# The Solar Origin of an In Situ Type III Radio Burst Event

Meiqi Wang (王美祺) Center for Solar-Terrestrial Research, New Jersey Institute
of Technology, Newark, NJ 07102, USA  Bin Chen (陈彬) Center for Solar-
Terrestrial Research, New Jersey Institute of Technology, Newark, NJ 07102,
USA  Sijie Yu (余思捷) Center for Solar-Terrestrial Research, New Jersey
Institute of Technology, Newark, NJ 07102, USA  Dale E. Gary Center for Solar-
Terrestrial Research, New Jersey Institute of Technology, Newark, NJ 07102,
USA  Jeongwoo Lee Center for Solar-Terrestrial Research, New Jersey Institute
of Technology, Newark, NJ 07102, USA  Institute for Space Weather Sciences,
New Jersey Institute of Technology, Newark, NJ 07102, USA  Haimin Wang Center
for Solar-Terrestrial Research, New Jersey Institute of Technology, Newark, NJ
07102, USA  Christina Cohen Space Radiation Laboratory, California Institute
of Technology, Pasadena, CA 91125, USA

###### Abstract

Solar type III radio bursts are generated by beams of energetic electrons that
travel along open magnetic field lines through the corona and into
interplanetary space. However, understanding the source of these electrons and
how they escape into interplanetary space remains an outstanding topic. Here
we report multi-instrument, multi-perspective observations of an
interplanetary type III radio burst event shortly after the second perihelion
of the Parker Solar Probe (PSP). This event was associated with a solar jet
that produced an impulsive microwave burst event recorded by the Expanded
Owens Valley Solar Array (EOVSA). The type III burst event also coincided with
the detection of enhanced in situ energetic electrons recorded by both PSP at
0.37 AU and WIND at 1 AU, which were located very closely on the Parker spiral
longitudinally. The close timing association and magnetic connectivity suggest
that the in situ energetic electrons originated from the jet’s magnetic
reconnection region. Intriguingly, microwave imaging spectroscopy results
suggest that the escaping energetic electrons were injected into a large
opening angle of about 90∘, which is at least nine times broader than the
apparent width of the jet spire. Our findings provide an interpretation for
the previously reported, longitudinally broad spatial distribution of flare
locations associated with prompt energetic electron events and have important
implications for understanding the origin and distribution of energetic
electrons in interplanetary space.

Solar flares (1496), Solar coronal transients (312), Solar radio emission
(1522), Solar energetic particles (1491)

††journal: ApJ††facilities: OVRO:SA, Parker, SDO, STEREO, WIND,
GONG††software: CASA (McMullin et al., 2007), Astropy (Astropy Collaboration
et al., 2018), SunPy (SunPy Community et al., 2020), pfsspy (Stansby et al.,
2020), Numpy (Harris et al., 2020), spacepy (Morley et al., 2022)

##  1 Introduction

Solar type III radio bursts are one of the most commonly observed types of
radio bursts from the Sun. In the radio dynamic spectrum, they feature a rapid
drift from high to low frequencies (Wild & McCready, 1950). Owing to their
fast frequency drift rates, type III bursts are believed to be associated with
fast electron beams propagating in the solar corona and interplanetary space
at a fraction of the speed of light ($\sim$0.1–0.5 c). The widely adopted
emission mechanism of type III bursts, first proposed by Ginzburg &
Zhelezniakov (1958) and further developed by many researchers over decades,
involves the generation of a bump-on-tail distribution by a propagating fast
electron beam leading to nonlinear growth of Langmuir waves via the two-stream
instability. These Langmuir waves are subsequently converted to transverse
electromagnetic waves near the local plasma frequency or its harmonic (see,
e.g., Reid & Ratcliffe, 2014, for a review). Theoretical and modeling studies
have suggested that such a bump-on-tail instability can naturally develop when
high-speed electron beams are traveling along magnetic field lines, leading to
a positive gradient in the electron velocity distribution ($\partial
f/\partial v>0$) around the “bump” at the electron beam velocity $v_{b}$
(Melrose, 1990; Reid et al., 2011). The presence of the bump-on-tail feature
in association with type III radio bursts has been supported by multiple in
situ observations (Gurnett & Frank, 1975; Lin, 1985; Ergun et al., 1998).

Since van Allen & Krimigis (1965), several analyses of solar energetic
electron (SEE) events with in situ observations have been reported (Reames et
al., 1990; Lin et al., 1996; Krucker et al., 1999, 2007; Simnett et al.,
2002). Wang et al. (2012) reported that almost all the observed in situ SEE
events are associated with type III radio bursts. For the energetic electron
beams to enter interplanetary space to produce the low-frequency type III
bursts $\sim$10 kHz to MHz and in situ energetic electron events, they need to
have access to open field lines. Solar jets, which manifest in extreme
ultraviolet (EUV) and X-ray images as collimated material ejecting along
apparently open field lines, provide evidence of the existence of such a
magnetic topology. Indeed, it has been reported that some type-III-burst-
producing in situ SEE events are closely associated with jets (observed in EUV
and/or X-ray) (Aurass et al., 1994; Raulin et al., 1996; Klassen et al.,
2011). For example, by combining in situ electron measurements made by the
three-dimensional Plasma and Energetic Particles (3DP) experiment onboard the
WIND spacecraft and remote-sensing hard X-ray (HXR) observations from the
Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), Krucker et al.
(2011) explored the source region of supra-thermal electron beams and
suggested that they are associated with interchange reconnection occurring
between open and closed magnetic field lines.

Although type III radio bursts have been frequently reported to show a close
temporal association with SEEs (Lin et al., 1973; Cane & Erickson, 2003; Wang
et al., 2016; Gómez-Herrero et al., 2021), identifying the source region of
the type-III-burst-emitting electron beams remains challenging. Many studies
utilize a magnetic field model to investigate the connection between the in
situ SEE measurements and features on the solar surface. Meanwhile, the source
region of the SEEs has also been located by comparing the release time
inferred from a velocity dispersion analysis or assuming the electrons’
scatter-free propagation along the Archimedean interplanetary magnetic field
line to the timing of the radio, EUV, or X-ray emission signatures obtained
via remote sensing observations (Krucker et al., 1999; Haggerty & Roelof,
2002).

More recently, radio imaging spectroscopy has started to play a more and more
important role in tracing the solar origin of energetic particles. A number of
studies have analyzed the source of type III radio bursts associated with jets
using radio imaging spectroscopy (Cairns et al., 2009; McCauley et al., 2017;
Mulay et al., 2019; Chen et al., 2013, 2018). Particularly, radio imaging
spectroscopy results in the hundreds of MHz to GHz range (or decimetric
wavelengths) have indicated that the decimetric type III bursts are emitted by
electron beams originating from the core region of the jets in the low corona,
presumably close to the magnetic reconnection site. For example, Carley et al.
(2016) have identified different acceleration sites of electrons associated
with an erupting jet and flux rope by imaging radio sources at frequencies
ranging from 150–445 MHz observed by Nançay Radioheliograph. In Chen et al.
(2018), using the observations from the upgraded Karl G. Jansky Very Large
Array (VLA) in the 1–2 GHz L band, they have derived detailed trajectories of
type III-emitting electron beams and interpret each beam-diverging site as a
reconnection null point. In addition, for low-frequency interplanetary type
III radio bursts which are not accessible by ground-based radio instruments
(as they occur at frequencies below the ionospheric cutoff at $\sim$20 MHz),
techniques such as radio triangulation (Fainberg et al., 1972; Gurnett et al.,
1978; Reiner & Stone, 1988) and ray-tracing (Thejappa & MacDowall, 2008, 2010;
Musset et al., 2021) have been used to locate their source locations in
interplanetary space.

