EVLAM_205.pdf, see
also Lacy et al., 2020). The extrapolation to $\lambda=0$ assumes a linear
dependence between polarization angle and $\lambda^{2}$ with slope $RM$ at all
wavelengths. We have no indication to the contrary, but the extrapolated
polarization angle is only as good as this assumption (Farnsworth et al.,
2011). Adding formal and absolute calibration errors in quadrature, we find an
intrinsic polarization angle of $97\arcdeg\pm 6\arcdeg$.

The intrinsic polarization angle is related to the projection of the mean
magnetic axis of the source on the plane of the sky. Wang et al. (2021) could
not absolutely calibrate their polarization angles. They reported a reference
source that could be used to calibrate the angle a posteriori. Unfortunately,
this reference source is well below the detection limit of THOR-GC.

ASKAP J173608.2$-$321635 was not detected in circular polarization in our
observation. We derive a 3$\sigma$ upper limit of 2.0 mJy in Stokes $V$ at
1248 MHz. As such, the fractional circular polarization of the source was less
than 10.1% on 2020 April 11. This upper limit is well below some of the
detections reported by Wang et al. (2021), before and after 2020 April 11
(Figure 1).

##  5 Discussion

###  5.1 RM variability

Compared to the findings of Wang et al. (2021), the data presented in this
paper reveal a much larger range of $RM$ variability in ASKAP
J173608.2$-$321635, notably changing the sign of $RM$. We also provide the
first absolute polarization angle measurement, corrected for Faraday rotation,
which may be important to establish whether the source has a stable magnetic
axis in the plane of the sky.

The significance of the variable RM is best illustrated by a numeric example.
$RM$ is an integral quantity over the complete line of sight, but $RM$
variability with amplitude of order $10^{2}\ \rm rad\ m^{-2}$ is rare. Its
origin must be sought in terms of a localized phenomenon associated with the
source, as opposed to the ISM on larger scales, since the RM of most sources
is not variable.

The distance traveled by relative motion with speed $v$ in one year is
$d\approx 10^{-3}v_{6}$ pc, where $v_{6}$ has units of 1000 km s-1. The
variation of $RM$ is $\sim 10^{2}\ \rm rad\ m^{-2}\ yr^{-1}$ between 2020
April 11 and 2021 February 9, and $\sim 10^{4}\ \rm rad\ m^{-2}\ yr^{-1}$
between the two measurements by Wang et al. (2021) in 2021 February. If this
change is effected by relative motion with speed of order $10^{3}\ \rm km\
s^{-1}$, the line of sight scale of $10^{-3}\ \rm pc$ indicates variation of
$n_{e}B_{\|}$ in the range $10^{5}\ \rm cm^{-3}\ \mu G$ to $10^{7}\ \rm
cm^{-3}\ \mu G$. In the regular warm ionized medium, $n_{e}\sim 0.1\ \rm
cm^{-3}$, $B\sim 5\ \rm\mu G$, a distance $10^{-3}\ \rm pc$ corresponds to a
rotation measure increment of order $2\times 10^{-4}\ \rm rad\ m^{-2}$, which
is six orders of magnitude smaller than the observed RM variability of ASKAP
J173608.2$-$321635\. Supernova remnants are believed to have
$n_{e}B_{\|}\lesssim 10^{3}$ (Reynolds et al., 2012), and no supernova remnant
is known to be associated with ASKAP J173608.2$-$321635 (Figure 2). The RM
variability on time scales of days to several months suggests that the $RM$
variability arises in an unusual plasma associated with the source.

###  5.2 Depolarization by diffractive scattering

Figure 5: Distributions of $n_{e}$ (left) and $B_{\|}$ (right) under the
condition that $\nu_{\chi S}$ and $\nu_{rs}$ match the conditions described in
the text. The blue histograms show the uniform distributions of the input
parameters. The red histograms show the distributions that satisfy the
conditions for both $\nu_{\chi S}$ and $\nu_{rs}$. In the left panel, the
green histogram shows the distribution that matches only the condition for
$\nu_{\chi S}$ and the black histogram shows the distribution that matches
only the condition for $\nu_{rs}$. These distributions are not shown on the
right, as they would both appear the same as the blue histogram.

