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PIC simulations of harmonic maser emissions by Ning et al.*

Electron cyclotron maser emission (ECME) represents a major class of coherent emission mechanism of solar radio bursts. ECME usually occurs in strongly magnetized plasmas with the frequency ratio $\omega_{pe} / \Omega_{ce} < 1$, induced by energetic electrons with $\partial f /\partial v >0$, where $f$ represents the velocity distribution function. In solar active regions, this mechanism has been applied to millisecond spikes which are characterized by high brightness temperatures, short durations, narrow bandwidths, and strong polarizations.

A long-standing problem of ECME accounting for spikes is the escaping difficulty: fundamental emissions ($\omega \sim \Omega_{ce}$) would be absorbed efficiently at the second-harmonic layer where the magnetic field strength is half that at the source (Melrose & Dulk 1982), and thus cannot escape. Emissions at second or higher harmonics ($\omega \sim n\Omega_{ce}$, n=2, 3, …) are more likely to escape. Previous studies using the loss-cone distribution concluded that only fundamental emissions (i.e., $n=1$) can grow via ECME (e.g., Aschwanden 1990).

To investigate the possibilities of harmonic ECME emissions ($n \ge 2$), we conducted fully kinetic electromagnetic 2D3V particle-in-cell (PIC) simulations, in large domains with a huge amount of macro-particles to lower the noise level. We employed horseshoe (Ning et al. 2021a) and loss-cone (Ning et al. 2021b) distributions as the driver of electron cyclotron maser instability (ECMI) to study the wave excitations and the subsequent nonlinear processes.

Figure 1. Snapshots of the velocity distribution at the beginning of the simulations with horseshoe (a) and loss-cone (b) distributions. The density ratio of energetic electrons to total electrons are set to be 10%.

Horseshoe distribution

According to in situ measurements, auroral kilometric radiations (AKRs) are released by the horseshoe ECME. As an analogy of the AKR, solar spikes have also been associated with energetic electrons of the horseshoe distribution that can form in flare loops with electrons travelling toward lower atmosphere (Melrose & Wheatland 2016).

The horseshoe distribution used to drive the simulation consists of a shell and a double-sided loss-cone distribution (Figure 1(a)). Setting $\omega_{pe} / \Omega_{ce} = 0.1$, we varied the density ratio of energetic electrons to total electrons ($n_e / n_0 $) from 1% to 50%, to simulate the ECME process.

Figure 2. $\omega$-k dispersion diagrams of $E_{y}$ in the perpendicular direction of the simulations with horseshoe distribution with varying $n_{e}/n_{0}$. “Z”, “X2”, “X3”, and “R” stand for the Z mode, second-harmonic X mode, third-harmonic X mode, and the relativistic mode branch.

According to the simulations (Figure 2), the horseshoe distribution can amplify waves in Z and X2 modes (at frequencies of 0.96 and 1.92 $\Omega_{ce}$) efficiently along the perpendicular direction. The X3 mode also grows yet with a lower energy. We note that the amplification of X2 and X3 modes get more efficient with increasing $n_{e} / n_{0}$. With $n_{e} / n_{0}$ ranging from 5% to 50%, we estimated the brightness temperatures of the obtained X2 to be $10^{11}$ K to $10^{15}$ K, consistent with observations of spikes.

Efficient amplification of harmonic emissions provides a solution to the escaping difficulty of the ECME theory. The simultaneous growths of X2 and X3 can explain the multi-harmonic structures observed in solar spikes.

Loss-cone distribution

The loss-cone ECME has been widely investigated by earlier studies, including linear and quasi-linear analyses. However, the non-linear wave-wave interaction has not been well studied. We performed PIC simulation with a long enough duration to study the wave excitations via the loss-cone cyclotron resonance instability, and subsequent wave-wave interaction processes.

We employed a double-sided loss-cone distribution (Figure 1(b)). In the simulation, the value of $\omega_{pe} / \Omega_{ce} = 0.25$, and $n_{e} / n_{0}$ was set to be 10%. The simulation lasts 8000 $\omega_{pe}^{-1}$, representing the longest duration for simulations ever conducted in studies on the same topic.

Figure 3. Wave dispersion diagrams of electric fields over 7500-8000 $\omega_{pe}^{-1}$ along different directions. Panels (a), (b), and (c) display the amplified waves in X1, Z, and X2 modes. $\theta$ represent the angle between the directions of wavevector and background magnetic field.

Figure 4. Maximal wave energies in $\vec{k}$ space over 7000–8000 $\omega_{pe}^{-1}$; blue and brown represent results in $E_x$ and $E_y$ components. Possible conditions of wavevectors matching the coalescence condition are overplotted as arrows in the same color. Black arrows represent the wavevector of the target mode to be generated. The values of $\theta$ of each wave vector is marked beside.

Figure 3 shows the dispersion diagrams of the amplified waves in the simulation. We found that the loss-cone distribution could amplify X1 (panel (a); $\omega$~1.06-1.1 $\Omega_{ce}$) and Z (panel (b) $\omega$~1.025 $\Omega_{ce}$) modes via ECMI. As a major result, we obtain strong emissions in X2 along oblique and perpendicular directions at frequencies of 2.05, 2.09, and 2.14 $\Omega_{ce}$, separately (panel (c)).

We suggest that the X2 emissions are produced by nonlinear coalescence processes of Z+X1 and/or Z+Z. This is supported by the following arugments/observations: (1) the matching conditions are well satisfied (Figure 4); (2) X2 emissions are amplified at separate frequencies and discrete angles; (3) X2 starts to grow later than Z and X1. The energy ratio of X2 to Z mode is ~30%, indicating the coalescing process is efficient in energy conversion

For the first time, we obtain efficient excitations of X2 induced by loss-cone electrons via efficient wave-wave coalescing process. Such process represents a novel mechanism of X2 emission in plasmas with a low $\omega_{pe} / \Omega_{ce}$.

Conclusion

We simulated wave excitations by energetic electrons with either horseshoe or loss-cone distribution. We found that the horseshoe distribution could generate X2 and X3 simultaneously via the direct ECME mechanism, while loss-cone distribution could generate X2 through the indirect nonlinear wave-wave coalescence process: the loss-cone ECMI amplify X1 and Z modes first, which then coalesce to generate X2 emissions. 

The two studies (Ning et al., 2021a, 2021b) shed new lights on the mechanism of harmonic emissions and the resolution of the long-standing escaping problem of ECME. In our simulations, we obtain efficient excitations of X2, with narrow bandwidth and propagation angles, accounting for high brightness temperatures and strong polarizations of spikes, and explains why only a few percent of the Hard X-ray bursts correlate with spikes.

Based on the recent papers: 

Ning, H., Chen, Y., Ni, S.L., Li, C.Y., Zhang, Z.L., Kong, X.L., & Yousefzadeh, M., Harmonic electron-cyclotron maser emissions driven by energetic electrons of the horseshoe distribution with application to solar radio spikes, A&A, 2021a, 651, A118, DOI: https://doi.org/10.1051/0004-6361/202140427

Ning, H., Chen, Y., Ni, S.L., Li, C.Y., Zhang, Z.L., Kong, X.L., & Yousefzadeh, M., Harmonic maser emissions from electrons with the loss-cone distribution in solar active regions, ApJL, 2021b, 920, L40, DOI: https://doi.org/10.3847/2041-8213/ac2cc6

References

Aschwanden, M. J. 1990, A&AS, 85, 1141

Melrose, D. B., & Dulk, G. A. 1982, ApJ, 259, 844

Melrose, D. B., & Wheatland, M. S. 2016, Sol. Phys., 291, 3637

*Full list of Authors: Hao Ning, Yao Chen, Sulan Ni, Chuanyang Li, Zilong Zhang, Xiangliang Kong, and Mehdi Yousefzadeh

Radio Interferometric Observations of the Sun Using Commercial Dish TV Antennas by G. V. S. Gireesh et al.*

Commercial dish TV antennas are parabolic structures designed to receive radio waves from a communication satellite. The antennas and the associated front end receiver systems have improved with advances in the TV systems. They operate typically over the frequency range 10.7 – 11.7 GHz (Ku-band) and provide very good signal-to-noise ratio (SNR). It is well known that the Sun emits intense radio emission in the above frequency range with brightness temperature $T_{b}{\sim}10^{4}$K. The emission is primarily due to thermal free-free mechanism and originates in the upper chromosphere. It is well established that $T_{b}$ is one of the basic properties of the Sun. Hence its routine monitoring is widely used as a diagnostic tool to understand the different types of temporal changes. We attempted observations of the Sun in the microwave frequency range with a pair of commercial dish TV antennas. The observations were made in the correlation interferometer mode since it provides better sensitivity.

Observation and Data

We had set-up a correlation interferometer with a separation of ${\approx}$ 2.5m between the two dish antennas. The baseline between the antennas is oriented in the East-West direction. So, the theoretical angular resolution in that direction (for observations near the zenith), specified by separation between the interference fringes, is ${\approx}37^{\prime}$ at 11.2 GHz. The angular size of the Sun at 11 GHz is ${\approx}33^{\prime}$ (Furst79). Since this is smaller than the aforementioned fringe spacing, Sun can be assumed to be a ‘point’ source for our observations. The corresponding resolution in the North-South direction is ${\approx}3.02^{o}$, i.e. the HPBW of the dish.

Figure 1. The commercial dish TV antennas used in the Gauribidanur observatory for solar observations in the correlation interferometer mode.

Trail observations of Moon and the Sun were carried out with the Ku-band interferometer. The gain variations of the receiver were by monitoring the Ku-band transmission from geostationary satellites INSAT 3A & 4A. The $T_{b}$ of the Moon and the Sun were thus estimated to be ${\approx}$227${\pm}$52K and ${\approx}$9266${\pm}$2108K, respectively. 

The solar eclipse of 21 June 2020 was partial at Gauribidanur observatory with magnitude  ${\approx} $0.493 and obscuration ${\approx}$38.33 %. The solar eclipses are always partial at radio frequencies since the angular sizes of the `radio’ Sun in the frequency range over which it is typically observed from the ground are larger compared to that of the Moon. The average angular size of the Moon is ${\approx}31^{\prime}$, the corresponding values for the ‘radio’ Sun at 11 GHz and 80 MHz are ${\approx}33^{\prime}$ and ${\approx}38^{\prime}$, respectively (Borovik 1980, Ramesh et. al. 2006). 

Figure 2. Positions of the Moon during the first contact, maximum phase, and fourth contact of the 21 June 2020 solar eclipse (as seen from Gauribidanur observatory) overlaid on the 211 Angstrom image of the Sun obtained the same day at ${\approx}$ 06:30 UT with the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO). North is straight up and east is to the left.

Figure 3. Observations of the Sun with Ku-band interferometer on 20, 21, & 22 June 2020 in the transit mode after tilting the antennas towards the direction of the Sun. 

Figure 3 shows the results of our observations on 20 June 2020 (the day before the eclipse), 21 June 2020 (during the eclipse), and 22 June 2020 (day after the eclipse). The observations on 21 June 2020 were during the maximum phase of the eclipse. The estimated $T_{b}$ of the Sun at $\approx$11.2 GHz (after calibration using observations of the Moon with the same set-up) on the above three days are ${\approx}$9266K, 4294K, and 9263K, respectively. The $T_{b}$ on 21 June 2020 is lesser by ${\approx}$54 %. There were three noticeable active regions in the northern hemisphere of the Sun were fully occulted during the maximum phase of the eclipse. This could be the reason for the aforementioned reduction in $T_{b}$ (though the eclipse obscuration was only 38 %) since radio emission associated with the active regions constitute a significant fraction of the total emission from the Sun (Covington 1947, Mayfield et. al. 1971).

Summary

We have reported successful radio interferometric observations of the Sun at  ${\approx}$ 11.2 GHz using two commercial dish TV antennas operating in the Ku-band (${\approx}$ 10.7-11.7 GHz). The results obtained are encouraging for our plans to set up an array of such antennas for dedicated and synoptic two-dimensional spectroscopic imaging observations of the Sun in the above frequency range with minimal budget. Work is in progress to fine tune the pointing accuracy of the dishes and develop a FPGA based spectrocorrelator to observe over the entire 10.7-11.7 GHz frequency band.

Based on the recent paper: Gireesh, et. al.:  Radio Interferometric Observations of the Sun Using Commercial Dish TV Antennas. Solar Physics, 296, 121 (2021), DOI: https://doi.org/ 10.1007/s11207-021-01871-9

References

Covington, A. E. (1947). Nature, Volume 159, Issue 4038, pp. 405-406 (1947).

Borovik, V. N. (1980). Soviet Astronomy Letters, vol. 6, July-Aug. 1980, p. 236-238.

*Full list of authors: G. V. S. Gireesh. C. Kathiravan, Indrajit V. Barve, R. Ramesh

Radio, X-ray and extreme-ultraviolet observations of weak energy releases in the ‘quiet’ Sun by Ramesh et. al.

Small scale energy releases on the Sun e.g., flaring bright points, active region transient brightenings, etc. have been studied using X-ray and radio observations. The observations of low frequency radio type III bursts in associated with X-ray bright point flares (Kundu et. al. 1980) and coronal X-ray jets (Aurass et. al. 1994) indicated that the latter are capable of accelerating particles to non-thermal energies, as well as producing the heated material detected in soft X-rays. These results imply that radio observations are an useful complimentary tool for observing signatures of weak, transient energy releases in the solar atmosphere since the related non-thermal emission can be easily detected (Benz 1995). X-ray microflares are another independent observational evidence for the small-scale energy releases in the solar atmosphere (Lin et. al. 1984). Recent spectroscopic imaging observations indicate that the weak non-thermal radio emission at low frequencies is more like type I radio bursts (Mondal et. al. 2020). However, there are not any detailed study about their other wavelength counterparts. In this work, we studied weak type I radio burst emission during the same time as soft X-ray observations of a sub-A class level flare and EUV brightening from the ‘quiet’ solar corona in the complete absence of active regions and flare/coronal mass ejection (CME) activity.

Analysis and Results

The radio observations were carried out using the different facilities operated by the Indian Institute of Astrophysics (IIA) in the Gauribidanur Observatory (Ramesh 2011). The patches of bright emission in the spectra (Figure 1) during the period  $\approx$ 05:09-05:11 UT are typical of  type I or noise storm bursts from the solar corona (see for e.g. Iwai et. al. 2013). It is widely believed that the bursts are due to plasma radiation at the fundamental plasma frequency (Melrose 1980). The bright patched in Figure 1 are similar to type I bursts. There were no active regions and no H$\alpha$ and/or GOES soft X-ray flares were reported during the burst interval.

Figure 1. GLOSS dynamic spectrum of the solar radio emission observed on 2020 April 21. The bright emission during the period $\approx$ 05:09 05:11 UT correspond to the type I solar radio bursts.

With the X-ray flare observed on 2020 April 21 at ${\approx}$05:10 UT, there was also an EUV brightening observed with the SDO/AIA at 94{\AA} around the same time as the type I radio bursts. The location of the northern radio contour with label ‘1’ in Figure 3 correspond reasonably well with the location of the EUV brightening. The observations of the type I radio bursts over a larger area compared to the EUV brightening could be due to the divergence of the associated field lines (Li et. al. 2017). We speculate that the presence of the two spatially separated radio contours 1 & 2 suggests interaction at two different locations between inclined, large magnetic loops with foot points in the same hemisphere, north in the present (Wild 1968).

Figure 2. The ‘green’ colour plot corresponds to the frequency averaged time profile of the GLOSS dynamic spectrum in Figure 1. The labels 1 & 2 indicate the epochs of maximum radio emission from the regions 1 & 2 in Figure 3, respectively. The ‘blue’ colour profile is the light curve of the soft X-ray emission from the Sun close to the same epoch as the radio observations.

Figure 3. A composite of the GRAPH difference image of the bursts in Figure 1 at 80 MHz and the EUV observations at 94{\AA} with the SDO/AIA around the same time as the radio and X-ray observations in Figures 1 & 2 on 2020 April 21. The bigger and smaller ‘boxes’ in the left panel image indicate the region around the EUV brightening and the location of maximum emission, respectively. The ‘zoomed’ version of the same brightening is shown in the right side panel. The peak flux density in the GRAPH observations is $\rm {\approx}\,241\,Jy$. Its nearly the same for the contours 1 & 2, which correspond to the two maxima 1 & 2 in the radio time profile in Figure 2, respectively.

The peak flux of the XSM flare is $\rm {\approx}6{\times}10^{-9}\,Wm^{-2}$ (weak event). The total duration of the event is ${\approx}$5 min. There appears to be two ‘peaks’ in the flare light curve with a noticeable difference between the corresponding count rates. The type I radio bursts are present only during the initial phase of the X-ray emission. The total duration of the radio event is smaller $({\approx}$2 min).  Assuming that both the X-ray and radio events are related to a common primary phenomenon, the comparatively shorter duration of the radio event indicates that the electrons responsible for its occurrence are probably thermalized quickly. As a result, they cannot travel to larger heights in the corona from where the low frequency radio emission primarily originates (Mondal et. al. 2020). The shorter duration of the radio bursts could be also due to the emission being non-thermal in nature as compared to the soft X-ray emission (Reid et. al. 2017).

The energy associated with the type I burst was $\rm E\,{\approx}\,8.1{\times}10^{22}$ erg (minimum value). Both the type I bursts and the associated X-ray emission were short lived. Therefore, it is likely that the electron acceleration responsible for the type I bursts were triggered by the same process responsible for the associated X-ray microflare (Crosby et. al. 1996).  We find that the area enclosed by the contours in Figure 3 is nearly same as that of the GRAPH ‘beam’ size at 80 MHz mentioned earlier, i.e. ${\approx}5^{’}{\times}7^{ ’}$, which is very large compared to other high resolution observation results (Melrose 1980, Mugundhan et. al. 2018). So, it is possible that the contours in Figure 3 correspond to an ensemble of type I burst sources, each of size ${\approx}14^{’}{\times}14^{’}$. We calculated the maximum possible total energy of the type I bursts as ${\approx}\,5.3{\times}10^{25}$ erg. This is in reasonable agreement with the range of energies for the soft X-ray microflares reported by Vadawale et. al. 2021. The above numbers and arguments confirm that the type I radio bursts are an independent ground based observational tool to probe weak activity in the `quiet’ regions of the corona also in addition to its known association with sunspot activity.

Conclusions

We presented co-temporal/co-spatial observations of weak type I radio bursts, X-ray microflare, and EUV brightening from the ‘quiet’ Sun which was completely devoid of any active regions. There is close agreement between the energy budgets estimated independently from the radio and X-ray observations. Combined investigations of weak energy releases observed at the same time in all the aforementioned domains would be helpful to understand the energies deposited at different levels in the solar corona in addition to the associated mechanisms themselves.