Thanks to the operation of the Expanded Owens Valley Solar Array (EOVSA; Gary
et al. 2018), microwave imaging spectroscopy observations of the full solar
disk has been available from 1 to 18 GHz in 451 spectral channels with 1 s
time resolution. The operation of EOVSA provides means of combining imaging
spectroscopy observations of microwave emission from nonthermal electrons in
the low corona with in situ observations from Parker Solar Probe (PSP),
STEREO-A, and WIND, offering an opportunity to form a more comprehensive
picture of where these energetic electrons are accelerated and how they are
transported from the low corona into interplanetary space.

Here we report a type III radio burst that was observed jointly by PSP,
STEREO-A, WIND, e-Callisto, and EOVSA. In Section 2, we present the multi-
instrument, wide-band dynamic spectroscopy observations of this type III burst
event. In Section 2.1, we give the overview of the jet and the active region.
In Section 2.2 and 2.3, we derive the propagation and directivity of the type
III burst event from near the solar surface to interplanetary space. In
Section 2.4, we present in situ measurements made by the PSP and WIND, which
suggest that the type-III-burst-emitting electron beams have reached the two
spacecraft located at 0.37 AU and 1 AU, respectively. In Section 2.5, we
discuss the magnetic connectivity between the PSP and the jet event supported
by a potential-field source-surface (PFSS) magnetic field model. Then, we
perform imaging spectroscopy of the type III bursts in the microwave regime by
using EOVSA data and identify the origin of the source electrons as those
accelerated in the jet event. Finally, in Section 3, we summarize our main
results and discuss their implications.

##  2 Observations

###  2.1 Event Overview

The interplanetary type III radio burst event under study was recorded by
three well-separated spacecraft as well as multiple ground-based radio
facilities on 2019 April 15 around 19:30 UT, which was during the outbound
phase of PSP’s second perihelion. Figure 1 shows the overall dynamic spectrum
obtained by PSP/FIELDS/RFS (Bale et al., 2016; Pulupa et al., 2017) at 50
kHz–20 MHz (panel (a)), e-Callisto/Greenland at 10 MHz–100 MHz (panel (b)),
and EOVSA 1–18 GHz (panel (c)).

Figure 1: (a)–(c): Composite radio dynamic spectra from 50 kHz to 18 GHz
featuring the interplanetary type III radio burst event observed by PSP/FIELDS
(0.05–19 MHz), e-Callisto/Greenland (19–100 MHz), and EOVSA (1–18 GHz) during
a GOES B3.4-class microflare on 2019 April 15 (d). An enlarged view of the
high-frequency component of the burst event is shown in (e). Red curves show
the frequency-drift fit for two individual type III bursts that can be traced
to microwave frequencies. The blue curve represents the EOVSA 1.6 GHz light
curve. The selected frequency is indicated by a blue horizontal dashed line.

Figure 2: (a) SDO/AIA 171 Å full disk image at 19:33 UT on 2019 April 15
around the peak of the B3.4 flare. (b) SDO/HMI full-disk line-of-sight
magnetogram at 19:22 UT. (c) Selected magnetic field lines from the PFSS
extrapolation model. Red curves show the open field lines rooted at the
leading sunspot with a negative magnetic polarity. (d)–(f) Detailed view of
the region of interest in (a)–(c) (white box). Note that in panel (e),
different from panel (b), the radial magnetogram is shown instead to mitigate
projection effects. The transformation is based on the full vector magnetogram
measurements of SDO/HMI

.

This type III radio burst event coincided with a GOES soft X-ray (SXR)
B3.4-class microflare, which started at $\sim$19:22 UT and peaked at 19:31 UT
according to the 1–8 Å SXR light curve shown in Figure 1(d). The microflare
was the only flare event during the day. It was associated with a solar jet
located in the periphery of AR 12738 featuring a long ($>$115 Mm) and
collimated jet spire observed by multiple EUV channels of the Atmospheric
Imaging Assembly (AIA; Lemen et al., 2012) onboard the Solar Dynamics
Observatory (SDO; Pesnell et al., 2012). Figure 2(a) and (d) show a full-disk
view and a more detailed view of the jet event in AIA 171 Å, respectively.

At the time of the type III burst event, AR 12738 was located at a latitude of
$6^{\circ}$ north and a longitude of $32^{\circ}$ west in heliographic
coordinates. The active region consists of an $\alpha$-type sunspot (with a
unipolar magnetic field configuration) surrounded by weak magnetic structures
with mixed polarities. The full-disk line-of-sight (LOS) magnetogram is shown
in Figure 2(b), which is obtained by the Helioseismic and Magnetic Imager
(HMI; Scherrer et al., 2012) onboard SDO. An enlarged view of the AR in EUV
171 Å and the HMI radial magnetogram (calculated from components of the HMI
vector magnetogram) is shown in Figures 2(d) and (e). The jet is clearly
visible at the west edge of the negative polarity sunspot and erupts in the
southwest direction.

Selected field lines from the full-disk PFSS magnetic model, obtained by using
the python package pfsspy; Stansby et al. 2020, are shown as gray lines in
Figure 2(c). The PFSS model is calculated using the HMI synoptic radial
magnetogram for Carrington rotation 2216 (based on HMI LOS magnetograms
collected over a 27-day solar rotation) as the input, which was then down-
sampled to a size 360 pix $\times$ 180 pix. The source surface height is set
at 2.5 $R_{\odot}$. An enlarged view is shown in Figure 2(f), with PFSS
extrapolated field lines overlaid on the SDO/AIA 171 Å image. A few selected
open field lines originating from the negative spot are shown as red curves
which, as expected, coincide well with the EUV jet spire. We note, however,
the highly-collimated EUV jet spire is much narrower than the full extent of
the open field lines seen in the PFSS results.

The event occurred during the period of a deep solar minimum. The background
GOES 1–8 Å SXR flux level remained very low and below the B level throughout
the day. In addition, AR 12738 was the sole active region visible on disk over
the period of 2019 April 10–17. The relatively quiet period, low background,
and the presence of a single, dominant active region make it convenient to
study the connections between the type III radio bursts and in situ particle
events, as well as identify their source region. AR 12738 was the source of
other published events. For example, Badman et al. (2022) reported a type III
radio burst event on 2019 April 9 jointly observed by PSP/FIELDS,
STEREO/WAVES, as well as the ground-based Low Frequency Array (LoFAR), and
traced the source electrons to AR 12738. Wiedenbeck et al. (2020) reported
3He-rich SEPs events recorded by PSP/IS$\odot$IS and ACE from 2019 April 20–21
and suggested that they all originated from AR 12738. Interestingly, on 2019
April 4, one day prior to its perihelion, PSP observed a small SEP event. The
source of this event was identified, by Leske et al. (2020), as the same
active region but was located nearly 80∘ east of the nominal PSP magnetic
footpoint, implying that the open magnetic field lines along which the
particles escape may extend over a wide longitudinal range.

