# Multifrequency microwave imaging of weak transients from the quiet solar
corona

Surajit Mondal Center for Solar-Terrestrial Research, New Jersey Institute of
Technology,
323 M L King Jr Boulevard, Newark, NJ 07102-1982, USA  Bin Chen Center for
Solar-Terrestrial Research, New Jersey Institute of Technology,
323 M L King Jr Boulevard, Newark, NJ 07102-1982, USA  Sijie Yu Center for
Solar-Terrestrial Research, New Jersey Institute of Technology,
323 M L King Jr Boulevard, Newark, NJ 07102-1982, USA

###### Abstract

Understanding the dynamics of the quiet solar corona is important for
answering key questions including the coronal heating problem. Multiple
studies have suggested small-scale magnetic reconnection events may play a
crucial role. These reconnection events are expected to involve acceleration
of electrons to suprathermal energies, which can then produce nonthermal
observational signatures. However, due to the paucity of sensitive high-
fidelity observations capable of probing these nonthermal signatures, most
studies were unable to quantify their nonthermal nature. Here we use joint
radio observations from the Very Large Array (VLA) and the Expanded Owens
Valley Solar Array (EOVSA) to detect transient emissions from the quiet solar
corona in the microwave (GHz) domain. While similar transients have been
reported in the past, their nonthermal nature could not be adequately
quantified due to the unavailability of broadband observations. Using a much
larger bandwidth available now with the VLA and EOVSA, in this study, we are
able to quantify the nonthermal energy associated with two of these
transients. We find that the total nonthermal energy associated with some of
these transients can be comparable to or even larger than the total thermal
energy of a nanoflare, which underpins the importance of nonthermal energy in
the total coronal energy budget.

††software: Numpy (Harris et al., 2020), Scipy (Virtanen et al., 2020), Python
3 (Van Rossum & Drake, 2009), Matplotlib (Hunter, 2007), Sunpy (The SunPy
Community et al., 2020), Astropy(Astropy Collaboration et al., 2013, 2018,
2022), Aiapy(Barnes et al., 2020) ††facilities: OVRO:SA, SDO, GOES

##  1 Introduction

The solar corona is generally classified into active regions and quiet solar
corona. Active regions are defined as those regions of the solar corona which
harbor strong magnetic fields and are bright in X-rays and extreme ultraviolet
bands. They are responsible for large explosive events like solar flares,
coronal mass ejections, etc. On the other hand, the quiet solar corona has
weak magnetic fields and does not show such explosive behavior. However, with
the development of each new generation of instruments, it has become
increasingly clear that the quiet sun also shows a plethora of dynamics. The
most recent example of this dynamics is the observation of “campfires”
(Berghmans et al., 2021) by the Extreme Ultraviolet Imager (Rochus et al.,
2020) onboard the Solar Orbiter (Müller et al., 2020). Quiet sun dynamics has
also been reported by other authors (e.g., Krucker et al., 1997; Kuhar et al.,
2018; Innes, 2001; Harrison et al., 1999; Berghmans et al., 1998; Parnell &
Jupp, 2000; Chitta et al., 2021; Mandal et al., 2021; Chen et al., 2019;
Rouppe van der Voort et al., 2016; Joshi et al., 2020; Phillips et al., 2000).
We refer readers to reviews by Shibasaki et al. (2011); Madjarska (2019);
Nindos et al. (2022) for a more detailed discussion on these topics.
Observations of such extensive dynamics in the quiet sun are increasingly
making the name “quiet” a misnomer.

There are also theoretical reasons as to why we expect to have a dynamic quiet
solar corona as well. The most important of these reasons probably comes from
the efforts made so far to understand the coronal heating problem (see
Klimchuk, 2015, for a review). All of the notable theories which try to
explain this process suggest some dynamics in the quiet solar corona, although
the exact dynamics can vary from theory to theory. For example, the nanoflare
hypothesis (Parker, 1988) suggests that a large number of nanoflares are
continuously happening throughout the quiet corona, which in turn are
responsible for maintaining the million-degree coronal temperature. This
scenario requires the presence of ubiquitous small-scale magnetic-
reconnection-driven nanoflare events throughout the corona. During the process
of magnetic reconnection, particles get accelerated, although the extent to
which this energization happens depends intimately on the details of the
reconnection process (see, e.g., Bakke et al., 2018; James & Subramanian,
2018; Glesener et al., 2020; Frogner et al., 2020). These accelerated
particles can either escape into the interplanetary space and contribute to
the suprathermal particle population observed in the solar wind (Wang et al.,
2016; Hou et al., 2021; Mitchell et al., 2020; Hill et al., 2020) or can get
thermalized in the solar atmosphere and contribute to the energy budget of the
quiet solar corona (e.g. De Pontieu et al., 2011; Frogner et al., 2020, etc.).
However, due to the rarity of studies regarding the energetics of these
accelerated nonthermal electrons from the small microflares and nanoflares,
their exact contribution to coronal heating is, as of now, unknown. Thanks to
the availability of new instruments with high angular resolution, the recent
detection of small-scale reconnection-driven spicules (Samanta et al., 2019),
“campfires” (Berghmans et al., 2021), and the suggestions that they might be
related to the hypothesized nanoflares also make studies regarding detection
of nonthermal electrons particularly interesting and timely.