Based on the recent paper: Ramesh, R., et. al.:  Radio, X-Ray, and Extreme-ultraviolet Observations of Weak Energy Releases in the “Quiet” Sun. The Astrophysical Journal Letters, Volume 918, Issue 1, id.L18, 6 pp, DOI: https://doi.org/10.3847/2041-8213/ac1da3

References

Kundu, M. R. & Gopalswamy, N. (1990). Solar Physics, Volume 129, Issue 1, pp.133-152

Mondal, S., Oberoi, D. & Mohan, A. (2020). The Astrophysical Journal Letters, Volume 895, Issue 2, id.L39, 7 pp.

Ramesh, R., Mugundhan, V. & Prabhu, K. (2020). The Astrophysical Journal Letters, Volume 889, Issue 1, id.L25, 5 pp. (2020)

First Frequency-time-resolved Imaging Spectroscopy Observations of Solar Radio Spikes by D. L. Clarkson et al.*

Solar radio spikes are short duration, narrowband radio bursts that are signature of the acceleration of non-thermal electrons in solar flares. They are observed over a wide range of frequencies from the tens of MHz (Melnik et al. 2014) to the GHz range (Benz et al. 1992), and have some of the shortest durations and narrow bandwidths of any solar radio bursts. The origin of spikes is not fully understood. Their short durations represent an upper limit for the energy release time, and coupled with their narrow frequency bandwidths, spikes are indicative of processes that occur on millisecond timescales, providing an avenue to study the fastest processes in the solar corona. The high brightness temperatures associated with spikes indicate coherent mechanisms; namely, plasma emission or electron cyclotron maser (ECM) emission.

In the recent paper, Clarkson et al. (2021) have reported for the first time, spatially, frequency, and time resolved observations of individual radio spikes associated with a coronal mass ejection (CME).

Observations and Analysis

Using the excellent time and frequency resolution of LOFAR, we were able to resolve individual radio spikes between 30-70 MHz (e.g. Figure 1), and analyse their various characteristics such as duration, frequency width, frequency drift, area, and apparent motion over tens of millisecond scales. The flaring event was associated with a series of Type III bursts along with a CME and Type II burst, thought to originate from a jet eruption (Chrysaphi et al. 2020). Spikes were observed both before and after the CME; with the bulk of the observed spikes occurring within the CME wake. The same analysis was performed on individual striae of Type IIIb bursts that occurred during the same period. Both the spikes and striae show similar characteristics; that being a decreasing duration, increasing bandwidth, and decreasing area, with frequency. We found that the spike drift rates infer exciter velocities of approximately 10-50 km s-1.

Figure 1: (a) Dynamic spectra of spike and Type IIIb bursts. (b) Type IIIb burst (post-CME) (c) Spike cluster (d) An individual spike. (e) Type IIIb burst (pre-CME).

One of the intriguing observations is that the spike (and striae) centroid motions are not radial, but parallel to the solar limb (Figure 2a). Analysing the temporal variation of the spike area and vertical motion in the image plane (Figure 2b,c), we find that both the change in areal extent and motion are most pronounced during the decay phase. This is consistent with previous radio fine structure observations (Kontar et al. 2017, Kuznetsov et al. 2020), as well as with scattering simulations (Kontar et al. 2019, Kuznetsov et al. 2020), where scattering was determined to be the dominant process affecting the observed radio emission properties. Moreover, the spikes show superluminal velocities between 0.76-1.8c, and superluminal expansion of the FWHM source sizes. As noted above, this is not the physical speed of the exciter, and can be explained in the context of the scattering of the radio-waves due to anisotropic density turbulence. In Kontar et al. (2019), it was shown that anisotropic density turbulence was required to explain both the observed Type III decay times and source sizes simultaneously. In a medium with anisotropic density fluctuations, radio-wave scattering induces a shift in the observed emission preferentially along the direction of the guiding magnetic field. Further, the scattering simulations predict that apparent superluminal motion is possible due to scattering effects, and show that at larger heliocentric angles, the observed emission is subject to greater induced shifts and apparent velocities.

Figure 2: Temporal properties of the spike shown in Figure 1d at 34.5 MHz. (a) Spike centroid motion (coloured triangles) overlaid on an SDO/AIA 171 Å image. The blue plus symbols show the peak centroid position of other spikes pre-CME, whilst white plus symbols show those post-CME. The grey lines with diamond (pre-CME) and triangle (post-CME) markers represent the centroid motion of two individual striae from Figure 1(b,e). (b) Observed FWHM area over time. (c) Spike vertical centroid motion over time. The red curves represent the normalised spike lightcurve. Figure adapted from Clarkson et al. (2021).

Conclusions

It is shown that low-frequency radio spikes are strongly affected by scattering due to the radiation escaping through anisotropic density turbulence, with scattering preferentially along the guiding magnetic field. For this event, the spike and striae motions indicate that the magnetic field lines are parallel to the solar limb. The spike emission originates in a region within the CME wake where the formation of extended post-reconnection loops could be the location of weak electron beam acceleration. The scattering dominance will act to extend the spike time profile, implying that the energy release time is shorter than what is often assumed in the literature. The simulations by Kuznetsov et al. (2020) show that stronger anisotropy leads to smaller observed peak source sizes and superluminal velocities. The spike and striae properties are therefore consistent with anisotropy $\alpha=0.1-0.2$, that is higher than typically required in open field configurations to explain Type III bursts. Consequently, the anisotropy of density turbulence in closed loop configurations could be higher than that along open field lines. The similarities and co-spatial origin of the spikes and striae indicate that they have a common exciter. In addition, the Type III, Type IIIb, Type II, and spikes bursts in this event share the same sense of polarization. Combined with the coronal height of the emission where the condition for ECM emission in unlikely to be satisfied, the spikes are likely to be produced via the plasma emission mechanism near the plasma frequency.

Based on the recent paper by: Clarkson, D. L., Kontar, E. P., Gordovskyy, M., Chrysaphi, N., Vilmer, N. First Frequency-time-resolved Imaging Spectroscopy Observations of Solar Radio Spikes, ApJL, 917, L32. DOI: 10.3847/2041-8213/ac1a7d

References

Benz, A. O., Su, H., Magun, A., Stehling, W. 1992, A&AS, 93, 3

Chrysaphi, N., Reid, H. A. S., Kontar, E. P. 2020, ApJ, 898, 115

Kontar, E. P., Yu, S., Kuznetsov, A. A., Emslie, G. A., et al. 2017, NatComm, 8, 1515

Kontar, E. P., Chen, X., Chrysaphi, N., et al. 2019, ApJ, 884, 122

Kuznetsov, A. A., Chrysaphi, N., Eduard, E. P., et al. 2020, ApJ, 898, 94

Melnik, V. N., Shevchuk, N. V., Konovalenko, A. A., et al. 2014, SoPh, 289, 1701

Full list of authors: Clarkson, D. L., Kontar, E. P., Gordovskyy, M., Chrysaphi, N., Vilmer, N.

Properties of High-Frequency Type II Radio Bursts and Their Relation to the Associated Coronal Mass Ejections by A.C. Umuhire et al.*

Type II radio bursts are slow-drifting and long-lasting radio emission produced by nonthermal electrons accelerated at shocks propagating through the solar corona and interplanetary medium (Nelson & Melrose, 1985). The accelerated electrons generate Langmuir waves, which get converted into electromagnetic radiation by the plasma emission mechanism first identified by Ginzburg & Zhelezniakov (1958). Currently, there is a common understanding that type II radio bursts are produced by shocks formed ahead of Coronal Mass Ejections (CMEs) moving with super-Alfvénic speeds (Gopalswamy, et al., 2012). In this study, 128 type II bursts are analyzed, with a special emphasis on the 40 high frequency bursts to check the drift–frequency relationship. Previous studies considered events with lower starting frequencies ($<$ 14 MHz), and upper starting frequency in metric domain $\sim 140$ MHz .

2. Data and methods

The metric type II bursts considered in this study occurred during the period from 2010 to 2016, in the weakly active Solar Cycle 24. We checked the occurrence of type II burst as reported on the website of the Space Weather Prediction Center and considered those which are having spectral data obtained by different ground-based radio spectrographs. For each type II burst, we identified the associated CME from STEREO and SOHO instruments that image in the corona in EUV and/or white light. By combining coronagraph and EUV images, we were able to track all CME sources to the solar surface. Figure 1 shows an example of a high-starting-frequency type II burst observed by the Green Bank Solar Radio Bursts (GBSRB) spectrometer and its associated CME observed by STEREO-B/EUVI instruments. The fundamental starting frequency of the type II burst in the dynamic spectrum was 420 MHz (f2) at 17:35:00 UT (t2). The ending frequency was 60 MHz (f1) at 17:40:30 UT (t1). The event was associated with a flare, which occurred at N20E04 on the solar disk (see Cho, et al., 2013, for details). The associated CME was at N20W90 in the STEREO-B EUVI field of view (FOV). The CME-driven shock was observed in EUV 64 seconds after the appearance of type II burst corresponding to a height of 1.22 Rs. The relationship between the starting frequency of type II bursts in Solar Cycle 24 with the corresponding CME shock height can be obtained using the procedure in Gopalswamy, et al. (2013)

Figure 1 – (a) A high-starting-frequency type II burst. The dynamic spectrum was obtained by the Green Bank Solar Radio Burst Spectrometer (GBSRBS). The fundamental starting frequency was 420 MHz at 17:35:00 UT. The high starting frequency implies the radio source closer to the solar surface, hence the associated CME originating in the lower corona. (b) STEREO-B/EUVI 195 Å difference image shown by white arrow. The time of the image in (b) is close to the starting time of the type II burst. STEREO-B was located at E94 at the time of the eruption.

3. Results and Conclusions

In this study, the high-starting-frequency events are associated with shocks closer to the surface. This may indicate propagation of the shock through a high-density magnetic structure. The shock heights of CMEs associated with low-frequency events are generally large, which confirms the results of the previous study by Gopalswamy, et al. (2013). The correlation coefficient between the average CME speeds from STEREO data and the speeds estimated from the dynamic spectra is 0.76 for all events and 0.77 by excluding the two outliers near v2 1500 km/s. The obtained correlation is significant. The average width of CMEs in the LASCO FOV is 172o, which is greater than 46o obtained in  Gopalswamy (2006). Since the width is proportional to the mass, this shows that analyzed CMEs associated with type IIs are wide and more energetic. Generally, many events are associated with M and C class flares. For CMEs associated with high-frequency type II bursts, 33 out of 40 are associated with highly energetic flares (M and X class flares), which is consistent with their speeds. Moreover, there is a clear increase in speed between the inner and outer corona as measured in the STEREO and LASCO FOVs, which shows that the CMEs accelerate at the appearance of the metric type II burst. This has implications for the behavior of drift rate spectrum of type II bursts  (Gopalswamy, et al., 2012). For a few events, the shock speeds at the time of metric type II bursts are smaller than the calculated average speeds within the STEREO/COR1 and EUVI FOV, which shows that the CME reached the peak speed before the appearance of type II bursts.

Figure 2 – (a) Scatter plot between CME heights and the high-starting-frequency type II burst with a power-law fit to the data. (b) Scatter plot between CME heights and type II starting frequency for low-starting-frequency events. (c) Scatter plot between CME heights and the starting frequency of type II for all events (i.e., combined data of low- and high-starting-frequency type II bursts). The correlation coefficient (CC) is 0.51. Excluding the highest starting frequency (d), the correlation coefficient becomes 0.53.

 

Figure 3 –  Scatter plot between speeds from STEREO data (v2) and the radio dynamic spectra (vDS). The correlation coefficient (cc) is 0.76. When we exclude the two outliers near v21500 km/s, cc=0.77.

In this study, we found that closer to the solar surface, where type II emission frequency is high, the CME speed increases due to fast acceleration and starts to decrease in the IP medium, which shows the relationship between these deviations from the universal drift rate spectrum of type II bursts and CME speeds. The high-starting-frequency type II bursts have high drift rates and are associated with fast CMEs, which is consistent with the CME driving shock regardless of the spectral domain of type II bursts.

Based on the recent paper: A.C, Umuhire, et. al.  Solar Physics, 296:27 (2021)Properties of High-Frequency Type II Radio Bursts and Their Relation to the Associated Coronal Mass Ejections, DOI:  10.1007/s11207-020-01743-8

Full list of Authors:  A.C. Umuhire, N. Gopalswamy, J. Uwamahoro, S. Akiyama, S. Yashiro, P. Mäkelä.

References

Cho, K.-S et al., 2013.   2013ApJ…765..148C

Ginzburg, V & Zhelezniakov, V., 1958. 1958SvA…..2..653G

Gopalswamy, N., 2006. 2006JApA…27..243G

Gopalswamy, N et al., 2012. 2012SoPh..277..459G

Gopalswamy, N et al., 2013. 2013AdSpR..51.1981G

Nelson, G & Melrose, D., 1985. 1985srph.book..333N

The active region source of a type III radio storm observed by Parker Solar Probe during encounter 2 by L. Harra et al*

During encounter 2 of NASA’s PSP mission there was a large amount of radio activity and, in particular, a noise storm of frequent, small type III bursts from 31 March to 6 April 2019. Our aim is to investigate the source of these small and frequent bursts. We studied the behaviour of active region 12737, whose emergence and evolution coincides with the timing of the radio noise storm and determined the possible origins of the electron beams within the active region. Although, this active region produces no significant flares, its evolution indicates it is a source of the electron beams causing the radio storm. They most likely originate from the area at the edge of the active region that shows strong blue-shifted plasma. This paper was the result of the ISSI team ‘Exploring the solar wind in regions closer than ever observed before’, and was published in Astronomy & Astrophysics.

Figure 1. PSP/RFS radio frequency data showing the type III bursts and storm on 2 April 2019. Top panel: normalised Stokes intensity above 18 MHz, second panel: full spectrogram, third panel: significant burst above the background, and bottom panel: frequency of maximum normalised intensity. This interval shows both more classical type III bursts and the weaker more localised features associated with type III radio storms. These data are described further in the text (see Harra et al., 2021).

In order to explore the cause of the type III bursts, we analysed data from the Hinode EUV Imaging Spectrometer, PSP FIELDS, and the Solar Dynamics Observatory Atmospheric Imaging Assembly. Figure 1 illustrates both larger intensity type III bursts, extending over the full frequency band and exhibiting the classical frequency drift and the more impulsive, frequency-localised features associated with type III radio storms. The frequency of the maximum radio intensity decreases with time over this interval. As shown in panel 7, this implies a source moving to higher altitudes (and hence lower heliospheric plasma density) or an expanding source region whose density decreases with lateral expansion. With these characteristics defined, we then studied the behaviour of active region 12737, whose emergence and evolution coincides with the timing of the radio noise storm and determined the possible origins of the electron beams within the active region. To do this, we probed the dynamics, Doppler velocity, non-thermal velocity, FIP bias, and densities, and carried out magnetic modelling.

Figure 2. EIS Fe XII 195.119 Å intensity maps of the active region as it crossed the disc from 1 to 6 April. Centre panel: Doppler velocity maps derived from the same line. The colour bar shows the velocity range. The white boxes indicate the outflow regions chosen for measuring the FIP bias. Bottom panel: non-thermal velocity maps also from Fe XII 195.119 Å.

Figure 2 shows the active region (AR) as observed by Hinode EIS. The AR 12737 was observed to develop out of a coronal bright point near the east limb on 31 March and to evolve and grow before reaching a more steady state on approximately 6 April. The AR is a radio source and its dynamical evolution coincides with the evolution of the peak emission frequency of the dominant type III radio storm observed by PSP at this time. The active region has just emerged and as it evolves, the magnetic field lines expand. The edges of the active region both show increased Doppler velocities, increasing areas of upflows and increasing the magnitude of upflows and non-thermal velocity between 1 April and 4 April. Finally, the active region does not flare or have jets. We conclude that the active region is the most likely source of the energetic electron beams causing the type III radio storm, and more precisely, that the extended blue-shifted region could be a source. We also conclude that the changing nature of type III bursts (peak emission at a higher altitude or lower density region) must be related to the evolution and expansion of the active region. Other features seen were that the area of the blue-shifted outflow region increased by an order of magnitude and the FIP bias increased in the blue-shifted region by a significant amount (consistent with an increase in SEPs; Reames 2018).

Conclusions

In this work, we connected small-scale type III bursts with a non-flaring active region. Active region have always upflows at their edges in the corona, and in this case these are of interest in creating type III bursts. Although we had an hour of high cadence observations with Hinode-EIS, and found fluctuations in the upflows regions on the time scale of the cadence of the observations, they are close to the measurement limit of the instrument. The high cadence aspect of these measurements is key to further understanding the sources of SEPs and we encourage the future observing campaigns with PSP to aim to have some fast cadence measurements.

Based on a recent paper by L. Harra, D. H. Brooks, S. D. Bale, C. H. Mandrini, K. Barczynski, R. Sharma, S. T. Badman, S. Vargas Domínguez, and M. Pulupa, Astronomy & Astrophysics, 650, id.A7, (2021) DOI: https://doi.org/10.1051/0004-6361/202039514

References

L. Harra, D. H. Brooks, S. D. Bale, C. H. Mandrini, K. Barczynski, R. Sharma, S. T. Badman, S. Vargas Domínguez, and M. Pulupa, 2021A&A…650A…7H

Reames, R.,  2018SSRv..214…61R 

*Authors: L. Harra, D. H. Brooks, S. D. Bale, C. H. Mandrini, K. Barczynski, R. Sharma, S. T. Badman, S. Vargas Domínguez, and M. Pulupa,

 

 

 

Langmuir wave motion observed in the most intense radio sources in the sky by H. Reid and E. Kontar

The Sun routinely produces energetic electrons in its outer atmosphere that subsequently travel through interplanetary space. These electron beams generate Langmuir waves in the background plasma, producing type III radio bursts that are the brightest radio sources in the sky (Suzuki & Dulk, 1985). These solar radio bursts also provide a unique opportunity to understand particle acceleration and transport which is important for our prediction of extreme space weather events near the Earth. However, the formation and motion of type III fine frequency structures (see Figure 1) is a puzzle but is commonly believed to be related to plasma turbulence in the solar corona and solar wind.