###  2.2 Type III Radio Burst Event: Spectro-Temporal Properties

Figure 3: (a) EOVSA cross-power dynamic spectrum from 1–14 GHz. The red and
blue dashed lines correspond to the start times of the two type III burst
branches in Figure 1. (b) The spectra extracted from the two selected times in
(a). (c): Stokes I (red) and V (blue) light curves at 1.5 GHz. At the peak
time of 19:30:55 UT, the maximum degree of circular polarization is around
9$\%$.

In the composite dynamic spectrum from 50 kHz to 18 GHz shown in Figure 1, the
PSP interplanetary type III burst event consists of at least two individual
branches that continue to the metric-microwave range measured by e-Callisto
and EOVSA. Their characteristic rapid frequency drift from high to low
frequencies can be understood by the propagation of electron beams from the
low corona to interplanetary space during which they encounter background
plasma with a decreasing density (Wild & McCready, 1950). The relationship
between the emission frequency $\nu$ (in Hz) and electron density $n_{e}$ (in
cm-3) is given by $\nu\approx s\nu_{pe}=8980s\sqrt{n_{e}}$ Hz, where
$\nu_{pe}$ is the plasma frequency and $s\approx 1$ or 2 is the harmonic
number for the fundamental or harmonic plasma radiation, respectively.

To model the frequency drift of the type III radio bursts, we adopt an
electron density model $n_{e}(r)$ by combining the Newkirk density model in
the low corona ($r=1.02$–1.5 $R_{\odot}$; Newkirk 1967) with a solar wind
density model in the upper corona and interplanetary space ($r>1.5\
R_{\odot}$; Saito et al. 1977). The low corona and solar wind density models
are scaled by a factor of 0.5 and 9, respectively, in order to ensure a smooth
transition at $1.5\ R_{\odot}$ and match the in situ measurement of the plasma
density made by PSP/SWEAP at 79 $R_{\odot}$. The exact form of our adopted
density model is

$n_{e}(r)=\begin{cases}2.1\times 10^{4}\times 10^{4.32/r}&\text{(1.02 $<$ r
$<$ 1.5)}\\\ &\\\ 4.62\times 10^{5}r^{-2}+4.74\times 10^{7}r^{-3.3}\\\
+3.19\times 10^{7}r^{-5.8}&\text{(1.5 $\leq$ r $<$ 215)}\end{cases}$ (1)

where $r$ is the heliocentric distance in solar radii.

Assuming a constant electron beam speed $v_{b}$, the distance of the type III
source from the Sun is

$r(t)=v_{b}(t-t_{0}),$ (2)

where $t_{0}$ is the release time of the electron beam. Therefore, by assuming
fundamental plasma radiation at $\nu\approx 1.2\nu_{pe}$ (e.g., Musset et al.
2021), the frequency variation in heliocentric distance $\nu(r)$ can be, in
turn, expressed as a function of time $t$.

By varying the electron beam speed $v_{b}$ and the release time $t_{0}$, we
fit the leading edge of the two interplanetary type III burst branches in the
dynamic spectrum from 100 kHz to $\sim$100 MHz. For the high-frequency range
($\sim$100 MHz–1 GHz) where the density model is out of range, we extrapolate
the same frequency drift curves beyond $\sim$100 MHz. The best-fit results are
shown as red curves in Figures 1(a) and (b). The first frequency drift curve
extends all the way from $<$2 GHz to 200 kHz. The second curve appears to stop
at a relatively higher frequency ($\sim$3 MHz). The fitted electron beam speed
$v_{b}$ values are 0.35c and 0.1c, respectively. The extrapolated start time
of the second frequency-drift curve coincides very well with the onset of the
strongest EOVSA 1–3 GHz microwave burst at 19:30:55 UT (blue curve in Figure
1(e)). The start time of the first curve also seems to coincide with a small
microwave peak at 19:30:37 UT, but the correspondence is relatively less
clear.

The well-correlated timing of the interplanetary type III radio bursts and the
EOVSA bursts in $\sim$1–3 GHz suggests that the latter may be the decimetric
counterpart of the type III bursts due to coherent plasma radiation. To
further elucidate the coherent nature of the decimetric bursts, we show a
detailed EOVSA Stokes I dynamic spectrum with full frequency resolution (451
frequency channels spread in 1–18 GHz) and time resolution (1 s) in Figure
3(a). The dynamic spectrum is obtained by taking a median over the cross-power
dynamic spectra of all baselines shorter than 1.55 km, which reveals the
relatively weak microwave bursts. In Figure 3(b), we show the cross-power
spectra for two selected times that correspond to the starting time of the two
type III burst branches (indicated by the red and blue dashed lines in Figure
3(a)). The spectra at high frequencies ($>$3 GHz) have a positive slope
followed by a negative slope at above $\sim$8 GHz, which is consistent with
incoherent nonthermal gyrosynchrotron emission (e.g., Dulk, 1985). At the same
time, the spectra at $<$3 GHz are notably different, with much greater
intensity and many fine structures. The characteristics of the EOVSA 1–3 GHz
bursts are highly consistent with decimetric type III bursts reported in the
literature (e.g., Young et al., 1961; Paesold et al., 2001), although EOVSA’s
temporal resolution (1 s) does not allow us to further resolve their
presumably sub-second fine structures as presented in the observations by Chen
et al. (2013, 2018) using the Jansky VLA.

To further elucidate the nature of the 1–3 GHz microwave bursts, we
investigate the circular polarization of the bursts. Although EOVSA is
equipped with broadband cross-dipole feeds to offer imaging spectropolarimetry
capabilities, it has antennas with dissimilar mount types: four of them are
equatorially mounted, while the others are azimuth-elevation mounted. The
different antenna mount types have resulted in polarization mixing caused by
the differential rotation of the feeds. To avoid the complexity, we derive the
Stokes V dynamic spectra by only using the six baselines of the four
equatorially mounted antennas. The Stokes V light curve at 1.5 GHz,
representing the median value of the six baselines, is shown as the blue curve
in Figure 3(c). The polarization degree remains consistently low throughout
the entire event. At 19:30:55 UT, the polarization degree reaches a maximum of
9%. We conclude that the weak polarization degree of the 1–3 GHz microwave
bursts is consistent with harmonic plasma radiation (e.g., Dulk & Suzuki,
1980). The positive Stokes V value indicates that the bursts are right-hand
circularly polarized (RCP). Considering the dominant negative sunspot, the
emission is likely polarized in the sense of ordinary mode, or $o$ mode.