While the presence of nonthermal electrons in the quiescent corona has been
inferred using observations at the (extreme) ultraviolet wavelengths (e.g.,
Testa et al., 2014), a more direct means of detecting these nonthermal
electrons is through their emission at X-ray and radio wavelengths. Detection
of X-ray transients from the quiet solar corona has already been reported
(e.g. Kuhar et al., 2018; Vadawale et al., 2021; Paterson et al., 2022, etc.).
Confirmed detection of nonthermal electrons has also been reported for weak
microflares with the Reuven Ramaty High Energy Solar Spectroscopic Imager and
Nuclear Spectroscopic Telescope Array (NuSTAR) X-ray telescope thanks to its
high sensitivity (Qiu et al., 2004; Kundu et al., 2006; Stoiser et al., 2007;
Hannah et al., 2008a; Glesener et al., 2020; Cooper et al., 2021). Radio
observations have also presented strong evidence regarding the presence of
nonthermal electrons in the quiet solar corona. Mondal et al. (2020); Sharma
et al. (2022); Mondal et al. (2023) reported the detection of Weak Impulsive
Narrowband Quiet Sun Emissions (WINQSEs) which the authors hypothesize are
weaker cousins of the well-known type III radio burst and originate due to
coherent plasma emission from nonthermal electrons generated in nanoflares
(Mondal, 2021). Recent studies at millimeter wavelengths have also revealed
the presence of small-scale transients in the quiescent solar chromosphere
(e.g. Nindos et al., 2020; Eklund et al., 2020; Nindos et al., 2021, etc.).
While these chromospheric transients generally occur due to thermal free-free
emission, they can be driven by the precipitation of nonthermal electrons
produced due to weak energy release events. For producing observable
nonthermal gyrosynchrotron emission in these frequencies, a sufficiently large
electron population with energy in the MeV range is required, which is not
expected in the case of small-scale flares (White & Kundu, 1992).

Studies of these weak radio transients from the transition region and the low
corona provide mixed results. While most studies suggest that these transients
are free-free in nature (see Madjarska, 2019, for a review), some suggest that
some fraction of them are nonthermal in origin (Krucker et al., 1997; Kundu et
al., 2006), implicating the acceleration of nonthermal electrons in small-
scale energy release events. However, these studies were done a few decades
back when broadband radio imaging spectroscopy observations were not
available. This posed challenges in identifying the emission mechanism of
these sources. Additionally, due to the weak nature of these sources, image
fidelity has always been an issue. Here we use simultaneous detection of such
sources with two instruments or over wide bandwidths to increase the fidelity
of the detections.

In this paper, we use simultaneous broadband radio imaging spectroscopy data
from the Very Large Array (VLA; Perley et al. 2011) and the expanded Owens
Valley Solar Array (EOVSA; Gary et al. 2018) to detect weak radio transient
sources and also obtain their spectral and temporal behavior when possible. We
supplement these data with that obtained from the Atmospheric Imaging Assembly
(AIA; Lemen et al. 2012) onboard the Solar Dynamics Observatory (SDO; Pesnell
et al. 2012) to search for counterparts of these sources in the Extreme
Ultraviolet (EUV) and use the EUV properties of these sources to delve deeper
in their nature than that had been possible earlier.

This paper is structured as follows. In Section 2, we briefly describe the
observation. Section 3 describes the details of the data analysis procedure.
In Section 4 we present the results obtained, which are then discussed in a
broader context in Section 5. Finally, we conclude with a brief summary in
Section 6.

##  2 Observations and context

The data presented here were acquired using the EOVSA and the VLA on February
1, 2020, between 19:00:00–23:00:00 UT. The Sun was extremely quiet on this
day. No X-ray flare was reported by the Geostationary Operational
Environmental Satellite (GOES). There was only one active region designated as
National Oceanic and Atmospheric Administration (NOAA) 12757 presenting on the
west limb. In addition, a bi-polar, but spotless magnetic structure is located
on the disk (at S10W10). Fig. 1 shows contours of the full-day integrated
radio map from the
EOVSA111http://ovsa.njit.edu/browser/?suntoday_date=2020-02-01 at 3 GHz over
an image from the Solar X-ray Telescope (XRT; DeLuca et al., 2000) onboard
Hinode with the Al-poly filter (left panel) and an SDO/AIA 171 Å image (right
panel). A radio counterpart is detected from each region against the quiet Sun
disk.

The VLA observed the Sun during this time in the subarray mode in its
C-configuration, with one subarray operating in the P band and another
operating in the L band (0.994–2.006 GHz). Here we present data from the
L-band. The entire band is divided into 8 spectral windows, each with a
bandwidth of 128 MHz. Each spectral window has 128 channels and each channel
has a width of 1 MHz. The maximum baseline length is 3.2 km, corresponding to
an angular resolution of 14′′–28′′ in 1–2 GHz. We have also analyzed EOVSA
data from this time period, focusing primarily on the band spanning
1.425–1.749 GHz, which has a frequency closest to the analyzed VLA L band
data.