A Recent work by Reid & Kontar, Nat Astro, 2021, combines a theoretical framework with kinetic simulations and high-resolution radio type III observations using the Low Frequency Array (LOFAR) and quantitatively demonstrates that the fine structures are caused by the moving intense clumps of Langmuir waves in a turbulent medium. These results show how type III fine structure can be used to remotely analyse the intensity and spectrum of compressive density fluctuations, and can infer ambient temperatures in astrophysical plasma, both significantly expanding the current diagnostic potential of solar radio emission.

Figure 1 – Dynamic spectra (left) and associated radio contours (right) of a solar type III radio burst observed by LOFAR on the 24 June 2015 at 12:18:20 UT.  The LOFAR contours are at 75% of the peak flux of the type III bursts going from 40 MHz to 30 MHz in the colour sequence white-blue-green-yellow-red. The LOFAR beam contour at 75% for 30 MHz is shown in the top left corner in white. The background is the Sun in EUV at 171 Angstroms observed by AIA. Image from Reid & Kontar, Nature Astronomy, 2021.

The radio fine structures you can see in Figure 1 have a small drift in frequency, caused by the motion of Langmuir wave clumps moving through space at their group velocity.  Measuring this frequency drift (Figure 2) allows us to deduce the Langmuir wave group velocity, and subsequently deduce the background thermal velocity.  This new technique increases the scope of solar radio bursts to be used as a remote plasma temperature diagnostic. The observation infers a corresponding coronal plasma temperature around 1.1 MK. The radio fine structure also provides an additional way to estimate the electron beam bulk velocity, which is mostly controlled by the beam energy density.

Figure 2 – Magnification of one type III fine structure from the LOFAR data (left) and the simulations (right).  The black dashed lines show a linear fit to the drift, estimating a constant velocity of 0.69 Mm/s for the observed type III burst and 0.6 Mm/s for the simulated type III burst.  Image from Reid & Kontar, Nature Astronomy, 2021.

Type III radio emission fluctuates because the background electron density turbulence modulates the growth of Langmuir waves from the electron beam.  The characteristic intensity of density turbulence parallel to the magnetic field, $\Delta n/n$ and the characteristic intensity of radio fine structure $\Delta I/I$ are analytically related via

\[\frac{\Delta n}{n} =\bigg(\frac{v_{\rm Th}}{v_b}\bigg)^2\frac{\Delta I}{I} \]

for the thermal velocity $v_{\rm Th}$ and the beam velocity $v_b$.  The simulations also find the same relation (Figure 3).  This new technique further increases the scope of radio fine structure to remotely determine the level of density turbulence, with the observations finding a level of 0.003.

Figure 3 – The relation between the radio fine structure $\Delta I/I$ and the level of density fluctuations $\Delta n/n$ found from different simulations.  The black triangle shows the predicted level of turbulence from observations and the black dashed line shows the analytical relation between $\Delta I/I$ and $\Delta n/n$ from observations.  Image from Reid & Kontar, Nature Astronomy, 2021.

In summary, the results create a framework for exploiting the diagnostic potential of radio burst fine structure to estimate plasma temperatures and density turbulence.   This new potential is especially relevant given the enhanced resolution of new-age ground-based radio telescopes that are resolving much more fine structure originating from the solar corona. Moreover, the closer proximity of Parker Solar Probe and Solar Orbiter to radio emission originating in the very high corona or solar wind, and hence higher sensitivity, allows fine structures to be detected in situ.

Based on a recent paper: Reid, H.A.S., Kontar, E.P. Fine structure of type III solar radio bursts from Langmuir wave motion in turbulent plasma, Nature Astronomy (2021). DOI: 10.1038/s41550-021-01370-8

References:

Suzuki, S. & Dulk, G. A. Bursts of Type III and Type V 289–332 (Cambridge Univ. Press, 1985).

Reid, H.A.S., & Kontar, E.P., Nature Astronomy, 2021.

Quasi-Periodic Particle Acceleration in a Solar Flare by B. Clarke et al.*

Quasi-periodic pulsations (QPPs) are defined as intensity modulations in the flare electromagnetic radiation as a function of time. These modulations have been found to have characteristic periodicities that range from < 1 s up to several minutes.

QPPs were first associated with the impulsive phase of flares and observed in the hard X-ray (HXR) and radio wavebands (Parks & Winkler 1969). They have more recently been observed within the thermal component of flares and have been identified to persist into the decay phase (Dennis et al. 2017). Hence studies that explore signatures of QPPs across the entire electromagnetic spectrum are important to help us build a picture of their underlying driver.

Recent studies have determined that a lower limit of ~46 % of the X-class flares in the last solar cycle contained QPPs (Hayes et al. 2020). Despite the ubiquity of QPPs in flares, the underlying mechanism that produces them remains unknown. Several models have been proposed as explanations for the presence of QPPs, which are typically categorized as oscillatory or self-oscillatory processes (McLaughlin et al. 2018).

Oscillatory processes encompass mechanisms in which magnetohydrodynamic (MHD) oscillations or waves modulate the electromagnetic emission, or stimulate magnetic reconnection on a time-dependent basis. These processes allow for seismological possibilities of using QPPs to probe solar and stellar flare sites to extract properties such as the electron density, magnetic field, and flare loop lengths.

Self-oscillatory processes are interpreted as a manifestation of time-dependent, intermittent magnetic reconnection. These processes allow for the existence of broad-band QPPs and if found to be occurring, would provide new insight into the nature of energy release in flares.

Observations & Results

In this work, we investigate a GOES M3.7 flare that occurred on 2015 November 4. The flare exhibited pronounced QPPs across a broad-band of wavelengths. We identify QPPs in the X-ray, low-frequency radio, and extreme ultraviolet (EUV) wavebands.

We determine that these QPPs are a consequence of intermittent particle acceleration, likely due to “bursty” magnetic reconnection. At the energy release site, accelerated electrons precipitate toward the chromosphere to produce the X-ray and EUV pulsations. The electrons accelerated towards interplanetary space escape along open magnetic field lines, resulting in low-frequency radio pulses in the form of type III radio bursts.

Figure 1 – (a) shows the dynamic spectrum of the radio emission containing a sequence of type III radio bursts and Figure 1(b) shows the EUV, soft X-ray (SXR), and HXR light curves in which we identify seven pulsations. The EUV light curves were extracted from the QPP source region identified in Figure 2. The HXR, SXR, and EUV QPPs were found to have the same period of ~2 minutes, indicating a common progenitor.

The green light curve in Figure 1(b) shows a slice from the dynamic spectrum at 2.5 MHz. Using an electron density model, we estimated the height at which this radio emission was emitted: ~ 16 solar radii. Lines drawn from the peaks of pulses 1 and 7 from the 171 Å curve indicate the time delay required for the electron beams to reach this height from the flare site. This analysis suggests that the beam speeds are equal to the typical value of ~0.3 c for type III radio bursts. Hence, we have related QPPs observed in the SXR, HXR, EUV, and low frequency radio regimes.

Locating the QPP Source

Figure 2 – Spatial analysis of the QPPs. Left: an AIA 171 Å image with RHESSI 35-70 keV image contours overlaid. The light curves on the right show the HXRs (full Sun) with the EUV emission extracted from two of the kernels marked in the image, showing K1 to be the primary source region.

RHESSI imaging was employed to determine where the non-thermal HXRs originated. It was found that there were three HXR sources on the map which are labelled as K1, K2, and K3. These sources are shown in red overlaid on the 171 Å SDO/AIA image in Figure 2.

To determine the location within the flare site predominantly producing the QPPs, we integrated the emission from each EUV image over each region of the active region using various kernel sizes, generated light curves for each of these kernels for the duration of the flare, and compared the profiles of the time series to that of the HXR emission. The emission from K1 produced the most prominent QPPs and was found to yield a periodicity that best matched the HXR pulsations.

A natural escape route

Figure 3  PFSS extrapolation showing the geometry of the magnetic field lines of the flaring region overlaid on the AIA 171 Å image.

The QPP source region, K1, is associated with open magnetic field lines, identified in the potential field source surface (PFSS) extrapolation shown in Figure 3. This magnetic field geometry allows for a mechanism for the escape of the electrons responsible for producing the radio emission.

Conclusions

Figure 4 – Cartoon of the flaring region illustrating the likely mechanism through which we observe the episodic particle acceleration resulting in QPPs in EUV, radio, SXR, and HXR.

We interpret the QPPs identified in this flare in terms of pulsed electron acceleration caused by time-dependent intermittent reconnection. In Figure 4 we show a cartoon scenario of the flare site to illustrate how the QPP sources are related to the magnetic field configuration. Following each burst of electron acceleration, those that escape upward along the open magnetic field lines result in the type III QPPs, and those that travel along closed lines precipitate in the chromosphere to cause the QPPs we observe in hard X-ray and EUV.

This work provides new evidence that oscillatory or time-dependent reconnection can naturally generate QPPs, providing an explanation for their presence across the entire spatial range of flaring emission. It shines light onto the nature of energy release in flares, provides insight into how QPPs be can localised to specific regions of flare sites, and that QPPs can manifest over vast distances via multiple emission mechanism.

Future work to investigate the details and conditions necessary for the triggering of magnetic reconnection in this bursty fashion is required.

Based on the recent paper: Brendan P. Clarke et al., 2021, ApJ, 910, 123

References

Dennis, B. R. et al. 2017, ApJ, 836, 84

Hayes, L.A. et al. 2020 ApJ, 895, 50

McLaughlin, J. A. et al. 2018 SSRv, 214, 45

Parks, G., & Winckler, J. 1969 ApJL, 155, L117

*Full list of authors:  Brendan Clarke, Laura A. Hayes, Peter T. Gallagher, Shane A. Maloney & Eoin P. Carley

New results on the direct observations of thermal radio emission from a solar coronal mass ejection by R. Ramesh et al.*

Coronal mass ejections (CMEs) are large scale and energetic eruptions in the solar atmosphere during which $\approx$10$^{12}$-10$^{16}$g of magnetized coronal plasma are ejected into the heliosphere at speeds ranging from $\approx$100-3000km/s. They are mostly observed in whitelight using coronagraphs which use an occulter to block the bright light from the solar photosphere so that structures like CMEs can be observed with better contrast. But the size of the coronagraph occulters till date has always been larger than that of the photosphere. This prevents observations of the corona present immediately off the solar limb, in addition to the corona above the solar disk. Radio observations are unique in this connection since there is no occulter, hence both ‘limb’ and ‘disk’ corona could be observed simultaneously. However, there are only a few reports of direct detection of CMEs at radio frequencies via thermal bremsstrahlung emission (see for example, Sheridan et. al. 1978, Gopalswamy et. al. 1992, Kathiravan et. al. 2005, Ramesh et. al. 2003). We studied the radio observations of thermal emission from a CME simultaneously at two different frequencies on 2016 May 1.

Observations and Analysis

The radio observations were carried out on 2016 May 1 using the different facilities operated by Indian Institute of Astrophysics (IIA) in Gauribidanur observatory. Observations in Extreme ultraviolet (EUV) at 211 A$^o$ with the Atmospheric Imaging Assembly (AIA; Lemen et. al. 2012) on board the Solar Dynamics Observatory (SDO), and in whitelight with the COR1 coronoagraph of the Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI; Howard et. at. 2008) on board the Solar TErrestrial RElationship Observatory (STEREO) and the Large Angle and Spectrometric Coronagraph (LASCO; Brueckner et. al. 1995) on board the Solar and Heliospheric Observatory (SOHO) were used to supplement the radio observations. The spatio-temporal correspondence between the radio contours and the whitelight CME (Figure 1) indicates that the radio emission could be due to the CME. The larger size of the radio contours, particularly at 53 MHz and in the north-south direction, are likely due to the comparatively limited angular resolution of GRAPH. The centroids of the radio emission are located at $r_{80}{\approx}$1.7$\pm 0.2\rm R_{\odot}$ (80 MHz) and  $r_{53}{\approx}$2.1$\pm0.2\rm R_{\odot}$ (53 MHz).  Any possible error in the position of the centroids due to propagation effects such as scattering by density inhomogeneities in the solar corona and/or refraction in the Earth’s ionosphere.

 

Figure 1 – A composite of the difference images obtained using EUV ($\approx$06:02-05:41 UT), radio ($\approx$06:47-06:42 UT), for 80 MHz contours in ‘cyan’ and $\approx$06:47-06:43 UT and whitelight ($\approx$07:00-06:00 UT) observations on 2016 May 1. The inner and outer ‘red’ circles indicate the solar limb (radius$\approx$1$\rm R_{\odot} $), and the occulter in the SOHO/LASCO-C2 coronagraph (radius$\approx$2.2$\rm R_{\odot} $). The bright emission above the occulter (indicated by ‘magenta’ arrow) is the whitelight CME. The inset in the upper left corner is a close-up view of the region indicated by the ‘yellow’ arrow on the SDO/AIA-211 A$^o$ image. The ‘cyan’ and ‘blue’ contours correspond to radio observations at 80 MHz and 53 MHz. The contour levels are ${\approx} $[63, 67, 71, 75, 79, 83, 87, 91, 95, 99] \% of $3.4{\times}10^{5}$K (80 MHz) and $0.8{\times}10^{5}$K (53 MHz).

The brightness temperatures ($T_{b}$) of the radio sources near their centroids are $T_{b}^{80} {\approx}3.4{\times}10^{5}$K (80 MHz) and $T_{b}^{53} {\approx}0.8{\times}10^{5}$K (53 MHz). The corresponding flux density ($S$) values are $S_{80} {\approx}0.14$sfu (80 MHz) and $S_{53} {\approx}0.06$sfu (53 MHz). The spectral index ($\alpha$) derived from the above flux densities is ${\approx}2.1$. Model calculations by Bastian et. al. 1997 also indicate that it is possible to observe enhanced thermal emission from particularly the off-limb CMEs using difference images as in the present case. The above $T_{b}$ values are reasonably consistent with those predicted by the aforementioned model for thermal emission from a ‘typical’ CME in the same frequency range.

 Figure 2 – Polarimetric GRIP observations of Stokes I (‘blue’) and V (‘green’) emission at 80 MHz in the transit mode around 06:48 UT. The asymmetry in the Stokes I observations on 2016 May 2 was due to a local radio frequency interference (RFI) around ${\approx}$06:40 UT. The `solid’ lines in black colour are the `fit’ to the respective data points.

Results and Conclusions

The separation between the centroids of the 80 MHz and 53 MHz radio sources (Figure1) suggests possible density gradient in the frontal structure similar to that in the background corona since it is well known that radio emission from the Sun at a particular frequency ($f$) can propagate towards the observer only from/above the critical level at which the plasma frequency ($f_{p}$) corresponding to the local electron density ($N_{e}$) equals $f$. It is known that the larger density gradient near the solar limb leads to refraction of low frequency radio waves. So, the contribution to observed thermal bremsstrahlung emission at any given frequency is primarily from regions well above the corresponding plasma level. This implies smaller optical depth ($\tau$) since the absorption coefficient and hence $\tau$ are maximum only near the plasma level (Smerd 1950, Aubier et. al. 1971). In the case of solar corona, $T_{b}$ and $\tau$ are related to its electron temperature ($T_{e}{\approx}10^{6}$K) as $T_{b}{\approx}T_{e}(1{-}e^{-\tau})$. Since $\tau$ above the limb is small as mentioned, $T_{b}{<}T_{e}$ although the spectral index could be indicative of optically thick thermal emission. The emission from CMEs too undergoes refraction and reflection near the plasma layer as described above (Bastian et. al. 1997). The fact that $T_{b}^{80}$ and $T_{b}^{53}$ in the present case  are lesser than $T_{e}$ also indicates the same. 

Using the aforementioned relation, we calculated $\tau$ corresponding to $T_{b}^{80}$ and $T_{b}^{53}$, and the values are  ${\tau}_{80}{\approx}$0.4 and ${\tau}_{53}{\approx}$0.1. Based on this, we then estimated $N_{e}$ at $r_{80}{\approx}$1.7$\pm0.2\rm R_{\odot}$ and  $r_{53} {\approx}$2.1$\pm0.2\rm R_{\odot}$ to be  $N_{e}^{80} {\approx} $2.2$\rm{\times }10^{7} cm^{-3}$ and  $ N_{e}^{53} {\approx}$1.0$\rm {\times} 10^{6}cm^{-3}$, respectively. We calculated the CME kinetic energy $E_{cme}^{radio}{\approx}2{\times}10^{30}$erg. The estimates of $M_{cme}^{radio}$ and $E_{cme}^{radio}$ agree reasonably with the mass and kinetic energy of the CME estimated using SOHO/LASCO-C2 observations. The density at $r{\approx}$2.1$\rm R_{\odot}$ is ${\approx}1.0{\times}10^{6}\rm cm^{-3}$ and the estimated $dcp$ due to CME associated enhanced radio emission is ${\approx}12\%$. Sastry (2009) had shown that if $B{\approx}$0.5G and electron density is ${\approx} 1.2{\times}10^{6}\rm cm^{-3}$, then it should be possible to observe circular polarized radio emission with $dcp{\approx}$12 %. 

 

Figure 3. CME h-t plot obtained using EUV, whitelight and radio observations.

In this study, we reported relatively rare observation of CME in low radio frequencies on 2016 May 1. No non-thermal radio burst activity was noticed, which provided an opportunity to observe the faint thermal radio emission from the CME, and hence we directly estimated the electron density, mass, and magnetic field strength of the plasma entrained in the CME. Future observations with low frequency radio antenna arrays with larger collecting area like LOFAR and SKA should be able to effectively exploit this possibility for CMEs against the solar disk also.

Based on the recent paper: Ramesh, R., Kumari, A., et. al.:  New results on the direct observations of thermal radio emission from a solar coronal mass ejection. Geophysical Research Letters, 48, e2020GL091048, DOI: https://doi.org/10.1029/2020GL091048

References

Sheridan, K. V., & McLean, D. J. (1985). Solar radiophysics: Study of emission from the sun at meter wavelength (pp. 443–466).

Gopalswamy, N., & Kundu, M. R. (1992). The Astrophysical Journal, 390, L37–L39.

Bastian, T. S., & Gary, D. E. (1997). Journal of Geophysical Research, 102, 14031–14040.

Sastry, C. V. (2009). The Astrophysical Journal, 697, 1934–1939.

*Full list of Authors:  R. Ramesh, Anshu Kumari, C. Kathiravan, D. Ketaki, T. J. Wang.

New treatment of gyroresonance and free-free radio emissions from multi-thermal multi-component plasma by A. Kuznetsov et al.*

Thermal plasma in the solar corona is often characterized by a range of temperatures. This plasma can be described by the differential emission measure (DEM), which is a distribution of the thermal electron density square over temperature. The DEM-based treatment is widely used in application to the optically thin EUV and X-ray emissions. However, there has been no corresponding treatment in the radio domain, where optical depth of emission can be large, and both free-free and gyroresonance thermal emission mechanisms are involved. A framework that accounts for a multi-thermal plasma composition is highly demanded for analyzing and modeling the currently available data, and needed to combine the EUV, X-ray, and radio models.

