# A Radio Study of Persistent Radio Sources in Nearby Dwarf Galaxies:
Implications for Fast Radio Bursts

Y. Dong (董雨欣) Center for Interdisciplinary Exploration and Research in
Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern
University, Evanston, IL 60208, USA  T. Eftekhari NHFP Einstein Fellow  Center
for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and
Department of Physics and Astronomy, Northwestern University, Evanston, IL
60208, USA  W. Fong Center for Interdisciplinary Exploration and Research in
Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern
University, Evanston, IL 60208, USA  S. Bhandari ASTRON, Netherlands Institute
for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The
Netherlands  Joint Institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD,
Dwingeloo, The Netherlands  Anton Pannekoek Institute for Astronomy,
University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands
CSIRO, Space and Astronomy, PO Box 76, Epping, NSW 1710, Australia  E. Berger
Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden St. Cambridge, MA
02138, USA  O.S. Ould-Boukattine ASTRON, Netherlands Institute for Radio
Astronomy, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands  Anton
Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904,
1098 XH, Amsterdam, The Netherlands  J.W.T. Hessels ASTRON, Netherlands
Institute for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The
Netherlands  Anton Pannekoek Institute for Astronomy, University of Amsterdam,
Science Park 904, 1098 XH, Amsterdam, The Netherlands  N. Sridhar Department
of Astronomy and Columbia Astrophysics Laboratory, Columbia University, New
York, NY 10027, USA  Theoretical High Energy Astrophysics (THEA) Group,
Columbia University, New York, New York 10027, USA  Cahill Center for
Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA
91106, USA  A. Reines eXtreme Gravity Institute, Department of Physics,
Montana State University, Bozeman, MT 59717, USA  B. Margalit School of
Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455,
USA  J. Darling Center for Astrophysics and Space Astronomy, Department of
Astrophysical and Planetary Sciences, University of Colorado, 389 UCB,
Boulder, CO 80309-0389, USA  A. C. Gordon Center for Interdisciplinary
Exploration and Research in Astrophysics (CIERA) and Department of Physics and
Astronomy, Northwestern University, Evanston, IL 60208, USA  J.E. Greene
Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08544, USA  C. D. Kilpatrick Center for Interdisciplinary Exploration and
Research in Astrophysics (CIERA) and Department of Physics and Astronomy,
Northwestern University, Evanston, IL 60208, USA  B. Marcote Joint Institute
for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD, Dwingeloo, The Netherlands  B.
D. Metzger Department of Physics and Columbia Astrophysics Laboratory,
Columbia University, New York, NY 10027, USA  Theoretical High Energy
Astrophysics (THEA) Group, Columbia University, New York, New York 10027, USA
Center for Computational Astrophysics, Flatiron Institute, 162 W. 5th Avenue,
New York, NY 10011, USA  K. Nimmo MIT Kavli Institute for Astrophysics and
Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139  A.
E. Nugent Center for Interdisciplinary Exploration and Research in
Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern
University, Evanston, IL 60208, USA  Z. Paragi Joint Institute for VLBI ERIC,
Oude Hoogeveensedijk 4, 7991 PD, Dwingeloo, The Netherlands  P.K.G. Williams
Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden St. Cambridge, MA
02138, USA

###### Abstract

We present 1 – 12 GHz Karl G. Jansky Very Large Array observations of 9 off-
nuclear persistent radio sources (PRSs) in nearby ($z\lesssim 0.055$) dwarf
galaxies, along with high-resolution European very-long baseline
interferometry (VLBI) Network (EVN) observations for one of them at 1.7 GHz.
We explore the plausibility that these PRSs are associated with fast radio
burst (FRB) sources by examining their properties — physical sizes, host-
normalized offsets, spectral energy distributions (SEDs), radio luminosities,
and light curves — and compare them to those of the PRSs associated with FRBs
20121102A and 20190520B, two known active galactic nuclei (AGN), and one
likely AGN in our sample with comparable data, as well as other radio
transients exhibiting characteristics analogous to FRB-PRSs. We identify a
single source in our sample, J1136$+$2643, as the most promising FRB-PRS,
based on its compact physical size and host-normalized offset. We further
identify two sources, J0019$+$1507 and J0909$+$5955, with physical sizes
comparable to FRB-PRSs, but which exhibit large offsets and flat spectral
indices potentially indicative of a background AGN origin. We test the
viability of neutron star wind nebulae and hypernebulae models for
J1136$+$2643, and find that the physical size, luminosity, and SED of
J1136$+$2643 are broadly consistent with these models. Finally, we discuss the
alternative interpretation that the radio sources are instead powered by
accreting massive black holes and outline future prospects and follow-up
observations for differentiating between these scenarios.

††software: AIPS (Greisen, 2003), Astropy (Astropy Collaboration et al., 2013,
2018, 2022), CASA (McMullin et al., 2007; CASA Team et al., 2022), DIFMAP
(Shepherd et al., 1994), GALFIT (Peng et al., 2002, 2010), Heimdall,
Matplotlib (Hunter, 2007), Numpy (Harris et al., 2020), PHOTUTILS (Bradley et
al., 2021), SAOImage DS9 (Joye & Mandel, 2003), SciPy (Virtanen et al.,
2020)††facilities: VLA, EVN, Keck (DEIMOS), MMT (Binospec)

##  1 Introduction

The extragalactic radio sky is primarily composed of galaxies powered by
recent star formation and active galactic nuclei (AGN; Condon et al. 2012). At
low flux densities, the abundance of faint radio sources is dominated by
ongoing star formation in spiral and irregular galaxies (Condon, 1992;
Padovani, 2016), while radio-emitting AGN powering relativistic jets in
elliptical galaxies become prominent at higher flux densities (Condon et al.,
2012; Magliocchetti, 2022). However, recent investigations into extragalactic
radio sources over the past decade have unveiled a distinct, third population
of compact, persistent radio sources (PRSs) that preferentially reside in
dwarf host galaxy environments.

First coined in association with fast radio bursts (FRBs; Law et al. 2022),
the PRS population is variegated into two sub-classes: one related to
intermediate mass (100 M⊙ – 10${}^{5}M_{\odot}$) black holes (IMBHs; Maccarone
2004; Greene et al. 2020) and the other linked to FRBs and other transient
phenomena. In the context of IMBHs, numerous studies have relied on
multiwavelength accretion signatures to gain demographic statistics on IMBHs,
leading to the identification of hundreds of AGN candidates in dwarf galaxies
(Barth et al., 2008; Reines et al., 2013; Moran et al., 2014; Sartori et al.,
2015; Baldassare et al., 2020), with some appearing as off-nuclear wanderers
(Mezcua & Domínguez Sánchez, 2020; Reines et al., 2020). Among those AGN
candidates identified in dwarf galaxies, some exhibit radio emission and
appear as compact radio sources. However, it remains challenging to firmly
establish the presence of such IMBHs, as they cannot be easily distinguished
from background interlopers and thus require follow-up observations at other
wavelengths.

At the same time, a subset of the PRS population has been associated with
transient phenomena. Indeed, two luminous compact PRSs have been unambiguously
associated to FRBs in dwarf galaxies: FRBs 20121102A and 20190520B (Chatterjee
et al., 2017; Niu et al., 2022). FRBs are luminous, millisecond-duration
pulses of coherent radio emission whose origin is still broadly debated
despite hundreds of sources identified thus far (Lorimer et al., 2007;
Bannister et al., 2017; Law et al., 2018b; CHIME/FRB Collaboration et al.,
2021; Petroff et al., 2022; Zhang, 2023). The presence of PRSs associated with
two FRBs have provided some of the most stringent constraints on their
progenitors to date. As demonstrated by the variable Faraday rotation measure
(RM) of the bursts, they also reside in turbulent magneto-ionic environments
(Michilli et al., 2018; Anna-Thomas et al., 2023). In both cases, the radio
counterparts have been interpreted as emission from nebulae surrounding a
central engine such as a magnetar (Yang et al., 2016; Beloborodov, 2017;
Margalit & Metzger, 2018; Li et al., 2020) or an accreting compact object
(Sridhar & Metzger, 2022; Sridhar et al., 2024).

Following the identification of the FRB-PRS class, a population of slowly
evolving radio sources in dwarf galaxies were discovered, including the
decades-long radio transient FIRST J141918.9$+$394036 (hereafter J1419$+$3940)
which has been postulated as an orphan long $\gamma$-ray burst (LGRB)
afterglow (Law et al., 2018a; Marcote et al., 2019); the superluminous
supernova (SLSN) PTF10hgi (Eftekhari et al., 2019), whose PRS was identified
nearly a decade post-explosion; and the pulsar wind nebula (PWN) candidate
J113706.19$-$033737.3 (hereafter VT 1137$-$0337; Dong & Hallinan 2023).
Together, these discoveries exemplify the rich diversity of extragalactic
radio sources within dwarf galaxies.

PRS discovery methods have thus far been largely heterogeneous, ranging from
targeted searches for radio emission from the locations of known transients
(Ofek, 2017; Eftekhari et al., 2019; Law et al., 2019) to systematic searches
in nearby dwarf galaxies (Reines et al., 2020; Vohl et al., 2023). Recently,
Reines et al. (2020) presented a sample of 19 PRSs discovered in dwarf
galaxies and offset from their galactic centers. They rule out star-forming H
II regions, supernova remnants (SNRs), and radio supernovae (SNe) as the
origin of the radio emission, and instead conclude that these PRSs represent a
population of off-nuclear accreting IMBHs. Conversely, Eftekhari et al. (2020)
argued for an alternative interpretation in which these sources are instead
analogs to PRSs associated with FRBs, as evidenced by the shared similarities
in the observed radio properties with the PRS coincident with FRB 20121102A
(i.e., PRS 20121102A). Studies like Reines et al. (2020) take advantage of the
shared dwarf host galaxy environments of PRSs as a criterion for systematic
PRS discovery, as opposed to relying on serendipitous transient discovery.
Here, we further explore the possibility that these radio sources share the
same origin as FRB-PRSs using multi-frequency radio observations obtained with
the Karl G. Jansky Very Large Array (VLA) and the European very-long baseline
interferometry (VLBI) Network (EVN).

The paper is organized as follows. We present our sample of radio sources in
Section 2 and report a compilation of VLA, EVN, and archival radio
observations in Section 3. In Section 4, we present the properties of the
sources, including their physical sizes, host-normalized offsets, spectral
energy distributions (SEDs), and light curves, and compare them to those of
PRSs 20121102A and 20190520B along with radio transients J1419$+$3940,
PTF10ghi, and VT 1137$-$0337\. Based on these properties, we identify a single
source, J1136$+$2643, as the most compelling FRB-PRS candidate. In Section 5,
we test the viability of our FRB-PRS candidate in the context of FRB
progenitor models. Finally, in Section 6, we consider the alternative
interpretation that the radio sources are instead powered by AGN, and
summarize our conclusions in Section 7. Throughout the paper, we adopt the
Planck cosmological parameters for a flat $\Lambda$CDM universe, with $H_{0}$
= 67.66 km s-1 Mpc-1, $\Omega_{m}=0.310$, and $\Omega_{\lambda}=0.690$ (Planck
Collaboration et al., 2020) for luminosity and physical size calculations.

Table 1: VLA and EVN Observations of the Persistent Radio Sources

Source | ID† | Telescope | Date | Flux Calibrator | Phase Calibrator | Fringefinder | tint
---|---|---|---|---|---|---|---
|  |  | (mm/dd/yyyy) |  |  |  | (minutes)
J0019$+$1507 | 2 | VLA-BnA | 11/24/2020 | 3C48 | J0010+1724 | $\ldots$ | 12.40
|  | EVN | 04/13/2021 | $\ldots$ | J1028+0255 | J0237+2848 | 194.6
J0106$+$0046 | 6 | VLA-BnA | 11/24/2020 | 3C48 | J0125$-$0005 | $\ldots$ | 12.47
J0903$+$4824 | 25 | VLA-BnA | 11/25/2020 | 3C147 | J0920$+$4441 | $\ldots$ | 13.07
J0909$+$5655 | 28 | VLA-BnA | 11/25/2020 | 3C147 | J0921+6215 | $\ldots$ | 12.47
J0931$+$5633 | 33 | VLA-BnA | 11/25/2020 | 3C147 | J0921+6215 | $\ldots$ | 12.40
J1027$+$0112 | 48 | VLA-BnA | 11/25/2020 | 3C147 | J1024$-$0052 | $\ldots$ | 11.80
|  | EVN | 04/13/2021 | $\ldots$ | J0010+1724 | J0237+2848 | 196.0
J1136$+$1252 | 64 | VLA-BnA | 11/25/2020 | 3C286 | J1120+1420 | $\ldots$ | 13.60
|  | EVN | 06/22/2021 | $\ldots$ | J1132+1023 | J1058+0133 | 168.34
J1136$+$2643 | 65 | VLA-BnA | 11/25/2020 | 3C286 | J1125+2610 | $\ldots$ | 10.90
J1200$-$0341 | 77 | VLA-BnA | 11/25/2020 | 3C286 | J1150$-$0023 | $\ldots$ | 12.40
J1220$+$3020 | 82 | VLA-BnA | 11/25/2020 | 3C286 | J1221+2813 | $\ldots$ | 11.53
J1226$+$0815 | 83 | VLA-BnA | 11/25/2020 | 3C286 | J1239+0730 | $\ldots$ | 11.77
J1253$-$0312 | 92 | VLA-BnA | 11/25/2020 | 3C286 | J1246$-$0730 | $\ldots$ | 11.77

Note. — † Galaxy identification number as assigned in Reines et al. (2020).