Figure 1: The full day integrated EOVSA 3 GHz radio map overlaid on the
Hinode/XRT soft X-ray map (left panel) and the SDO/AIA 171Å EUV map (right
panel).

##  3 Data analysis

###  3.1 Calibration, imaging and source detection

The VLA observation on this day did not have a flux calibrator observation.
Hence, approximate flux densities were estimated assuming that the flux of the
phase calibrator, J1941-1524, is the same as that given in the VLA Calibrator
manual222http://www.vla.nrao.edu/astro/calib/manual/csource.html at all
frequencies. The flux density at 20 cm and 6 cm were used to determine the
spectral index, which was then used to obtain the frequency-dependent flux
density at each spectral window. All analysis was done using the Common
Astronomy Software Applications (CASA, McMullin et al., 2007). At the time of
the observation, spectral windows 1 (centered at 1.185 GHz) and 4 (centered at
1.557 GHz) were heavily affected by radio frequency inference (RFI) and were
excluded from further analysis. Details of the calibration and data analysis
procedure are provided in the Appendix. Calibrated EOVSA data were obtained
from the observatory for this day following the standard calibration
procedure.

Due to the large volume of data, automated techniques were used both for
deconvolution and source identification purposes. For imaging the VLA data, we
divided the entire duration into 15-minute chunks and imaged each chunk using
the image deconvolution task tclean with the auto-masking mode. Unless
specified otherwise, the time integration and frequency integration is 15
minutes and 128 MHz, respectively. Details of the imaging procedure are
provided in the Appendix. However, we find this technique is not very useful
for processing the EOVSA data for the weak radio transients due to the
particularly high sidelobe levels ($\sim 70$%). Hence the EOVSA data were
imaged manually and sources were identified with visual inspection.

###  3.2 Filtering scheme to remove probable spurious sources

Careful considerations were taken to ensure that no spurious source is
included in the imaging results used for further analysis. The automasking
algorithm of tclean which was used to identify real sources during the
deconvolution procedure was tuned such that it only identifies sources that
are higher than the 1.5 times the maximum sidelobe level of the brightest
sources identified earlier. During the image deconvolution, frequent major
cycles (Schwab, 1984)333The CLEAN algorithm has two major steps, namely the
minor cycle and major cycle. During the minor cycle, model sky components are
found in the image plane iteratively. After each model component is found, a
scaled and truncated copy of PSF centered at that component is subtracted.
During the major cycle, all the found components are Fourier transformed to
the visibility plane and then subtracted from the observed visibilities. For
more details, we refer the reader to
https://science.nrao.edu/science/meetings/2018/16th-synthesis-imaging-
workshop/talks/Wilner_Imaging.pdf. were performed to ensure that the artifacts
due to inaccurate subtraction of the instrumental point spread function are
minimal. However, in the spirit of additional caution, we considered the
possibility that still some sources might be sidelobes of real sources. The
possibility of spurious source detection is much more in the EOVSA data. The
sidelobe levels are very high ($\sim 70\%$ at $\sim$1′ away from the main beam
at 1.5 GHz) and hence it often becomes impossible to determine the true
location of a source when multiple closely spaced sources are present in the
image. While care was taken to minimize these effects, we found that the best
way to find true sources is to compare the images obtained using data having
very different uv-distributions and PSFs. Both the uv-distribution and image
artifacts change significantly between images with very different frequencies.
Hence if a source is detected at different frequencies, it is considered to be
a real source. If a source is detected at a single frequency in the VLA/EOVSA,
we investigate if the source is also detected by the other instrument. For
additional caution, we also compare the flux density of the source in both
images if it is detected by both instruments. Due to the difference between
the frequency and flux scale of the two instruments we assume a 15% and 10%
systematic flux uncertainty in the case of EOVSA and VLA, respectively. If
under these assumptions the flux and location of the source match in the EOVSA
and VLA, it is considered to be a real source. Additionally, the brightest
source in each image is also believed to be real as it is highly unlikely that
other real sources in the image conspire such that their sidelobes merge
together to produce the brightest source in the image. To summarize a source
is considered to be real if it satisfies at least one of the following
criteria:

  1. 1.

It is the brightest source in the deconvolved image.

  2. 2.

The same source is detected at multiple frequencies over a wide bandwidth.

  3. 3.

The same source is detected in both EOVSA and VLA deconvolved images and their
flux densities are consistent within uncertainties.

##  4 Results

Using the techniques described in the previous section, we have detected
several sources with high confidence, some lying on coronal holes, some
associated with coronal bright points, some located beyond the limb, and some
lying above the network regions. Below we discuss examples of these different
types of sources. We have not included sources associated with active regions
as these sources have been studied quite extensively and are not the focus of
this work.