Another important factor that is often neglected but can affect the free-free radio emission is the contribution of heavy (highly-ionized) ions. Although abundances of heavy elements relative to Hydrogen are relatively small, their contribution to the free-free emission can be significant due to dependence of the emission on Z2 (the charge square). This contribution depends on both the plasma composition (i.e., the element abundances) and the temperature (i.e., the ionization states).

Method

We have extended the “classical” theory of the thermal free-free and gyroresonance radio emission to the case of a multi-temperature plasma; the new theory has been implemented in a freely-available computer code (Kuznetsov et al. 2021). For the free-free emission, the new theory and code include:

  • the multi-temperature plasma composition (described by the DEM), which is applied to both optically thin and thick emissions;
  • the temperature-dependent ionization of the elements composing the plasma (which includes the dependence on the element abundances), see Figure 1;
  • exact values of the Gaunt factor which determine the Coulomb logarithm, see Figure 1;
  • contributions of electron collisions with both ions and neutral (hydrogen and helium) atoms;
  • effect of the ambient magnetic field.

 

Figure 1 – Dependence of the free-free emissivity at 1 GHz on temperature: green line shows the result for a hydrogen plasma taking into account the exact Gaunt factor, while the blue line also accounts for the temperature-dependent ionization of heavier elements in the solar corona. For comparison, the dotted line shows the T-0.5 dependence.

For the gyroresonance emission mechanism, we have introduced a new measure – the differential density metrics (DDM), which represents a distribution of the thermal electron density over temperature. The new theory and code use this DDM to compute the gyroresonance radio emission from a multi-temperature plasma (the gyroresonance mechanism is insensitive to the element abundances or Gaunt factor).

Similarly to our previous numerical tools for simulating the solar radio emission (Fleishman & Kuznetsov 2010; Fleishman & Kuznetsov 2014), the new computer code computes the radio emission from one or more lines-of-sight by solving the radiation transfer equation. The code also accounts for possible depolarization or polarization reversals when the emission crosses quasi-transverse magnetic field regions.

The new theory is presented in a paper recently published in ApJ (Fleishman et al. 2021). The corresponding computer code is implemented as executable libraries callable from IDL; it is available on GitHub and in the Zenodo repository (Kuznetsov et al. 2021).

Results

Figure 2 shows an example of DDM and DEM distributions obtained from an updated EBTEL code (courtesy of J. Klimchuk; private communication); these distributions will be used below to compute the model emission spectra. The corresponding average plasma temperatures (computed as moments of the distributions) are of about 2.6-2.8 MK, but there are significant amounts of particles with the temperatures considerably above the average values.

   Figure 2 – Model DDM and DEM distributions (courtesy of Jim Klimchuk) used in the simulations. The distributions correspond to the plasma heating parameters typical of a solar active region.

   

Figure 3 – Model radio emission spectra computed using the electron distributions shown in Figure 2. a) Free-free emission (no magnetic field); b) gyroresonance emission (magnetic field varying linearly with height from 1000 to 300 G along the line of sight). The emissions were computed both for the multi-thermal DEM/DDM approach and for an isothermal case corresponding to DDM-averaged temperature and density.

In Figure 3, we compare the free-free and gyroresonance radio emission spectra computed using the new multi-thermal approach and the corresponding (DDM-based) isothermal approximation. For both emission mechanisms, the multi-thermal plasma produces considerably higher emission fluxes, due to the contribution of particles with above-average energies; the difference is up to a factor of ~1.5 for the free-free emission and up to a factor of 2-6 for the gyroresonance emission. For the free-free emission, we have also considered the element abundances typical of either the solar corona or the photosphere/chromosphere; in the corona, due to higher abundances of low-FIP heavy elements (primarily – iron) and hence stronger contribution of highly-ionized ions, the emission intensity is higher by up to 10%.

Additional info: Based on the recent paper by Fleishman, Kuznetsov, & Landi, “Gyroresonance and Free-Free Radio Emissions from Multithermal Multicomponent Plasma”, ApJ, 914, 52 (2021). DOI: 10.3847/1538-4357/abf92c

References

Fleishman, G.D., Kuznetsov, A.A.: 2010, ApJ, 721, 1127

Fleishman, G.D., Kuznetsov, A.A.: 2014, ApJ, 781, 77

Fleishman, G.D., Kuznetsov, A.A., Landi, E.: 2021, ApJ, 914, 52

Kuznetsov, A., Fleishman, G., Landi, E.: 2021, Zenodo:4625572

*Full list of authors: Alexey Kuznetsov, Gregory Fleishman, and Enrico Landi

Energy budget of plasma motions, heating, and electron acceleration in a three-loop solar flare by G. Motorina et al.*

The solar flare phenomenon is a complex process in the solar atmosphere where non-potential magnetic energy is released and converted into other forms of energy, such as nonthermal energy of accelerated particles, thermal energy of heated flaring plasma, kinetic energy of eruptions, jets, up/down flows, and stochastic (turbulent) plasma motions. The processes lying behind initial division between energy components, distribution of these components among flaring loops and their evolution are not yet fully understood. A recent statistical study by Lysenko et al. (2018) described a class of early impulsive ‘cold’ flares, where the direct heating is weak and most of plasma heating is driven by accelerated electrons. Such flares offer the cleanest way to study the electron acceleration in flares and the thermal plasma response driven by the nonthermal electron population. 

Here we quantify the energy partitioning and spatial distribution in a SOL2014-02-16T064620 solar flare of class C1.5, which has relatively weak thermal response similar to cold flares. This event is a rare case when a rather simple flare with a ‘single-spike’ impulsive phase was observed with IRIS so we can quantify the kinetic energy of turbulent and bulk plasma motions in the flare footpoints. 

Analysis of Observations

In the study we analyze SDO/AIA and RHESSI data to take into account both moderately heated and hot components of the flaring plasma in the coronal part of the flare. Applying the regularized inversion code to the SDO/AIA data (Hannah & Kontar 2012, 2013) and the methodology described in Motorina et al. (2020) we calculate the spatial distribution of temperature, emission measure, and thermal energy density (Figure 1, a). The main contribution to the thermal energy comes from the flare area (box 2 in Figure 1, a, upper left panel) which can be divided into two regions (marked with green/magenta lines) corresponding to two different flaring loops. The bulk of the thermal energy contained in the flare region is equally divided between these two loops (Figure 1, b). Evolution of this energy (from box 2) is shown in Figure 1(c) in black with its peak value at ~7×1028 [erg].

Given that RHESSI missed the impulsive phase due to being in the orbital night, we use the X-ray data from RHESSI only in the decay phase. To calculate the thermal energy detected by RHESSI, we use the emission measure and temperature obtained from the RHESSI fit and volume of the corresponding Loop II from a 3D flare model. The evolution of this energy is shown in Figure 1(c) in green with the peak value of ~5×1028 [erg]. 

Hard X-ray observations of the impulsive phase are only available in the Konus-Wind wide G1 channel covering 21–80 keV range. These observations in conjunction with the NoRP, RSTN, and BBMS data in microwave range and a built 3D model of the flare are employed to estimate the nonthermal energy deposition in the flare (Figure 1, c, blue line). The nonthermal energy deposition derived from the RHESSI fit (Figure 1, c, dark blue dashed line) during the decay phase does not contradict any available data.

The IRIS data show activity (impulsive enhancements in the flare area) temporally coinciding with the impulsive emission from Konus-Wind and microwaves. We analyze the spectral lines Si IV, O IV, and Fe XXI which form at different transition region to coronal temperatures. We fit a Gaussian function to each pixel for each spectral line to determine their Doppler velocities and Doppler widths and thus to quantify the kinetic energy of the plasma flows and turbulent motions. Because of weak signatures of Fe XXI, we cannot use this spectral line to estimate a coronal portion of the kinetic energy. The considered temperature range 104.8-105.1 K belongs to the flare footpoints. Thus, these data quantify only a fraction of the total kinetic energy in the flare. We determine which IRIS pixels lie inside the 50% RHESSI 6-9 keV contour and calculate this energy 3 × 1024 [erg]. Then we found the total turbulent kinetic energy for the same volume as less than 7 ×1025 [erg].

Figure 1 – (a) Spatial distributions of plasma parameters derived from SDO/AIA: temperature (top left panel), emission measure (top right panel), chi-square (bottom left panel), thermal energy density (bottom right panel). (b) Components of the thermal energy inside box 2 defined in Figure 1(a): green/magenta lines correspond to green/magenta ROIs. The red and green symbols indicate the model values of thermal energies Loops I and II, respectively. (c) Evolution of the energy components in the February 16, 2014 flare. 

3D Modeling

Based on the NLFFF extrapolation code (Fleishman et al. 2017) initiated with an SDO/HMI vector magnetogram taken at 06:34:12 UT and GX Simulator (Nita et al. 2015) we built a 3D flare model (Figure 2). The GX Simulator functionality permits computation (and visualisation) of selected magnetic field lines such as to match available flare images. With the use of the AIA and RHESSI images we identified three loops and filled them with thermal plasma. The red, green, and yellow symbols in Figure 1 (c) indicate the model values of thermal energies in Loops I, II, and III respectively. 

Based on the only available microwave spectral data at 06:44:41UT we found that energetically dominant fraction of the nonthermal electrons must be located in Loop II. The built model is consistent with all available observational constraints and, thus, validated by the data. 

 

Figure 2 – The 3D model with three flux tubes labeled with their numbers (I–III). (a) Magnetic flux tubes. (b) Distribution of thermal number density in the flux tubes. (c) Distribution of nonthermal number density in the flux tubes (in Loop II only). (d) Distribution of the temperature in the flux tubes.

Conclusions

In this study, we have analyzed the SOL2014-02-16T064600 flare which has three distinct consecutive heating episodes, where the second one appeared as a response on the nonthermal impulsive peak. From the timing of the event, we can conclude that only a portion of the flaring plasma heating was driven by nonthermal electron losses, while the remaining portion was driven by another agent.

We found that the flare occurred in a multi-loop system that included at least three distinct flux tubes. The nonthermal electron population was only detectable in the largest and hottest Loop II, while two other loops remained thermal. The distribution of the energy components over the three flaring loops involved in the event was highly uneven. The accounted forms of the kinetic energy in the flare footpoints constituted only a minor fraction compared with the thermal and nonthermal energies.

Nonthermal energy input was sufficient for the postimpulsive heating in the flaring loop with nonthermal electrons, but insufficient for the overall thermal response in the flare. 

Based on the recently published paper: Gregory D. Fleishman, Lucia Kleint, Galina G. Motorina, Gelu M. Nita, and Eduard P. Kontar, Energy budget of plasma motions, heating, and electron acceleration in a three-loop solar flare, The Astrophysical Journal, 913, 97 (2021) (https://doi.org/10.3847/1538-4357/abf495)  

References 

Hannah I.G. & Kontar E.P. 2012, A&A, 539, A146 https://doi.org/10.1051/0004-6361/201117576 

Hannah I.G. & Kontar E.P. 2013, A&A, 553, A10 https://doi.org/10.1051/0004-6361/201219727 

Lysenko A.L.  et al. 2018, ApJ, 856, 111 https://doi.org/10.3847/1538-4357/aab271 

Motorina G.G. et al, 2020, ApJ, 890, 75 https://doi.org/10.3847/1538-4357/ab67d1 

Fleishman G.D. et al. 2017, ApJ, 839, 30 https://doi.org/10.3847/1538-4357/aa6840 

Nita, G. M.  et al. 2015, ApJ, 799, 236 https://doi.org/10.1088/0004-637X/799/2/236 

*Full list of authors: Gregory D. Fleishman, Lucia Kleint, Galina G. Motorina, Gelu M. Nita, and Eduard P. Kontar

Narrowband Spikes Observed during the 2013 November 7 Flare by M. Karlicky et al.

Narrowband dm-spikes belong to the most interesting fine structures of solar radio bursts that are closely connected to primary flare energy-release processes (Krueger 1979) and observed in some cases near the Type III burst starting frequency. They occur in clouds of narrowband bursts with a typical duration less than 100 ms, frequency relative bandwidth 1-3 %, and brightness temperature up to $10^{15}$ K.

For them several radio emission models were suggested. Earlier models suggested emission by the electron cyclotron maser mechanism for $Y=\omega_{pe} / \omega_{ce} < 1$, where $\omega_{pe}$ is the electron plasma frequency, $\omega_{ce}$ is the electron cyclotron frequency (Melrose & Dulk 1982). In this model, emission occurs near the harmonics of the electron cyclotron frequency. However, non-integer ratios between spike bands were observed by Krucker & Benz (1994). Therefore, a model based on emission at Bernstein mode frequencies was proposed by Willes & Robinson (1996). Moreover, the model of emission at upper-hybrid frequencies was suggested  for $Y > 1$ by Stepanov et al. (2001). In this model, emission regions are separated in height, and thus they emit at separate frequencies.

We investigate the 2013 November 7 spike event showing unique very narrow bands with non-integer frequency ratios. In interpretation of this event we consider two models: (1) with the emission from one emission source at Bernstein mode frequencies and (2) with the emission from separated emission sources at upper-hybrid frequencies.

Observation

We study the 2013 November 7 spike event  where spikes were clustered in unique very narrow bands (Figure 1). This spike event belongs to 53 spike events that were registered by Ondřejov radiospectrographs in the range 0.8-2 GHz during 1992-2020 years. The frequencies of its four narrow bands are 1003, 1276, 1572, and 1877 MHz, giving ratios between adjacent bands as 1.275, 1.23, and 1.19. Figure 2 shows the radio flux evolution of these bands and their cross-correlations.

Figure 1 – Observed spike event on 2013 November 7. (a) Broadband cloud of spikes followed by unique four very narrow bands of spikes. (b) Detail of the radio spectrum in 1 – 2 GHz range with 1 s duration. The arrow shows the band frequency variation for which the form is synchronized with the similar forms in all four bands. The spectrum is not smoothed and thus shows bins in the record.

Results

We computed growth rates for both our models. For the Bernstein model (Figure 3), we found the corresponding Bernstein modes cross regions of positive growth rates. Moreover, these modes have a non-integer frequency ratios, and their positions fit well with the observed band frequencies. The parameters in this model correspond to the plasma density $9 \times 10^{9}$ cm$^{-3}$ and magnetic field strength 113 G. In the upper-hybrid model, we also estimated growth rates  (Figure 4). The corresponding plasma density and magnetic field strength are in the range $1.1 – 2.9 \times 10^{10}$ cm$^{-3}$ and  119-111 G, respectively.

Figure 2 – (a) Evolution of radio flux at 1877 MHz (black line), at 1572 MHz (red line) +400 au, at 1276 MHz (blue line) +800 au, and at 1003 MHz (orange line) +1200 au, starting at 12:26:55 UT and lasting 1 s. (b) Cross-correlations of the radio flux profiles on 1877 and 1572 MHz (black line), 1572 and 1276 MHz (red line), and 1276 and 1003 MHz (blue line).

 

Figure 3 – Growth rates of the Bernstein modes as a function of the frequency and perpendicular wavenumber for parameters $\omega_{pe}/\omega_{ce} = 2.7$, $f_{pe} = 855$ MHz, $v_{tb}/c = 0.02$, $v_{t}/c = 0.25$, $n_{e}/n_{h} = 10$. Frequency corresponds to the radio emission on Bernstein mode frequencies. Green lines: dispersion modes, $s$ is the gyro-harmonic number of each branch. White dashed horizontal line denotes the plasma frequency.

 

Figure 4 – Growth rate of the upper-hybrid waves vs. the upper-hybrid to electron cyclotron frequency ratio; $s$ denotes the gyro-harmonic number of the most unstable wave.

Conclusions

We found that the Bernstein mode model better explains the observed spikes than the upper-hybrid model, at least in the studied event. It fits very well with the observed frequencies for reasonable plasma parameters and produces well the observed band frequency difference of 300 MHz. Moreover, it is not very probable that four separated regions give these ratios in the upper-hybrid model. Another argument against upper-hybrid model is that it requests Alfvén speed $\sim 200.000$ km s$^{-1}$ to obtain $\leq 0.01$ s cross-correlation time lag between frequency bands (Figure 2b) when we assume typical density scale height in the corona.

Based on the recent paper

Karlický, M., Benáček, J., & Rybák, J. 2021, ApJ, 910, 108.doi:10.3847/1538-4357/abe62b

References

Krucker, S. & Benz, A. O. 1994, A&A, 285, 1038. 

Krueger, A. 1979, Geophysics and Astrophysics Monographs, Dordrecht: Reidel, 1979

Melrose, D. B. & Dulk, G. A. 1982, ApJ, 259, 844. doi:10.1086/160219

Stepanov, A. V., Kliem, B., Krüger, A., et al. 1999, ApJ, 524, 961. doi:10.1086/307835

Willes, A. J. & Robinson, P. A. 1996, ApJ, 467, 465. doi:10.1086/177620

*Full list of authors: Marian Karlický, Jan Benáček and Ján Rybák

Statistics of Low Frequency Cutoffs for Type III Radio Bursts Observed by Parker Solar Probe during Its Encounters 1–5 by Bing Ma et al

Interplanetary (IP) type III radio bursts are deemed to generate in the interplanetary space because of their lower emission frequency ($0.01 – 10$ MHz) in terms of plasma emission. However, using the electron cyclotron maser emission (ECME), Wu et al. (2004) presented that IP type III radio bursts may generate in the low corona. The low frequency cutoffs is an important parameter to research the generation mechanism of type III emission.

Leblanc et al. (1995) and Dulk et al. (1996) investigated the low frequency cutoffs of IP type III bursts observed by Ulysses and Wind spacecraft located in 1–4.3 AU to the Sun. Their results show that: (1) the cutoff frequencies of type III radio bursts $f_{lo}$ are almost all higher than spacecraft’s local plasma frequency $f_p$. (2) The $f_p$ decreases with the distance of spacecraft from the Sun. (3) The $f_{lo}$ mainly ranges from 20 to 300 kHz and it is independent of the location of spacecraft.

NASA’s Parker Solar Probe (PSP) is a spacecraft that was launched on 2018 August 12 and could fly to a closer distance to the Sun than any other previous spacecraft. In this paper, we use the radio data observed by the PSP within 0.25 AU (during PSP’s encounter phases) to study the low frequency cutoffs of the IP type III bursts and preliminarily discuss the possible reasons of the different results from previous studies. 