###  2.3 Type III Radio Burst Event: Location and Directivity

Figure 4: Multi-spacecraft observations of the interplanetary type III radio
burst event. (a) Locations of PSP, WIND, and STEREO-A in the Heliocentric
Earth Ecliptic (HEE) coordinate system. The gray curves in the background show
the Parker spiral magnetic field lines in the ecliptic plane, equally spaced
in longitude by 18 degrees. A solar wind speed of 350 km s-1 is assumed. Solid
green, red, and purple curves are the magnetic field lines connected to PSP,
Wind, and STEREO A. (b) Dynamic spectrum recorded by PSP/FIELDS, WIND/WAVES,
and STEREO-A/WAVES. The light-travel delays and the intensity due to the
different spacecraft positions have been corrected as if they are observed
from 1 AU. The horizontal bars show the six selected frequencies (576, 625,
723, 815, 925, and 1040 kHz) used for the calculation of the type III burst
source position.  Figure 5: Locations of the interplanetary type III radio
bursts. (a) Enlarged view of the inner heliosphere (corresponds to the black
box in Figure 4). Color circles show the derived source locations of the type
III bursts at six selected frequencies based on a joint analysis of
observations made by all three spacecraft. The light green lobe at each burst
location illustrates the derived emission pattern. The half-power beam width
of each lobe represents the FWHM width of the estimated type III radio
emission pattern. The solid red, green, and purple curves are the magnetic
field lines connected to WIND, PSP, and STEREO-A, constructed by combining
PFSS extrapolation and Parker spiral ballistic mapping results joining at a
source surface of 2.5$R_{\odot}$ (dashed circle). WIND and PSP are
magnetically connected to the jet region, while STEREO is not (see Section
2.5). Straight dashed lines are the line of sight directions of the three
spacecraft. (b) Measured type III burst intensities by the three spacecraft,
scaled to 1 AU, at different HEE longitudes and the corresponding fit results
of their angular emission patterns at the six selected frequencies. The
vertical dashed lines mark the derived source longitudes at their respective
peaks. A relative uncertainty of 10% for the observed intensity is assumed,
shown as the error bars.

This type III radio burst event was recorded by three spacecraft—PSP/FIELDS,
WIND/WAVES, and STEREO-A/WAVES observing the Sun from different viewing
perspectives and heliocentric distances. The locations of the three spacecraft
in the Heliocentric Earth Ecliptic (HEE) coordinate system are shown in Figure
4(a). At the time of the event, all three spacecraft were located within (WIND
and STEREO-A) or very close to (PSP) the ecliptic plane. Both WIND/WAVES and
STEREO-A were located at a radial distance of $\sim$1 AU, while PSP was much
closer at 0.37 AU away from the Sun. Figure 4(b) shows the radio dynamic
spectra of the type III burst event observed by PSP/FIELDS, WIND/WAVES, and
STEREO-A/WAVES, respectively, in 10 kHz–20 MHz. The data in the units of
measured voltage power ($\mathrm{V}^{2}\ \mathrm{Hz}^{-1}$) have been
calibrated to physical values in solar flux units (sfu) (Dulk et al., 2001;
Hillan et al., 2010; Eastwood et al., 2009; Pulupa et al., 2017). The widely-
separated, multi-vantage-point observations from the three spacecraft makes it
possible to constrain the location and directivity of the type III radio burst
as it propagates in interplanetary space by using their relative intensity and
timing (see, e.g., recent studies by Musset et al. 2021; Badman et al. 2022).

Here we follow the method used in Musset et al. (2021) to perform the position
and directivity analysis. First, we assume that the angular emission pattern
of the type III bursts at a source location $\vec{r}$ follows the form:

$I(\vec{r},\mu)=C_{0}\exp\left(-\frac{1-\mu}{\Delta\mu}\right),$ (3)

where $\mu=\cos(\varphi-{\varphi}_{0})$ describes the longitudinal angle of
the emission pattern $\varphi$ with regard to the peak direction
${\varphi}_{0}$. $\Delta\mu$ is a parameter for the width of the emission
pattern. Because the active region is located at a low solar latitude and all
probes are located within or very close to the ecliptic plane, for simplicity,
we only consider the longitudinal dependence of the radio emission pattern.

The radio waves generated at the source location $\vec{r}$ then propagate
through interplanetary space and reach the radio instruments onboard the three
spacecraft. Assuming free-space propagation of the radio waves from the
source, the intensity of the observed radio intensity at the location of a
spacecraft $i$ $\vec{r}_{i}^{obs}$ follows an inverse square law
$I_{i}^{obs}\propto 1/(\vec{r}_{i}^{obs}-\vec{r})^{2}$. In addition, a
spacecraft located at a larger distance from the source would have observed
the burst with a larger time delay due to the longer light travel time. Such
an effect is clearly shown when comparing the dynamic spectra obtained by,
e.g., PSP and WIND.

To correct for these effects associated with the different source–spacecraft
distances, before we carry out the directivity analysis, we scale the radio
intensities of all three spacecraft to what would have been measured if the
spacecraft was positioned at 1 AU. We also shift all the spectra in time
accordingly to compensate for the light travel time. We select six frequencies
(576, 625, 723, 815, 925, and 1040 kHz) that are clearly observed by all three
spacecraft. The scaled intensities at the six frequencies are shown in Figure
5(b) as square, circle, and triangle symbols. The measurements made by the
three spacecraft at each frequency are fitted using a least-square-based
minimization technique, shown as color curves in Figure 5(b). The dashed
vertical lines correspond to the longitudes of the peak intensity
$\varphi_{0}$ at the six selected frequencies, which range from 38 to 47
degrees. The fitted values of $\Delta\mu$ in Equation 3 at different
frequencies range from 0.28–0.35, corresponding to an average full width at
half maximum (FWHM) angle of 73–81∘. Such an angular extent is consistent with
those shown in Musset et al. (2021) for another type III burst event. The
radial distances of the type III burst source are calculated using the density
model of Equation 1, again assuming fundamental plasma radiation emitted at
$1.2\nu_{pe}$.

Figure 5(a) shows the derived type III burst source locations and the
directions of their emission pattern at the six selected frequencies as color
circles and light green lobes, respectively. The half-power beam widths of the
lobes represent the FWHM width of each fitted angular emission pattern shown
in Figure 5(b). Type III emission theories suggest that the emission pattern
of type III bursts resembles approximately a dipole or quadrupole shape and is
generally aligned with the tangent of the magnetic field line along which the
type-III-emitting electron beams are propagating (Zheleznyakov & Zaitsev,
1970; Thejappa et al., 2012; Thejappa & MacDowall, 2015), although the exact
source location and directivity pattern of the radio emission is strongly
modulated by propagation effects in the inhomogeneous turbulent corona (e.g.,
Kontar et al., 2019). We conclude that the derived type III directivity is
consistent with the scenario in which the type-III-emitting electron beams are
directed toward the general direction of PSP and WIND. We note that, in our
analysis, we have assumed that the type III bursts are due to fundamental
plasma radiation, which has a dipole-shaped emission pattern (Zheleznyakov &
Zaitsev, 1970). The situation would be different for harmonic radiation as the
emission pattern would have a more complex quadrupole-type shape.

###  2.4 Type III Radio Burst Event: In Situ Signatures at 0.37 AU and 1 AU

Figure 6: (a) Electron count rate from the EPI-Lo instrument onboard
PSP/IS$\odot$IS. The data shown is background subtracted and smoothed using
the Savitzky–Golay method. (b): Composite radio dynamic spectrum using data
from PSP/FIELDS. The white curve shows where the local plasma frequency lies
at the vicinity of the spacecraft. (c) Electron pitch angle distribution
integrated over the energy range of 132–751 eV, obtained by the SPAN-E
instrument onboard PSP/SWEAP. The two vertical dashed lines demarcate the
estimated arrival times of the 132–751 eV electrons at the PSP spacecraft if
we assume these electrons propagate freely along the Parker spiral. (d)
PSP/FIELDS measurements of the magnetic field at the spacecraft. Three
magnetic components in the radial–tangential–normal (RTN) coordinates are
shown.