###  4.1 Beyond the limb source

While the integration time of EOVSA is 1 second, we have averaged the data
over 15 minutes for this work. This was done in order to increase the image
signal-to-noise ratio (SNR), and also for the ease of exploring the entire 4
hours of data with manual imaging. This source was first identified at 1.5 GHz
using EOVSA data by averaging over 15 minutes between 21:15:00–21:30:00. It
was also detected at a few other frequencies, although significant spatial
averaging was needed for this. In the right panel of Fig. 2 radio contours of
this source are overlaid on a nearby AIA 171Å image. The spectrum of the
source is shown in the left panel. The spectrum has been determined by taking
the peak value of this source after smoothing each image to a resolution of
$150^{{}^{\prime\prime}}\times 150^{{}^{\prime\prime}}$. At this resolution,
the source becomes unresolved, and hence the peak value (in units of Jy/beam)
is equal to the integrated flux density (in units of Jy). The error bars were
obtained by adding the rms of the image and a 15% flux uncertainty in
quadrature. We have done a differential emission measure analysis using
publicly available code444https://github.com/ianan/demreg/tree/master/python
following Hannah & Kontar (2012, 2013) and use the output of that to calculate
the expected free-free emission using the code developed in Fleishman et al.
(2021). The expected flux density due to free-free emission is shown using a
black dashed line. It has been calculated directly from the model solar
emission, by summing the pixel values inside the outermost contour shown in
the right panel of Fig. 2. It is evident that the expected flux density is
much lower than that observed in the EOVSA radio images. However, it should be
noted that there can be small differences because the EUV limb and the radio
limb do not lie at the same location. Additionally, the EUV images do not seem
to have a counterpart to the observed radio source. We have also simulated an
EOVSA observation using the free-free emission model and produced simulated
images using the same procedure as that followed while producing the observed
EOVSA map. No structure, similar to that observed in the EOVSA map, is
detected in the simulated map, even though the rms of both the simulated and
observed maps are comparable. Based on this we rule out free-free emission as
the dominant emission mechanism behind the observed source.

Next, we investigate if a gyrosynchrotron model can explain the observed
spectrum. The gyrosynchrotron model was obtained using the code available in
Kuznetsov & Fleishman (2021); Fleishman et al. (2021). The source is assumed
to be homogeneous and isotropic. The nonthermal electron distribution is
assumed to be a powerlaw between $E_{min}$ and $E_{max}$ with powerlaw index
$\delta$. The magnetic field (B), $\delta$, and number density of nonthermal
electrons were kept as free parameters during the fitting procedure. We also
manually adjust other parameters to obtain a good fit to the data. The density
of the thermal and nonthermal electrons are denoted as $n_{\rm th}$ and
$n_{\rm nth}$ respectively. The angle between the LOS and the magnetic field
is denoted as $\theta$. The parameters used for modeling the spectra are given
in Table 1 in the top row, marked with the label S1. The fitted spectrum is
shown in the left panel of Fig. 2 using a blue line. It appears that for this
source, $n_{\rm nth}$ is greater than $n_{\rm th}$, which, while rather
uncommon, has been reported earlier in some flare events (Krucker et al.,
2010; Fleishman et al., 2016). We have been unable to find a valid model in
which $n_{\rm nth}$ is smaller than the assumed thermal density, even when the
magnetic field is allowed to be as high as 5 kG. While we have provided the
formal uncertainties for the fitted parameters, due to the insufficient
frequency sampling and bandwidth coverage, the fit is highly under-
constrained. The fit parameters given in the table are certainly non-unique
and should only be taken as representative values. Thus the primary source of
uncertainties in those fit parameters is largely due to the systematic
uncertainties due to the under-constrained fitting. Using these representative
fit parameters, we calculate that the total nonthermal power of this source is
$2.6\times 10^{26}\,$ergs s-1. Assuming a constant power over the entire
integration time, we estimated the total nonthermal energy associated with
this source to be $2.3\times 10^{29}\,$ergs, which is comparable to that
estimated in the case of microflares based on X-ray data (Hannah et al.,
2008a, b; Glesener et al., 2020).

Figure 2: Left panel: The red points show the observed spectrum of the above-the-limb source (S1 in table 1) between 21:15–21:30. The blue line shows the fitted gyrosynchrotron model. The black dashed line shows the expected spectrum if the emission due to optically thin free-free radiation. Right panel: Contours of the radio source at 1.6 GHz overlaid over a SDO/AIA 171Å image.  |  Magnetic field (G) | $\delta$ |  Emax (MeV) |  $\theta$ (deg) |  $\log_{10}$($nth$ (cm-3)) |  Temper- ature (MK) |  LOS depth (arcsec) |  Area (arcsec2) |  $\log_{10}$($nnth$ (cm-3) |  Emin (keV)
---|---|---|---|---|---|---|---|---|---|---
S1 |  47$\pm$7 | 6.4$\pm$0.3 |  10 |  50 |  9.5 |  3 |  6.41 |  326 |  9.8$\pm$0.2 |  30
S2 |  129$\pm$12 | 5.7$\pm$0.2 |  10 |  70 |  9.4 |  3 |  5 |  100 |  9$\pm$0.7 |  1
Table 1: Parameters used to obtain the model gyrosynchrotron spectrum shown in
Figs. 2 and 5. Note due to the under-constrained nature of the spectral
fitting, they should only be regarded as representative values.