Observation and Analysis

We use the data observed by the Radio Frequency Spectrometer on PSP during the encounter phases of its first five orbits and obtain 176 type III radio bursts and their cutoff frequency $f_{lo}$ and spacecraft’s local plasma frequency $f_p$ by automatic program recognition and manual checking.

The scatter plot of $f_{lo}$ and $f_p$ versus the distance of PSP from the Sun is shown in Figure 1. It is obvious that the distribution of the cutoff frequency is higher than that of the PSP’s local plasma frequency. One can also find that the cutoff frequency is independent of the spacecraft’s position and $f_p$ decreases with the distance if the events with relatively lower $f_p$ in $35-40R_{\odot}$ circled by the black dashed line are excluded, which are associated with a high velocity solar wind stream with low density. These results are consistent with previous studies. 

On the other hand, the $f_p$ mainly ranges from 50 to 250 kHz, which is much higher than that observed by Ulysses and Wind (3-50 kHz). It is easy to understand because PSP is much closer to the Sun than Ulysses and Wind, and its ambient electron density is higher. However, there is a significant difference between the distributions of $f_{lo}$ observed by PSP (200 kHz−1.6 MHz) in this study and in previous work based on Ulysses and Wind (20-300 kHz) by Leblanc et al. (1995) and Dulk et al. (1996). We propose three possible reasons:

Figure 1 – Measurements of characteristic frequencies ($f_{lo}$ and $f_p$) of 176 type III events vs. the corresponding distances of PSP from the Sun. The solid triangle and the hollow circle indicate $f_{lo}$ and $f_p$, respectively. Different colors of marks denote different encounter phases of PSP. Some events with relatively lower $f_p$ in 35-40 $R_{\odot}$ during E02 are circled by the black dashed line. The correlation coefficient $R_{flo} = -0.2246$ implies that $f_{lo}$ is independent of the PSP’s location. And $R_{fp} = -0.7748$ implies there is apparent dependency between $f_p$ and distance of PSP from the Sun.

(1) Solar activity intensity in different observation periods is different and it can influence the magnetic energy release and the propagation distance of electron beams in active regions. Therefore, solar activity intensity may affect the cutoff frequency of type III radio bursts.

(2) The criteria of event selection may also play an important role. We consider many events with shorter duration and weaker intensity than previous studies. These events may have much higher $f_{lo}$.

(3) The spacecraft located further from the Sun may be hard to receive the emission of weak bursts with higher cutoff frequencies due to the radiation attenuation effect, and thus the statistics of $f_{lo}$ observed especially by Ulysses only covered the stronger events with lower $f_{lo}$. 

The statistics of multipoint observation by spacecraft like PSP, Wind, or Solar Orbiter may provide more details about the influence factors of the low frequency cutoffs of type III bursts in the future.

Based on a recent paper Bing Ma et al 2021 ApJL 913 L1 DOI: https://doi.org/10.3847/2041-8213/abfb77

References

Wu, C. S., Reiner, M. J., Yoon, P. H., Zheng, H. N., & Wang, S. 2004, ApJ, 605, 503

Leblanc, Y., Dulk, G. A., & Hoang, S. 1995, GeoRL, 22, 3429

Dulk, G. A., Leblanc, Y., Bougeret, J.-L., & Hoang, S. 1996, GeoRL, 23, 1203

PIC Simulation of Double Plasma Resonance and Zebra Pattern of Solar Radio Bursts by Li et al.*

Zebra patterns (ZPs) represent a spectral fine structure with equidistant or almost-equidistant stripes of enhanced intensity against a broadband emission background, frequently observed in the dynamic spectra of solar radio bursts such as type IVs. There exist many scenarios for ZPs. The most-accepted one is the model of double plasma resonance (DPR) which, as its name indicates, means simultaneous actions of two kinds of resonance instabilities, i.e., the cyclotron resonance and the upper-hybrid (UH) resonance. DPR is also a result of the electron cyclotron maser instability (ECMI) driven by energetic electrons in plasmas with large ratio of characteristic frequencies ($\omega_{pe} / \Omega_{ce} >> 1$). The DPR process generates plasma waves with sharply-increased growth rates at frequencies close to the upper hybrid (UH) frequency and also an integer times of $\Omega_{ce}$, with $\omega \approx \omega_{UH} \approx s \Omega_{ce}$, where $s$ is an integer. ZPs are suggested to be generated through the conversion process of these plasma waves into escaping radiations, along a large-scale loop structure with gradually-varying $\omega_{pe} / \Omega_{ce}$ (Zheleznyakov & Zlotnik 1975).

Previous studies on DPR are mostly based on linear analysis without considering the generation of escaping radiations due to the non-linear plasma emission process. In a recent study using the fully kinetic electromagnetic particle-in-cell (PIC) simulation, Ni et al. (2020) presented significant plasma emissions at both the fundamental (F) and harmonic (H) branches, via the ECMI process in plasmas with $ \omega_{pe} / \Omega_{ce} = 10$. The process starts from the excitation of various waves, including the UH, Z, and whistler (W) modes, followed by the nonlinear wave–wave coupling process to release the fundamental (F) and harmonic (H) plasma emissions. Ni et al. (2020) suggested that the F emission is generated by the coalescence of almost-counter-propagating Z and W modes, and the H emission is given by the coalescence of almost-counter-propagating electrostatic UH modes.

To investigate the complete generation process of ZPs from the excitation of the DPR instability, the growth of non-escaping wave modes, to the release of escaping radiations, we conduct PIC simulations with values of $\omega_{pe}/\Omega_{ce} $ varying within two adjacent gyro-harmonic bands (9.5–11.5). This also allows us to further examine the occurrence of the above ECMI-plasma emission process through detailed parameter study.

According to the simulations (see Figures 1 and 2), the growths of the UH and Z modes are indeed dominated by the DPR effect, as demonstrated by the variations of their growth rates as well as their intensities with $\omega_{pe}/ \Omega_{ce}$. It was further found that the intensity of the H emission is stronger than that of the F emission by about 2 orders of magnitude. The intensity of the H emission also varies with $\omega_{pe}/\Omega_{ce}$, quasi-periodically, while the F emission is too weak to be significant. This indicates that the ZPs arise from the H emission, rather than the F emission as assumed in many earlier studies. Furthermore, the peak-valley contrast of the total intensity of the H emission (pr ZPs) is about 4, consistent with some observational reports (e.g., Tan et al. 2014). These results are critical to the understanding of the origin of solar ZPs and further diagnostic efforts using radio data with ZPs.

Figure 1 – (a) The wave intensity map in ($k_\parallel, \ k_\perp$) space with $\omega_{pe}/\Omega_{ce} = 9.5 – 11.5$, and (b)–(c) the $\omega-k$ dispersion curves for different modes. “UH” stands for upper hybrid mode, “W” for whistler mode, “Z” for Z mode, “H” for harmonic plasma emission, and “O-F” stands for O mode around the fundamental plasma frequency.

Figure 2 – (a)–(c) The temporal energy profiles of the five modes normalized to the initial kinetic energy of total electrons ($E_{k0} $). (d) The fitted exponential growth rate of UH, Z, and W modes. (e) The variation of final energy of Z and H modes with $ \omega_{pe} / \Omega_{ce} $. (f) The ZPs generated according to the simulated variation of the H emission, assuming $\Omega_{ce}=14$ MHz and $ \omega_{pe} / \Omega_{ce} =9.5-19.5$. The fluctuations of the simulated ZPs are caused by prescribed fluctuations of plasma densities (or $\Omega_{ce}$).

Based on the recent paper: Li, C., Chen, Y., Ni, S., Tan, B., Ning, H., & Zhang, Z., PIC Simulation of Double Plasma Resonance and Zebra Pattern of Solar Radio Bursts, The Astrophysical Journal Letters, 2021, 909, L5, DOI: https://doi.org/10.3847/2041-8213/abe708

References

Ni, S., Chen, Y., Li, C., et al. 2020, ApJL, 891, L25

Tan, B., Tan, C., Zhang, Y., et al. 2014, ApJ, 790, 151

Zheleznyakov, V. V., & Zlotnik, E. Y. 1975, SoPh, 44, 461

*Full list of Authors: Chuanyang Li, Yao Chen, Sulan Ni, Baolin Tan, Hao Ning, and Zilong Zhang

Parametric simulation studies on the wave propagation of solar radio emission: the source size, duration, and position by Zhang et al.*

The imaging and spectroscopy observations of solar radio bursts can provide information on the non-thermal electrons associated with the transient energy release in the solar active region and the parameters of the background plasma. However,  the corona plasma is an inhomogeneous refractive media for solar radio waves. Propagation effects, namely the refraction and scattering of waves, can cause the deformation of the observed radio source, including the expansion of the source size, and the offset of the visual source position from the “real source” at the wave generation site.

Ray-tracing simulation is an effective method to investigate the wave propagation effects, which can help us in interpreting the imaging and spectroscopy observation and in diagnosing the solar corona properties from the observation results (Steinberg et al.1971; Arzner & Magun,1999; Kuznetsov et al., 2020). Figure 1 shows an example of simulation results of a point pulse source generated at the limb with highly anisotropic fluctuation of the background plasma density, on the basis of the anisotropic radio-wave scattering model developed by Kontar et al. (2019). With this method we can obtain the source size, position, duration and visual speed.

Figure 1 – [GIFmovie] Temporal variations of  the 2D-flux distribution of the apparent source in the sky plane (upper panel) and the total flux (lower panel) in a simulation with a point pulse source for fundamental emission at 35 MHz. The starting position angle of the source is 45 Degree. The parameter set is $\epsilon=0.27$ and $\alpha=0.104$.

In this work, we perform ray-tracing simulations on radio wave transport in the corona and interplanetary region, and compare the simulation results with previous observations to estimate the property of the background plasma. For the first time, the variation of the apparent source size, burst duration, and source position for the fundamental emission and harmonic emission at the frequency of 35 MHz are simulated as a function of the anisotropic parameter α and the angular scattering rate coefficient $\eta=\frac{\epsilon^2}{h_0}$ , where $\epsilon = \frac{\langle \delta n^2 \rangle}{n^2}$  is the density fluctuation level and $h_0$  is its correlation length near the wave excitation site.

Simulation Results

1. Source Size and Duration

The source size and duration are the most common information that can be extracted from imaging and spectroscopy observations of solar radio bursts. Figure 2 shows the source size and decay time of the simulation results for the fundamental emission. The simulation results in the parameter space can be used to constrain the background plasma properties near the wave generation site. By comparing the observed duration and source size with the simulation results, we can estimate the scattering coefficient and the anisotropic parameter η=8.9×10−5 km−1 and α=0.719 with a point pulse source assumption.

 

Figure 2 – The source size and decay time of the simulation results for the fundamental emission. Purple lines in the left panel show the contour of source size, and black lines in the right panel show the contour of the decay time for the simulation data. The green square marks the cross point of the bold contour lines at $\epsilon= 0.277$ and  $\alpha= 0.719$. The equivalent scale length of density fluctuation $h_0$ is about 860 km near the wave generation site.

2. Offset of Source Position

Figure 3 shows the offset of the reconstructed source centroid from the starting point.  We can see that for the same frequency, the source of fundamental emission is more outward shifted than that of the harmonic emission. This may produce the co-spatial positions of the fundamental and harmonic waves in the observation of some type III radio bursts.

Figure 3 – The offset of the reconstructed source centroid from the starting point of the fundamental emission (left panel) and the harmonic emission (right panel). The equivalent scale length of density fluctuation $h_0$ near the wave generation site are about 860 km and 1010 km for the fundamental emission and the harmonic emission respectively.

3. Visual speed of the source

The propagation effects can also be (partially) responsible for the high speed motion of the observed source in the sky plane at a given frequency (Zhang et al, 2020). One can see from Figure 4  that the maximum visual speed is about 0.65 R$_{\odot}$ s$^{-1}$ or 1.5 c with largely anisotropic fluctuation of the background density.

Figure 4 – The visual speed of the source for the fundamental emission. The positive value represents the outward motion from the solar disk center, while the negative value represents the inward motion in this figure.

Conclusion

1.  For the fundamental emission, both the source size and decay time increase with the scattering rate coefficient or the variance of density fluctuation. The isotropic fluctuation can produce a larger decay time than a highly anisotropic fluctuation, while the source size is not sensitive to the level of anisotropy for α > 0.2. For the harmonic emission, both the source size and decay time are largely determined by the variance of the density. The decay time of the harmonic emission is significantly smaller than that of the fundamental emission for the same background parameters.

2.  By comparing the source size and decay time derived from simulation results to the observational statistics, we obtained the estimation of $\eta=8.9\times 10^{-5}\,km^{-1}$  and  $\alpha=0.719$ near the source region of the fundamental emission at the frequency of 35 MHz.

3.  The statistical results of the offset show that the source of the fundamental emission is more outward shifted than that of the harmonic emission by the propagation effect, which could account for the co-spatial positions of the fundamental and harmonic emission in some observations.

4.  The observed source position and size can have significant visual motion and expansion due to the wave propagation effects. Both the visual speed and the expansion rate tend to be large for highly anisotropic medium. For the fundamental emission, the visual speed of the source size can reach about 1.5c at  $\eta=8.9\times 10^{-5}\,km^{-1}$ and  $\alpha=0.2$.

Based on recent paper: Zhang P.J., Wang C.B., Kontar E.P. 2021, ApJ., 909, 195

References

Arzner K., & Magun A., 1999, A&A, 351, 1165

Kontar E. P., Chen X., Chrysaphi N., et al.. 2019, ApJ, 884(2): 122.

Kuznetsov A. A., Chrysaphi N., Kontar E. P., & Motorina G., 2020, ApJ, 898, 94.

Steinberg J., Aubier-Giraud M., Leblanc Y., & Boischot A., 1971, A&A, 10, 362.

Zhang P., Zucca P., Sridhar S. S., et al., 2020, A&A, 639, A115

*Full list of authors: PeiJing Zhang, ChuanBing Wang, Eduard P. Kontar

Harmonic Electron Cyclotron Maser Emission Excited by Energetic Electrons Traveling inside a Coronal Loop by M. Yousefzadeh et al.*

Solar spikes are radio bursts closely associated with the impulsive stage of solar flares. They are characterized by extremely high brightness temperature of up to 1015 K, narrow-band, and short duration. Thousands of spikes could exist in an event. This leads researchers to suggest that solar spikes represent elementary energy release events during solar flares.

Earlier studies have suggested the electron-cyclotron-maser emission (ECME) driven by energetic electrons with the loss-cone distribution to be the emission mechanism of spikes (Holman et al. 1980). Yet, the loss-cone maser mainly excites the fundamental X mode (X1), and it is difficult for X1 to pass through the second harmonic absorption layer during its escape from the source (Melrose & Dulk 1982). This gives the so-called escaping difficulty of ECME when it is applied to solar radio spikes as well as other types of radio bursts associated with similar magnetic configurations.

Another problem is that most earlier studies employed prescribed analytical velocity distribution function (VDF) while any solar radio bursts are a consequence of a multiscale process starting from large-scale magnetic eruptive activities in the astronomical to MHD scale, followed by particle acceleration via magnetic reconnection or shocks in the particle kinetic scale and further excitation and propagation of electromagnetic radiations. In this study, as a starting point to bridge the large-scale dynamics and small-scale plasma kinetic maser instabilities associated with solar radio bursts, in particular, solar spikes, we developed a numerical scheme combining techniques including (1) the magnetic field extrapolation to describe the magnetic configuration of a normal loop within a well-studies active region (see Figure 1); (2) the guiding-center (GC) method to infer the temporal evolution of VDFs along various sections of the loop while taking the effect of pitch-angle scattering into account; and (3) the particle-in-cell (PIC) simulation to further explore the kinetic instabilities driven by electrons with the obtained VDFs. This represents a significantly simplified approach for the proposed study.

Figure 1 – (a) The magnetogram of HMI/SDO for AR 11283 before the eruption of the major X2.1 flare on 2011 September 6, overplotted with field lines given by the NLFFF extrapolation; (b) the selected loop structure for the GC simulation of energetic electrons. The color in panels (b) represents the field strength (in units of Gauss). The letters “A–D” represent the sections within which VDFs will be examined, and the letter “I” represents the region of injection.

It was found that the VDFs of energetic electrons injected from the loop top manifest interesting strip-like feature with significant positive velocity gradient, together with the familiar loss-cone feature (see upper panels of Figure 2). The strip-like features of VDFs are formed due to the bouncing motion of energetic electrons during the early stage of the VDF relaxation toward a well-developed loss-cone distribution. According to further PIC simulations fed by the corresponding VDFs in plasmas with the parameter setup of ωpece = 0.25, the strip-like feature is essential for efficient excitation of ECME at harmonic X mode (in the weak scattering case), while the loss-cone feature can be efficient in exciting the fundamental X mode (in the strong-scattering case). See Figure 2 for the PIC results.

Efficient amplification of X2 favors the escape of ECME radiation from the corona, and this effectively reduces the limitation of applying ECME to solar spikes. The study provides new insight into how escaping radiation, in particular, the harmonic X mode, can be generated within a coronal loop. The scenario presented here may also be useful to other types of radio bursts generated within similar astrophysical and space circumstances.

Figure 2 – (a-c) VDFs at t = 1000 wpe-1 obtained by the PIC simulation for cases with various levels of scattering: W for weak, M for moderate, and S for strong scattering case; (d-f) temporal profiles of energies of various wave modes (X2, X1, and Z), normalized to the total energy of energetic electrons (Ek0).

This nugget is based on the paper by Yousefzadeh, M., Ning, H., & Chen, Y. 2021, APJ, 909 3 doi: 10.3847/1538-4357/abd8d5

References:

Holman, G. D., Eichler, D., & Kundu, M. R. 1980, in IAU Symp. 86, Radio Physics of the Sun, ed. M. R. Kundu & T. E. Gergely (Cambridge: Cambridge Univ. Press), 457

Melrose, D. B., & Dulk, G. A. 1982, ApJ, 259, 844

*Full list of Authors: Mehdi Yousefzadeh, Hao Ning, and Yao Chen

Discovery of correlated evolution in noise storm source parameters: Insights on $\vec{B}$ dynamics during a microflare by A. Mohan

Solar noise storms are known to be related to small and large scale magnetic field enhancements at active regions (Elgaroy 1977, Li et al.,2017). However, the mechanism still remain unclear. Their high spectro-temporal variability and ubiquity of weak events demanded sub-second and sub-MHz scale imaging with high dynamic ranges (DRs) to reliably study emission from individual sources. Using high DR snapshot spectroscopic images from the Murchison Widefield Array, this work explores the complete structural evolution of a noise storm source associated with a microflare for the first time. Combining this with the earlier results on the event from EUV analysis and magnetic field $\vec{B}$ modelling presented in Mohan et al.,2019 (M19; CESRA nugget), this work draws insights on the local $\vec{B}$ evolution during the event.