##  2 Sample of Compact Radio Sources

We derive our sample from a catalogue of compact radio sources initially
discovered by Reines et al. (2020) using the VLA. In particular, they
identified a sample of 19 compact radio sources that exhibited the strongest
evidence for accreting wandering IMBHs while also being inconsistent with a
star formation origin. We aim to leverage the similarities between the known
PRSs and the compact radio sources found in dwarf galaxies, some of which
demonstrate spatial offsets from their host centers akin to the PRSs.
Motivated by the dwarf host environment of PRSs, we only consider 13 of the
initial 19 that were in bona fide (M∗ $\lesssim$ 3 $\times$ 109 M⊙) dwarf
galaxies with robust redshifts (“Sample A” in Reines et al. 2020). However, as
discussed in Reines et al. (2020) and Eftekhari et al. (2020), only one out of
the 13 dwarf galaxies, J0906+5610, is securely in the AGN region on the
Baldwin-Phillips-Terlevich (BPT) diagram (Baldwin et al., 1981) and was
previously identified as a broad-line AGN (Reines et al., 2013). We therefore
exclude J0906$+$5610 as a potential FRB-PRS candidate in this work. The rest
of the sample falls in the region occupied by star-forming galaxies.

More recently, among the parent sample of 13 radio sources in dwarf galaxies,
J1220$+$3020 and J1136$+$1252 have been confirmed as AGN based on
spectroscopic data. In particular, J1220$+$3020 shows the presence of coronal
line [Fe X] and enhanced [O I] emission (Molina et al., 2021), while
J1136$+$1252 is associated with an optical counterpart in deep Hubble Space
Telescope (HST) imaging at a spectroscopic redshift of $z=0.76$ (Sturm et al.
2024, in prep.), pointing to a background quasar origin. Nevertheless, we
include them in our analysis as they provide useful comparisons by
representing the known AGN in our sample. Lastly, archival optical imaging
reveals a red optical counterpart at the position of J1027$+$0112, hinting at
a possible background AGN origin (Section 3.5).

Our final sample therefore includes 9 radio sources excluding the two
confirmed AGN and one likely AGN. In the following sections, we refer to all 9
sources as PRSs and explore them as potential FRB-PRSs. To constrain the size
of the sources in our sample down to sub-arcsecond scales, we separately
construct a subset of three targets for follow-up with the EVN. We expand upon
the details of this sub-sample in Section 3.2.

##  3 Observations

###  3.1 VLA Continuum Observations

We observed our sample of 12 radio sources with the VLA under program 20B-228
(PI: T. Eftekhari) in the hybrid BnA configuration. The sample was grouped
into three scheduling blocks ranging between $\sim$ 1–2 hours each, with on-
source integration times of $\approx$ 11–14 min per source. The observations
were taken between 2020 November 24 and 25 UTC in four frequency bands
centered at 1.5 (L-band), 3.0 (S-band), 6.0 (C-band), and 10.0 GHz (X-band).
At the higher frequencies (4$-$12 GHz), we utilized the 3-bit samplers which
provide the full 4 GHz of bandwidth across the observing band. At the lower
frequencies, we employed the 8-bit samplers to achieve 1 and 2 GHz of
bandwidth at L- and S-band, respectively.

We processed the data using the standard VLA pipeline (version 2022.2.0.64) as
part of the Common Astronomy Software Applications (CASA; McMullin et al.
2007; van Bemmel et al. 2022) software package. We performed bandpass and flux
density calibration using 3C48, 3C147, and 3C286 in each scheduling block,
respectively. Details of the observations, including complex gain calibrators
for individual sources and on-source integration times are listed in Table 1.
We split the calibrated data in each frequency band into two subbands and
imaged each subband separately using CASA’s tclean task out to the first null
of the primary beam. We set a pixel scale of 0.43, 0.22, 0.11, and
0.07″pixel-1 at 1.5, 3, 6, and 10 GHz, respectively. We performed
deconvolution using standard gridders, a Briggs visibility weighting scheme
with a robust parameter of 0, and multi-term multi-frequency synthesis (MTMFS;
Rau & Cornwell 2011) with two Taylor terms.

We extracted the flux densities at the source positions and image root-mean-
square (rms) values using the imtool task as part of the pwkit package
(Williams et al., 2017). We also applied an additional 5$\%$ error to the
measured uncertainties to account for the accuracy of the absolute flux
calibration scale of the VLA (Perley & Butler, 2017). We detect unresolved
radio emission at the positions of all the sources in our sample with the
exception of J0903+4824, which appears to be resolved into two components. A
summary of our VLA observations is given in Table 2.

Figure 1: EVN-detected source J0019$+$1507 at 1.7 GHz with contour lines
depicting rms levels starting from $3.5\sigma$, where $\sigma$ is 50 $\upmu$Jy
beam-1. A small bar in the top-right of the image shows the physical scale
assuming that the sources are at the same redshift of the associated dwarf
galaxy. The synthesized beam of size 6 mas $\times$ 5 mas is represented by
the grey ellipse in the lower left corner.

###  3.2 EVN VLBI Observations

We observed three sources from our sample with the EVN, including e-MERLIN
stations. Sources J0019$+$1507 and J1027$+$0112 were observed on 2021 April 13
UTC (EO018A, PI: O. Ould-Boukattine), and source J1136$+$1252 was observed on
2021 June 22 UTC (EO018B, PI: O. Ould-Boukattine). The sample was chosen to be
unresolved by the VLA, have a minimum flux density of 2.5 mJy at 9 GHz and a
relatively flat spectral index. In addition, they exhibit relatively small
physical offset from the center of their host galaxies. The observations
included regular EVN stations.111Full list of EVN stations: Mark II Jodrell
Bank (Jb), Westerbork single dish (Wb, RT1), Effelsberg (Ef), Medicina (Mc),
Onsala (O8), Tianma (T6), Toruń (Tr), Hartebeesthoek (Hf), Svetloe (Sv),
Zelenchukskaya (Zc), Badary (Bd), Irbene (Ir), Sardinia (Sr) and e-MERLIN
stations: Cambridge (Cm), Darnhall (Da), Knockin (Kn) and Pickmere (Pi). Of
these, the Russian stations (Sv, Zc and Bd), Sr and Cm did not participate in
the second session. At the time of observation, the likely background AGN
J1027+0112 and the confirmed background AGN J1136$+$1252 were still considered
FRB-PRS candidates with unknown origins. All of our observations were
conducted at 1.7 GHz (L-band) with $4\times 32$ MHz sub-bands. Details of the
observations, including fringe finder and phase calibrator sources as well as
on-source integration times are listed in Table 1.

We correlated the interferometric data using the software correlator SFXC
(Keimpema et al., 2015) at the Joint Institute for VLBI ERIC (JIVE), with an
integration time of 2s and 128 channels per 32 MHz subband. We calibrated the
data following standard procedures in AIPS (Greisen, 2003) and CASA (McMullin
et al., 2007; van Bemmel et al., 2022). Using the FITLD task, we loaded the
correlated visibilities in FITS-IDI format into AIPS and applied the a-priori
amplitude calibration and a-priori flagging table from the table generated by
the EVN AIPS pipeline and used VLBATECR in AIPS to correct for ionospheric
dispersive delays. We then performed the rest of the calibration in CASA
following the steps described in Bhandari et al. (2023a).

We imaged all three targets using Difmap (Shepherd et al., 1994). Source
J0019$+$1507 along with the background sources, J1027$+$0112 and J1136$+$1252,
were all detected in our EVN observations. Figure 1 shows the continuum image
of J0019$+$1507 at 1.7 GHz (see the Appendix for EVN images of sources
J1027$+$0112 and J1136$+$1252). We constrained the apparent angular sizes and
measured the flux densities of all three sources in Difmap by
$\chi^{2}$–fitting of a circular Gaussian model in the $uv$-plane using
modelfit. The flux densities of the sources are presented in Table 2. We note
that the uncertainty on the flux density is the quadrature sum of the rms
noise and 15% of the absolute flux error, which is typical for VLBI
observations.