###  4.2 Source associated with coronal bright point

This source was detected at 4 frequencies in the VLA data between
19:00:00-19:15:00. Radio contours of this source (S2 in table 1) are overlaid
on an SDO/AIA 193Å image at 19:06:16 in the left panel of Fig. 3. The blue,
white, magenta, and cyan contours correspond to images made at 1.057, 1.313,
1.441, and 1.685 GHz respectively. This source also had a signature in the
soft X-ray wavelengths, shown on the right, where the radio 1.441 GHz contour
is overlaid on a Hinode/XRT Al-poly image. This source was only detected at
1.4 GHz in the later time period 19:15:00–19:30:00 and is not detected at any
frequency at later times. In Fig. 4, we show the 193 Å and 1.4 GHz light
curve. The 1.4 GHz light curve was obtained by making images with a time
integration of 5 minutes. The coronal bright point (CBP) shows a clearly
decreasing flux, which implies that it was in the decay phase during this
time. Interestingly we find that during the time when radio data were
available and the source was detected, the 1.4 GHz light curve of this source
and the EUV light curve show very similar trends.

Figure 3: Radio contours of the source (S2 in table 1) described in Sec 4.2
are overlaid on a AIA 193Å image (left panel) and a XRT Al-poly image (right
panel). The blue, white, magenta and cyan contours correspond to images made
at 1.057, 1.313, 1.441 and 1.685 GHz respectively. Figure 4: Light-curve at
193Å from a 24${}^{"}\times$14" box centered on the black cross shown in Fig.
3 is shown in blue. The 1.4 GHz light curve is shown in red.

In the upper panel of Fig. 5, the spectrum of this source is shown. The
absolute value of the stokes V/I spectrum of this source is also shown in the
bottom panel. The error bars have been determined by adding a 10% systematic
flux uncertainty in quadrature to the rms of the image. The red triangles
denote the upper limits obtained using the 3 times the error in the estimated
V/I and are shown when stokes V is not detected with at least an SNR of 3. The
blue curve shows a model gyrosynchrotron spectrum which can account for the
detected flux and the degree of circular polarization at different
frequencies. It is evident that the model predicts a higher degree of circular
polarization at 1.68 GHz, than that expected from the upper limit at that
frequency. Such behavior is possible if there are inhomogeneities in the
source, leading to a decrease in the observed circular polarization. However,
exploring the details of this is beyond the scope of this work. The parameters
used for modeling the spectra are given in Table 1 in the top row, marked with
the label S2. The nonthermal energy flux estimated using the model parameters
is $7\times 10^{22}\,$erg s-1. Again assuming a constant power over the entire
integration time, we estimate the nonthermal energy associated with this
source as $6\times 10^{25}\,$ergs. The average thermal energy estimated from
DEM analysis for this source is $5\times 10^{25}\,$ergs, comparable to the
estimated nonthermal energy of the microwave source.

Past studies of CBPs have assumed that the radio emission associated with them
is generated due to free-free emission (Habbal et al., 1986). A high degree of
circular polarization, if detected, was explained by propagation effects
through a magnetized plasma. We investigate this possibility using simulated
free-free emission maps, generated by the procedure described in Section 4.1.
We assume that the medium has a uniform magnetic field of 100 G. The black
dashed line shows the expected degree of circular polarization from this
simulation. It is evident that the simulated values are much lower than those
observed. Hence we conclude that free-free emission cannot be the emission
mechanism behind the observed source.

Figure 5: Red and blue indicate the observed values and the modeled
gyrosynchrotron spectrum respectively for the source described in Sec 4.2. The
red triangles denote the upper limits obtained using the 3 times the rms in
the Stokes V image. The black dashed line shows the expected value assuming
free-free emission and a medium with a magnetic field of 100 G.

###  4.3 Sources associated with coronal holes

While several sources were detected in coronal holes, three sources were
chosen for further analysis because these are the brightest sources in the
respective images and hence were unlikely to be significantly affected by the
sidelobes of other sources. The radio contours of these three sources have
been overlaid on SDO/AIA images at a similar time, and are shown in the first
row of Fig. 6. The sources in the right, middle, and left panels are detected
at 1.313, 1.941, and 1.941 GHz respectively. In the second and third rows, the
light curves of these radio sources and those of the EUV sources (centers of
the cyan dashed circles drawn in the upper panels) are shown. The EUV sources
have been identified through visual inspection such that they are located
close to the radio source and their light curve shows qualitative similarity
with that of the corresponding radio source. However, it is quite possible
that multiple EUV sources lying within the instrumental resolution element of
the radio instruments may contribute to the observed radio emission. Hence
while identification of the EUV source bolsters the fidelity of the detected
sources, their exact location is only accurate up to the instrumental
resolution of the radio data. In the fourth row, the GOES light curve is
shown. The black dotted line shows the time when the radio flux density is
maximum. It should be noted that while this line has a spread of 5 minutes,
which is the integration time of the radio images, the spread has not been
shown in these plots. Interestingly we find that for each source, we find an
X-ray peak at the same location as the radio peak. However, it should also be
noted that at these low flux levels GOES light curve has a lot of
contamination due to electrons and in absence of independent confirmation, the
mere presence of these X-ray peaks does not confirm an X-ray signature. Movies
showing the variability in EUV at the location of these three sources are
provided in the supplementary material. , where we overlay contours of these
three radio images over AIA 171Å base difference images. The cyan circles
shown are the same ones shown in the upper panel of Fig. 3. The movies span
the same time duration as the light curves shown in the second row of Fig. 3,
with a cadence of 1 minute. Still frames of these movies are given in Figs. 7,
8 and 9. The name of the movie is same as the respective figure number of its
still frame.