Event & Analysis

Figure 1 summarises the event and analysis. The noise storm source had a 2D Gaussian morphology in the images (e.g. Fig. 1a) made across 15 MHz band (df = 160 kHz) centred around 200 MHz for 12 min duration (Nov 3, 2014; 06:08 – 06:16 UT) at a cadence of 0.5 s. NLFF modelling by M19 had showed that a bright active region loop that underwent a microflare was linked to the noise storm via a common magnetic footpoint.

Figure 1 – (a) The noise storm source overlaid on AIA 94 Angstrom image showing its association with the flaring loop. (b) NLFF extrapolation with radio and EUV sources marked. (c) Spatially Resolved Dynamic spectrum for the radio source. (d) GOES data (blue) with spectral averaged radio source light curve (red: full data; black: 20s running mean filtered). 

2D Gaussian fitting was done to the images and the spectro-temporal evolution of the source area, integrated flux density and position angle were derived. Fig. 1c shows the evolution of integrated flux density during the flare. Fig. 1d shows the GOES (1-8 Angstrom) light curve with event phases marked. The red curve shows the spectral averaged light curve for the noise storm source. Black curve, obtained by applying a 20s running mean window, brings out the 30s QPPs. M19 had hypothesised that the radio source region could be braided at a dominant scale of ~12 Mm and, magnetic stresses could build up across them and be released via particle acceleration events at the local Alfve’n timescale of 30s. The clumped episodes of type-I bursts within QPP periods could signify this.

Figure 2 – (a-c): Normalised cross-correlation with respect to area. (d): Frequency averaged evolution of parameters. Vertical lines are marked every 30s (e): “T” mode schematic

The current study discovered simultaneous and often correlated evolution in the area, position angle and intensity of the noise storm source with simultaneous 30s QPPs clearly seen in the running mean filtered light curves (Fig. 2c). To quantify this correlated evolution, a normalised cross correlation (NCC) analysis was done for parameter evolution curves at each observation frequency. Area was chosen as the base parameter for NCC analysis. Fig. 2a-c show the results. The sub-bands with lot of bad parameter estimates are masked. The similarity in NCC across the band could be because it corresponds to less than 10% of the pressure scale height in the regions probed. The mean dynamical properties would hence be similar. The line plots below each panel show the  band averaged NCC. Two dominant modes of correlated evolution are discovered: an area and integrated flux density anticorrelated mode (“S”); an area and position angle correlated mode (“T”). Fig. 2e depicts the “T” mode as a winding-unwinding motion of the braid loop. The pre-flare phase shows the dominance of torsional-like “T” mode which gets converted to sausage-like “S” via the flare.

Interpretation

Source area is a proxy to the region illuminated by particle beams, position angle to their overall directionality and integrated flux density to their energy flux. In the pre-flare phase, the braided loop is pumped with free energy mainly in the “T” mode. This is released as particle acceleration events at Alfve’n timescales. In the flare phase, the loop  was possibly driven into a critically braided state. This triggered an internal restructuring  with a redistribution of excess energy in “T” modes to “S”, and particle energisation. In the post-flare phase, “S” mode becomes dominant in the restructured loop.

Conclusions

The first study of noise storm structural evolution is presented. Source parameters show two dominant modes of correlated evolution: a winding-unwinding like “T” mode; a sausage-like “S” mode. Flare mediates a mode conversion from “T” to “S” accompanied by enhanced particle acceleration and a microflare. This hints at the restructuring of an internally braided loop. Tracing evolutionary modes in the associated noise storm sources could hence be used to track the internal dynamics during flares, irrespective of their energy budget.

*Based on recent paper by Atul Mohan, 2021, ApJL, 901, L1

References

Elgaroy, E.,O., 1977, Solar Noise Storms (Oxford: Pergamon Press)

Li, C. Y., Chen, Y., Wang, B., et al. 2017, SoPh, 292, 82

Mohan, A., McCauley, P.,I., Oberoi, D. & Mastrano, A. 2019a, ApJ, 883, 45

Radio and X-ray Observations of Short-lived Episodes of Electron Acceleration in a Solar Microflare by R. Sharma et al.

In a solar flare, the plasma is locally heated and particles are accelerated to energies from a few tens of keV to MeVs. X-ray bremsstrahlung emission and radio gyrosynchrotron emission are highly complementary and provide diagnostics of the timing, location and spectral properties of flare-accelerated electrons in a broad energy range.

Here we present comprehensive observations of multiple individual bursts during a GOES B1.7-class (back-ground subtracted) microflare observed jointly in radio by the VLA, in X-rays by RHESSI, and in the ExtremeUltraviolet (EUV) by the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al. 2012). The observations are indicative of multiple co-temporal acceleration episodes during the impulsive phase of a solar microflare. The X-ray and radio burst sources likely originate from separate electron distributions in different magnetic loops.

Figure 1 – Temporal evolution of radio and X-ray emission during the B1.7-class flare on 2012 February 25 (SOL2012-02-25T20:50:34). Top: VLA dynamic spectrum showing the total flux computed from the radio images for each frequency-time pixel in the observation. Each pixel has a size of 4 MHz and 1 s in frequency and time respectively. The second panel shows the frequency averaged VLA spectrum from 1.65 GHz to 2.03 GHz. The inset shows 5 distinct radio bursts marked by letters. The third panel shows X-ray light curves from RHESSI and GOES.

Spatial-temporal Evolution of Radio and X-ray Sources

The radio lightcurves show six distinct short-lived radio bursts (labeled A, B, C, D, E, and F in Figure 1) associated with increased X-ray emission. The flare shows distinct spatial-temporal features at EUV, X-rays and radio wavelengths. The EUV 193 Å images show two separate ribbons (Figure 2A). The radio emission shows six distinct short-lived radio bursts (labeled A, B, C, D, E, and F in Figure 1). During the radio bursts, the observed compact clustering suggests a bright common radio source for all shown radio frequencies (Figure 2B). Both X-ray sources and radio bursts A, B and C appear near the northern ribbon, but they are not co-spatial with each other. The location of these burst sources projected onto the flare ribbon suggests a low coronal origin of the emission. Using a magnetic extrapolation model, the altitude of the radio sources is inferred to be ~2700 km.

Figure 2 – Panel (A): HMI magnetogram at 20:51:45 UT. The red and blue contours are emission observed by AIA 304 Å at 20:51:32 UT for northern and southern ribbons, respectively. The contour level shown is at 18% of the maximum brightness. Panel (B): Evolution of the AIA 94 Å EUV ribbons (black and white image, color table inverted), X-ray RHESSI sources (magenta and blue contours), and VLA radio centroid (crosses) positions. The RHESSI contour levels are at 65%, 75%, 85%, and 95% w.r.t map’s peak. Panel (C): The spectra of the brightness temperature for the three fitted, individual bursts (labeled A, B, and C) are shown in blue, green and red respectively. The solid lines shows the optimum MCMC fit represented in their colors.

RHESSI and Gyro-Synchroton Fits

RHESSI X-ray and VLA gyrosynchrotron fits provide the properties of the accelerated electron spectra, like spectral index, total electron flux, and low-energy cutoff. The RHESSI spectrum was fit between 20:47:00 UT and 20:47:28 UT. Note that radio bursts A, B, and C occurred during this time. A weak nonthermal component is present in the spectrum up to about 20 keV (Figure 3A), with an electron spectral index $\delta$ of 8.6 ± 3.2 and a low-energy cutoff ($E_{low}$ ) of 13.5 keV.

The radio spectra for burst A to C developed a positive slope, indicative of optically thick nonthermal gyrosynchrotron radiation (see, e.g., Dulk 1985). For calculating the model gyrosynchrotron spectrum, the user-friendly and computationally inexpensive fast GS code (Fleishman & Kuznetsov 2010) was used. Further, we adopted the MCMC method described in Chen et al. (2020) for the spectral fitting. Here, we assumed a homogeneous nonthermal source. We treated magnetic field strength ($B$), nonthermal density ($n_{nth}$), thermal density ($n_{th}$), electron spectral index ($\delta$), and low-energy cutoff ($E_{low}$) as free parameters. We note that the low-energy cutoff of the nonthermal electron distribution Elow is smaller than that inferred from the RHESSI X-ray spectrum by a factor of ∼4, while the nonthermal density from the gyrosynchrotron fit is two orders of magnitude higher than the RHESSI estimates. At the same time, the total electron density, and as a result, the total electron flux from the gyrosynchrotron fit, is a factor of 10 to 100 higher than from the X-ray fit. This discrepancy in Elow and nnth is present in burst A through C, a possible indication that the two instruments observe two different electron populations.

Figure 3 – Left: RHESSI spectrum along with the fitted thermal and nonthermal components between 20:47:00 UT and 20:47:28 UT. The black crosses show the RHESSI spectrum, while the green curve shows the sum of the thermal (blue line) and nonthermal (purple line) components. The yellow histogram shows the background spectrum. Middle: nonthermal power as a function of low-energy cutoff for the spectral parameters inferred from the X-ray fit (RHESSI) and from the gyrosynchrotron fits of bursts A to C. The symbols mark the nonthermal power calculated from the observed low-energy cutoff. Right: model electron spectra inferred from X-rays (RHESSI) and radio bursts A to C. The vertical lines give the position of the low-energy cutoff.

Conclusions

Our observations support a scenario with multiple acceleration events, possibly in different magnetic loops, since even though the X-ray emission was observed co-temporally with the radio bursts, the observed spectra are very different. Two factors contribute to this interpretation:
1. The spectral parameters inferred from the X-ray observations are different from the properties inferred from the radio observations to an extent that cannot be explained by uncertainties or by the fact that the X-ray spectrum was time-integrated over the 28 s during which bursts A to C were observed. For a given spectral index δ, total electron flux $F_e$ ($s^{−1}$), and cutoff energy $E_{low}$ in erg, the nonthermal power can be found as $P = (\delta-1)F_e E_{low}/(\delta-2)$. Figure 3B shows the nonthermal power inferred from the X-ray fit is a factor of 10 lower. However, both values lie within the range of nonthermal powers found in a statistical analysis of sub-C class flares by Hannah et al. (2008).
2. Both X-ray and radio sources show a remarkable footpoint asymmetry. Such asymmetries are unfeasible in a standard single reconnecting magnetic loop scenario. A possible explanation would be the presence of different electron distributions in separate magnetic loops.

Overall, the contrasting spectral properties and spatial displacements suggest two distinct electron populations. This microflare study demonstrates that even microflares can exhibit complex characteristics and behaviors.

This nugget is based on the paper by Sharma, R., Battaglia, M., Luo, Y., Chen, B., Yu, S., 2020 ApJ 904 94

References

Benz, A. 2002, Plasma Astrophysics, 2nd ed, Vol. 279 (Dordrecht: Kluwer)

Chen, B., Shen, C., Gary, D. E., et al. 2020, NatAs, 2020, Nature Astronomy, 4, 1140-1147

Dulk, G. A. 1985, ARA&A, 23, 169

Krucker, S., Hudson, H. S., Glesener, L., et al. 2010, ApJ, 714, 1108

White, S. M., Benz, A. O., Christe, S., et al. 2011, SSRv, 159, 225

Hannah, I. G., Christe, S., Krucker, S., et al. 2008, ApJ, 677, 704

Huang, J., Yan, Y., & Tsap, Y. T. 2014, ApJ, 787, 123

Fleishman, G. D., & Kuznetsov, A. A. 2010, ApJ, 721, 1127

Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, SoPh, 275, 17

Masuda, S., Kosugi, T., Hara, H., Tsuneta, S., & Ogawara, Y. 1994, Nature,371, 495

Pesnell, W. D., Thompson, B. J., & Chamberlin, P. C. 2012, SoPh, 275, 3

*Full list of authors: Rohit Sharma, Marina Battaglia, Yingjie Luo, Bin Chen and Sijie Yu

Analyzing the propagation of EUV waves and their connection with type II radio bursts by combining numerical simulations and multi-instrument observations by A. Koukras et al.*

EUV (EIT) waves are wavelike disturbances of enhanced extreme ultraviolet (EUV) emission that propagate away from an eruptive region. Recent years have seen much debate over their nature, with three main interpretations: the fast-mode MHD wave, the apparent wave (reconfiguration of the magnetic field), and the hybrid wave (combination of the previous two). Observations of such waves are often accompanied by type II radio bursts, which are widely considered as signature of coronal shock waves. However, their link to EUV waves is uncertain and the association holds clearly only for the fastest EUV waves.

By studying the kinematics of EUV waves and their connection with type II radio bursts, we aim to examine the capability of the fast-mode interpretation to explain the observations, and to constrain the source locations of the type II radio burst emission.

Methodology

To investigate the association between EUV  waves and type II radio bursts we follow the formalism of Wang (2000) in the modeling of EIT waves, but depart from it by using a global MHD model for the ambient corona. We model the propagation of EUV waves as a fast-mode MHD wave and identify the ray paths that are compatible with the drift rates deduced from the radio observations.  Uchida (1968) showed, in the WKB approximation, (short-wavelength limit) that an MHD wave may be regarded as being propagated along rays that are refracted by the nonuniform medium.

In our model, the simulation of the propagating wave front takes as input the coronal data from the global MHD model, the coordinates of the origin point of the EUV wave and a distribution of initial wave vectors that determine the initial directions of propagation (initially uniformly distributed). The output of the simulation is a collection of ray paths representing the successive spatial positions in time of the different wave vectors. For a given time, we can therefore derive the EUV wave front.

To compare the simulated wave front with actual EUV observation, a visualization scene was created where EUV spectroheliograms were mapped onto a 3D representation of the Sun. With this method we can simultaneously view the computed wave front and the real observations.

The analysis of the frequency drift of type II bursts (plasma emission) gives us access to the variation in electron density along the path of the shock wave. Inversely, we can infer from the model, the electron density along each calculated ray path and convert it into a temporal evolution in frequency and deduce which instantaneous position along each ray path could be responsible for the observed radio emission at the same moment. For that we identify the boundaries of the type II in the radio spectrum fit third-degree polynomials to them, and then identify the ray-path points that are inside this frequency domain.

Analysis and results

In this study we analyzed 2 events that present two different geometrical configurations, one edge-on (SOL2017-04-03T14:20:00) and one face-on (SOL2017-09-12T07:25:00). The main analysis methods are the same for both events.

The coordinates of the origin point for the EUV wave was identified by combining  EUV  (PROBA2/SWAP, SDO/AIA) and RHESSI observations. To account for the uncertainty in height of the X-ray source, the RHESSI peak coordinates were deprojected, as if the source was located at different heights. This way a sample of “possible” origin points, derived from observations, was created. After testing, the origin point that provided the best match with the EUV observations was selected to continue the analysis.

In order to examine the behavior of the wave front, we created a number of visualizations scenes, which also produced synthetic movies for the duration of the events. An example for the first event is shown below in Fig. 1.

Figure 1 – Left: images of PROBA2/SWAP 174 Å for three different times during Event 1 (from top to bottom: 14:26:10 UT, 14:28:00 UT, 14:37:10 UT). Right insets: zoom into the region of interest. The simulated wave front is displayed with white and red points on top of a background of PROBA2/SWAP running-difference images. Two different viewing angles for the same moment are shown, one that represents the PROBA2 viewing position and one tilted viewing position that was selected to optimize the visibility of the simulated wave front. The red points are identified candidates for the type II radio burst emission.

Additionally, we calculated the angle between the wave vector (K) and the magnetic field (B) for every ray-path point. The results (right panel in Fig. 2) show that for almost all the ray-path points whose density matches that of the source of the radio burst (in red), the corresponding wave vectors are quasi-perpendicular to the magnetic field.                                                                                              

Figure 2 – Left: dynamic radio spectrum from the Humain station, showing the signature of the type II radio burst during Event 1. The three vertical lines correspond to the time of the snapshots in Fig. 1. Blue crosses represent manually selected points and the dashed black lines the fitting curves. Right: angles between the magnetic field and the wave vector for every ray-path point. Red indicates the ray-path points that are identified as the potential source of the type II radio burst emission based on the local electron density matching the plasma frequency.

Conclusions

Our main conclusions are that: 1) even a fairly simple ray-path model of fast-mode MHD waves displays a good qualitative match with the observations, 2) the location of the type II radio burst emission on the propagating wave front can be derived for the duration of the event, 3) the position of the type II radio burst source on the wave front is not stationary but evolves with time, meaning that different areas of the wave front can be responsible for different parts of the radio burst signature and 4) the wave vectors of the ray-path points that are identified as the potential source of the radio type II burst emission are quasi-perpendicular to the magnetic lines.

This study serves as an initial examination of a framework for the analysis of the association between EUV (EIT) waves and type II radio bursts, and is planned to be extended in the future, specifically: by refining the fast-mode model and by the comparison of the localized type II radio burst source with radio images, which will be the main validation test for the aforementioned results.

Additional info

Based on the recent paper: Alexandros Koukras, Christophe Marqué, Cooper Downs, Laurent Dolla (2020) “Analyzing the propagation of EUV waves and their connection with type II radio bursts by combining numerical simulations and multi-instrument observations”, 2020, A&A, 644, A90. DOI: https://doi.org/10.1051/0004-6361/202038699 .

The movies of this study are available in https://www.aanda.org  and in http://solweb.oma.be/users/akoukras .

*Full list of authors: Alexandros Koukras, Christophe Marqué, Cooper Downs and Laurent Dolla

References

Uchida, Y. 1968, Sol. Phys., 4, 30

Wang, Y.-M. 2000, ApJ, 543, L89

On the occurrence of type IV solar radio bursts in the solar cycle 24 and their association with coronal mass ejections by A. Kumari et al. *

Coronal mass ejections are large eruptions of magnetized plasma from the Sun (Webb et. al. 2012) that are often accompanied by radio emission, generated by the energetic electrons produced during these eruptions (Gopalswamy et. al. 2004). These electrons can generate radio emission in the corona through various emission mechanisms (Melrose, 1980). The most common radio bursts associated with CMEs are type II and type IV bursts. CMEs are often accompanied by broadband continuum emission at decimetric and metric wavelengths which are known as type IV radio bursts (Pick, 1986), that can have either stationary or moving sources and various emission mechanisms (Bastian et. al. 1998). The association of CMEs with type IV bursts is also poorly understood. We perform a statistical study on the association of type IV radio bursts to CMEs in solar cycle 24.