Table 2: Radio Observation Catalog  Source | R.A. | Decl. | Frequency | Beam Size | Beam Angle | RMS | Flux Density
---|---|---|---|---|---|---|---
| (J2000) | (J2000) | (GHz) | (arcsec2) | (deg) | ($\upmu$Jy/beam) | (mJy)
J0019$+$1507 | 00h18m59.985s | $+15^{\circ}07^{\prime}11.02^{\prime\prime}$ | 1.3 | 4.04 $\times$ 1.24 |  $-$80.36 | 42 | 2.19 $\pm$ 0.13
|  |  | 1.7 | 0.006$\times$0.005 |  $-$78.85 | 50 | 1.30 $\pm$ 0.20
|  |  | 1.8 | 2.73 $\times$ 0.93 |  $-$82.03 | 54 | 2.00 $\pm$ 0.13
|  |  | 2.6 | 2.13 $\times$ 0.62 |  $-$80.32 | 40 | 2.24 $\pm$ 0.13
|  |  | 3.4 | 1.78 $\times$ 0.46 |  $-$79.50 | 35 | 2.23 $\pm$ 0.12
|  |  | 5 | 1.08 $\times$ 0.32 |  $-$81.05 | 38 | 2.08 $\pm$ 0.12
|  |  | 7 | 0.78 $\times$ 0.22 |  $-$81.38 | 40 | 2.13 $\pm$ 0.12
|  |  | 9 | 0.70 $\times$ 0.16 |  $-$81.87 | 38 | 2.06 $\pm$ 0.11
|  |  | 11 | 0.52 $\times$ 0.14 |  $-$82.65 | 30 | 2.00 $\pm$ 0.11
J0106$+$0046 | 01h06m07.308s | $+00^{\circ}46^{\prime}34.320^{\prime\prime}$ | 1.3 | 5.97 $\times$ 1.18 |  $-$69.56 | 66 | 1.91 $\pm$ 0.13
|  |  | 1.8 | 4.37 $\times$ 0.90 |  $-$71.54 | 66 | 1.48 $\pm$ 0.12
|  |  | 2.6 | 3.00 $\times$ 0.65 |  $-$70.63 | 38 | 0.96 $\pm$ 0.07
|  |  | 3.4 | 2.13 $\times$ 0.52 |  $-$70.45 | 37 | 0.85 $\pm$ 0.07
|  |  | 5 | 1.48 $\times$ 0.34 |  $-$71.01 | 37 | 0.59 $\pm$ 0.06
|  |  | 7 | 1.14 $\times$ 0.22 |  $-$74.21 | 21 | 0.45 $\pm$ 0.04
|  |  | 9 | 0.86 $\times$ 0.19 |  $-$73.98 | 24 | 0.28 $\pm$ 0.04
|  |  | 11 | 0.75 $\times$ 0.14 |  $-$74.92 | 30 | 0.24 $\pm$ 0.04
J0903$+$4824 | 09h03m12.967s | $+48^{\circ}24^{\prime}13.716^{\prime\prime}$ | 1.3 | 1.94 $\times$ 1.16 |  $-$65.49 | 377 | 6.51 $\pm$ 0.62
|  |  | 1.8 | 1.40 $\times$ 0.84 |  $-$66.80 | 415 | 4.18 $\pm$ 0.62
|  |  | 2.6 | 0.98 $\times$ 0.60 |  $-$66.00 | 245 | 2.48 $\pm$ 0.37
|  |  | 3.4 | 0.75 $\times$ 0.46 |  $-$65.96 | 148 | 1.79 $\pm$ 0.23
|  |  | 5 | 0.52 $\times$ 0.32 |  $-$60.08 | 79 | 1.46 $\pm$ 0.16
|  |  | 7 | 0.53 $\times$ 0.23 | 87.09 | 19 | 0.99 $\pm$ 0.06
|  |  | 9 | 0.29 $\times$ 0.17 |  $-$68.23 | 39 | 0.76 $\pm$ 0.09
|  |  | 11 | 0.23 $\times$ 0.14 |  $-$69.41 | 19 | 0.68 $\pm$ 0.06
J0909$+$5655 | 09h09m08.689s | $+56^{\circ}55^{\prime}19.750^{\prime\prime}$ | 1.3 | 2.00 $\times$ 1.19 |  $-$60.16 | 56 | 1.53 $\pm$ 0.11
|  |  | 1.8 | 1.43 $\times$ 0.87 |  $-$60.35 | 58 | 1.37 $\pm$ 0.11
|  |  | 2.6 | 1.00 $\times$ 0.62 |  $-$65.65 | 31 | 1.32 $\pm$ 0.08
|  |  | 3.4 | 0.76 $\times$ 0.48 |  $-$64.39 | 33 | 1.29 $\pm$ 0.08
|  |  | 5 | 0.54 $\times$ 0.33 |  $-$64.79 | 34 | 1.09 $\pm$ 0.07
|  |  | 7 | 0.74 $\times$ 0.23 | 76.50 | 19 | 0.91 $\pm$ 0.05
|  |  | 9 | 0.30 $\times$ 0.17 |  $-$65.11 | 19 | 0.73 $\pm$ 0.05
|  |  | 11 | 0.24 $\times$ 0.15 |  $-$71.81 | 22 | 0.65 $\pm$ 0.04
J0931$+$5633 | 09h31m38.419s | $+56^{\circ}33^{\prime}19.872^{\prime\prime}$ | 1.3 | 2.01 $\times$ 1.20 |  $-$60.15 | 65 | 9.37 $\pm$ 0.48
|  |  | 1.8 | 1.44 $\times$ 0.87 |  $-$60.22 | 54 | 7.70 $\pm$ 0.39
|  |  | 2.6 | 1.05 $\times$ 0.59 |  $-$59.62 | 51 | 5.84 $\pm$ 0.30
|  |  | 3.4 | 0.80 $\times$ 0.46 |  $-$58.73 | 40 | 4.90 $\pm$ 0.25
|  |  | 5 | 0.53 $\times$ 0.33 |  $-$64.34 | 97 | 3.63 $\pm$ 0.23
|  |  | 7 | 0.74 $\times$ 0.23 | 77.24 | 31 | 2.75 $\pm$ 0.14
|  |  | 9 | 0.29 $\times$ 0.17 |  $-$64.94 | 27 | 2.17 $\pm$ 0.11
|  |  | 11 | 0.24 $\times$ 0.15 |  $-$71.22 | 21 | 1.88 $\pm$ 0.10
J1027$+$0112 | 10h27m41.378s | $+01^{\circ}12^{\prime}06.444^{\prime\prime}$ | 1.3 | 3.75 $\times$ 1.40 | 81.13 | 119 | 4.38 $\pm$ 0.28
|  |  | 1.7 | 0.006$\times$0.004 | 21.93 | 62 | 2.80 $\pm$ 0.40
|  |  | 1.8 | 2.9 $\times$ 0.95 | 84.12 | 70 | 3.94 $\pm$ 0.22
|  |  | 2.6 | 2.08 $\times$ 0.69 | 84.13 | 65 | 3.23 $\pm$ 0.19
|  |  | 3.4 | 1.77 $\times$ 0.54 | 82.66 | 43 | 3.46 $\pm$ 0.18
|  |  | 5 | 1.03 $\times$ 0.38 | 74.97 | 29 | 3.16 $\pm$ 0.16
|  |  | 7 | 0.98 $\times$ 0.24 | 80.25 | 22 | 3.07 $\pm$ 0.16
|  |  | 9 | 0.57 $\times$ 0.20 | 78.41 | 25 | 2.88 $\pm$ 0.15
|  |  | 11 | 0.50 $\times$ 0.15 | 82.75 | 28 | 2.72 $\pm$ 0.14
J1136$+$1252 | 11h36m48.526s | $+12^{\circ}52^{\prime}39.900^{\prime\prime}$ | 1.3 | 8.15 $\times$ 1.27 | 58.25 | 77 | 2.78 $\pm$ 0.18
|  |  | 1.7 | 0.022 $\times$ 0.005 | 80.10 | 65 | 1.60 $\pm$ 0.30
|  |  | 1.8 | 5.58 $\times$ 0.82 | 59.08 | 76 | 2.48 $\pm$ 0.16
|  |  | 2.6 | 3.74 $\times$ 0.71 | 57.37 | 51 | 2.48 $\pm$ 0.14
|  |  | 3.4 | 2.68 $\times$ 0.47 | 59.50 | 49 | 2.62 $\pm$ 0.14
|  |  | 5 | 2.22 $\times$ 0.34 | 59.02 | 34 | 3.00 $\pm$ 0.16
|  |  | 7 | 1.56 $\times$ 0.25 | 57.91 | 41 | 3.16 $\pm$ 0.17
|  |  | 9 | 0.56 $\times$ 0.23 |  $-$88.97 | 103 | 3.12 $\pm$ 0.21
|  |  | 11 | 0.46 $\times$ 0.18 |  $-$89.03 | 121 | 3.19 $\pm$ 0.23
J1136$+$2643 | 11h36m42.576s | $+26^{\circ}43^{\prime}35.652^{\prime\prime}$ | 1.3 | 7.19 $\times$ 1.35 | 55.80 | 79 | 1.33 $\pm$ 0.13
|  |  | 1.8 | 4.77 $\times$ 0.87 | 57.30 | 67 | 1.64 $\pm$ 0.13
|  |  | 2.6 | 3.44 $\times$ 0.70 | 56.78 | 43 | 1.99 $\pm$ 0.12
|  |  | 3.4 | 2.36 $\times$ 0.49 | 57.25 | 36 | 1.88 $\pm$ 0.11
|  |  | 5 | 0.87 $\times$ 0.32 | 74.83 | 26 | 1.48 $\pm$ 0.08
|  |  | 7 | 1.38 $\times$ 0.24 | 56.56 | 27 | 0.95 $\pm$ 0.06
|  |  | 9 | 1.14 $\times$ 0.20 | 55.92 | 22 | 0.63 $\pm$ 0.04
|  |  | 11 | 0.97 $\times$ 0.15 | 56.43 | 26 | 0.48 $\pm$ 0.04
J1200$-$0341 | 12h00m58.301s | $-03^{\circ}41^{\prime}18.456^{\prime\prime}$ | 1.3 | 4.25 $\times$ 1.44 | 64.98 | 82 | 4.67 $\pm$ 0.26
|  |  | 1.8 | 7.61 $\times$ 0.94 | 55.92 | 91 | 3.93 $\pm$ 0.23
|  |  | 2.6 | 5.42 $\times$ 0.68 | 56.10 | 49 | 3.41 $\pm$ 0.18
|  |  | 3.4 | 3.86 $\times$ 0.49 | 56.10 | 38 | 2.92 $\pm$ 0.16
|  |  | 5 | 3.06 $\times$ 0.35 | 55.98 | 31 | 2.25 $\pm$ 0.12
|  |  | 7 | 0.79 $\times$ 0.25 | 66.19 | 34 | 1.84 $\pm$ 0.10
|  |  | 9 | 2.06 $\times$ 0.20 | 55.12 | 30 | 1.65 $\pm$ 0.09
|  |  | 11 | 1.67 $\times$ 0.16 | 56.25 | 30 | 1.43 $\pm$ 0.08
J1220$+$3020 | 12h20m11.266s | $+30^{\circ}20^{\prime}08.304^{\prime\prime}$ | 1.3 | 6.56 $\times$ 1.39 | 56.45 | 75 | 0.90 $\pm$ 0.11
|  |  | 1.8 | 4.27 $\times$ 0.90 | 56.97 | 71 | 0.95 $\pm$ 0.11
|  |  | 2.6 | 3.07 $\times$ 0.69 | 57.65 | 48 | 0.82 $\pm$ 0.08
|  |  | 3.4 | 2.21 $\times$ 0.50 | 56.99 | 36 | 0.72 $\pm$ 0.06
|  |  | 5 | 1.78 $\times$ 0.37 | 56.19 | 30 | 0.59 $\pm$ 0.05
|  |  | 7 | 1.30 $\times$ 0.24 | 55.64 | 24 | 0.46 $\pm$ 0.04
|  |  | 9 | 0.46 $\times$ 0.17 | 75.97 | 22 | 0.41 $\pm$ 0.04
|  |  | 11 | 0.90 $\times$ 0.16 | 56.41 | 26 | 0.28 $\pm$ 0.04
J1226$+$0815 | 12h26m03.643s | $+08^{\circ}15^{\prime}19.008^{\prime\prime}$ | 1.3 | 4.02 $\times$ 1.25 | 70.63 | 66 | 1.22 $\pm$ 0.11
|  |  | 1.8 | 7.04 $\times$ 0.82 | 57.41 | 69 | 1.14 $\pm$ 0.11
|  |  | 2.6 | 4.68 $\times$ 0.67 | 57.98 | 47 | 0.93 $\pm$ 0.08
|  |  | 3.4 | 3.53 $\times$ 0.48 | 58.85 | 40 | 0.80 $\pm$ 0.07
|  |  | 5 | 2.76 $\times$ 0.35 | 56.70 | 30 | 0.65 $\pm$ 0.05
|  |  | 7 | 2.29 $\times$ 0.23 | 56.54 | 28 | 0.47 $\pm$ 0.05
|  |  | 9 | 0.62 $\times$ 0.19 | 68.93 | 26 | 0.43 $\pm$ 0.04
|  |  | 11 | 1.55 $\times$ 0.16 | 56.53 | 28 | 0.33 $\pm$ 0.04
J1253$-$0312 | 12h53m05.969s | $-03^{\circ}12^{\prime}58.752^{\prime\prime}$ | 1.3 | 4.53 $\times$ 1.45 | 64.51 | 200 | 3.26 $\pm$ 0.26
|  |  | 1.8 | 8.57 $\times$ 0.92 | 56.86 | 127 | 2.91 $\pm$ 0.19
|  |  | 2.6 | 5.55 $\times$ 0.68 | 55.85 | 110 | 2.56 $\pm$ 0.17
|  |  | 3.4 | 4.15 $\times$ 0.48 | 56.51 | 102 | 2.24 $\pm$ 0.15
|  |  | 5 | 3.32 $\times$ 0.36 | 55.78 | 68 | 1.80 $\pm$ 0.11
|  |  | 7 | 0.84 $\times$ 0.25 | 64.30 | 94 | 1.31 $\pm$ 0.11
|  |  | 9 | 2.06 $\times$ 0.19 | 55.29 | 61 | 1.05 $\pm$ 0.08
|  |  | 11 | 1.84 $\times$ 0.16 | 55.63 | 57 | 0.95 $\pm$ 0.07

###  3.3 Additional Archival Data

In conjunction with our VLA and EVN observations, we searched the positions of
all sources in our sample in the LOFAR Two-metre Sky Survey (LoTSS) Data
Release 2 (DR2), which consists of over 4 million radio sources at a central
frequency of 144 MHz (Shimwell et al., 2022). The LoTSS DR2 observations cover
27$\%$ of the Northern sky with an angular resolution of $\sim$ 6″ and a
median rms sensitivity of $\sim$ 80 $\upmu$Jy/beam. We found three out of 12
of our targets were located within the LoTSS footprint: J0903+4824,
J0909+5655, and J0931+5633, with integrated flux densities of 36.4 $\pm$ 0.4
mJy, 2.2 $\pm$ 0.1 mJy, and 9.3 $\pm$ 0.3 mJy, respectively. The positions of
the remaining nine sources were not covered by LoTSS.

In addition, we included all detections from Epochs 1 through 3 of the the VLA
Sky Survey (VLASS; Lacy et al. 2020) at 3 GHz for each source. VLASS offers an
angular resolution of 2.5″ and a sensitivity of $\approx$ 120 $\upmu$Jy rms
per epoch. We extracted the flux densities at the source positions from the
Quick Look image products, and applied corrections of 10$\%$ and 3$\%$ to the
flux uncertainties in the first and subsequent epochs, respectively, to
account for a systematic inaccuracy for sources below $\approx$ 1 Jy (Lacy et
al., 2019). The uncertainties on the flux densities reflect the quadrature
sums of the flux error and the systematic error, as described above.

Lastly, we included data from FIRST (Becker et al., 1995), the NRAO VLA Sky
Survey (NVSS; Condon et al. 1998), and archival VLA observations, including
upper limits and detections, for J0106$+$0046, J1136$+$2643, J1200$-$0341, and
J1220$+$3020, as originally compiled in Eftekhari et al. (2020). For the flux
uncertainties, we adopt the rms values reported in the FIRST catalog, and
include an additional 5$\%$ systematic error to account for the larger
integrated flux density errors observed in bright sources (Becker et al.,
1995). The archival observations were used in Sections 4.3 – 4.5.

###  3.4 Single-pulse Searches

In addition to standard continuum observations with the EVN, we utilized the
most sensitive telescope in the EVN array, Effelsberg, to search for FRBs in
the direction of our EVN-observed target J0019$+$1507 within the frequency
range $1.6-1.7$ GHz. Employing the custom data search pipeline detailed in
Kirsten et al. (2024), we processed raw voltages into 8-bit Stokes I
filterbank files with a time resolution of $0.128$ ms and a frequency
resolution of $62.5$ kHz. We also applied a static mask to excise channels
with known radio frequency interference (RFI).