We find that the radio sources are located near the coronal bright points in
the coronal hole region. From the top panel, it is evident that the EUV source
is co-located with the radio source and also shows variability in similar
times. The variability is always observed in the 171Å , and sometimes in the
193Å , and 211Å , but not observed in the other AIA wavebands. It should
however be noted that due to the huge difference between the instrumental
resolution of AIA and the radio observations presented here, it is extremely
hard to identify a unique EUV counterpart to the radio source and it is
possible that the observed radio emission has a contribution from other nearby
sources as well. All of these radio sources are circularly polarized, with the
one in the left column showing a degree of circular polarization of $-56\pm
11\%$. The sources in the middle and right columns are only detected in the
right circular polarization and using the 5$\sigma$ as the upper limit of the
flux in the left circular polarization we estimate that the stokes V fraction
is greater than 11% and 23% respectively. The high circular polarization of
the source can be explained either by optically thin free-free emission due to
propagation effects through the magnetic field (e.g. Habbal et al., 1986;
Sastry, 2009), or due to gyrosynchrotron emission. Extremely impulsive
narrowband emissions with flux densities comparable to the sources studied
here were detected only in one circular polarisation (Bastian, 1991) and were
attributed to plasma emission mechanism. While those emissions were solely
associated with active regions, plasma emission from the weak reconnection
events happening in the quiet Sun has been reported at lower frequencies
(Mondal et al., 2020, 2023; Sharma et al., 2022) and can happen at our
observing frequencies as well. Hence the polarization data alone are
insufficient to determine the emission mechanism of these sources. However,
for the first source shown in the left column, we can rule out free-free
emission by combining the polarization and spectral information. Fig. 10 shows
the observed flux density and the corresponding degree of circular
polarization at 1.313 GHz where we have a detection of confidence. The upper
limits of the flux density of the source at neighboring frequencies are also
computed as 5 times the noise in the image, shown as red triangles. While the
source spectra (observed flux at 1.313 GHz and the upper limits at other
frequencies) may be explained by optically thick free-free emission, the high
degree of circular polarization cannot be explained. On the other hand, while
the polarization signal can be explained with optically thin free-free
emission due to propagation effects, the spectral structure cannot be
explained as the spectrum is not flat. However, a gyrosynchrotron model can
explain both properties simultaneously. A representative gyrosynchrotron
spectrum which satisfies the spectral constraints and also shows a high degree
of circular polarization is shown as the blue curve in Fig. 10. Note that this
model spectrum shown here is not a best-fit spectrum due to the lack of
spectral constraints. It is provided with the sole intention of demonstrating
that a nonthermal gyrosynchrotron spectrum can possibly meet the observational
constraints in a much better manner than a thermal free-free emission
mechanism.

Figure 6: Radio transients in the coronal hole region detected by VLA. First
row: Overlay of radio contours over SDO/AIA images at similar times. Second
row: Light curves of radio sources at 1.313 (left panel) and 1.987 GHz (middle
and right panels). The red points show the peak flux at the location of the
radio source. The blue triangles show the 3$\sigma$ value, where $\sigma$ is
the estimated noise on the corresponding radio image. Third row: Light curves
of the box centered on the red dashed point shown in the upper panel in the
SDO/171 Å image. Fourth row: GOES lightcurve during the relevant times are
shown. The dotted black line is used to mark the peak of the radio light
curve. Each column corresponds to the same source.  Figure 7: Base difference
EUV image at 171Å corresponding to the source shown the left panel of Fig. 6.
This figure is available as an animation in the supplementary material. The
animation shows the variability seen in the difference image with time. The
animation spans from 19:54:00–20:27:00 UT and shows the AIA images at a
cadence of 1 minute. Figure 8: Base difference EUV image at 171Å corresponding
to the source shown in the middle panel of Fig. 6. This figure is available as
an animation in the supplementary material. The animation shows the
variability seen in the difference image with time. The animation spans from
19:35:00–20:10:00 UT and shows the AIA images at a cadence of 1 minute. Figure
9: Base difference EUV image at 171Å corresponding to the source shown in the
right panel of Fig. 6. This figure is available as an animation in the
supplementary material. The animation shows the variability seen in the
difference image with time. The animation spans from 20:35:00–21:10:00 UT and
shows the AIA images at a cadence of 1 minute. Figure 10: Flux density
spectrum of the source in the left panel of Fig. 6. The red circular points
shows the observed values. The red triangles show the upper limits to the flux
density estimated as 5 times the noise in the image. The blue line shows a
representative gyrosynchrotron model which satisfies the observational
constraints.