Observations and Data Analysis

We use CMEs detected with the Large Angle and Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric Observatory (SOHO) and the Cor1 and Cor2 coronagraphs from the Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI) onboard the Solar Terrestrial Relationship Observatory (STEREO). The radio bursts are provided by the event lists from the Space Weather Prediction Center, which catalogues radio events since the year 1996.

Figure 1 – Left panel: Solar radio dynamic spectra of a moving type IV burst on October 18, 2017. The duration of the burst is $\sim 7 $ minutes and it shows a frequency drift of $\sim 0.09$ MHz/s from 160 MHz to 60 MHz. Right panel: Solar radio dynamic spectra of a stationary type IV burst on October 03, 2011. The duration of the burst is $\sim 7 $ hours.

We divided the type IV bursts into moving type IV bursts (IVm) and stationary type IV bursts (IVs) based on their spectral characteristics (drift rates and duration). For the stationary/moving type IV bursts classification, in addition to the drift rate, we also considered the duration of the moving type IV bursts as mentioned by Robinson (1978) and Gergely (1986). To study the association of type IV bursts with CMEs, we used the temporal criteria: a CME should appear in LASCO-c2 coronagraph FOV within  $\approx 2 $ hours of the start time of the type IV burst. In the case that these criteria were not enough to determine a CME association within SOHO/LASCO-c2 and STEREO-cor2, the STEREO-cor1/cor2 coronagraph data was investigated manually.

Results and Conclusions

There were total 16107 CMEs reported with SOHO/LASCO and additional 5944 with STEREO-A and B combined. There was total 446 type IV bursts in this solar cycle. We categorized all CMEs based on their linear speeds and angular widths as ‘Fast’, ‘Slow’, ‘Wide’ and ‘Narrow’ CMEs. CMEs with linear speed $\geq 500$ km/s are classified as ‘Fast’ CMEs, with the remaining classified as ‘Slow’. Similarly the CMEs with angular width $\geq 60^{\circ}$ are classified as ‘Wide’ CMEs, with the remaining classified as ‘Narrow’ CMEs.

Figure 2 – The distribution of CMEs and type IV bursts in the solar cycle 24. Histogram for: (a) all CMEs; (b) all type IVs bursts; (c) all type IVm bursts; (d) all type IV bursts; (e) all type IVs bursts with CMEs; (f) all type IVm bursts with CMEs.

Out of 80 type IVm bursts observed, 73 ($\sim 91 \%$) were accompanied by white-light CMEs. However, only $\sim 0.5\%$ of the total CMEs in this solar cycle were accompanied by type IVm bursts. $\sim62\%$ were associated with ‘Fast’ CMEs and $\sim38\%$ were associated with ‘Slow’ CMEs, unlike type II radio bursts where the majority are associated with ‘Fast’ CMEs (Kahler et. al. 2019). Out of 366 type IVs bursts, 286 bursts ($\sim78 \%$) were accompanied with white-light CMEs. Only $\sim1.8\%$ of the total CMEs in this solar cycle were accompanied with type IVs bursts. Type IVs bursts are almost equally associated with ‘Fast’ and ‘Slow’ CMEs, with $\sim 46\%$ and $\sim 54\%$, respectively, and also have quite similar associations with ‘Wide’ and ‘Narrow’ CMEs, with $\sim 59\%$ and $\sim 41\%$, respectively. Most of the type IVm bursts ($\sim85 \%$) had duration of a few minutes. Contrary to this, the duration of type IVs varies from a few minutes to a few hours. Our analysis shows that $\sim 95 \%$ of type IVm bursts had drift rates $\leq 0.5$ MHz/s. The correlation between the occurrence of these CMEs and type IV bursts is $\sim 92 \%$, which indicates that the occurrence of type IV bursts closely follows the occurrence of CMEs. Thus, we conclude that a CME eruption may be necessary for the generation of type IV emission as opposed to non-eruptive flares.

In this work, we present the first comprehensive long-term statistical study of type IV radio bursts during solar cycle 24, where we find a significant correlation between the occurrence of type IV radio bursts and CMEs, with $\sim$81\% of the observed bursts being accompanied by CMEs, based on a temporal association with white-light CME observations. However, we found that only $\sim 2.2 \%$ of the CMEs are accompanied by type IV radio bursts. We categorized the type IV bursts as moving or stationary based on their spectral characteristics and found that only $\sim 18 \%$ of the total type IV bursts in this study were moving type IV bursts.  Our study suggests that type IV bursts can occur with both ‘Fast’ ($\geq 500$ km/s) and ‘Slow’ ($< 500$ km/s), and also both ‘Wide’ ($\geq 60^{\circ}$) and ‘Narrow’ ($< 60^{\circ}$) CMEs. However, the moving type IV bursts in our study were mostly associated with ‘Fast’ and ‘Wide’ CMEs ($\sim 52 \%$), similar to type II radio bursts. Contrary to type II bursts, stationary type IV bursts have a more uniform association with all CME types. This study also provides the typical duration of type IV bursts and drift rates of moving type IV bursts.

Figure 3 – The number of CMEs (per year) and type IV bursts (per year) from 2009-2019. The number of type IV bursts are very less as compared to the number of CMEs however, there is a very strong correlation ($92 \%$) between the occurrence of the white-light feature and radio emission.

Based on the recent paper: Kumari, Anshu, et. al. 2021 ApJ 906, 79: On the occurrence of type IV solar radio bursts in the solar cycle 24 and their association with coronal mass ejections. The Astrophysical Journal, DOI: https://doi.org/10.3847/1538-4357/abc878.

Additional info: Homepage: https://researchportal.helsinki.fi/en/persons/anshu-singh Acknowledgement: A.K. acknowledges the ERC under the European Union’s Horizon 2020 Research and Innovation Programme Project SolMAG 724391.

References

Gergely, T. E. (1986).  Solar Physics, 104, 175.

Kahler, S. W., Ling, A. G. and Gopalswamy, N. (2019). Solar Physics, 294, 134.

Robinson, R. D. (1978).  Solar Physics, 60, 383.

*Full list of Authors:  Anshu Kumari, Diana E. Morosan, Emilia K. J. Kilpua

VLA Measurements of Faraday Rotation through a Coronal Mass Ejection Using Multiple Lines of Sight by J. E. Kooi et al.*

The Sun is the main source of space weather, and one type of solar event that is critical to space weather is a coronal mass ejection. Coronal mass ejections (CMEs) are large eruptions of magnetized plasma from the Sun that produce energetic particles, which can cause geomagnetic storms on Earth. One method that has proven successful in determining the strength and structure of the coronal magnetic field is Faraday rotation (FR), which is the rotation of the plane of polarization when linearly polarized radiation propagates through a magnetized plasma. Previous observations of CME Faraday rotation have all been limited to a single line of sight (LOS, such as Howard et al., 2016, and Kooi et al., 2017), whereas we report the first successful observations of Faraday rotation through a CME using multiple lines of sight: 13 LOS across seven target radio fields.  These observations were made using the “triggered” observation mode of the Karl G. Jansky Very Large Array (VLA) of the National Radio Astronomy Observatory (NRAO). Triggered observations ensured that there would be multiple sources present to probe different regions of the solar wind and CME when a CME suddenly appeared.

Modeling the Coronal and CME Faraday Rotation

The 2015 observations were made during solar maximum and, therefore, the Sun was extremely active. Multiple CMEs were present leading up to our observations. Two particularly large CMEs that initially erupted on 30 July 2015 and early 31 July 2015 caused noticeable restructuring of the corona off the eastern limb of the Sun in both LASCO-C2 and C3 images. Included in this restructuring was a southward shift in heliographic latitude of the southeastern streamer belt. The southward shift did not affect the impact parameter for a given LOS but did alter the angle [βc] at which the LOS crosses the heliospheric current sheet (HCS), especially for LOS with heliographic latitudes proximate to the HCS. Fig. 1 shows the model HCS shift applied to the synoptic chart neutral line data.

Thomson-scattering brightness (TSB) is the observed radiation from the photosphere that has been Thomson-scattered by electrons in the coronal plasma. TSB can be directly measured using coronagraph images from LASCO-C2/C3. TSB is a LOS integral that can be inverted to solve for the plasma density and, therefore, determine its contribution to the observed Faraday-rotation measurement. In order to calculate the plasma density of the corona, before occultation by the CME, we performed a χ2-minimization process to determine which of four models accurately described the TSB profile; single-term power law, coronal streamer model, coronal hole model, and LDB model. The single-term power law model consists of a single-term power law and provides good predictions of Faraday rotation measurements at heliocentric distances ranging from 6-20 solar radii. The streamer and hole models use two-term power laws for dense coronal streamers and tenuous holes, taken from Mancuso & Spangler (2000). The LDB model employs a three-term power law and is typically used for the quiescent corona, much like the single-term model. The LDB model was determined by Leblanc, Dulk, and Bougeret (1998) by measuring the onset time of Type III radio bursts measured by the WAVES instrument onboard the WIND spacecraft.

To model the magnetic structure of the CME, we assumed a force-free flux rope configuration for the magnetic field. We explored three models for the plasma density structure: constant density, thin-shell, and thick-shell. The reason we explored three plasma density models was because a strong shock front was present, as evidenced by the presence of a Type II radio burst associated with the CME. The fundamental harmonic was detected at ~15:50 UT, lasting until 22:30 UT, and was followed by a second harmonic Type II radio burst that began at ~17:00 UT on 31 July, lasting until ~6:00 UT on 1 August. We could not determine the exact morphology of the CME in white light images; consequently, we assumed simple geometric configurations for the CME’s orientation with respect each LOS.

Figure 1 – Synoptic chart used to calculate βc  for coronal conditions in 2015 (Carrington rotation 2166) and demonstrate the effect of the HCS shift on Fields 1 and 6. The solid lines are LOS to Field 1 (northern latitudes) and Field 6 (southern latitudes) projected onto the Sun’s surface in Heliographic Latitude and Longitude at 23:45 UT. The black dotted line gives the location of the neutral line near the beginning of the observations (18:20 UT) and the red dotted line gives the full 8$^\circ$ shift of the neutral line near the end of the observations (23:45 UT). The solid diamonds give the midpoint of the LOS (β = 0) and βc is measured where the LOS and neutral line intersect. This appears as Fig. 5 in Kooi et al. (2021).

In order to compare our observational results from white-light coronagraph images and radio Faraday-rotation measurements to the coronal and CME models, we plotted the TSB (t) and RM(t) of each source as well as the models. Fig. 2 presents the data as well as the modeling results for Fields 5, 6, and 7, in which each were occulted by one leg of the CME and the shifting HCS (Fields 1 – 4 are also reported in Kooi et al., 2021)Our shifting HCS model only includes effects of the shifting neutral line (Fig. 1) and therefore the shifting HCS has a negligible effect on our coronal models for the TSB(t).  TSB(t) data for Field 6 is unusable because it was corrupted by imaging artifacts shortly after occultation by the CME. However, the small increase in TSB magnitude is consistent with the model CME TSB(t).

Figure 2 – Above are TSB(t) (top panels) and RM(t) (bottom panels) for Fields 6 (left panels), 5 (middle panels), and 7 (right panels) on 31 July 2015. TSB(t) is given for one LOS to the Field center. RM(t) is given for LOS 1 of Field 6 and LOS 1 & 2 of Fields 5 and 7. The models for coronal contribution only (dashed black curve), the coronal and constant density CME model (solid black curve), the coronal and thick shell CME model (dashed red curve), and the coronal and thin shell CME model (solid red curve) are plotted as well. The vertical lines (LE) give the times at which occultation by the CME begins, assuming a linear speed of ~750 km s-1 for the CME. TSB is given in units of TSBU (1 TSBU = 10-12 solar brightness). This appears as Fig. 10 in Kooi et al. (2021).

Our shifting HCS model has the strongest impact on the source closest to the Sun (Field 6). By the end of the observations, the HCS shifted ~8$^\circ$, which increased the expected coronal contribution by a factor of two. Without including the HCS shift, the CME and coronal FR models would not be consistent with the data, especially for Field 6. The second data point at ~19:40 UT for Field 5 is not consistent with the coronal FR model: either the CME arrived earlier than expected at this field or this is a plasma sheath, as we likely saw in Kooi et al. (2017) and discussed in Wood et al. (2020). The constant density CME model is the most consistent with the data. Between the two shell models, the thin shell is much more consistent with the data reported here as well as the other radio fields discussed in Kooi et al. (2021).

Conclusions

The observations presented in Kooi et al. (2021) represent the first observations of CME Faraday rotation along multiple lines of sight and the first triggered VLA observations of CME Faraday rotation. The advantage of multiple LOS is that we can definitively determine the CME strength and helicity, therefore removing ambiguity surrounding the absolute sign of the CME’s axial magnetic field. 

The only model that successfully reproduces the RM(t) results for all sources is the one in which: the northern leg (in heliographic latitude) is angled away from the Earth (βcme < 0) and the southern leg is angled toward the Earth (βcme > 0); the axial magnetic field is directed out from the Sun into the northern leg and directed into the Sun from the southern leg; the helicity is +1 (right handed). TSB(t) and RM(t) data both strongly favor the constant density and thin shell models over the thick shell model, as the thick shell model is not consistent with the observed RM(t) for Fields 1, 2, 6 and 7. We were therefore able to determine that at the Sun, Ncme 476 x 103 cm-3 and Bcme 2,575 mG and at Earth, Ncme   0.01 x 103 cm-3 and Bcme 0.05 mG assuming frozen-in flux. The use of multiple LOS also proved a strong test for our model of the shifting HCS. Data for the LOS presented in Fig. 2 show strong evidence that this shift occurs at Carrington longitudes between 50$^\circ$– 140$^\circ$. Because the LOS provided by Fields 5-7 each sample different regions of the corona, there is limited ambiguity of the nature of the shifting HCS.

Radio remote-sensing ground-based measurements of Faraday rotation have the potential for great synergy with in situ measurements of space-based platforms such as the Parker Solar Probe (PSP) and Solar Orbiter (SO).  PSP and SO can measure the micro-scale physics of the corona whereas Faraday rotation measurements can provide information about the macro-scale physics.

*Based on the accepted paper: Jason E. Kooi, J. E., Madison L. Ascione, Lianis V. Reyes-Rosa, Sophia K. Rier, and Mohammad Ashas: “VLA Measurements of Faraday Rotation through a Coronal Mass Ejection Using Multiple Lines of Sight,” 2020, Solar Phys., 296, 11 (2021). https://doi.org/10.1007/s11207-020-01755-4

References

Howard, T.A., Stovall, K., Dowell, J., Taylor, G.B., White, S.M.: 2016, Measuring the Magnetic Field of Coronal Mass Ejections Near the Sun Using Pulsars. Astrophys. J., 831, 208.

Kooi, J.E., Fischer, P.D., Buffo, J.J., Spangler, S.R.: 2017, VLA Measurements of Faraday Rotation through Coronal Mass Ejections. Solar Phys., 292, 56.

Leblanc, Y., Dulk, G.A., Bougeret, J.-L.: 1998, Tracing the Electron Density from the Corona to 1au. Solar Phys. 183, 165.

Mancuso, S. Spangler, S.R.: 2000, Faraday Rotation and Models for the Plasma Structure of the Solar Corona. Astrophys. J. 539, 480.

Wood, B.E., Tun-Beltran, S., Kooi, J.E., Polisensky, E.J., Nieves-Chinchilla, T.: 2020, Inferences About the Magnetic Field Structure of a CME with Both In Situ and Faraday Rotation Constraints. Astrophys. J. 896, 99.

Propagation Effects in Quiet Sun Observations at Meter Wavelengths by R. Sharma and D. Oberoi

The quiet Sun coronal emission dominantly comes from thermal bremsstrahlung. As this radiation traverses the coronal medium on its way to the Earthbound observer, the coronal optical depth, τ, along typical ray paths is neither low enough to be approximated as optically thin, nor high enough to be treated as optically thick. On its way to the observer, it gets modified substantially due to propagation effects —primarily refraction and scattering—through the magnetized and turbulent coronal medium, leading to the redistribution of the intensity in the image plane.

Figure 1 – Panel (a): Schematic showing the features of the radio Sun and the presence of scattered flux in a PSF-sized region from its surrounding regions. The red region represents region R1. The total flux within a PSF-sized region is the sum of its intrinsic flux (red arrow) and the scattered flux (yellow arrows).  Panel (b) & (c):  AIA 193 Å EUV map along with MWA solar contours at 108 MHz and 217 MHz. The 9 Contour levels are at 25%, 35%, 45%, 55%, 65%, 75%, 85% and 95% level w.r.t the image maximum.

By studying the differences in the observed quiet Sun maps with thermal bremsstrahlung models, we can quantify the effect of scattering and derive some of the scattering parameters.  We compare high-quality solar radio images from an exceptionally quiet period with the corresponding thermal bremsstrahlung maps obtained using data-driven MHD simulations. The radio images come from the Murchison Widefield Array (MWA), which represents the state of the art in solar imaging in this band (Mondal et al. 2019, 2020a, 2020b; Mohan et al. 2019a, 2019b). The corresponding simulated thermal bremsstrahlung maps are obtained using the FORWARD software (Gibson et al. 2015 ,Gibson et al. 2016), which models the radio brightness distribution (TB ).

Interesting Radio-EUV features at meterwavelengths

At the higher frequency end of our observations, the large-scale correspondence between the EUV and radio emissions is seen (217 MHz MWA map, Figure 1). The EUV bright regions also tend to have regions of higher TB nearby. The large coronal hole, occupying much of the northern hemisphere, is clearly seen in the EUV with a thin tongue dipping into the southern hemisphere. At 217 MHz, the coronal hole region is associated with lower TB, though by 108 MHz, the same region has higher TB values than its neighboring regions. In fact, at 108 MHz, the enhanced TB sits atop the thin coronal hole tongue (108 MHz MWA map, Figure 1).

Thermal Bremsstrahlung model 

The thermal bremsstrahlung emission depends directly on the local plasma parameters like electron density, temperature, and the local magnetic field. For thermal bremsstrahlung, which is always included in a FORWARD radio emission calculation, opacity results from collisions between electrons and ions. However, FORWARD does not incorporate any propagation effects, i.e., it does not take into account the scattering and refraction caused by the coronal density structures that are a part of the PSIMAS model or the refraction due to the large-scale density decrease with coronal height.