Compared to the $RM$ variability, the data indicate a very modest but non-zero
Faraday depth dispersion. Our value is marginally smaller than that of Wang et
al. (2021) at $\sigma_{\phi}\lesssim 5.7\ \rm rad\ m^{-2}$. Faraday depth
dispersion arises from differences in Faraday rotation between lines of sight
that are combined within the beam. Instrumental Faraday depth dispersion
arising from frequency-averaging the visibilities to 4 MHz channels and
fitting Equation 3 is less than $0.15\ \rm rad\ m^{-2}$ for a source with
$RM=63.9\ \rm rad\ m^{-2}$. Equation 3 refers, strictly speaking, to a screen
of turbulent cells with angular size much smaller than the angular size of the
background source. Considering the shortest known variability time scale of
ASKAP J173608.2$-$321635, its angular size is of the order of a light day, or
21 milli-arcseconds at the distance of the Galactic center, 8.3 kpc. This is
so small that we may suspect that the origin of the observed Faraday depth
dispersion is different from the assumptions made in Equation 3.

Diffractive scattering is the distortion of the wave front by an intervening
plasma, analogous to the effect of Earth’s atmosphere on the light of a star
causing seeing and scintillation (Williamson, 1972; Rickett, 1990). It gives
rise to multiple signal paths through the interstellar medium from the source
to the observer. Several frequency-dependent effects are observable, such as
pulse broadening for a pulsed source and scintillation, which occurs for any
source (pulsed or not) with angular size smaller than a minimum angular size
defined by the scattering plasma. These multiple signal paths also result in
Faraday depth dispersion (c.f. Equation 1).

Galactic pulsars usually have negligible Faraday depth dispersion (Sobey et
al., 2019). There are some exceptions, with pulsars displaying wavelength-
dependent depolarization comparable to or more than what is measured for ASKAP
J173608.2$-$321635 (Sobey et al., 2021). Noutsos et al. (2009) found that the
RM of some bright pulsars depends on pulse phase with a range of order $10\
\rm rad\ m^{-2}$, and attributed this to scattering. The effects of scattering
of radio waves on Faraday rotation of a source with very small angular size
were recently described by Beniamini et al. (2022) in the context of Fast
Radio Bursts. We analyze the Faraday depth dispersion of ASKAP
J173608.2$-$321635 in the context of their model.

Beniamini et al. (2022) modeled diffractive scattering for FRBs, for which
Feng et al. (2022) have presented a relation between pulse broadening and
Faraday dispersion. The scattering in these sources occurs in a plasma close
to the source, not in the Galactic ISM. Since ASKAP J173608.2$-$321635 is a
compact source in a special environment, we can apply the model of Beniamini
et al. (2022). A necessary but insufficient condition for depolarization is
that the mean Faraday rotation angle $\Delta\theta\geq 1\ \rm rad$. Taking the
RM variability amplitude as a lower limit of the mean RM of the plasma, this
condition is satisfied for $\lambda^{2}\gtrsim 6.7\times 10^{-3}\ \rm m^{2}$,
or $\nu\lesssim 3.7\ \rm GHz$. Wang et al. (2021) found depolarization for
$\lambda^{2}\gtrsim 0.05\ \rm m^{2}$, roughly coincident with the emergence of
detectable circular polarization at the $\gtrsim 10\%$ level. The total
fractional polarization, including Stokes $V$, dropped significantly below
100%.