To identify burst candidates, we applied the Heimdall222
https://sourceforge.net/projects/heimdall-astro/ search algorithm with a
signal-to-noise (S/N) threshold of $7$, searching over a broad dispersion
measure (DM) range of $10-1500$ pc cm-3. To approximate a DM value for source
J0019$+$1507, we assumed the combined Milky Way (MW) halo and host
contribution to be 100 pc cm-3 and determined the Galactic interstellar medium
(ISM) contribution to be $\approx$ 37 pc cm-3 with the NE2001 model (Cordes &
Lazio, 2002). We inferred a DM value of $\approx$ 170 pc cm-3, which is
significantly lower than the maximum of the search range. Lastly, we
classified and refined the burst candidates ($>5000$) identified by Heimdall
with a machine learning classifier, FETCH, using models A and H and a
probability threshold of $0.5$ (Agarwal et al., 2020). Additionally, we
manually inspected all Heimdall reported candidates and found them to be
either RFI or false positives.

No pulses were detected in $\approx 203$ minutes of on-source integration
time. Thus, we place an upper limit using the radiometer equation (Equation 15
in Cordes & McLaughlin 2003), with a S/N of $7$, two summed polarizations,
$\Delta\nu=128$ MHz, a nominal duration of $1$ ms for the burst width, and a
typical Effelsberg system temperature of $20$ K and gain of $1.54$ Jy
$\textrm{K}^{-1}$, yielding a fluence of $<0.18$ Jy ms.

###  3.5 Optical Imaging

As discussed in Reines et al. (2020), the dwarf galaxy population is selected
from the NASA-Sloan Atlas with available optical imaging from the Sloan
Digital Sky Survey (SDSS; Blanton et al. 2017). To ascertain the potential
presence of background interlopers among our sources, we examined the full
sample with the DESI Legacy Imaging Surveys Data Release 10 (Dey et al.,
2019). We find no apparent optical sources at the locations of our sources
except for source J1027$+$0112, which is coincident with an apparently red
point-like source with a dereddened $r$\- and $z$-band brightness of 23.96 AB
mag and 21.88 AB mag, respectively. Based on the spatial coincidence and
color, we conclude that source J1027$+$0112 is likely a background AGN
unconnected to the dwarf galaxy. We thus remove the source from our sample as
a potential FRB-PRS candidate, and instead use it as a source for comparison.

For sources J0019$+$1507 and J0909$+$5655 that are compact on milliarcsecond
(mas) scales and highly offset from their host galaxies, we obtained deep
ground-based observations with Binospec mounted on the 6.5 m MMT telescope
(2023B-UAO-G201-23B, PI: A. Nugent) and DEIMOS on the 10 m Keck telescope
(O438, PI: A. Gordon). For data reduction and stacking, we utilized the
POTPyRI software333https://github.com/CIERA-Transients/POTPyRI. We further
confirm the absence of any obvious coincident optical source in $z$-band at
the locations of sources J0019$+$1507 and J0909$+$5655.

##  4 Analysis $\&$ Results

In this section, we examine various properties of the 12 radio sources in our
sample including their physical sizes, host-normalized offsets, SEDs, spectral
luminosities, and light curves. We compare them to the known PRSs associated
with FRBs: PRS 20121102A (Chatterjee et al., 2017) and PRS 20190520B (Niu et
al., 2022) to assess the likelihood that they share a common origin. In our
comprehensive analysis, we also include additional radio transients discovered
within dwarf host galaxies including the decades-long transient J1419$+$3940
(Law et al., 2018a), the PRS associated with the SLSN PTF10hgi (Eftekhari et
al., 2019), and the PWN candidate VT 1137$-$0337 (Epoch 2; Dong & Hallinan
2023). Noteworthy for their similar host environments, these transients also
exhibit radio properties reminiscent of PRSs, hinting at a potential common
origin with the PRSs associated with FRBs. We further include a sample of
compact radio sources in nearby dwarf galaxies, as identified by Vohl et al.
(2023) with LOFAR, akin to our PRS population and those associated with an
FRB, to serve as a point of comparison. Our main aim is to assess which
sources are most plausibly associated with FRBs, and thus we refer to our
sample as “PRS candidates” unless proven otherwise.

###  4.1 Characteristics of PRSs

We first summarize the key defining characteristics of PRSs to identify
sources in our sample that share these properties. PRSs are typically compact
continuum radio sources and, thus far, only two have been identified in
association with FRBs (Chatterjee et al., 2017; Niu et al., 2022). A third PRS
was recently claimed to be associated with the active FRB 20201124A (Bruni et
al., 2023). However, the apparent offset of the PRS from the FRB location and
a lack of definitive evidence as to its compact nature makes this association
more tentative.

The compact nature of PRSs 20121102A and 20190520B was established through
high-resolution VLBI radio observations, placing constraints on their physical
sizes down to pc and sub-pc scales (Marcote et al., 2017; Bhandari et al.,
2023a). The two FRB-PRS pairs were notably discovered in dwarf host
environments (Chatterjee et al., 2017; Niu et al., 2022). PRSs 20121102A and
20190520B exhibit angular offsets from their host centers of 0.2″ and 1.3″,
respectively, indicating that they do not reside directly in their galaxy’s
cores. Moreover, Law et al. (2022) proposed a specific luminosity threshold of
Lν $>$ 1029 ergs s-1Hz-1 for PRSs based on the two known FRB-PRSs, effectively
excluding radio emission from ongoing star formation and individual SNRs which
are significantly less luminous. However, given the uncertainty of the
intrinsic luminosity function of PRSs, we do not enforce the proposed
luminosity threshold in ruling out PRS candidates. Thus, we use the following
observed properties of known FRB-PRSs as general guidelines to characterize
the sources in our sample:

  1. 1.

Compact on mas scales

  2. 2.

Projected offset from the center of the host galaxy of $<$ 2 re

where re is the half-light radius of the host galaxy. We subsequently divide
our sample into three tiers based on their observed properties. From here on,
we refer to sources that satisfy all of our above criteria as “Tier A”.
Sources in “Tier B” satisfy only the first criterion, whereas “Tier C” sources
do not satisfy the first criterion, i.e., are resolved out on mas scales.
Based on our criteria, we identify a single source in Tier A (J1136$+$2643),
two sources in Tier B (J0019$+$1507 and J0909$+$5955), and six sources in Tier
C (J0106$+$0046, J0903$+$4824, J0931$+$5933, J1200$-$0341, J1226$+$0815, and
J1253$-$0312). We note that we do not include J1027$+$0112, J1136$+$1252 and
J1220$+$3020 in our classification scheme given their classification as
confirmed or likely AGN, but we nevertheless summarize their observed
properties in the following sections as compact radio sources of known origin.

Table 3: Radio Source Comparisons

Source | z | Size | Tier | $r_{\mathrm{norm}}$ | $L_{\mathrm{3\,GHz}}$ | SED shape | $\alpha$ | $\nu_{\mathrm{b}}$ | References
---|---|---|---|---|---|---|---|---|---
|  | (pc) |  | ($r_{\mathrm{e}}$) | ($\mathrm{ergs~{}s}^{-1}~{}\mathrm{Hz}^{-1}$) |  |  | (GHz) |
PRS 20121102A | 0.1927 |  $<$0.7 |  | 0.4 | $2.3\times 10^{29}$ | BPL | [$-$0.07, $-$1.31] |  $\sim$ 9 | 1$-$4
PRS 20190520B | 0.241 |  $<$9 |  | 1.3 | $3.0\times 10^{29}$ | SPL |  $-$0.33 | $\ldots$ | 5$-$7
VT 1137$-$0337 | 0.0276 |  $<$6.1 |  | 0.8 | $2.3\times 10^{28}$ | SPL |  $-$0.35 | $\ldots$ | 8
PTF10hgi | 0.098 |  $<$2060 |  | $\ldots$ | $1.2\times 10^{28}$ | SPL |  $-$0.14 | $\ldots$ | 9
J1419$+$3940 | 0.0196 | 1.6 |  | 0.7 | $9.5\times 10^{27}$ | SPL | $\lesssim-0.65$ | $\ldots$ | 10, 11
J0019+1507 | 0.0376 |  $<$1.95 | B | 5.3 | $7.8\times 10^{28}$ | SPL |  $-$0.03 $\pm$ 0.02 | $\ldots$ | 12, This work
J0106$+$0046 | 0.0171 | [11, 87] | C | 0.6 | $6.3\times 10^{27}$ | SPL |  $-$0.92 $\pm$ 0.04 | $\ldots$ | 13, This work
J0903$+$4824 | 0.0272 | [17, 102] | C | 1.6 | $3.8\times 10^{28}$ | SPL |  $-$0.92 $\pm$ 0.01 | $\ldots$ | 13, This work
J0909$+$5655 | 0.0315 |  $<$1.33 | B | 3.0 | $3.2\times 10^{28}$ | BPL | [$-$0.18 $\pm$ 0.01, $-$0.73 $\pm$ 0.10] | 4.8 $\pm$ 0.6 | 12, 13, This work
J0931$+$5633 | 0.0494 | [30, 200] | C | 4.1 | $3.3\times 10^{29}$ | BPL | [0.0 $\pm$ 0.01, $-$0.78 $\pm$ 0.03] | 1.4 $\pm$ 0.1 | 13, This work
J1136$+$2643 | 0.0331 |  $<$1.43 | A | 1.3 | $5.3\times 10^{28}$ | BPL | [0.77 $\pm$ 0.24, $-$1.65 $\pm$ 0.19] | 3.6 $\pm$ 0.2 | 11, 13, This work
J1200$-$0341 | 0.0257 | [17, 182] | C | 1.2 | $5.1\times 10^{28}$ | SPL |  $-$0.55 $\pm$ 0.02 | $\ldots$ | 13, This work
J1226$+$0815 | 0.0241 | [16, 111] | C | 0.0 | $1.2\times 10^{28}$ | SPL |  $-$0.59 $\pm$ 0.04 | $\ldots$ | 13, This work
J1253$-$0312 | 0.0221 | [14, 102] | C | 0.1 | $2.9\times 10^{28}$ | BPL | [$-$0.35 $\pm$ 0.09, $-$0.83 $\pm$ 0.08] | 3.8 $\pm$ 0.6 | 13, This work
J1027$+$0112 | $\ldots$ | $\ldots$ | AGN(?) | $\ldots$ | $3.7\times 10^{28}$ | SPL |  $-$0.19 $\pm$ 0.03 | $\ldots$ | 13, This work
J1136$+$1252 | 0.76 |  $<$9.86 | AGN | $\ldots$ | $7.2\times 10^{31}$ | SPL | 0.12 $\pm$ 0.04 | $\ldots$ | 13, 14, This work
J1220$+$3020 | 0.0269 | [17, 101] | AGN | 0.1 | $1.4\times 10^{28}$ | SPL |  $-$0.51 $\pm$ 0.07 | $\ldots$ | 13, This work

Note. — Radio-inferred properties of our 9 PRS candidates, 2 AGN and 1 likely
AGN sources in our sample, PRSs associated with FRBs, and radio transients
VT1137$-$0337, PTF10hgi, and J1419$+$3940\. The SED shape is either a single
power law (SPL) or a broken power law (BPL). Column 1: source name. Column 2:
physical size. Column 3: classification based on criteria discussed in Section
4.1. Column 4: host-normalized offsets. Column 5: spectral luminosity at 3
GHz. Column 6: shape that best characterizes the SED. Column 7: best-fit
spectral indices. Column 8: break frequency $\nu_{b}$ (if applicable). Column
9: references. References (1) Chatterjee et al. 2017, (2) Marcote et al. 2017,
(3) Resmi et al. 2021, (4) Tendulkar et al. 2017, (5) Bhandari et al. 2023a,
(6) Niu et al. 2022, (7) Zhang et al. 2023, (8) Dong & Hallinan 2023, (9)
Eftekhari et al. 2019, (10) Law et al. 2018a, (11) Marcote et al. 2019, (12)
Sargent et al. 2022, (13) Reines et al. 2020. (14) Sturm et al. 2024, in prep.

###  4.2 Physical Sizes $\&$ Host-normalized Offsets

We take advantage of our high-resolution observations to constrain the
physical sizes of the 9 PRS candidates in our sample under the assumption that
they are at the redshifts of the dwarf galaxies. Beginning with the EVN-
detected source, J0019$+$1507 (Figure 1), we find that it is unresolved on mas
scales, with corresponding constraints on its physical size of $<$ 3.5 pc.
J0019$+$1507 is also detected with the VLBA at 9 GHz taken at a slightly
higher resolution (Sargent et al., 2022); we adopt the more constraining size
limit of $<$ 1.95 pc for this source. Two additional sources (J0909$+$5655 and
J1136$+$2643) are detected with the VLBA, with physical sizes of $<$ 1.33 pc
and $<$ 1.43 pc, respectively (Sargent et al., 2022). We therefore identify a
total of three sources in our sample (J0019+1507, J0909+5655, and
J1136$+$2643) that satisfy criteria #1 in Section 4.1 (i.e., compact on mas
scales), with physical extents of $\approx$ 1.3 – 2 pc. The physical sizes of
these sources are comparable to those of both known PRSs ($<9$ pc), the pulsar
wind nebula candidate VT 1137$-$0337 ($<6.1$ pc), and the decades-long radio
transient J1419$+$3940 (1.6 pc).