###  4.4 Sources associated with network regions

Several other radio transients were detected in the quiet sun network regions
where no apparent dynamic features were detected either in EUV or soft X-ray.
Here we show two examples of these sources in Fig. 11. The source in the left
panel is detected both in the EOVSA and VLA, while the source in the right
panel is detected in multiple VLA bands. Hence both of these sources are high-
fidelity sources and hence chosen for further analysis using the EUV and X-ray
data. In Fig. 11 the details of these two sources are shown in the same format
as that in Fig. 6. In the top left panel, the VLA and EOVSA data are shown
with blue and white contours respectively. In the top right panel, blue,
white, and magenta contours correspond to images at 1.057, 1.313 and 1.441 GHz
respectively. Dashed cyan circles have been drawn such that their centers show
the location from where the EUV light curves shown in the bottom panel are
extracted. Movies showing the EUV variability at the location of these sources
are provided in the supplementary material. The format of these movies is the
same as that in Figs. 7, 8 and 9. Still frames of the movies are provided in
Figs. 12 and 13. For the source in the left panel, we see a clear peak in the
X-ray light curve at the same time as the peak in the radio. For the source in
the right panel, while we have marked the numerical peak of the radio light
curve, the fluxes are comparable at the times when the source was detected.
Additionally, there are multiple X-ray peaks during this time interval, making
it hard to identify a probable X-ray counterpart to the radio source. However,
as mentioned earlier due to the high contamination from electrons, these
signatures in the GOES lightcurve should not be treated as confirmatory
signatures.

Figure 11: Image shown is in same format as that in Fig. 6 for the sources
described in Section 4.4. The left panel correspond to the source detected
both in VLA and EOVSA images and the right panel correspond to the source
detected in multiple frequencies. Figure 12: Base difference EUV image at 171Å
corresponding to the source shown in the left panel of Fig. 11. This figure is
available as an animation in the supplementary material. The animation shows
the variability seen in the difference image with time. The animation spans
from 20:00:00–20:45:00 UT and shows the AIA images at a cadence of 1 minute.
Figure 13: Base difference EUV image at 171Å corresponding to the source shown
in the right panel of Fig. 11. This figure is available as an animation in the
supplementary material. The animation shows the variability seen in the
difference image with time. The animation spans from 20:55:00–21:40:00 UT and
shows the AIA images at a cadence of 1 minute.

##  5 Discussion

In this paper, we take advantage of simultaneous broadband radio imaging
spectroscopy observations made with the EOVSA and VLA to detect and analyze
weak (a few times 0.01 sfu) radio transients from the quiescent solar corona
in the microwave range. Reports of such microwave transients are very rare in
the literature, and our study marks the first in which they are detected in
multiple frequencies simultaneously. With these measurements, we are able to
pinpoint the emission mechanisms and show that they are generally consistent
with a nonthermal gyrosynchrotron origin. The nonthermal nature is also true
for one radio transient event associated with a CBP (discussed in Section
4.2). We note that, however, in the past works, the radio counterparts of CBPs
were usually attributed to the free-free emission mechanism (see, e.g.,
Madjarska, 2019, and references therein). We caution that, due to the small
number of sources studied here, one can not attribute most of the radio
transients at these frequencies to nonthermal emission. Nevertheless, the
detection of gyrosynchrotron emission from these small scales transients does
provide strong evidence of the presence of nonthermal electrons in the
quiescent solar corona. The nonthermal electron energies estimated in this
work indicate that these nonthermal electrons are either comparable to or
weaker than those detected even during regular flares and microflares
(Glesener et al., 2020). These results are also consistent with the recent
detection of WINQSEs, which are hypothesized to be produced due to coherent
plasma emission from very weak nonthermal electron beams in the quiet solar
corona (Mondal et al., 2020; Sharma et al., 2022; Mondal et al., 2023) and
X-ray detection of quiet sun transients (Glesener et al., 2020; Cooper et al.,
2021; Paterson et al., 2022).

In Section 4.3 we present robust detection of radio transients from CBPs lying
in coronal holes. To the best of our knowledge, this is the first detection of
such sources in microwave wavelengths. In one instance, we have also shown
that the spectrum is inconsistent with a free-free emission origin and may be
explained by a nonthermal gyrosynchrotron model. The presence of nonthermal
emission implies the occurrence of weak energy release events in the coronal
hole region due to yet-to-determined mechanisms such as interchange
reconnection (e.g. Fisk & Schwadron, 2001; Upendran & Tripathi, 2022).

Measuring the magnetic field in the solar corona has always been very
difficult and routine measurements of this nature are not possible yet. While
there are techniques to measure the magnetic field using EUV, infrared, and
optical data, these are limited to regions beyond the solar disc (Casini et
al., 2017). On the other hand, most radio measurements reported till date has
only measured the magnetic field from active regions, or, are associated with
explosive events like solar flares and coronal mass ejections (Alissandrakis &
Gary, 2021). To the best of our knowledge, this work is the second work that
constrains the coronal magnetic field in the quiet on-disk solar corona using
radio observations (the first one was done by Habbal et al. (1986)). The
availability of more sensitive and wideband radio instruments thus raises the
hope that this technique of using quiet sun radio transients can be used in a
much more routine manner to constrain the magnetic field in the quiescent
solar corona.