Beniamini et al. (2022) defined a critical frequency $\nu_{rs}$ for
wavelength-dependent depolarization by a scattering screen, and frequency
$\nu_{\chi S}$ below which circular polarization may arise from the
scattering. Figure 5 shows the results of a parameter search that varied the
electron density $n_{e}$, line-of-sight component of the mean magnetic field,
$B_{\|}$, distance $d$ and size of the scattering screen $L$. The distance was
varied between 0.1 kpc and 10 kpc, while the size of the scattering screen was
varied between $10^{-4}\ \rm pc$ and 1 kpc. The spectral resolution
$\mathcal{R}$ was set to the THOR-GC resolution ($4\ \rm MHz$). All other
model parameters were kept at the values assumed by Beniamini et al. (2022)
(their Figure 3). We then constrained the models according to $1.1<\nu_{\chi
S}<1.3\ \rm GHz$ and $1.5<\nu_{rs}<2.5\ \rm GHz$. The distribution of allowed
values for $n_{e}$ and $B_{\|}$ are shown as red histograms in Figure 5. We
find that both constraints are met if the density and magnetic field are
within a factor $\sim 3$ of $n_{e}=2\ \rm cm^{-3}$ and $B_{\|}=2\times 10^{5}\
\rm\mu G$. Interestingly, the strongest constraint on $n_{e}$ comes from
$\nu_{rs}$, while both constraints are required to place limits on $B_{\|}$.
The depth of the screen and the distance are not constrained by this
experiment.

The model of Beniamini et al. (2022) thus implies a plasma with density that
is normal for the ISM in the Galactic center region (Yao et al., 2017) but a
magnetic field that is several orders of magnitude stronger than typical ISM
magnetic fields. We find $n_{e}B_{\|}\sim 10^{5}-10^{6}\ \rm cm^{-3}\mu G$,
which is roughly consistent with the range estimated from the RM variability.
The models approximately but not precisely reproduce the observed polarization
of ASKAP J173608.2$-$321635\. To give a specific example, assuming $n_{e}=1.5\
\rm cm^{-3}$, $B_{\|}=3.5\times 10^{5}\ \mu$G, $L=10^{-3}\ \rm pc$, $d=8.3\
\rm kpc$, velocity of the source $10^{3}\ \rm km\ s^{-1}$ and eddy velocity
$100\ \rm km\ s^{-1}$ yield 1.39 GHz linear polarization 89%, circular
polarization 4.5%, while at 1.0 GHz, the linear polarization is 76% and the
circular polarization is 17%. These values approximate the observed fractional
polarization and upper limits, but the frequencies $\nu_{\chi S}=0.91\ \rm
GHz$ and $\nu_{rs}=1.2\ \rm GHz$ appear lower than the observations indicate.

The low-frequency spectral break reported here may be due to synchrotron self-
absorption. Following Kellermann & Pauliny-Toth (1981) for the frequency of
the peak brightness of a compact synchrotron source, with $B=3\times 10^{5}\
\rm\mu G$, peak flux density $100\ \rm mJy$, and angular size less than 21
milli-arcseconds, we find the peak brightness occurs at 220 MHz. With the same
parameters, but angular size of the source half the upper limit set by
causality, the peak would occur near the VLITE frequency. So the parameters we
find are consistent with the interpretation of the observed low-frequency
spectral break in terms of synchrotron self absorption. It should be kept in
mind though, that the emission mechanism in ASKAP J173608.2$-$321635 may be
more complex than the standard assumptions about synchrotron emission.

###  5.3 Nature of ASKAP J173608.2$-$321635
and the scattering screen

The upper range of magnetic field strength in supernova remnants is believed
to be of order $1\ \rm mG$ (Reynolds et al., 2012) and the product
$n_{e}B_{\|}\sim 10^{3}\ \rm cm^{-3}\mu G$ is adopted for supernova remnants
as environments for some Fast Radio Bursts (Feng et al., 2022; Yang et al.,
2022b). The observed linear and circular polarization of ASKAP
J173608.2$-$321635 requires a scattering screen with a magnetic field that is
two orders of magnitude stronger, but one that is still weaker by many orders
of magnitude than the magnetic field of a typical pulsar $\sim 10^{12}\ \rm G$
(e.g. Philippov & Kramer, 2022). Bearing in mind that the emission of ASKAP
J173608.2$-$321635 may not be incoherent synchrotron emission, the synchrotron
cooling time for electrons emitting GHz frequency synchrotron emission in a
magnetic field of $10^{6}\ \rm\mu G$ is of the order of a month, which is too
long to explain the observed variability on time scales of a day.