Of the remaining six sources in our sample with VLA observations, none were
observed with the EVN at 1.7 GHz, and all six were non-detections with the
VLBA (Sargent et al., 2022). For these sources, we derive both upper and lower
limits on the physical sizes of each source. Specifically, we calculate an
upper limit from the VLA A-configuration observations using the semi-major
axes of the synthesized beams (Reines et al., 2020) and a lower limit from
VLBA non-detections using the largest angular scale (LAS) of $\sim$ 30 mas at
9 GHz (Sargent et al., 2022). The larger upper limits of 87 – 200 pc can be
attributed to either the absence of high-resolution observations or an
intrinsically larger physical size. Finally, we note that J0903$+$4824 (Tier
C) is resolved in our VLA observations over 2 – 12 GHz (S-, C-, and X-bands),
consistent with previous findings (Reines et al., 2020). All derived physical
sizes are calculated assuming the radio sources are at the redshift of their
dwarf host galaxies, and are only valid under this condition.

We note that in addition to the PRSs in our sample, we also detected the
background source J1027$+$0112 and the background AGN J1136$+$1252 in our EVN
observations. J1136$+$1252 has a physical size of $<$ 9.86 pc at a redshift of
$z=0.76$ (Sturm et al. 2024, in prep.), indicating that the radio emission is
core-dominated. Interestingly, J1136$+$1252 is not detected with VLBA at 9
GHz. A potential explanation is refractive scintillation of the compact core
due to small-scale irregularities in the interstellar medium. Indeed, given
the Galactic latitude of the source, variations in the flux density of up to
60$\%$ at higher frequencies are expected (Walker, 1998). The scintillation
level may be even higher depending on the observation time, as the timescale
is modulated by the Earth’s orbit (Cordes & Rickett, 1998). We therefore
attribute the VLBA non-detection to scintillation-induced variability. The
non-detection of the AGN source J1220$+$3020 with VLBA indicates that the
radio source is effectively “resolved out”, exhibiting a physical extent
beyond the LAS of the VLBA observations. We report the source sizes of our
sample in Table 3.

Next, we consider the relative locations of these sources within their host
galaxies. For sources detected with either the EVN or VLBA, we calculate the
angular offsets from their host centers using these more precise positions.
When unavailable, we adopt the values compiled in Reines et al. (2020) using
high-resolution VLA observations in A-configuration. We find that more than
half of the sources exhibit spatial offsets of $\gtrsim$ 2″ from their host
optical centers. Among the three VLBA-detected sources, J0909$+$5655 and
J1136$+$2643 exhibit offsets $\lesssim$ 3″ from the photocenters of their host
galaxies, while J0019+1507 is offset by $>$ 4″. The large offset is consistent
with the off-nuclear locations of the FRB-PRSs (Eftekhari et al., 2020). On
the other hand, in the context of AGN (Reines et al., 2020), the large spatial
offsets may be attributable to the weaker gravitational potentials in less
massive dwarf galaxies (Shen et al., 2019), and/or high velocity kicks caused
by merging black holes.

Despite sharing similar stellar masses, the dwarf hosts in our sample exhibit
diverse galaxy morphologies and sizes (see Figure 7 in Reines et al. 2020). To
enable a fair comparison across our sample and provide a more standardized
offset measurement, we therefore compute the host-normalized offset (rnorm)
for each source, in which the angular offset is normalized by re. For the
half-light radii of the dwarf galaxies, we utilize the semi-major axes
reported NASA/IPAC Extragalactic Database
(NED)444https://ned.ipac.caltech.edu/ using an exponential light profile.

For comparison, we employ the host-normalized offsets of the two known FRB-
PRSs. For PRS 20121102A, we adopt rnorm = 0.4 re (Mannings et al., 2021). For
PRS 20190520B, we derive re for the host galaxy by modeling the archival
CFHT/MegaCam R-band imaging with Galfit (v3.0.5; Peng et al. 2002, 2010). We
first model the empirical point spread function (ePSF) of the image using the
EPSFBuilder module of photutils (v0.6; Bradley et al. 2021). Next, we
initialize Galfit with the ePSF and a single Sérsic surface brightness profile
(Sersic, 1968) at the position of the host with a fixed Sérsic index of n = 1
and position angle of $-30^{\circ}$ 555We note that due to the faintness of
the galaxy, the fit does not converge on reasonable values if we let the
Sérsic index be free., leaving all other default parameters as free. The
resulting best-fit model yields re = 0.98″, corresponding to a host-normalized
offset rnorm = 1.3 re (for an angular offset of 1.3″ ; Niu et al. 2022). We
also include in Figure 2 the host-normalized offsets for J1419$+$3940 (Law et
al., 2018a) and VT1137$-$0337 (Dong & Hallinan, 2023), where we adopt angular
offsets of 0.5 pc and 0.4 pc, respectively, and normalize them by the sizes of
their hosts as reported in NED. We exclude PTF10hgi from this analysis due to
the lack of a reported host size for this source.

Figure 2: Host-normalized offset distribution of the 9 radio sources in our
sample. Hatched bins represent sources that are confirmed as compact on mas
scales. Sources with rnorm values $\gtrsim$ 3 re are boxed in yellow as
potential background AGN. The magenta and green lines denote the the host-
normalized offsets of PRSs 20121102A and 20190520B, while the rnorm values of
J1419$+$3940 and VT1137$-$0337 are indicated by the red and orange arrows,
respectively. Based on its comparable physical size and spatial offset, we
identify J1136$+$2643, represented by the blue hatched bin, as the most
promising FRB-PRS candidate among the observed sources.

In Figure 2, we plot the host-normalized offset distribution for all 9
sources. We find a wide range of r${}_{\mathrm{norm}}\approx
0~{}$–$~{}5.3~{}\rm r_{e}$ with upper and lower bounds set by J0019$+$1507 and
J1226$+$0815, respectively, and a median of 1.3 re. Among the entire
population, J1136$+$2643 (denoted by the blue hatched bin) is the only source
that shares both a similar host-normalized offset and compact physical size
with the FRB-PRSs. Three sources (J0019$+$1507, J0909$+$5655, and
J0931$+$5633) exhibit rnorm values $\gtrsim 3~{}\rm r_{e}$, larger than those
of PRSs 20121102A and 20190520B by at least a factor of 2. Two of these highly
offset sources are confirmed as compact with VLBI as represented by the black
hatched bins in Figure 2. The large spatial offsets observed for these sources
indicate a likely background origin (Sargent et al., 2022). In contrast,
sources J0106+0046, J1200$-$0341, J1226$+$0815 and J1253$-$0312 in Tier C are
located closer to the host nucleus with rnorm values comparable to both FRB-
PRSs as well as transients J1419$+$3940 (0.7 re) and VT1137$-$0337 (0.8 re).
Finally, while the sample of compact radio sources presented by Vohl et al.
(2023) predominantly (16 out of 27 sources) exhibit an angular offset of
$\lesssim$ 2″ due to the nature of selection, their host-normalized offsets
are not available for comparison.

Based on our selection criteria as defined in Section 4.1, we therefore find
J1136$+$2643 to be the most promising analog to PRSs associated with FRBs.
Conversely, although J0019+1507 and J0909+5655 are compact on similar spatial
scales, they exhibit large host-normalized offsets and their origin as
background sources cannot be ruled out. Thus, these sources are relegated to
Tier B. Individual values for rnorm are provided in Table 3.

###  4.3 Spectral Energy Distributions

Figure 3: SEDs for the 9 PRS candidates, 2 confirmed AGN and 1 likely AGN in
our sample using flux densities from our VLA observations (1$-$12 GHz). We
also include flux densities at 144 MHz for the three sources detected in
LoTSS. Blue dashed lines correspond to power law fits with the derived
spectral indices and $1\sigma$ uncertainties listed in each panel. Yellow
shaded panels denote sources that are compact on mas scales. The confirmed and
possible AGN are highlighted in grey. The letter in the bottom right corner in
each panel indicates the tier to which each source belongs based on our
selection criteria. For comparison, we also show the SEDs of the PRSs
associated with FRB 20121102A (diamonds) and FRB 20190520B (pentagons) with an
arbitrary flux scaling. The SED of the Tier A source J1136$+$2643 exhibits a
turnover at 3.6 GHz and shape that is indicative of SSA, in agreement with its
compact size. Sources in Tier B and C are characterized by both simple and
broken power laws with spectral indices ranging from 0.12 to $-$0.92,
demonstrating a diversity in the spectral shape.

In Figure 3, we plot the radio SEDs spanning 1–12 GHz for all 9 sources,
including the two confirmed AGN and the one likely AGN, using the VLA
observations detailed in Section 3. We complement the SEDs for sources
J0903$+$4824, J0909$+$5655, and J0931$+$5633 with LoTSS data at 144 MHz with a
temporal separation with the VLA data of up to $\sim$ two years, which we
consider negligible given the apparent lack of variability in the light curves
of radio transients at $<1$ GHz on these timescales (Bell et al., 2014;
Rowlinson et al., 2016). For comparison, we plot the SEDs of PRSs 20121102A
and 20190520B with an arbitrary flux scaling in each panel. In particular, we
construct the SED of PRS 20121102A with data from the Giant Metre-wave Radio
Telescope (GMRT) between 400 MHz and 1.4 GHz (Resmi et al., 2021) and the VLA
between 1.6 and 22 GHz (Chatterjee et al., 2017). Similarly, we plot the radio
SED of PRS 20190520B using VLA data between 1.3 and 6 GHz (Niu et al., 2022).

To characterize the shape of the SEDs, we employ the curve$\\_$fit function
within the SciPy.optimize package (Jones et al., 2001) and fit the data with a
single power law, $F_{\nu}\propto\nu^{\alpha}$. For sources that exhibit a
break in the SED, we adopt a smoothed broken power law of the form:

$F_{\nu}=C\left[\left[\frac{\nu}{\nu_{b}}\right]^{-s_{1}\alpha_{1}}+\left[\frac{\nu}{\nu_{b}}\right]^{-s_{1}\alpha_{2}}\right]^{-1/s_{1}}$
(1)

where C is the normalization constant, $\nu_{b}$ is the break frequency,
$\alpha_{1}$ and $\alpha_{2}$ are the spectral indices before and after the
break, respectively, and $s_{1}$ is the smoothing parameter. Individual fits
and best-fit parameters are shown in Figure 3 and listed in Table 3.

We find that our Tier A source J1136$+$2643 is best characterized by a broken
power law that becomes optically thin above a break frequency of $\nu_{b}$ =
3.6 $\pm$ 0.2 GHz. Such a spectral shape is a hallmark of synchrotron self-
absorption (SSA; Condon & Ransom 2016) which is indicative of a compact
emission region. Interestingly, the SED of PRS 20121102A also features a break
in which it steepens from $\sim\nu^{-0.1}$ to $\sim\nu^{-1.3}$ at $\sim$ 9 GHz
(Resmi et al., 2021), possibly indicative of synchrotron cooling. In contrast,
the absence of a clear SSA feature in the SEDs of PRSs 20121102A and 20190520B
implies that such a turnover is located at frequencies below $\lesssim 1$ GHz.

Among our two Tier B sources, the SED for J0019$+$1507 is fairly flat across 1
– 12 GHz with spectral index of $\alpha=-0.03$ while J0909$+$5655 displays a
flat spectrum ($\alpha=-0.18$) from $1-4.8$ GHz followed by a steepening with
$\alpha=-0.73$ at $\nu_{b}$ $\gtrsim 4.8$ GHz. Such SEDs are broadly
consistent with the flat spectral shapes observed in PWNe, generally
characterized by spectral indices flatter than $-$0.5 (Gaensler & Slane,
2006). Indeed, such a model has been proposed for PRS 20121102A (Dai et al.,
2017; Yang & Dai, 2019). Furthermore, the flat spectral indices cannot be
explained by diffusive shock interactions (DSA; Bell 1978; Blandford & Eichler
1987), which typically yield steep spectral indices with $\alpha\lesssim-$0.5,
in line with most synchrotron transients (e.g., Chevalier & Irwin 2011;
Margutti et al. 2019; Fang et al. 2020). Among our sample, we also find that
the likely AGN J1027$+$0112 and background AGN J1136$+$1252 are the only other
sources exhibiting a flat SED.