In the previous subsection, the derived locations of the type III sources and
their emission patterns have implied that the type-III-burst-emitting electron
beams may be propagating along magnetic field lines that are connected to PSP
at 0.37 AU and WIND/Earth at 1 AU, which were located very closely on the
Parker spiral longitudinally. In this subsection, we will discuss in situ
measurements made by PSP and WIND with a focus on signatures of the energetic
electrons.

First, we examine whether the type III burst event indeed constitutes an in
situ event as seen by the PSP spacecraft. One of the main signatures of an in
situ type III burst event is the presence of a low-frequency cutoff near the
local plasma frequency (e.g., Dulk et al., 1998; Cane & Erickson, 2003). As
the type-III-burst-emitting electron beam reaches the vicinity of the
spacecraft, the plasma emission is produced near the local plasma frequency.
No emission at lower frequencies is allowed to propagate, forming a low-
frequency cutoff. Figure 6(b) shows the composite dynamic spectrum in 10
kHz–20 MHz obtained by PSP/FIELDS. It is evident that the type III burst does
show such a low-frequency cutoff near the local plasma frequency line (white
curve) derived using the quasi-thermal noise data from PSP/FIELDS (Moncuquet
et al., 2020). This observation implicates that the escaping electron beams
have reached at least the same radial distance from the Sun as that of PSP.

In Figure 6(a), we show the $>$17 keV energetic electron count rate recorded
by PSP’s Integrated Science Investigation of the Sun (IS$\odot$IS; McComas et
al. 2016). The curve shown is obtained by the IS$\odot$IS Energetic Particle
Instrument that measures the energetic particles with relatively lower energy
(EPI-Lo). The data are first integrated within the energy range of 17–400 keV
after performing background subtraction. Then, following the method in
Mitchell et al. (2020), a Savitzky–Golay smoothing technique with a 7-minute
smoothing window is used to reduce the noise. The horizontal dashed line marks
the 1$\sigma$ deviation above the mean. A small enhancement above the
1$\sigma$ level indicated by the black arrow in Figure 6(a) appears $\sim$20
minutes after the onset of type III radio burst. However, owing to its low
signal-to-noise ratio, we consider this enhancement at best a marginal
detection. Nevertheless, we note that this enhancement occurs very close to
the time when the low-frequency cutoff of the type III radio burst is
observed. Such a temporal coincidence is another possible indication of the
arrival of the energetic electrons at the PSP spacecraft.

Figure 7: (a) Electron pitch-angle distribution in different energy bins from
132 eV to 751 eV as measured by PSP/SWEAP. The differential energy flux has
been normalized to the maximum at each energy bin. Note that the distribution
in 180∘–360∘ is mirrored from the measurements for 0∘–180∘. (b) Differential
electron flux spectrum made at times during the peak (black and red solid
curves) and just prior to the peak (dashed curve). An angle of zero degree is
aligned with the direction of the magnetic vector. The green curve is the
thermal distribution calculated with PSP/FIELD plasma measurements (with a
temperature of $k_{B}T\approx 20\ \mathrm{eV}$). Figure 8: Time profiles of
the in situ energetic electron flux at 40 and 60 keV observed by Wind/3DP. The
horizontal solid and dashed lines mark, respectively, the average pre-event
background level and the $3\sigma$ level above the background. The orange
rectangle indicates the range of the estimated onset time of the energetic
electron event at 60 keV. The black circle indicates the estimated onset time
at 40 keV.

PSP is also equipped with electrostatic analyzers (referred to as Solar Probe
ANalyzers, or SPANs) onboard the Solar Wind Electrons Alphas and Protons
(SWEAP; Kasper et al. 2016) instrument suite that can measure the energy
spectra and directivity of lower energy electrons ($\lesssim$1 keV). Figure
6(c) shows the evolution of the pitch angle distribution of the 132–751 eV
electrons using SWEAP/SPAN-E data. The direction of the magnetic field is at
the 0-degree pitch angle. Although the electrons are more concentrated along
the direction of the magnetic field, representing the ubiquitous electron
“strahl” population in the solar wind (Feldman et al., 1975; Rosenbauer et
al., 1977; Pilipp et al., 1987), such a field-aligned concentration shows an
evident enhancement after 20:20 UT. To further elucidate the pitch angle
distribution of the electrons as a function of energy, we make a polar plot by
averaging the SWEAP/SPAN-E data during the peak time between 20:19 UT and
21:18 UT, shown in Figure 7(a). The different concentric rings in the polar
plot correspond to nine energy channels ranging from 132 eV to 751 eV. The
differential energy flux of each channel has been normalized to their
respective maximum. The anti-sunward beam-like electron distribution can be
seen clearly in all energy channels except for the highest energy channel (751
eV) where the signal is very weak. The pitch angle width at half maximum of
the beam-like distribution decreases slightly from $65^{\circ}$ to
$57^{\circ}$ in increasing energy.

In Figure 7(b), we show 1-D slices of the electron distribution made during
the peak time for directions parallel (red solid curve) and anti-parallel
(black solid) to the magnetic field. The thermal electron distribution at the
respective time period is shown as the solid green curve, calculated using the
thermal electron temperature derived from the plasma measurements made by
PSP/FIELDS. In comparison, the red dashed curve in Figure 7(b) shows the time
just prior to the enhancement of electron flux (averaged from
18:05:00–19:15:00 UT). While a suprathermal electron population is present at
all times (both prior to and during the peak), the electron flux is greater by
a factor of 2 at all energies during the enhancement and is predominant along
the magnetic field direction. The enhancement of the low-energy, $\sim$0.1–1
keV electron flux with a beam-like distribution closely resembles properties
of the low-energy “solar electron burst” events reported in the literature
(Gosling et al., 2003, 2004; de Koning et al., 2006), which have been found to
be strongly associated with the occurrence of type III radio bursts that
extended to the local plasma frequency. The low temporal resolution of our
data (recorded 11 days after the perihelion) does not allow us to distinguish
signatures of systematic time-of-the-flight delays in decreasing electron
energy of the in situ electrons as reported in, e.g., Gosling et al. (2003).
However, the timing of the enhancement is consistent with the period expected
for the arrival of the $\sim$0.1–1 keV electrons (20:23–21:43 UT, indicated by
the interval demarcated by the dashed vertical lines in Figure 6(c)), if we
assume that they originate close to the solar surface at the start time of the
type III radio bursts and propagate along the Parker spiral freely (shown as
the double-sided arrow in Figure 6(d)).

Now we turn to in situ signatures of energetic electrons obtained at 1 AU
using measurements made by the 3D Plasma and Energetic Particle Instrument
onboard the WIND spacecraft (WIND/3DP; Lin et al. 1995). In Figure 8, we show
the time profile of the energetic electron flux from 19 UT to 24 UT in two
energy bands at 40 keV and 60 keV. An enhancement is observed around 20:10 UT,
$\sim$40 minutes after the start of the type III radio bursts. Following the
method discussed in Miteva et al. (2014), we use a straight slope to fit the
logarithm of the 60 keV electron flux profile shown in Figure 8. The
intersection of the fitted slope with the average pre-event background is used
as the estimated earliest onset time of the energetic electron event, or
19:53:49 UT. In addition, we also find the flux that corresponds to three
times the standard deviation of the pre-event background flux (or the
$3\sigma$ level), shown as the horizontal dashed lines. The intersection
between the same slope and the $3\sigma$ level is used to be our estimate for
the latest onset time, found to be 20:03:06 UT. For the 40 keV profile, the
rise can not be described by a single slope. In this case, we simply use the
$3\sigma$ threshold above the background flux to identify the onset time,
marked as a black circle in Figure 8(a).