In the context of a compact source behind a scattering screen, a Faraday depth
dispersion that is small compared with $RM$ has been suggested as evidence of
a large-scale magnetic field, or additional Faraday rotation in a separate
plasma along the line of sight. However, when the $RM$ is variable with a
large amplitude over a short time scale, we must associate the $RM$ itself
with small-scale structure, and its variability with relative motions as
outlined above. The implied plasma density $n_{e}\sim 2\ \rm cm^{-3}$ is also
too small to provide significant free-free opacity to explain the low-
frequency spectral break reported in Section 3. The thermal emission of the
scattering screen is undetectable because its filling factor in the
synthesized beam is very small. In summary, we find that the scattering model
by Beniamini et al. (2022) implies a plasma with unremarkable density but
strong magnetic field associated with ASKAP J173608.2$-$321635.

ASKAP J173608.2$-$321635 may be a high-velocity neutron star moving through
the inner Galaxy. The physical scale for structure in the screen, $\sim
10^{-3}\ \rm pc$ is not strongly constrained by the data, but it follows from
the RM variability and a plausible but high speed. A highly supersonic neutron
star, possibly with a pulsar wind, would create a bow shock structure. The
distance between a highly supersonic pulsar and the apex of the contact
discontinuity between a pulsar wind and the shocked interstellar medium was
given by Kargaltsev et al. (2017) as

$R_{a}=6.5\times 10^{16}n^{-1/2}(f_{\Omega}\dot{E}_{36})^{1/2}v_{7}^{-1}\ \rm
cm,$ (5)

and with $n=2$ the particle density in $\rm cm^{-3}$, $v_{7}=10$ the speed in
$10^{7}\ \rm cm\ s^{-1}$, $\dot{E}_{36}=1$ the mechanical luminosity of the
pulsar wind and $f_{\Omega}=1$, a dimensionless anisotropy factor, we find
$R_{a}=4.6\times 10^{15}\ \rm cm$ or $R_{a}=1.5\times 10^{-3}\ \rm pc$. The
approximate scale of the screen and the relative speed of order $10^{3}\
\rm\rm km\ s^{-1}$ match the shocked interstellar medium in the bow shock of a
high-velocity neutron star. The implied high magnetic field strength and
modest density could arise in a turbulent wake.

The size of the radio emission region is less than a light day ($8.4\times
10^{-4}\ \rm pc$) because of causality constraints and the rapid variability
time scale reported by Wang et al. (2021). The emission of ASKAP
J173608.2$-$321635 is more highly polarized than the theoretical maximum for
optically thin incoherent synchrotron emission, which has fractional
polarization $\lesssim 70\%$ to $\lesssim 85\%$ (higher if the power law
electron energy spectrum is steeper Pacholczyk, 1977). Our data show that the
source reached a maximum brightness in 2020 before dimming by a factor $\sim
30$ and brightening again to the 2021 peak observed by Wang et al. (2021).
This supports the idea of occasional brief enhanced injection (acceleration)
of relativistic electrons into the emission region and that the variable,
steep to ultra-steep, spectral index is related to the time of an observation
since the injection of relativistic electrons.

The origin of the bursts requires speculation on the reason for brief
intermittent injection (acceleration) of relativistic electrons. The time
scale between peak brightness appears to be months to years, suggested by a
combination of modest sampling in time, detectable low-level emission in the
period between the 2020 and 2021 peaks, and the fact that ASKAP
J173608.2$-$321635 was not observed before 2020. Wang et al. (2021) did not
detect pulsed emission but their observations were inconclusive because of the
variability of the source. Absence of pulsation of (most of) the burst
emission is significant because the physical scales derived from the
variability allow an emission region that is orders of magnitude larger than
the radius of the light cylinder, $R_{\rm LC}=1.5\times 10^{-9}P\ \rm pc$ with
$P$ the pulsar’s rotation period in seconds.

