Multifrequency microwave imaging of weak transients from the quiet solar corona

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.

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.

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).

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.

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.

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.

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.