Figure 9: PFSS model mapped to the synoptic HMI magnetogram for Carrington
Rotation 2216. The blue, red, and purple dots denote the location of the PSP,
WIND, and STEREO-A spacecraft ballistically mapped from 0.37 AU, 1 AU, and 1
AU, respectively, to the source surface at 2.5 $R_{\odot}$ following the
Parker spiral. They are all magnetically connected to AR 12738, as shown by
the PSFF field lines (green, red, and purple curves). However, while both WIND
and PSP are well connected to the jet region (marked by the yellow open
circle), STEREO-A is connected to the opposite side of the AR far away from
the jet region. The black solid line is the source surface magnetic neutral
line mapped to the solar surface.

.

If assuming scatter-free propagation along the Parker spiral with a path
length of 1.2 AU (The green line shown in Figure 4(a)), the release time of
the 60 keV electrons near the solar surface would be $\sim$19:33 UT, which is
delayed by $\sim$11 minutes after the onset of the microflare/type III radio
bursts at $\sim$19:22 UT (19:30:37 UT as observed from 1 AU, corrected with
the light traveling time of 8.3 minutes). If we assume the electrons detected
by WIND are released at the same time as the onset of the type III radio burst
event, the estimated path length for 60 keV electrons is approximately 1.68
AU, which is greater than the expected distance of 1.2 AU along the Parker
spiral. Such a delay has been frequently observed in the past for impulsive
SEE events (e.g., Haggerty & Roelof, 2002; Cane & Erickson, 2003; Kahler &
Ragot, 2006; Kahler et al., 2007; Klassen et al., 2012), and has been
interpreted as either a delayed injection through, e.g., acceleration by
coronal shocks developed in the upper corona (Haggerty & Roelof, 2002) and/or
effects due to transport, which increase the effective path length of the
energetic electrons (Cane & Erickson, 2003).

STEREO-A also carries an energetic particle instrument: the Solar Electron and
Proton Telescope (SEPT; Müller-Mellin et al. 2008). However, it did not detect
any enhancement in the measured energetic electron flux in the 30–400 keV
range. As we will discuss in the next subsection, the magnetic field line
connecting to STEREO-A is rooted at the opposite side of the active region far
away from the jet location, which might explain the non-detection of energetic
electrons arriving at the spacecraft.

###  2.5 The Solar Source: Nonthermal Electrons Escaped from a Solar Jet

In Section 2.3, we have shown that the source trajectory of the type III radio
burst event likely follows magnetic field lines in interplanetary space that
are generally connected to PSP at 0.37 AU and WIND (Earth) at 1 AU. Then, in
Section 2.4, we have shown that both PSP and WIND observed in situ signatures
of energetic electrons that arrived at the spacecraft, while STEREO-A did not.
Here we further discuss the solar source of the type-III-burst-emitting
energetic electrons by examining the magnetic connectivity of the three
spacecraft and concurrent microwave imaging spectroscopy observations of the
solar jet/microflare event.

Figure 10: (a) SDO/HMI radial field magnetogram of the main sunspot. The black
curve corresponds to the dark filament seen in the H$\alpha$ image shown in
(b) and the SDO/AIA 304 Å image in (c). (d) SDO/AIA 1600 Å image shown in
reversed color scale (black is bright). Two ribbons are marked, which are also
outlined as green contours in (a). The red curve represents the magnetic
polarity inversion line. (e) SDO/AIA 131 Å image shown in reversed color
scale. Blue and red contours show radial magnetic field of $-$500 G and 300 G
respectively. (f) EOVSA microwave source at multiple frequencies (50$\%$
contours) overlaid on SDO/AIA 171 Å image. They are colored from red in blue
according to the color bar on the right. The EOVSA beam sizes at different
frequencies are shown at the bottom left corner with the same color scheme.
Figure 11: Evolution of the multi-frequency EOVSA microwave source from 1.6
GHz to 12 GHz, shown as 50$\%$ contours colored from red to blue for (a) pre-
flare phase and (c)–(e) during the peak time. All the background is SDO/AIA
171 Å image. The corresponding times in (c)–(e) are shown as red arrows in the
cross-power microwave dynamic spectrum in (b). The white curve shows the 1.6
GHz light curve. The two orange dashed lines in (b) show the initiation times
of the interplanetary type III radio bursts discussed in Section 2.2. The
EOVSA beam sizes are shown at the bottom left corner in (a).

First, we investigate the solar source region of the in situ SEE event
observed by PSP and WIND. We follow the widely-used PFSS extrapolation method
(see, e.g., Stansby et al., 2020; Gieseler et al., 2022) to first
ballistically map the spacecraft locations following the Parker spiral to the
source surface where the field lines are predominantly radial (taken to be at
a heliocentric distance of 2.5$R_{\odot}$). Then, we trace the field lines
back to the solar surface using the PFSS-extrapolated potential field model
based on the same SDO/HMI synoptic map discussed in Section 2.1. The solar
wind speed is assumed to be 350 km s-1. Figure 9 shows our results. The green,
red, and purple circles mark the locations of the PSP, WIND, and STEREO-A
spacecraft ballistically mapped using the nominal Parker spiral from the
spacecraft’s respective location to the source surface at 2.5$R_{\odot}$. As
shown in Figure 9, PSP and WIND are both well connected magnetically to AR
12738 where the jet occurs. Meanwhile, STEREO-A is connected to the remote
northeast edge of the same active region with a positive polarity. The lack of
magnetic connectivity between the STEREO-A and the jet region explains the
non-detection of energetic electrons by STEREO-A. In addition to the temporal
coincidence discussed in Section 2.2, the PFSS magnetic modeling results
reaffirm that the solar source of the type III burst event and the associated
in situ SEE signatures did indeed originate from the active region which
produced the microflare-related solar jet. As shown in Figure 2(f), the jet
has a favorable magnetic geometry featuring widely open field lines toward the
west, which allows the nonthermal electrons to access interplanetary space and
eventually reach PSP and WIND.

Before the jet eruption at 19:15 UT, a dark mini-filament can be seen in the
H$\alpha$ image taken by the Cerro Tololo station of the Global Oscillation
Network Group (GONG; Figure 10(b)). This mini-filament is located in a mixed
polarity region off the southwest side of the main sunspot, shown in the HMI
radial magnetogram in Figure 10(a). The same mini-filament is also visible in
the SDO/AIA 304 Å image (Figure 10(c)), which is sensitive to plasma at
chromospheric temperatures. This filament starts to rise at $\sim$19:20 UT
followed by the jet eruption at 19:30 UT. Meanwhile, two bright footpoints
start to appear in the SDO/AIA 1600 Å image (Figure 10(d)). The footpoints
reside at opposite ends of the northern leg of the mini-filament with opposite
magnetic polarities (Figure 10(a)). After the jet eruption at $\sim$19:33 UT,
a bright, arcade-like loop appears in the SDO/AIA 131 Å image (Figure 10(e)),
indicative of flare-heated hot plasma at $\sim$10 MK. The magnetic, H$\alpha$,
and EUV signatures of the jet eruption are all broadly consistent with the
mini-filament-driven jet scenario discussed in, e.g., Sterling et al. (2015).