The variability of ASKAP J173608.2$-$321635 is unlike normal pulsars, so the
mechanism of the bursts may be related to special conditions. It is
interesting that the upper limit to the size of the emission region is
comparable to the distance between the neutron star and the vertex point of
the contact discontinuity between the pulsar wind and the swept-up medium.
This leaves the possibility of injection of new particles into the
magnetosphere because of a change in environment, for example if ASKAP
J173608.2$-$321635 runs into a structure in the interstellar medium that
changes the density or relative velocity of the surrounding medium. For a time
scale of 1 year between observed bursts, and a relative velocity of $10^{3}\
\rm\rm km\ s^{-1}$, the scale of a plasma structure would be of order
$1.0\times 10^{-3}\ \rm pc$ or $\sim 200\ \rm AU$. Such plasma structures are
known to exist from extreme scattering events (e.g. Coles et al., 2015). The
physical scale is also similar to the size of the Solar heliopause.

If ASKAP J173608.2$-$321635 is approximately at the distance of the Galactic
center, it must be located well within the Fermi and eROSITA bubbles (Zhang &
Guo, 2020). The environment of ASKAP J173608.2$-$321635 may be very different
from the interstellar medium in the solar neighborhood, with a higher density
of gas and stars, possibly stirred up by activity of Sgr A* within the past
$\lesssim 3$ Myr (Guo & Mathews, 2012; Yang et al., 2022a). This makes it
plausible that the environment of ASKAP J173608.2$-$321635 changes on time
scales shown in Figure 1 and required by the $RM$ variability, when moving at
its implied high speed.

The above picture of a highly supersonic pulsar running into a plasma
structure, or perhaps the outskirts of another solar system, suggests it may
be a rare kind of source with activity on a time scale of a year that may come
to an end. Magnetohydrodynamic simulations of supersonic pulsars (Barkov et
al., 2019; Bucciantini et al., 2020) model the interaction region as a steady,
anisotropic pulsar wind that is generated at the light cylinder. Emission from
the much larger interaction region between the pulsar wind and the
interstellar medium is not expected to be pulsed. We note that much older
pulsars with a negligible pulsar wind may be better described by a
magnetosphere interacting with the interstellar medium, in analogy to a
planetary magnetosphere that interacts with the solar wind.

Direct observations of rapid evolution of the spectral index and possible time
evolution of the spectral break reported here would provide valuable
information on the emission mechanism and the particle acceleration process.
This can be achieved by continued monitoring of this source and a more
complete statistical sample of Galactic radio transients. The latter is a
prospect for new radio telescopes with high survey speed, such as the Square
Kilometre Array.

##  6 Summary and Conclusions

ASKAP J173608.2$-$321635 was detected with the VLA on 2020 April 11 with flux
density $20.6\pm 1.1\ \rm mJy$ at 1.23 GHz and spectral index $\alpha=-3.1\pm
0.2$ (THOR-GC) and 339 MHz flux density $122.6\pm 20.4$ mJy (VLITE). The
linear polarization at 1.23 GHz was $76.7\pm 3.9\%$ and a $3\sigma$ upper
limit for the circular polarization $|V|/I<10.1\%$ was found.

On 2020 April 11 the rotation measure of ASKAP J173608.2$-$321635 was $63.9\pm
0.3\ \rm rad\ m^{-2}$. The rotation measure of ASKAP J173608.2$-$321635 is
more variable than previously thought, and it changes sign. A basic geometric
argument of relative motion of a plasma and a compact source suggests that the
Faraday rotation occurs in a plasma with $n_{e}B_{\|}$ of order $10^{5}$ to
$10^{7}\ \rm cm^{-3}\ \mu G$, which is several orders of magnitude higher than
the warm ionized ISM (WIM) and also 2 orders of magnitude beyond the range of
$n_{e}B_{\|}$ thought to be representative for supernova remnants.