Finally, we find that all of the SEDs in our remaining six Tier C sources are
characterized by fairly steep power laws with $\alpha\geq-0.92$. As discussed
in Section 4.2, source J0903$+$4824 is resolved in our VLA observations at
higher frequencies and in VLA X-band observations from Reines et al. (2020).
The slight feature between $\sim$ 1 and 3 GHz in the SED is therefore likely a
result of two distinct components. We note that although sources J1200$-$0341,
J1226$+$0815, and J1253$-$0312 exhibit spectral indices similar to PRS
20190520B across the frequency range $\sim 1-3$ GHz, they do not show evidence
for flattening at $\lesssim$ 2 GHz. Considering the diversity in the spectral
shapes observed across all tiers and their notable similarities to the known
FRB-PRSs, we do not exclude these sources as plausible PRS candidates solely
based on their SEDs.

Figure 4: Radio spectral luminosities of the sample of PRS candidates (blue),
where we highlight our Tier A source, J1136$+$2643\. Also shown for comparison
are PRS 20121102A (pink; Chatterjee et al. 2017; Resmi et al. 2021), PRS
20190520B (green; Niu et al. 2022; Zhang et al. 2023), VT 1137$-$0337 (orange;
Dong & Hallinan 2023), PTF10hgi (purple; Mondal et al. 2020), and J1419$+$3940
(dark orange; Mooley et al. 2022). Grey triangles represent all existing PRS
luminosity upper limits (Law et al., 2022, 2023). The radio sources in our
sample are overall less luminous than the FRB-PRSs, with the exception of
J0931$+$5633, but comparable to other radio transients.

###  4.4 Radio Luminosities

As shown in Table 3, the sources in our sample, along with other known PRSs,
occupy a wide range of radio luminosities at 3 GHz. Motivated by the diversity
in luminosity and SED shapes (Section 4.3), we plot the spectral luminosities
of the 9 PRS candidates at the redshifts of the dwarf galaxies in comparison
to those of FRB-PRSs, including limits on PRSs associated with FRBs (Law et
al., 2022, 2023), as well as known transients VT 1137$-$0337, PTF10hgi, and
J1419$+$3940 in Figure 4. We compile the spectral luminosities of VT
1137$-$0337 from VLA observations taken in 2019 (Epoch 2 in Dong & Hallinan
2023) over $\sim$ 1 – 18 GHz. Similarly, the broad-band SED of the radio
source associated with PTF10hgi is plotted utilizing VLA data from 2020 across
the range $\sim$ 1 – 15 GHz (Mondal et al., 2020). Lastly, the SED for
J1419$+$3940 is based on radio observations obtained in 2019 with LOFAR, VLA,
and VLBA spanning 150 MHz – 9 GHz (Mooley et al., 2022). These specific epochs
provide the broadest, contemporaneous spectrum for each radio transient.

The 9 PRS candidates in our sample span about three orders of magnitude in
luminosity, ranging from $\approx$ 1027 to 1030 erg s-1 Hz-1. While the Tier A
source, J1136$+$2643, highlighted in Figure 4, is less luminous than both PRSs
known to be associated with FRBs, it does not significantly differ from those
of the other sources in our sample and is comparable to the radio luminosity
of VT 1137$-$0337\. When compared to the known FRB-PRSs, all but J0931$+$5633
(Tier C) are less luminous by at least a factor of 10 (above 1 GHz). Only two
radio sources at the lower end of the luminosity distribution are dimmer than
PTF10hgi, and none are less luminous than the decades-long transient
J1419$+$3940.

In terms of the PRS limits associated with FRBs, a majority of them are
shallower than our radio sources with only three being deeper by $\sim$ an
order of magnitude. We also note that most of these limits are lower than
those of PRSs 20121102A and 20190520B. This supports the notion that if these
PRSs exist, they exhibit lower luminosities, possibly similar to what is
observed for our sources. Lower luminosities could easily be explained by
factors such as older age or intrinsic lower energy output (Margalit et al.,
2019).

We conclude that our sample of sources span a wide spectral luminosity range
in which only the brightest source (J0909$+$5633, Tier C) is comparable to the
luminosities of the FRB-PRSs. The remaining sources, including J1136$+$2643 in
Tier A, are notably less luminous but in agreement with the spectral
luminosities of VT 1137$-$0337 and PTF10ghi and more luminous than
J1419$+$3940\. Compared to the PRS limits, our sample is deeper than the
majority of limits, with the exception of three deep limits at $\lesssim
10^{27}\ \rm erg\ s^{-1}\ Hz^{-1}$. Overall, we cannot rule out any of the
sources in our sample as FRB-PRS candidates in the phase space of radio
luminosities alone. More importantly, this highlights the presence of sub-
luminous radio sources relative to the known FRB-PRSs in dwarf galaxies, most
of which would have been ruled out by the PRS luminosity threshold proposed by
Law et al. (2022).

Figure 5: Radio light curves of the PRS candidates shown at 1.4 (blue), 3
(purple), and 9 GHz (orange). The light curves at 1.4 GHz are drawn from
FIRST, NVSS, and archival VLA data as detailed in Eftekhari et al. (2020), and
our own VLA data at 1.4 GHz. The panels highlighted in yellow are Tier A and B
sources compact on mas scales. Data at 3 and 9 GHz include observations from
VLASS and Reines et al. (2020), in addition to our VLA observations. The 1.4
GHz light curves cover the longest baseline, spanning approximately three
decades, while the 3 and 9 GHz light curves illustrate the temporal evolution
over a shorter span of approximately 5$-$10 years. Detections are shown as
circles, while upper limits are represented as triangles. Overall, the light
curves at 1.4 GHz are generally flat or gradually declining, including Tier A
source J1136$+$2643, over a span of 3 decades. On shorter timescales, most
light curves at 3 and 9 GHz remain flat with minor variability. Due to the
sparse data coverage and inhomogeneous comparison timescales, we do not
eliminate any source as a PRS candidate.

###  4.5 Light Curves

The precise localizations of FRBs 20121102A and 20190520B have facilitated
continued monitoring campaigns to characterize the temporal evolution of their
associated PRSs over various timescales, spanning from days/weeks to years. To
explore whether the 9 PRS candidates in our sample exhibit temporal
variability similar to the PRSs associated with FRBs, we compile the light
curves at 1.4, 3, and 9 GHz using the radio observations presented in Sections
3.1 and 3.3. We also include archival upper limits and detections for sources
J0106$+$0046, J1136$+$2643, and J1200$-$0341 at 1.4 GHz as compiled in
Eftekhari et al. (2020) along with VLA data at 9 GHz from Reines et al.
(2020). The light curves for all 9 PRS candidates are shown in blue (1.4 GHz),
purple (3 GHz), and orange (9 GHz) in Figure 5.

Based on prevailing FRB progenitor models (see Section 5), PRSs coincident
with FRBs are expected to evolve on timescales of $\sim$ decades to centuries
following the supernova explosion that gives rise to a compact central engine
(Margalit & Metzger, 2018; Sridhar & Metzger, 2022). Thus motivated, we first
inspect the light curves at 1.4 GHz which span the longest temporal baseline
of $\sim$ 3 decades. To first order, the compact source J1136$+$2643 in Tier A
exhibits a slight increase by a factor of 1.5 at early times followed by a
gradual decrease in flux. In Tier B, sources J0019$+$1507 and J0906$+$5655
demonstrate a monotonic decline with a flux reduction of $\approx$ 40 and
20$\%$ spanning roughly 2 decades, respectively. The upper limit in the light
curve of J0906$+$5655 does not preclude a rise at early times. In Tier C, we
find that the light curves of sources J0909$+$4824 and J1253$-$0312 depict a
markedly similar secular decline in flux. This is in contrast to sources
J0106$+$0046, J1200$-$0341, and J1226$+$0815 which all display some level of
variability in the light curves. Specifically, source J1226$+$0815 exhibits
the most drastic decrease in flux of $\sim$ 75$\%$ over a $\sim 2$-decade
timescale.

Compared to J1419$+$3940, the decades-long radio transient which decays to
half of its peak flux value in 3 years (Law et al., 2018a), our source
population is fading more gradually and is less luminous by a factor of 10 at
early times. We stress that such comparisons on $\sim$ decade timescales
cannot be extended to the FRB-PRSs; due to their recent discovery dates,
constraints on their long-term variability are not yet tenable. We note that
neither of the FRB-PRSs are detected in FIRST or NVSS, with 3$\sigma$ limits
of 3 mJy and 7.5 mJy, respectively.

To assess the level of variability for the PRS candidates on shorter $\sim 5$
year timescales, we turn to the light curves at 3 and 9 GHz. In Tier A, the
light curve of J1136$+$2643 does not show variability and remains relatively
constant at 3 GHz. However, a minor increase of 20$\%$ is observed at 9 GHz.
Furthermore, the light curve of Tier B source J0019$+$1507 remains relatively
constant with a moderate variability of $\lesssim$ 20$\%$. In contrast, source
J0909$+$5655 demonstrates a notable rise by a factor of 2 over a span of
approximately 3 years, followed by a drop in the flux by a factor of 1.5. This
rise and decline is reminiscent of the flux measurements of PRS 20121102A
observed on a time baseline of $\sim 7$ years with MeerKAT which revealed an
increase of $\sim$ 30$\%$ and then a similar decline over a 3-year period,
based on one epoch so far (Rhodes et al., 2023). In this case, the observed
temporal variability in PRS 20121102A is likely intrinsic to the system (e.g.,
due to the interaction between a PWN terminal shock and the surrounding
supernova ejecta; Rhodes et al. 2023). However, it is worth mentioning that
the observed variabilities in the known FRB-PRSs are not yet well-established
and observed trends are based on limited time sampling. Factors such as
scintillation also cannot be ruled out as the source of observed variability
with present data alone.

In Tier C, the short-term light curves of sources J0106$+$0046 and
J1200$-$0341 exhibit a secular decline at 3 GHz, analogous to the decrease in
luminosity (20%) observed for PRS 20190520B from a multi-frequency (1 – 12
GHz) monitoring campaign between 2020 and 2021, alongside a 3.2$\sigma$ flux
decrease at 3 GHz (Zhang et al., 2023). In contrast, the light curve of source
J0931$+$5633 at 3 GHz is characterized by an apparent, continual rise. While
this trend could still be consistent with the flux increase observed in the
light curve of PRS 20121102A, it presents a challenge for scenarios such as
the PWN model in which the flux is expected to decrease over time (Yang et
al., 2016; Dai et al., 2017)

Finally, at 9 GHz, the light curve of the Tier A source J1136$+$2643 is
marginally rising over a $\sim$ 7 year period, in contrast to the declining
behavior at lower frequencies. None of the sources in Tier B show evidence of
substantial variability and out of the sources in Tier C, notable cases are
J0903$+$4824, which exhibits a significant increase of $\sim$ 50$\%$, while
J1226$+$0815 shows a decline of $\sim$ 50$\%$ over the span of 6.5 years.

In conclusion, on a temporal baseline of $\lesssim 3$ decades, the light
curves at 1.4 GHz are generally flat or gradually decaying across all sources.
At 3 and 9 GHz, most light curves remain relatively constant with minor
variability, comparable to the observed behaviors in the light curves of the
known PRSs. Given the sparse and uneven data coverage across all frequencies,
the diversity of PRS light curve behavior, and the inhomogenous comparison
timescales, the light curves at present do not offer obvious distinguishing
power in determining the origin(s) of the radio sources in our sample. If most
of the radio sources in our sample are in fact FRB-PRSs, this demonstrates
diverse behavior across timescales and frequencies that cannot be easily
explained with a single model.

###  4.6 Coincident FRBs

To identify potential FRBs coincident with the locations of the PRS candidates
in our sample, we utilized the Transient Name Server (TNS)666https://www.wis-
tns.org/ to search for FRBs detected in the CHIME/FRB catalog (CHIME/FRB
Collaboration et al., 2021) as well as FRBs detected by the by the Commensal
Real-Time ASKAP Fast-Transients (CRAFT) survey (Macquart et al., 2010). Our
search did not yield any results from other experiments. For the CHIME/FRB
catalog, we adopt a conservative search radius of $3^{\circ}$ centered around
each radio source to accommodate the large sky localizations of CHIME FRBs and
the non-Gaussian nature of the localization regions. For CRAFT, we impose a
smaller search radius of 10″ to match the largest CRAFT FRB localization
uncertainty (6″; Prochaska et al. 2019). Our initial search yielded a total of
four unique, non-repeating CHIME FRBs coincident with three PRS candidates in
our sample. Conversely, we find no CRAFT FRBs co-located with the sources in
our sample.

To account for the non-Gaussian nature of the CHIME/FRB localization regions,
we next manually check whether the matched sources fall within the
localization regions for each FRB using the HDF5 localization files (CHIME/FRB
Collaboration et al., 2021) and the CHIME/FRB Open Data Python
package777https://chime-frb-open-data.github.io/. We find that only one
source, J0106$+$0046 (Tier C), falls within the 95$\%$ confidence interval of
the localization region for FRB 20190531E, while the rest are not spatially
coincident with the FRB localization regions.