At the time of the event, EOVSA was observing the Sun with 451 science
spectral channels spanning the 1–18 GHz range at a 1-s time cadence. For
imaging spectroscopy, we combine the fine spectral channels into 51 spectral
windows, each of which has a bandwidth of 325 MHz. As the frequency range at
$>$12 GHz has a weak response, in this study, we only show the results from
the first 30 spectral windows ranging from 1.6 GHz to 12 GHz. The EOVSA data
were first calibrated using a celestial source and then were self-calibrated
and averaged to a cadence of 2 s. The multi-frequency EOVSA microwave sources
during the peak are shown in Figure 10(f) as color contours (red to blue
indicate increasing frequency). In Figures 11(c)–(e), we show four snapshots
of the multi-frequency EOVSA images obtained during the pre-event quiescent
period (panel a), the initiation phase of the event (panel c), the first 1.6
GHz peak (panel d), and the second 1.6 GHz peak (panel e, which is identical
to Figure 10(f)), respectively.

Prior to the event, the microwave sources are located at the main sunspot
(Figure 11(a)) likely due to gyroresonance emission from the quiescent thermal
plasma (Zheleznyakov, 1962; Kakinuma & Swarup, 1962; Lee, 2007). At the
beginning of the jet/microflare event, a small extension of the microwave
source along the direction of the jet material starts to be visible (Figure
11(c)). During the peaks of the event, the pre-event sunspot source is still
present, but a new microwave source becomes clearly visible at the location of
the jet eruption. The source morphology in the low and high-frequency regimes
appears distinctly different. At high frequencies (above $\sim$3 GHz), the
microwave source coincides very well with a bright arcade-like structure at
the base of the jet spire. In contrast, at low frequencies ($<$3 GHz) the
microwave source (red contour marked by the blue arrow in Figure 11(d) and the
first three red contours in Figure 11(e)) is located above the arcade. The
low-frequency source appears at the first peak time of the 1.6 GHz emission at
19:30:37 UT and lasts about half a minute. It coincides with the jet peak but
has a much wider angle up to about $90^{\circ}$, indicated by the yellow
dashed lines in Figure 11(e).

##  3 Summary and Discussion

In this study, we have presented a multi-instrument, multi-perspective
observation of an interplanetary type III radio burst event accompanied with
in situ energetic electrons. We then identify the source region of the event
as a solar jet in the periphery of a solar active region through the analysis
of temporal association and magnetic connectivity. Our observations are
briefly summarized as follows:

  1. 1.

By utilizing observations from three well-separated spacecraft (PSP/FIELDS,
WIND/WAVES, and STEREO-A/WAVES), we find that the source motion and emission
pattern of the interplanetary type III radio burst are generally directed
toward PSP at 0.37 AU and WIND at 1 AU.

  2. 2.

PSP/FIELDS observations of the type III radio burst event show that the
electromagnetic radiation reaches the local plasma frequency line, which
suggests that the escaping electron beams have reached at least the same
radial distance from the Sun as that of PSP. Meanwhile, PSP/SWEAP recorded an
enhanced low-energy ($<$1 keV) suprathermal electron burst event with a beamed
anti-sunward angular distribution, implicating that the electron beams have
reached the close vicinity of the PSP.

  3. 3.

WIND/3DP at 1 AU recorded a weak in situ SEE event at 40–60 keV. The onset
time, which occurs about 30 minutes after the type III event, shows a
characteristic energy dependence, implying a solar origin. The inferred
release time of the energetic electrons at the solar surface (assuming free
propagation) is within $\sim$10 minutes of the microwave burst onset,
suggesting a common source.

  4. 4.

STEREO-A/SEPT did not detect any enhancement of energetic electrons at 30–400
keV.

  5. 5.

The onset time of the interplanetary type III radio burst coincides very well
with the occurrence of a solar jet in AR 12738. PFSS extrapolation results
show that PSP and WIND were magnetically connected to the jet region, but
STEREO-A was not, which may explain the detection/non-detection of the
energetic electrons by the three spacecraft.

  6. 6.

The solar jet occurs in an open field line region at the periphery of the AR
and is accompanied by a co-located EOVSA nonthermal microwave source. In
particular, the 1–2.6 GHz microwave source, which we interpret as the
decimetric counterpart of the interplanetary type III radio bursts, features a
morphology that subtends a large angle of 80–90∘ in the open field region,
which is 8–9 times wider than the EUV jet spire itself ($\sim\\!10^{\circ}$).

Figure 12: Schematic of the solar jet event associated with escaping energetic
electrons. (a) Before the jet eruption, a mini-filament lies at the southwest
side of the main sunspot where an opposite magnetic polarity is present. (b)
During the jet eruption, a bright flare arcade is formed due to magnetic
reconnection trailing the erupting mini-filament. Energetic electrons trapped
in the arcade produce the high-frequency microwave (MW) source via incoherent
gyrosynchrotron emission (blue shade). In addition, breakout-type external
reconnection occurs between the erupting mini-filament and the open field
lines, facilitating the eruption and allowing the energetic electrons to
escape. As a result, a low-frequency microwave source is formed due to
coherent plasma radiation (red shade), which appears to subtend a much wider
angle than that of the highly collimated EUV jet spire.

In the following, we incorporate the multifaceted remote-sensing and in situ
observations and discuss them in a coherent picture, shown as a schematic in
Figure 12. The event is driven by the eruption of a mini-filament, or a small-
scale magnetic flux rope, shown as the yellow feature in Figure 12(a). As
depicted by Sterling et al. (2015) and Wyper et al. (2017), the eruption may
lead to magnetic reconnection occurring at locations both trailing and above
the erupting filament/flux rope, referred to inner and outer reconnection,
respectively. The inner reconnection, which is akin to that in the standard
CSHKP eruptive flare scenario (Carmichael, 1964; Sturrock, 1966; Hirayama,
1974; Kopp & Pneuman, 1976), leads to the formation of a post-reconnection
flare arcade with a pair of conjugate footpoints, shown in Figure 2(e) and (d)
respectively. The outer reconnection between the filament and ambient field
allows the eruption to “break out” and untwist, forming the jet material seen
in EUV. The reconnection-driven energy release produces energetic electrons.
They may be accelerated at the reconnection null point(s) (Drake et al., 2006;
Browning et al., 2010; Stanier et al., 2012; Chen et al., 2018; Che et al.,
2021) or in the reconnection-driven outflows or shocks (Yokoyama & Shibata,
1996; Glesener et al., 2012; Chen et al., 2015; Kong et al., 2019). The
accelerated nonthermal electrons trapped in the post-reconnection arcade emit
incoherent gyrosynchrotron radiation, observed as the compact, high-frequency
($>$3 GHz) EOVSA microwave source (depicted as the blue-shaded region).

The upward-directed nonthermal electrons, in contrast, have access to the open
field lines in the direction of the jet eruption. Thanks to their close
magnetic connectivity with the jet region (c.f., Figure 9), some of the
electrons reach the PSP and WIND spacecraft and are recorded as in situ
energetic electron events. STEREO-A was not magnetically connected to the jet
region and did not record any energetic electron event.