The simultaneous THOR-GC L-band and VLITE 339 MHz data reveal a low-frequency
break in the spectrum of ASKAP J173608.2$-$321635\. If this break is caused by
free-free absorption, the free-free opacity at 1 GHz is $\tau=0.4\pm 0.06$.
The thermal emission of such a plasma can only remain undetected if the
filling factor within our beam is much smaller than 1. Such a plasma would
almost certainly be associated with the source. However, free-free absorption
is not consistent with our analysis of a scattering screen with modest density
$n_{e}\sim 2\ \rm cm^{-3}$. The spectral break may be the result of
synchrotron self-absorption in a source with angular size less than 21 milli-
arcseconds, magnetic field $\sim 3\times 10^{5}\ \rm\mu G$ and peak flux
density $100\ \rm mJy$ at a few hundred MHz.

The in-band depolarization of ASKAP J173608.2$-$321635 is quantified by
Faraday depth dispersion $\sigma_{\phi}=4.8^{+0.5}_{-0.7}\ \rm rad\ m^{-2}$,
marginally smaller than the value reported by Wang et al. (2021). If this
Faraday dispersion arises from scattering of radio waves in a plasma, the
model by Beniamini et al. (2022) suggests the scattering plasma has a density
that is comparable to WIM density near the Galactic center, but strongly
magnetized with magnetic field of the order of $3\times 10^{5}\ \rm\mu G$.

We conclude that the variable $RM$ and the Faraday depth dispersion of ASKAP
J173608.2$-$321635 are consistent with the presence of a highly magnetized
plasma associated with the source. This kind of plasma may be found in the
wake of a high-velocity neutron star interacting with its environment.

## acknowledgments

The National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. Construction and installation of VLITE was supported by the Naval
Research Laboratory Sustainment Restoration and Maintenance fund. $RM$-Tools
is maintained by the Canadian Initiative for Radio Astronomy Data Analysis
(CIRADA; cirada.org). This work is based on data from eROSITA, the soft X-ray
instrument aboard SRG, a joint Russian-German science mission supported by the
Russian Space Agency (Roskosmos), in the interests of the Russian Academy of
Sciences represented by its Space Research Institute (IKI), and the Deutsches
Zentrum für Luft- und Raumfahrt (DLR). The SRG spacecraft was built by
Lavochkin Association (NPOL) and its subcontractors, and is operated by NPOL
with support from the Max Planck Institute for Extraterrestrial Physics (MPE).
The development and construction of the eROSITA X-ray instrument was led by
MPE, with contributions from the Dr. Karl Remeis Observatory Bamberg & ECAP
(FAU Erlangen-Nuernberg), the University of Hamburg Observatory, the Leibniz
Institute for Astrophysics Potsdam (AIP), and the Institute for Astronomy and
Astrophysics of the University of Tübingen, with the support of DLR and the
Max Planck Society. The Argelander Institute for Astronomy of the University
of Bonn and the Ludwig Maximilians Universität Munich also participated in the
science preparation for eROSITA. J.M.S. acknowledges the support of the
Natural Sciences and Engineering Research Council of Canada (NSERC),
2019-04848, and a generous private donor of a substantial server for data
processing. M.R.R is a Jansky Fellow of the National Radio Astronomy
Observatory, USA. W.M.P., K.E.N., and T.E.C. acknowledge that basic research
in radio astronomy at the U.S. Naval Research Laboratory is supported by 6.1
Base funding. This work was performed in part at the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the
National Aeronautics and Space Administration (80NM0018D0004). S.A.D.
acknowledge the M2FINDERS project from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant No 101018682). M.C.S acknowledges financial support from the Royal
Society (URF\R1\221118) and the European Research Council under the ERC
Starting Grant “GalFlow” (grant No 101116226).

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