To assess whether source J0106$+$0046 and FRB 20190531E are plausibly related,
we estimate the redshift probability distribution for FRB 20190531E based on
its DM of 328.2 pc cm-3 (CHIME/FRB Collaboration et al., 2021). Following the
Macquart relation (Macquart et al., 2020), we calculate the Galactic ISM
contribution to be $\approx 33$ pc cm-3 from NE2001 (Cordes & Lazio, 2002) and
assume the DM contribution from the MW halo and the host to be 100 pc cm-3. We
find a redshift range for a confidence interval of 2.5$\%$ and 97.5$\%$ to be
z = [0.12, 0.38] with a mean value of z = 0.28. This is well above the
spectroscopic redshift of the dwarf host galaxy (z $\approx$ 0.02) associated
with J0106$+$0046\. Thus, if a plausible connection between source
J0106$+$0046 and FRB 20190531E exists, this requires an excess DM contribution
(e.g., from the host) of $\approx$ 190 pc cm-3. While this is not out of the
question given other excess DM FRBs (e.g., an extreme case such as FRB
20190520B with a foreground galaxy cluster contribution up to $\sim$ 640 pc
cm-3; Lee et al. 2023), the majority of FRBs with known redshift do not
exhibit such strong excess DM. Thus, we cannot conclusively associate any of
the PRS candidates with coincident FRBs.

##  5 FRB Progenitor Models

At present, the emission mechanisms responsible for producing both FRBs and
their associated PRSs are uncertain. A multitude of theoretical models have
been proposed, typically invoking a compact neutron star as the central engine
that powers a synchrotron nebula leading to the observed PRS emission (Yang et
al., 2016; Margalit & Metzger, 2018; Li et al., 2020). In this section, we
explore a few FRB progenitor models known to produce PRSs and test the
viability of these models for our Tier A source J1136$+$2643, the strongest
PRS candidate in our sample.

###  5.1 Magnetar and Pulsar Wind Nebulae

The magnetar wind nebula model was first invoked to explain the observed
properties (e.g., size and flux) of the PRS emission associated with FRB
20121102A in which the non-thermal radio emission is powered by a magnetized
nebula inflated by the flaring magnetar and confined behind the ejecta shell
(Beloborodov, 2017; Margalit & Metzger, 2018; Zhao & Wang, 2021). The
formation channel of the magnetar, whether prompt or delayed, dictates the
nature of the ejecta, which can arise from the core-collapse of a massive star
(and which could potentially be associated with a SLSN/LGRB), binary neutron
star (BNS) merger, or the accretion-induced collapse (AIC) of a white dwarf
(Margalit et al., 2019).

We adopt the analytic approach of Margalit et al. (2019) for the expanding
nebula in which the nebula luminosity depends on the energy injection rate of
the magnetar $\dot{E}$ and the density of the surrounding medium. We use
$\zeta\equiv$ Mej/v${}^{3}_{\mathrm{ej}}$ as a proxy for the ejecta density
($\rho_{\mathrm{ej}}\sim\zeta t^{-3}$) where Mej and vej are the total mass
and mean velocity of the expanding ejecta, respectively. The primary
difference between the SLSN/LGRB, BNS and AIC scenarios is the lower Mej and
higher vej in the latter two cases which sets a shorter free-free transparency
time. To satisfy the observed peak luminosity $\simeq$ 5.4 $\times$ 1028 erg
s-1 Hz-1 of source J1136$+$2643 at the break frequency $\nu_{b}$ = 3.6 GHz,
the energy injection rate must satisfy:

$\dot{E}\simeq 2.15\times
10^{41}~{}\mathrm{erg\,s^{-1}}\times\zeta_{-5}^{-41/144}$ (2)

based on Equation 23 in Margalit et al. (2019) where $\zeta\equiv
10^{-5}\zeta_{-5}\times(M_{\rm ej}/M_{\odot})(v_{\rm ej}/10^{4}\,{\rm
km\,s}^{-1})^{-3}$, and we have assumed that the mean energy per ion ejected
in the magnetar wind and the wind magnetization are $\chi$ = 0.2 GeV and
$\sigma$ = 0.1, respectively. For these fiducial parameters, this implies an
internal magnetic field for the putative magnetar of $\approx$ 2 $\times$ 1016
G for a normal-mass NS within an expanding nebula that is 100 years old. (see
Equation 2 of Margalit et al. 2019). This is consistent with the inferred
values for both PRSs 20121102A and 20190520B ($\approx$ 1016 G). Such a strong
field points to a highly magnetized magnetar as a plausible central engine
that could support the persistent radio emission on the observed timescale of
decades for source J1136$+$2643.

The observational constraints of J1136$+$2643 also allow us to rule out a
significant portion of the $\dot{E}$-$\zeta$ phase space that corresponds to
different progenitor formation channels as shown in Figure 4 of Margalit et
al. (2019). In particular, we find that magnetars born from core-collapse SNe
and BNS mergers remain plausible. In the first case, a higher ejecta density
necessitates a $\dot{E}$ value between 1039-40 erg s-1 whereas the lower
$\zeta$ in the BNS merger scenario permits a rate of energy injection in the
range of 1041-42 erg s-1. Lastly, we rule out the AIC scenario as it occupies
the region where $\dot{E}$ and $\zeta$ values are both low and is thus
inconsistent with the observed spectral luminosity of J1136$+$2643.

If instead, the energy deposited into the wind nebula is powered by the spin-
down of a pulsar, as in the case of a pulsar wind nebula (Dai et al., 2017;
Yang & Dai, 2019), we infer an external dipole field of $\approx$ 5 $\times$
1012 G assuming a central ionizing source equal to the spin-down luminosity of
the pulsar. This inferred value is expected for an ordinary pulsar with a
moderate spin period (P $\sim$ 0.1 – 1 s, Gaensler & Slane 2006).
Additionally, this poloidal field strength is improbable for the LGRB scenario
as it falls short of that demanded by the spin-down luminosity from the
relativistic jet of a LGRB which is usually much stronger (1015 G) for a rapid
spin period of P $\sim$ 1 – 2 ms (Metzger et al., 2017).

###  5.2 Hypernebula

Another paradigm proposed to explain PRSs associated with FRBs is the
‘hypernebula’ model, which involves a stellar-mass NS/BH accreting at super-
Eddington rates from a stellar companion, leading to intense mass-loss which
inflates a nebula of relativistic electrons (Sridhar & Metzger, 2022; Sridhar
et al., 2024). This model has been used to self-consistently explain the
observed properties of the PRSs associated with FRBs 20121102A, 20190520B
(Bhandari et al., 2023a), as well as the radio bursts themselves (Sridhar et
al., 2021). This model is also consistent with the burst properties for FRBs
20210117A (Bhandari et al., 2023b) and 20201124A (Dong et al., 2024), and the
limits on PRS emission at their locations. Additionally, the proposed
hypernebula resembles the Galactic microquasar SS 433 – W50 system (Dubner et
al., 1998).

Applying the model to source J1136$+$2643, we consider a BH of mass
$M_{\bullet}=10\,M_{\odot}$ accreting matter from a companion donor star of
mass M⋆ = $30\,M_{\odot}$ at a super-Eddington rate $\dot{M}$. Such mass
transfer is expected to drive large-angled slow winds from the accretion disk,
which interact with the upstream circumstellar medium (with an assumed density
$n_{\rm csm}\sim 10\,{\rm cm^{-3}}$) and accumulate an ejecta shell. The
kinetic luminosity of the disk-wind with velocity $v_{\rm w}$ is $L_{\rm w}$
$\approx\frac{1}{2}\dot{M}v_{\rm w}^{2}$ (Equation 7 in Sridhar & Metzger
2022). In addition to the slower disk winds, the accreting BH launches a
faster, collimated jet along the spin axis (with speeds $v_{\rm j}\gg v_{\rm
w}$), corresponding to a jet luminosity $L_{\rm j}\approx\eta L_{\rm w}$, with
the jet efficiency being $\eta<1$. The radio synchrotron emission in the
hypernebula arises from the collision between the collimated jet and the
slower disk-wind shell that heats relativistically hot electrons behind the
shell. The luminosity of the shock-heated electrons can be taken as $L_{\rm
e}\approx\varepsilon_{\rm e}L_{\rm j}$, where $\varepsilon_{\rm e}\sim 0.5$ is
the heating efficiency of the electrons (Sironi & Spitkovsky, 2011) in a
mildly-magnetized electron-ion shock.

Figure 6: Hypernebula model constraints in accretion rate-evolutionary age
parameter space for the Tier A source J1136$+$2643\. Critical regions of the
accretion rate - age map where the accretion rates are normalized to the
Eddington accretion rate $\dot{M}_{\rm Edd}\equiv L_{\rm Edd}/(0.1c^{2})$,
where $L_{\rm Edd}\simeq 1.5\times 10^{39}\,{\rm
erg\,s^{-1}}(M_{\bullet}/10\,M_{\star})$ is the Eddington luminosity. The
assumed fiducial set of parameters for the system is listed in the top right
of the figure. The blue shaded area is the only region that likely represents
the putative hypernebula associated with J1136$+$2643 based on the observed
constraints on the size, luminosity, radio SED, and light curve (more on this
in §5.2).

We place constraints on the accretion rate $\dot{M}$ (normalized to the
Eddington accretion rate for a $10\,M_{\odot}$ BH) and evolutionary timescale
of a putative hypernebula using the size constraint and luminosity of source
J1136$+$2643 in Figure 6. We adopt a fiducial set of parameters as listed in
the top right of the panel. First, accretion onto the BH by the donor star
sets an active lifetime for the hypernebula (brown shaded region) given by
Equation 3 of Sridhar & Metzger (2022). Next, using the available constraint
on the physical size of J1136$+$2643 ($<1.43$ pc) and Equation 10 of Sridhar &
Metzger (2022) which bridges the free-expansion phase and deceleration phases
of the ejecta, we rule out the black hatched region. We can further eliminate
the parameter space corresponding to $t\lesssim$ 27 years based on the 1.4 GHz
light curve (purple region). This eliminated region also includes the values
of $\dot{M}$ and the ages of the system that yield inefficient synchrotron
emission (i.e., a synchrotron cooling timescale $>$ the adiabatic cooling
timescale; Equation 49 of Sridhar & Metzger 2022) and optical depth of free-
free absorption ($\tau_{\mathrm{ff}}$) $<1$ at $\nu_{b}$ (3.6 GHz). Finally,
using the observed radio luminosity of J1136$+$2643, we rule out the $\dot{M}$
range where $L_{\rm e}\lesssim 2\times 10^{38}\,{\rm erg\,s^{-1}}$ (grey
region).

The remaining narrow blue region in Figure 6 denotes the allowed parameter
space for Tier A source J1136$+$2643\. For low accretion rates of
$\dot{M}/\dot{M}_{\rm Edd}$ $\lesssim 10^{4}$, the hypernebula can be
considerably older $\sim$ 30 – 300 years. Given the compact nature of the
source, however, it instead suggests that the nebula is likely younger with a
moderate mass-transfer rate. While a high accretion rate of
$\dot{M}/\dot{M}_{\rm Edd}\approx 10^{5-6}$ is possible, the nebula age is
confined to a very narrow range of $\sim$ 30 – 50 years.

###  5.3 Energy Equipartition

Independent of any progenitor models, we can use the SSA feature in the radio
SED of J1136$+$2643 to place meaningful constraints on the source properties.
Specifically, for self-absorbed emission, we can indirectly constrain the size
$R$, magnetic field $B$, and magnetic energy $U$ of the emitting region under
the assumption of energy equipartition between radiating particles and the
magnetic field (Scott & Readhead, 1977; Chevalier, 1998).

For an observed flux density of 2 mJy at $\nu_{b}$, we estimate a source size
of $R=0.05$ pc, consistent with the upper limit of 1.43 pc inferred from VLBA
observations (Sargent et al., 2022). In a similar fashion, we estimate a
magnetic field strength of $B$ $=$ 0.28 G (Equation 14 in Chevalier 1998) and
a corresponding magnetic energy of $U\sim 10^{49}~{}\rm erg$. For those
calculations, we assume a fiducial value for the emission volume filling
factor of $f=0.5$, a ratio of relativistic electron energy density to magnetic
energy density of $\alpha=1$, and an energy conversion efficiency parameter of
$\epsilon_{B}$ = $\frac{1}{3}$.

The inferred magnetic strength is a factor of $\sim 10^{2}$ higher than the
average magnetic field strengths of PRSs 20121102A and 20190520B derived from
the RM and host contribution to DM ($\approx$ 1 – 6 mG; Michilli et al. 2018;
Anna-Thomas et al. 2023). We stress that these estimated values for the known
FRB-PRS limits are only lower limits as the host DM is likely dominated by
star formation within the host rather than the immediate surrounding
environments. For comparison, our inferred magnetic field strength is similar
to that expected from the magnetar wind nebulae model of PRS 20121102A (e.g.,
Equation 17 in Margalit & Metzger 2018). The inferred energy, implies an
average energy-injection rate $\dot{E}\gtrsim 10^{40}\,{\rm erg\,s}^{-1}$ over
the $>30\,{\rm yr}$ age of the source.