The nonthermal electrons propagating along open field lines can quickly
develop into a beam-like distribution with bump-on-tail instabilities and emit
coherent plasma radiation near the plasma frequency or its second harmonic
(Lin, 1990; Reid et al., 2011). Assuming harmonic plasma radiation, the
estimated plasma density of the observed 1–2.6 GHz microwave source is
$3\times 10^{9}$–$3\times 10^{10}$ cm-3, which is typical for the low corona
in an active region. The escaping nonthermal electrons enter interplanetary
space and generate the meter-decameter wave type III radio bursts observed by
e-Callisto, PSP, WIND, and STEREO in a broad frequency range from $\sim$100
MHz down to $<$0.1 MHz. We note that each electron beam can generate a type
III radio burst with a broad, dipole-like, or quadruple-like emission pattern
(Zheleznyakov & Zaitsev, 1970). In addition, particle and radio wave
instruments have different capabilities in detecting weak signal against the
background noise. Therefore, it is not surprising that STEREO-A recorded a
weak type III radio burst event, despite not detecting the energetic electrons
_in situ_.

We also point out that the 1.6–3 GHz EOVSA microwave source located above the
post-reconnection arcade is likely different from that reported by Glesener &
Fleishman (2018), interpreted by the authors as a source due to incoherent
gyrosynchrotron radiation. Based on the spectral properties shown in Figure 3,
we have concluded that our 1–2.6 GHz microwave source should resemble the
previously reported decimetric type III radio bursts observed by VLA in a
similar frequency range (1–2 GHz L band), which had a much higher frequency
and time resolution to reveal their detailed spectral, temporal, and
polarization properties (Chen et al., 2013, 2018).

One striking finding is that, contrary to most existing jet models in which
nonthermal electrons are often assumed to escape along the highly collimated
jet spire, the morphology of our observed 1–3 GHz microwave source is by no
means collimated. In stark contrast, the source features a fan-like morphology
with an opening angle of $\sim$80–90 degrees at any instant (2-s snapshot in
our case), rather than the narrow EUV jet that opens by only $\sim$10 degrees.
Note that, in Chen et al. (2018), with an ultra-high time resolution of 50 ms
provided by the VLA, the decimetric type III bursts were resolved into a group
of $>$10 individual bursts within a duration of $\sim$1 s. Although the
trajectory of the individual electron beam generating each burst (in 50 ms)
formed a highly collimated, nearly straight line, all the beams of the
$\sim$1-s-duration type III burst group were shown to fan out to a much wider
angle ($\sim\\!30^{\circ}$ in their event). In addition, although they seemed
to propagate along the same general direction, the electron beams did not show
an exact co-alignment with the EUV jet spire. With EOVSA’s limited time
resolution, we are unable to resolve these individual bursts in our event.
However, it remains a possibility that our case could be similar to the
previously reported VLA event.

Our observations imply that the accelerated, upward-going nonthermal electrons
have access to a far wider angle than that of the jet spire itself, by as much
as one order of magnitude (or two orders of magnitude in solid angle). The
wide opening angle of the escaping, type-III-burst-emitting electron beams has
the following broader implications:

  1. 1.

Energetic electrons may be injected into a broad range of interplanetary
magnetic field lines near their source at the solar surface. Therefore, the
wide spread of flare events that produce observed SEE events at a single
observer location (e.g., Anderson & Lin, 1966; Lin, 1974; Reames, 1999) or
SEE/SEP events that deviate significantly from their nominal magnetic field
footpoints (Wiedenbeck et al., 2013; Leske et al., 2020) does not necessarily
have to be interpreted solely in terms of cross-field diffusion effects or
secondary acceleration site(s) in the upper corona. In Lin (1974), flares
associated with impulsive SEE events observed in 1964–1972 are shown to
distribute in a wide longitudinal range from $\sim\\!30^{\circ}$ east to
$90^{\circ}$ west, with a full width of $70^{\circ}$. A more recent
statistical study of ${}^{3}{He}$-rich impulsive SEE events from 1995 to 2005
observed by WIND/3DP (Wang et al., 2012) also suggests that the longitudinal
distribution of such SEE-associated flares distribute widely from $90^{\circ}$
east to $90^{\circ}$ degrees west. Such an observed longitudinal width, which
can be interpreted as the (statistically averaged) width of the injection cone
of energetic electrons in a single event, is broadly consistent with our
findings based on direct microwave imaging spectroscopy.

  2. 2.

When comparing the number of flare-accelerated nonthermal electrons and those
that escaped into interplanetary space, care must be taken to properly account
for the injection angle of the upward-going electrons. For example, if one
only uses the narrow EUV jet spire for the angle estimate, the derived total
upward-going electron number based on the same measured in situ electron flux
would be underestimated by as much as two orders of magnitude. Despite this,
it is worth noting that the conclusion reached by several previous studies,
including Lin & Hudson (1971), Krucker et al. (2007), and Wang et al. (2021)
likely still holds. These studies estimated that the number of energetic
electrons escaping to interplanetary space is only a small fraction of those
generating HXR/microwave emission in the post-reconnection flare arcade or
footpoints. These cited studies correctly based their estimates of the
injection cone of the escaping energetic electrons on the width of the
statistical longitudinal distribution of the SEE-generating flares rather than
that of the EUV jets themselves.

For our event, a comparative study between the escaping in situ energetic
electrons ($>$10s of keV) and those that remain at the flare site in a manner
similar to Wang et al. (2021) (and references therein) is challenging, if not
impossible, due to the lack of in situ measurements with sufficient signal-to-
noise over a wide range of energies and the unavailability of hard X-ray data.
However, a rough estimate using WIND/3DP data recorded at two channels (40 keV
and 60 keV) and assuming a 90∘ opening angle of the upward-directed electrons,
the estimated power of $>$25 keV nonthermal electrons at the peak time is
approximately $1\times 10^{21}$ ergs s-1. Consistent with earlier findings,
the nonthermal power of upward-directed electrons is orders of magnitude lower
than that of downward-directed nonthermal electrons produced in microflares
inferred from the X-ray data, which has a nonthermal power of $>$25 keV
electrons ranging from 1022–1027 ergs s-1 (Hannah et al., 2008). We are
extending our investigations to larger impulsive SEE events that are well
connected to their source regions on the Sun and will report our results in
future studies.

The authors acknowledge Drs. Sophie Musset, Radoslav Bučík, Sung Jun Noh, and
Marc Pulupa for helpful discussions. The work by MW and BC is mainly supported
by NASA grant HSO Connect 80NSSC20K1282, NASA grant HSO PSP data support
80NSSC20K0026, and NSF CAREER grant AGS-1654382 to NJIT. SY, JL, and HW
acknowledge additional support by NASA HSO Connect grant 80NSSC20K1283, NSF
grants AGS-2114201, and AGS-2229064 to NJIT. CMSC is supported in part by
NASA’s Parker Solar Probe Mission, contract NNN06AA01C. EOVSA operations are
supported by NSF grants AST-1910354 and AGS-2130832 to NJIT. Parker Solar
Probe was designed, built, and is now operated by the Johns Hopkins Applied
Physics Laboratory as part of NASA’s Living with a Star (LWS) program.

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