##  6 Conclusion

In this work, we have presented a study on weak radio transients from the
quiet sun in the microwave range. We take advantage of imaging spectroscopy
observations made by VLA and EOVSA along with available EUV data to unravel
features of some of these transients. We show that at least 3 of the detected
radio transients observed at 1–2 GHz are powered by nonthermal gyrosynchrotron
emission. We have modeled the spectrum using a gyrosynchrotron model whenever
possible and using the modeled parameters to estimate the nonthermal electron
energy, which varies between $10^{26}-10^{29}\,$ergs. While this result is
obtained from only a handful of events, our results strongly suggest the
presence of a significant nonthermal electron population even during these
quiet times. For the two sources where we were able to calculate both thermal
and nonthermal energy, we find that they are comparable. This suggests that
the nonthermal energy budget should also be taken into account when
calculating the total coronal energy budget.

We also present the first detection of radio transients associated with
coronal holes and show that at least in one instance the source is due to
gyrosynchrotron emission. We suggest that the source may be due to interchange
reconnection in the vicinity of coronal holes, a scenario suggested to explain
solar wind formation from the coronal holes.

In addition, this work also shows that these radio transients can be used to
constrain the coronal magnetic field in the quiet sun. Recent advances with
the EOVSA have already demonstrated the technique of using microwave imaging
spectroscopy to constrain the coronal magnetic field based on nonthermal
gyrosynchrotron radiation theories (e.g. Chen et al., 2020; Kuroda et al.,
2020; Yu et al., 2020; Wei et al., 2021; Chen et al., 2021; Fleishman et al.,
2022; Zhang et al., 2022). However, due to the limit in sensitivity, dynamic
range, and image fidelity of current instruments, such studies have largely
been limited to active regions and solar flares. We hope that with the
availability of more sensitive and broadband instruments with a much lower
sidelobe level and higher image fidelity, similar studies can be extended even
to the quiet solar corona. While due to the isolated nature of these radio
transients, this technique can not be used to map the coronal magnetic field
of the full solar disk, these measurements will add new constraints which we
hope would ultimately lead to a better understanding of the magnetic field
structure of the solar corona.

This work makes use of public VLA data from the observing program VLA/19B-338.
The NRAO is a facility of the National Science Foundation (NSF) operated under
a cooperative agreement by Associated Universities, Inc. The authors
acknowledge Dr. Tim Bastian for leading the VLA observing program and helpful
discussions. SM also acknowledges Dr. Stephen White for discussions regarding
intricacies of the GOES data. This work is supported by NSF grant AGS-1654382
and NASA grants 80NSSC20K0026, 80NSSC20K1283, and 80NSSC21K0623 to NJIT. EOVSA
operations are supported by NSF grants AST-1910354 and AGS-2130832 to NJIT.
This research used version 4.0.5 (Mumford et al., 2022) of the SunPy open
source software package (The SunPy Community et al., 2020). This research used
version 0.6.4 (Barnes et al., 2020) of the aiapy open source software package
(Barnes et al., 2020). This research has made use of NASA’s Astrophysics Data
System Bibliographic Services.

##  Appendix A VLA Data analysis and Imaging procedure

All analysis were done using the Common Astronomy Software Applications (CASA,
McMullin et al., 2007). A combination of manual flagging and an automated
flagging routine, tfcrop, was used for the initial flagging. Calibration was
non-trivial as the phase calibrator becomes resolved at baselines above
3$k\lambda$, a threshold below which many antennas had very few baselines.
Hence to determine robust and accurate antenna gains self-calibration
technique was applied on the phase calibrator data. We initially calibrated
the data using baselines smaller than $\sim 5k\lambda$ at 1.05 GHz (translates
to a scale of $\sim 40^{{}^{\prime\prime}}$) and used progressively higher
thresholds at higher frequencies so as to ensure that sufficient baselines
were present for all antennas within this threshold. Each spectral window was
calibrated independently assuming that the calibrator source flux is constant
within each spectral window. After the initial calibration of bandpass and
temporal variability of gain using baselines below the chosen threshold, the
obtained gains were refined using a self-calibration based approach. During
the self-calibration approach, all baselines were used. We also assumed that
the bandpass obtained earlier using the uv-based threshold is correct and
time-invariant. Flagging was done using the task rflag when needed. After the
self-calibration converged, we fitted a Gaussian function to the source using
the task imfit and obtained a scaling factor to match the observed flux and
true flux obtained from the VLA calibrator manual. The obtained gains from the
phase calibrator and complex gains due to the 20 dB attenuators were then
applied on the solar data555See Chen (2013) for a more detailed discussion on
the use and calibration of the 20 dB attenuators.. A round of flagging was
done using the task rflag to remove bad data in solar scans.

Imaging was done using the task tclean. We have used the auto-masking mode for
deconvolving only “real” sources. However, the point spread function, or
synthesized beam, generally had a sidelobe level of about 40%, which was
larger than that typically observed in full-day synthesis images. Hence
different auto-masking parameters of the task tclean were tuned so that the
emission could be better captured. Specifically, sidelobethreshold,
noisethreshold, minbeamfrac, and cyclefactor were set to 1.5, 3, 0.2, and 5,
respectively666Detailed description of these parameters are provided in
https://casadocs.readthedocs.io/en/stable/notebooks/synthesis_imaging.html.

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