##  6 Alternative origin for the radio emission: On a possible IMBH origin

Based on our findings presented in Sections 4 and 5, we have identified source
J1136$+$2643 as our most compelling FRB-PRS candidate. However, we cannot rule
out the possibility that source J1136$+$2643 and the remaining sources in our
sample have an alternative origin. In particular, as mentioned in Section 2,
our sample of radio sources were first suggested to be “wandering” accreting
IMBHs by Reines et al. (2020) based on their compact nature and apparent
offset from their host centers. This motivates us to consider their origin in
the context of IMBHs as there are also several notable features in the
observed SEDs of the radio sources which may corroborate such an
interpretation.

For the Tier A source, J1136$+$2643, the SSA turnover feature shown in the SED
(Figure 3), is similar to the spectral breaks observed in gigahertz peaked
spectrum (GPS) and compact steep-spectrum sources, which exhibit a defining
break frequency between 1 – 5 GHz from young AGN (O’Dea, 1998; Murgia, 2003).
The observed turnovers in the radio SEDs of GPS sources are generally ascribed
to SSA (Snellen et al., 2000), driven by the compact size of AGN cores. The
presence of such a feature in the radio SED of J1136$+$2643, also from SSA,
combined with the compact size, are thus broadly consistent with a GPS
interpretation with an AGN origin.

We now turn to Tier B sources, which primarily exhibit flat spectral indices
($\alpha\approx-0.20~{}{\rm to}~{}-0.03$), reminiscent of the flat spectrum
radio cores of AGN. Indeed, it is widely accepted that the radio emission from
AGN is anisotropic and orientation-dependent as evidenced by the discoveries
of relativistic jets launched by the central BHs (Urry & Padovani, 1995). In
this framework, the compact base of the approaching jet observed close to the
jet-axis and the BH-accretion disk nucleus as viewed down the jet axis both
result in a flat SED (de Zotti et al., 2010). We note that the Tier B source
SEDs are similar to that of the known compact AGN source J1126$+$1252 as well
as the likely AGN source J1027$+$1027 (also compact) in our sample. Thus, the
spectral similarities, together with the large host-normalized offsets,
suggests a potential association between Tier B sources and background AGN. It
is worth noting that the compact sizes and large offsets in Tier B sources are
also in line with the “wandering” IMBHs scenario. However, as discussed in
Reines et al. (2020), it is difficult to distinguish between background
interlopers and “wandering” IMBHs based only on radio observables.

If, however, the AGN is viewed in the plane of the disk, then the radio
emission would instead be dominated by the radio lobes, which exhibit a steep
radio spectrum (de Zotti et al., 2010). This is analogous to the observed
steep spectral indices in our Tier C sources. Moreover, the non-compact nature
of these sources is consistent with the extended jet structure in this
scenario. This interpretation is further reinforced by their similarity to the
known AGN source J1220$+$3020 in our sample, which exhibits a steep spectral
index and extended radio emission.

Thus, while we identify a number of similarities between the radio sources in
our sample and known FRB-PRSs, as well as viable models for their emission, we
cannot discount their resemblance to “wandering” BHs and background AGN, which
can also exhibit a diversity of radio SEDs. Hence, it is imperative to obtain
follow-up observations in other wavelengths such as X-ray and optical bands,
as they offer additional BH diagnostics when searching for PRSs coincident
with FRBs. This is highlighted by the identification of at least two known AGN
in our sample through optical observations. Similarly, the discovery of FRBs
at the locations of these radio sources would provide unambiguous evidence for
their origins and association with FRBs.

##  7 Conclusions

We have presented VLA and EVN observations of 9 FRB-PRS candidates in dwarf
galaxies at low redshifts ($z\lesssim 0.055$), two radio sources of known AGN
origin, and one radio source with a probable AGN origin. All sources that were
observed are detected with the VLA and EVN (where applicable). We divided the
sample into three tiers based on their observed properties and shared
similarities with known FRB-PRS pairs, and further assessed the likelihood
that any of the sources share a common origin with PRSs associated with FRBs
20121102A and 20190520B. We also tested the viability of NS wind nebula and
hypernebula models for our most promising FRB-PRS candidate J1136$+$2643\. Our
main conclusions are as follows:

  * •

We identify a single source (J1136$+$2643) as the most promising FRB-PRS
candidate in our sample, classified in Tier A (compact on milliarcsecond
scales and small galactocentric offset). Additionally, we identify two sources
(J0019$+$1507 and J0909$+$5955) in Tier B (compact) and six sources
(J0106$+$0046, J0903$+$4824, J0931$+$5633, J1200$-$0341, J1226$+$0815, and
J1253$-$0312) in Tier C (not obviously compact based on existing
observations). Source J0019$+$1507 is detected, but unresolved, in our EVN
observations.

  * •

The radio sources exhibit host-normalized offsets of 0 re $\leqslant$ rnorm
$\leqslant$ 5.3 re. The Tier A source has r${}_{\rm norm}=1.31~{}\rm r_{e}$,
consistent with those of PRSs 20121102A and 20190520B, whereas both Tier B
sources have rnorm $>3~{}r_{e}$, which may indicate a background AGN origin.
While not compact, almost all Tier C sources are within 2 re of the dwarf
hosts, comparable to the host-normalized offsets of FRB-PRSs and transients
J1419$+$3940 and VT1137$-$0337.

  * •

The peak luminosity at $\nu_{b}$ of the Tier A source, J1136$+$2643, is
consistent with NS wind nebula models. Within the magnetar nebula model we
constrain the energy injection rate and ambient density. From this, we are
able to rule out the AIC scenario as a potential formation pathway, while a
core-collapse SNe or BNS merger origin remain plausible. In the hypernebula
paradigm, constraints derived from the compact size ($<$ 1.43 pc) and spectral
luminosity of J1136$+$2643 imply a nebula age of $\sim$ 50 yr for moderate
$\dot{M}/\dot{M}_{\rm Edd}$, slightly older than the inferred ages of FRB-
PRSs. Despite some differences from the known FRB-PRSs, the observed
properties of J1136$+$2643 are consistent with multiple FRB progenitor models.

  * •

The spectral radio luminosities of the sample span roughly there orders of
magnitude ranging between $\approx 10^{27}$ and 1030 erg s-1Hz-1. Across all
tiers, the radio sources are sub-luminous relative to the known FRB-PRSs (with
the exception of source J0909$+$5633 in Tier C). Moreover, the luminosities
are comparable to those of VT 1137$-$0337 (PWN candidate) and PTF10ghi (SLSN),
but brighter than the decades-long transient J1419$+$3940\. Additionally, the
radio luminosities for our sample are comparable to existing PRS limits for
well-localized FRBs, suggesting that these FRBs could harbor lower luminosity
PRSs.

  * •

On a temporal baseline of $\approx 30$ years, the light curves at 1.4 GHz of
all radio sources are generally flat or gradually decaying, with the Tier A
source exhibiting slight variability. At 3 and 9 GHz, the short-term light
curves of the full sample remain relatively constant with no evidence of
variability, comparable to the observed behaviors in the light curves of the
known FRB-PRSs. Given the sparse and uneven data coverage across all
frequencies, the diversity in the light curve behavior, and the inhomogenous
comparison timescales, the light curves do not offer obvious distinguishing
power in determining the origin(s) of the radio sources in our sample.

  * •

The turnover observed in the radio SED of Tier A source, J1136$+$2643, at
$\nu_{b}=$ 3.6 GHz can likely be attributed to SSA. This spectral shape
contrasts with what is observed in the SED of PRS 20121102A at $\sim$ 9 GHz,
caused by synchrotron cooling, but aligns with turnovers seen in GPS sources.
In Tier B, the presence of flat spectral indices ($\alpha\approx-0.1$) is
broadly consistent flat-spectrum PWNe, as well as core-dominated radio AGN.
Conversely, the steep spectral indices ($\alpha$ $\approx-0.5~{}{\rm
to}~{}-1.0$) observed for the Tier C sources are reminiscent of extended radio
lobes associated with AGN.

With only a couple of definitive FRB-PRSs to date, both identified through the
initial localization of an FRB, it is important to explore alternative avenues
for new identifications of FRB-PRSs to fully delineate the characteristics of
the population and their connection to FRB progenitors. Through multi-
frequency radio observations, we find that even our most promising source,
J1136$+$2643, differs from known FRB-PRSs in terms of spectral evolution and
radio luminosity, potentially indicative of diversity in the FRB-PRS
population. Moreover, while we identify a number of similarities in the
observed properties between our sample and known FRB-PRSs, we do not discount
the fact that they could also be consistent with wandering BHs and background
AGN.

Our work has highlighted that even among a sample with a fairly uniform
selection of compact radio sources in spectroscopically confirmed dwarf
galaxies, there is great diversity in observed radio spectral and temporal
behavior that can be challenging to interpret. In addition, there remains
great flexibility in current FRB-PRS emission models and mechanisms. This
highlights the importance of high-resolution VLBI observations to confirm the
compactness of candidate radio sources, coupled with X-ray observations and
optical spectroscopy, to complement future radio searches of FRB-PRSs and
reduce contamination from background interlopers. At the same time, the
increased attention to blind searches of radio sources on many timescales from
ThunderKAT, VLASS, and FRATS (Fender et al., 2016; ter Veen et al., 2019; Law
et al., 2023) will place these compact radio sources into context with the
entire source population.

##  8 Acknowledgments

The authors are grateful for the helpful discussions with Dillon Dong and
Joseph Michail. Y.D. is supported by the National Science Foundation Graduate
Research Fellowship under Grant No. DGE-1842165. The Fong Group at
Northwestern acknowledges support by the National Science Foundation under
grant Nos. AST-2206494, AST-2308182, and CAREER grant No. AST-2047919. T.E. is
supported by NASA through the NASA Hubble Fellowship grant HST-HF2-51504.001-A
awarded by the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., for NASA, under
contract NAS5-26555. S.B. is supported by the Dutch Research Council (NWO)
Veni Fellowship (VI.Veni.212.058). Research by the AstroFlash group at the
University of Amsterdam, ASTRON, and JIVE is supported in part by a Vici grant
from the Dutch Scientific Research Council (Nederlandse Oranisatie voor
Wetenschappelijk Onderzoek or NWO; PI Hessels; VI.C.192.045) as well as the
European Union’s Horizon 2020 research and innovation programme through the
ERC Advanced Grant ‘EuroFlash’ (PI Hessels; Grant Agreement No. 101098079).
W.F. gratefully acknowledges support by the David and Lucile Packard
Foundation, the Alfred P. Sloan Foundation, and the Research Corporation for
Science Advancement through Cottrell Scholar Award #28284. N.S. acknowledges
the support from NASA (grant number 80NSSC22K0332), NASA FINESST (grant number
80NSSC22K1597), Columbia University Dean’s fellowship, and a grant from the
Simons Foundation. B.M. acknowledges financial support from the State Agency
for Research of the Spanish Ministry of Science and Innovation under grant
PID2019-105510GB-C31/AEI/10.13039/501100011033 and through the Unit of
Excellence María de Maeztu 2020–2023 award to the Institute of Cosmos Sciences
(CEX2019- 000918-M). The Berger Time-Domain Group at Harvard is supported by
NSF and NASA grants.

The National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc. The European VLBI Network is a joint facility of independent European,
African, Asian, and North American radio astronomy institutes. Scientific
results from data presented in this publication are derived from the following
EVN project code(s): EO018. W. M. Keck Observatory and MMT Observatory access
was supported by Northwestern University and the Center for Interdisciplinary
Exploration and Research in Astrophysics (CIERA). The authors wish to
recognize and acknowledge the very significant cultural role and reverence
that the summit of Maunakea has always had within the indigenous Hawaiian
community. We are most fortunate to have the opportunity to conduct
observations from this mountain. , SFXC (Keimpema et al., 2015)

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We also observed the source J0134$-$0741 as a part of our EVN observations.
This source is included in sample B of the Reines et al. (2020) sample of
compact radio sources and therefore does not satisfy our selection criteria
for further analysis. The source is detected with the EVN with a flux density
of $10.0\pm 1.5$ mJy at 1.7 GHz. We constrain the angular size of the source
to be $<1.9$ mas which translates to a physical size of $<0.62$ pc at
$z=0.0156$. We measure the luminosity of the source to be $5.8\times 10^{28}$
erg s-1 Hz-1. We show the EVN radio image of source J0134$-$0741 and the
identified probable and confirmed background AGN sources J1027$+$0112 and
J1136$+$1252 in Figure 7.

Figure 7: EVN images of the identified likely and confirmed background AGN
sources, J1027$+$0112 and J1136$+$1252, along with the additional source
J0134$-$0741 at 1.7 GHz with contour lines depicting rms levels starting from
$3.5\sigma$. The synthesized beams are displayed in the bottom left corner in
each panel with sizes 6 mas $\times$ 4 mas, 22 mas $\times$ 5 mas, 24 mas
$\times$ 3 mas for J1027$+$0112, J1136$+$1252, and J0134$-$0741, respectively.