Figure 2 – Top panel: Averaged brightness temperature solar maps for three MWA frequency bands at 108, 162 and 217 MHz. The maps, which these are the average of, were made with frequency and time averaging of 2 MHz and 0.5 seconds, respectively. Middle panel: FORWARD brightness temperature solar maps for three frequency bands at 109, 162 and 217 MHz. Note that only TB > 0.2 MK are shown. Circles mark 1 and 2 R. Contour levels in all the maps are at 70, 75, 80, 85, 90 and 95 % of the peak. The peak MWA TB for 108, 162 and 217 MHz are 0.92, 1.20 and 1.50 MK, while for FORWARD maps peak TB are 1.59, 1.60 and 1.61 MK respectively.

Comparison of FORWARD and MWA maps

We find a good agreement between them at highest two frequencies at 217 MHz and 240 MHz, but below 200 MHz FORWARD overestimates the flux densities.     For 217 and 240 MHz, assuming FORWARD models to be true representations of solar emission, we obtain a lower limit on the fraction of scattered emission. We find smallest fraction of 14% for AR, and the largest is 300% at the same frequency for coronal hole at 217 MHz. Large values for quiet Sun and coronal hole regions imply that scattering/refraction plays an important role in redistributing the flux density. We further quantify impacts of propagation due to the estimated level of inhomogeneities in the coronal medium. The strength of scattering is well known to depend on the level of density inhomogeneities, parameterized by ε = ΔN N, where N is the local average electron density and ΔN is a measure of the departure from it. We assume that the inhomogeneities have a Gaussian distribution with a characteristic correlation length scale h (Chandrasekhar 1952; Hollweg 1968; Steinberg et al. 1971; Chrysaphi, N. et al. 2018; Kontar et al. 2019). For the disk center, we compute the optical depth due to scattering using FORWARD modelled densities and temperature for a range of values for  ε2/h.  These optical depth values were fed into radiative transfer equations and optimised for the observed MWA brightness temperature of the disk center. 

Figure 3 – Left panel: The brightness temperature obtained by radiative transfer for disk-centre LoS by varying ε2/h. The points on the curve are the MWA TB for disk-centre LoS. Middle panel: The optimised values of  ε2/h for MWA frequency bands. The errorbars are the propagated uncertainties in MWA fluxes to brightness temperatures and  ε2/h. The dashed line shows the power-law fit. Right panel: The optimised values of  for MWA frequency bands. Note that here h ≈ 40 km. The dashed line shows the power-law fit to the  datapoints.

Conclusions

Scattering and refractive effects redistribute the radio emission on the solar disk, significantly, changing the appearance of the radio Sun (e.g., Aubier et al. 1971; Rahman et al. 2019; Kontar et al. 2019). The peak of the emission associated with the active regions shifts by 8–11ʹ between the observed and modeled maps closer to the disk-center, but in non-radial direction (Figure 2). Coronal refraction tends to shift sources closer to the disk center, while scattering not only increases the apparent observed size, it also tends to shift the apparent location of sources farther from the disk center. Anisotropic scattering from nonradial coronal structures can give rise to nonradial shifts in the apparent locations of sources. The angular size of the Sun in MWA images is also found to be larger than that in FORWARD images by 25–30%. 

We estimate that for coronal holes, the observed TB could be dominated by a factor between 2 and 3 by the radiation which has been scattered into these lines of sight from the neighboring regions; while for active regions, up to half of the flux density might be scattered out of these lines of sight. Thus, the observed TB depends not only on the intrinsic TB of the region from where the radiation is originating, but also on the TB of the neighboring regions (Figure 1a). Recently, ubiquitous impulsive emissions of flux densities down to ∼mSFU levels have been reported (Mondal et al. 2020a). In this context, we note that the significant smearing in the image caused by scattering will make it harder to detect intrinsically low-level variations in solar radio images. 

The coronal density inhomogeneities arise due to turbulence, and it is interesting to quantify the level of density fluctuations.  We estimate an average inhomogeneity parameter  ε2/h towards

the central LoS to be (4.9±2.4)×10-5 km-1(Figure 3). Using h = 40 km (Steinberg et al. 1971) leads to an average value of ε = (4.28±1.09)%, which is consistent with earlier estimates (Figure 3). Variations in the estimated values of ε could reflect the diversity of coronal physical conditions. The coronal inhomogeneities observed close to the Sun advect away into the solar wind and evolve. Recently, in-situ measurements by the Parker Solar Probe have yielded ε≈6–7% (Krupar et al. 2020), implying that ε has not evolved significantly even out to much larger solar distances.

Additional info: Based on the recent paper by Sharma, R. & Oberoi, D., “Propagation Effects in Quiet Sun Observations at Meter Wavelengths”, ApJ, 903, 2 (2020). DOI: 10.3847/1538-4357/abb949

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Electromagnetic Emission Produced by Three-wave Interactions in a Plasma with Continuously Injected Counterstreaming Electron Beams by Vladimir Annenkov and Igor Timofeev

Weakly turbulent processes of three-wave interactions between Langmuir and electromagnetic waves in plasma with unstable electron flows are believed to be the main cause of type II and III solar radio emissions. The narrow band of type II bursts requires assuming that this radiation is generated in some local regions of shock fronts traveling in the solar corona, where the specific conditions for the enhancement of electromagnetic emissions near the plasma frequency harmonics are created. The reason for such enhancement at the second harmonic may be the formation of counterstreaming electron beams Ganse et al. [1]. Indeed, in the case of a single beam, before generating EM radiation in three-wave interactions, the vast majority of the beam energy is wasted on the excitation of a wide spectrum of nonradiating electrostatic oscillations through the electrostatic decay of primary unstable Langmuir waves and consequent plasma heating. The energy sink from the resonant to nonresonant part of the wave spectrum can be, in principle, reduced if both electrostatic waves participating in the three-wave process are excited directly by two counterstreaming electron beams. However, Ziebell et al. [2] have studied the generation of EM waves by counterstreaming beams by solving equations of weak turbulence and found that its enhancement is not that pronounced compared to the single-beam case as reported by Ganse et al. [1]. In  our work, we show that there are two reasons why the efficiency of the second harmonic emission from a plasma with counterstreaming electron beams should be higher than in previous works. The first reason is the fundamentally nonuniform character of beam–plasma interaction, which is not accounted for in models with periodic boundary conditions assuming that the beam is uniformly distributed in the whole space.  In the case of continuous beam inflow from local acceleration sites, instead of excitation of low-amplitude waves with stochastic phases, we observe the formation of coherent wave packets with higher densities of Langmuir wave energy. This affects not only EM emission, but also ion dynamics, which can no longer be described in terms of sound waves and is more governed by ponderomotive forces of high-frequency fields even for relatively small beam densities $10^{-3}$. The second reason is the possibility of tuning the system parameters in such a way that the most unstable (and most energetic) colliding beam-driven modes begin to participate in the nonlinear coalescence process.

We carried out particle-in-cell simulations of the collision of two symmetric electron beams in plasma with open boundary conditions [3] and show that the efficiency of beam-to-radiation power conversion can be significantly increased up to the level of a few percent if three-wave interactions with electromagnetic waves near the second harmonic of the plasma frequency becomes available for the most unstable, oblique, beam-driven modes. To prove the feasibility of this efficient regime, we first find the system parameters at which the maximum linear growth rate (Fig. 1a) calculated in the framework of the relativistic kinetic theory [4]  lies in the region of three-wave interaction and then compare this regime with less efficient ones in which the most unstable modes drop out of this resonance (Fig.1b).

Figure 1: (a) The growth rate map for the beam-plasma instability $\Gamma\left(k_\parallel,k_\perp\right)$  in the efficient regime. The black line $k_\perp=k_\perp(k_\parallel)$ marks the maximal growth rate achieved for each $k_\perp$.  The arrows $k^l_1$ and $k^l_2$ correspond to the wave vectors of the most unstable beam-plasma modes. The wave vector of radiated EM wave $k^t_3$ is the result of their summation.(b) $\Gamma(k_\perp)$  along the line of the local maximum (red points indicates the  region of the three-wave interaction) for all considered regimes with different magnetic fields characterized by the dimensionless electron cyclotron frequency $\widehat{\Omega}=\Omega_e/\omega_p$. Adapted from: Annenkov et al. [5]

PIC simulations of beams collision confirmed the dominance of oblique modes in the efficient regime and demonstrated the formation of spatially localized relaxation regions. EM emission near $2\omega_p$ is observed when such regions of both beams intersect with each other  (Fig. 2). At later stages of the interaction, we also observe generation of higher harmonics  at $3\omega_p$ and $4\omega_p $ (Figure 3a-3d). For each case, we carry out several (from three to five) runs with identical initial macro-parameters, but with a different specific implementation of the particle distribution function.

Figure 2: PIC results in a time moment of emission maximum for the efficient regime. (a) Density of both beams in units of unperturbed plasma density $n_0$. (b) Electric field $E_x$. Langmuir waves in plasma column and $2\omega_p$ emission in vacuum.

Figure 3: (a)-(d) The frequency spectrum of the produced radiation in the single point in vacuum. (c) The efficiency of beam-to-radiation power conversion as a function of time for all runs.  The methodology for constructing these dependencies is as follows. In each moment of time, from all the runs corresponding to one regime, the highest and lowest radiation efficiencies are found and placed on the graph. The thick line indicates the average value between them. Adapted from: Annenkov et al. [5]

Figure 3 (e) shows the beam-to-radiation power conversion efficiency. Despite the significant scatter of results for the efficient regime, the typical value of the generation efficiency is several percent while the maximum efficiency reaches 4%. When switching to regimes with lower magnetic fields, the efficiency decreases several times. In the case of a strong field the beam instability becomes purely longitudinal and there is no noticeable radiation.

Based on the recently published paper: V. V. Annenkov, E. P. Volchok, and I. V. Timofeev. Electromagnetic emission produced by three-wave interactions in a plasma with continuously injected counterstreaming electron beams. The Astrophysical Journal, 904 (2):88, nov 2020. doi: 10.3847/1538-4357/abbef2.

References:

[1] Urs Ganse, Patrick Kilian, Felix Spanier, and Rami Vainio. Nonlinear wave interactions as emission process of type II radio bursts. The Astrophysical Journal, (2):145, jun . ISSN 15384357. doi: 10.1088/0004-637X/751/2/145.

[2] L. F. Ziebell, L. T. Petruzzellis, P. H. Yoon, R. Gaelzer, and J. Pavan. Plasma emission by counter-streaming electron beams. The Astrophysical Journal, 818(1):61, feb 2016. ISSN 1538-4357. doi: 10.3847/0004-637X/818/1/61.

[3] V. V. Annenkov, E. A. Berendeev, I. V. Timofeev, and E. P. Volchok. High-power terahertz emission from a plasma penetrated by counterstreaming different-size electron beams. Physics of Plasmas, (11):113110, nov . ISSN 1070-664X. doi: 10.1063/1.5048245.

[4] I. V. Timofeev and V. V. Annenkov. Exact kinetic theory for the instability of an electron beam in a hot magnetized plasma. Physics of Plasmas, 20(9): 092123, sep 2013. ISSN 1070664X. doi: 10.1063/1.4823722.

An Explanation of Subsecond Time Evolution of Type III Solar Radio Burst Sources at Fundamental and Harmonic Frequencies by X. Chen et al

Recent studies (Kontar et al. 2017) of a Type III–IIIb burst observed by LOFAR (van Haarlem et al. 2013) indicated that the temporal variations in the positions and source sizes do not fit into the standard picture of type III solar radio bursts and require a better understanding of radio-wave transport. With the aim of explaining the observed properties of type III–IIIb solar radio bursts, we use radio-wave simulations of radio-wave propagation to investigate the time evolution, positions, and sizes of the apparent solar radio burst sources for both the fundamental and harmonic components at subsecond scales. The radio waves can be strongly affected by the inhomogeneous density fluctuations while they propagate away from the Sun. Those propagation effects, including the refraction due to plasma density gradients and scattering by small-scale density fluctuations, can significantly affect the apparent properties of the radio sources, including their time evolution, position, and size (Steinberg et al. 1971; Arzner & Magun 1999; Thejappa et al. 2007; Krupar et al. 2020Bian et al. 2019).

The radio waves were treated as a series of photons propagating through the turbulent corona. Their positions and wave vector were derived from the same theoretical expressions and numerical approach as in Kontar et al. (2019). A histogram of the ray arrival times can be regarded as the time profile of radio emissions. The temporal evolution, apparent sizes, and locations of radio sources simulated assuming an anisotropic turbulence with different spectrum-averaged mean wavenumbers (Cq), heliocentric angles (θ) and anisotropy parameters(α) are shown in Figure 1 for the fundamental emission. Here, Cq characterizes the density fluctuation properties that is a composite of the density fluctuation levels ε, the lo and li, the outer and inner scales of the inhomogeneities. Anisotropic scattering description with an α is required because the isotropic scattering cannot simultaneously describe all the observed radio emission characteristics, seen in the details from Chen et al. (2020).

Figure 1. Simulations of fundamental plasma emission from an instantaneous point source scattered by anisotropic turbulence, with the effects of, (a) different mean wavenumbers Cq of the density fluctuations, (b) varying the heliocentric angle θ, and (c) the anisotropy parameter α. The time profiles (top row), the shifts of the apparent source centroids (middle row), and the apparent source areas (bottom row) with respect to time were compared with LOFAR observations (red data) of the type III–IIIb radio burst at 32.5 MHz from Kontar et al. (2017).

We found that radio-wave scattering due to turbulence with Cq=2300 R-1, θ=5° and α~0.25 can simultaneously match the main characteristics of the fundamental sources observed by LOFAR, seen in the red lines from Figure 1. We also simulated the harmonic emission using the same parameters, and found that it can be explained by the same parameters of turbulence when the harmonic has a finite source area of 200 arcmin2 and finite emission time. Using the obtained parameters to simulate both the fundamental and harmonic sources, we successfully reproduce the observed sources, presented in Figure 2.

Figure 2. Observed (left panel, from Kontar et al. (2017)) and simulated (right panel, from Chen et al. (2020)) radio sources of the fundamental (red contour) and harmonic (blue contour) components, overlaid on an SDO/AIA 171 Å image. The fundamental sources were simulated using Cq=2300 R-1, θ=5° and α~0.25. The harmonic source was simulated using the injection profile of a finite emission area of 200 arcmin2 shown in Figure 5 from Chen et al. (2020). Both the simulated fundamental and harmonic sources were considered to add a beam size of 110 arcmin2.

 

By matching simultaneously the main characteristics (time profile, position and size) of the observed sources with those observed by LOFAR, we have estimated the properties of plasma turbulence in the solar corona. Given that the observed radio properties do not represent the intrinsic source properties, radio-wave propagation effects should be taken into account when inferring physical parameters using solar radio-imaging observations. The comparison of simulations to observations of source sizes and positions at subsecond timescales allows us to understand the propagation of radio waves, and provide a useful tool to diagnose the turbulence in the solar corona.

Based on the recently published paper: Xingyao Chen, Eduard P. Kontar, Nicolina Chrysaphi, Natasha L. S. Jeffrey, Mykola Gordovskyy, Yihua Yan, and Baolin Tan, Subsecond Time Evolution of Type III Solar Radio Burst Sources at Fundamental and Harmonic Frequencies, The Astrophysical Journal, 905:43  (2020) DOI: 10.3847/1538-4357/abc24e

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Estimate of Plasma Temperatures across a CME-driven Shock from a Comparison between EUV and Radio Data by F. Frassati et al.*

Type II radio bursts, produced near the local plasma frequency and/or its harmonic by energetic electrons accelerated by shock waves moving outward through the inner heliosphere, have long been recognized as evidence of shock waves origin and propagation in the solar corona.

In this work, we analyze the early evolution of a coronal shock wave, associated with a prominence eruption, with the aim of investigating the properties of the compressed plasma through both radio and Extreme-Ultra Violet (EUV) data.

Observations and Analysis

On 2014 October 30, a solar eruption occurred at the east limb in active region NOAA 12201 (S04E70) involving a C6.9 flare, a CME, and a type II radio burst starting at about 13:08 UT.

Analysis of Radio data

The type II radio burst, also observed by  the Nancay RadioHeliograph (NRH), was rather complex, as evinced by inspecting the compound radio dynamic spectrum obtained by combining data from the Compound Astronomical Low-cost Low-frequency Instrument for Spectroscopy and Transportable Observatory (CALLISTO) station located in Birr, Ireland (BIR) and the USAF Radio Solar Telescope Network (RSTN) spectrometer located in San Vito, Italy (see Figure 1).

Figure 1   Radio dynamic spectrum obtained from CALLISTO (mid and high frequencies) and RSTN (low frequencies).

The harmonic component was split into two sub-bands, a lower (L) and an upper (U) frequency component, most probably due to shock/streamer interactions (discussion in Mancuso et al. 2019 paper). The further splitting of the upper harmonic band, visible in the time interval between 13:08.5 UT and 13:08.7 UT, is instead attributable to simultaneous radio emission occurring in the upstream (ahead) and downstream (behind) regions of the shock front. Under the above assumption, we calculated the compression ratio Xradio of the expanding front as:

\[X_{radio}=\frac{n_{e}^{D}}{ n_{e}^{U}}=\frac{f_{U}^{2}}{ f_{D}^{2}} \tag{1} \]

The calculated Xradio values lie between 1.1 and 1.4 in the temporal range [13:08:30 – 13:09:00] UT.

Analysis of Extreme Ultra-Violet data

EUV data from SDO/AIA (Figure 2, left panel) were used to estimate the temperature of the emitting plasma and to infer the density compression ratio, XEUV, from emission measure (EM) modeling.

Temporal variations of the observed EUV intensities related to the evolution of the electron density and ionization state (depending on temperature) of the plasma were used to infer the presence of the shock from the images.

                                      Figure 2 – Left Panel:SDO/AIA running difference EUV images of the event at 171 Å (top), 193 Å (middle), and 211 Å (bottom).  Right Panel:  Temporal dependence of the intensity fluxes in the 171 Å, 193 Å, and 211 Å channels as measured in the red filled-dot region marked by a red arrow in the left panel.

The shock wave front was clearly detected in three of the SDO/AIA channels (171 Å, 193 Å, and 211 Å) and it was distinctly separated from the CME bubble represented by the observed expanding EUV front. Moreover, given the temperature response of each of the used AIA filters, the emitting plasma temperature was estimated in the range of 1.75 – 4.00 MK.

From the EM (Eq. 2), representing the amount of emitting material as a function of coronal plasma temperature along the line of sight (LOS), we calculated the plasma electron density and the compression ratio XEUV (Eq 3., see Frassati et al. 2019 and Frassati 2020 for more details).

\[EM\simeq\int_{\rm LOS}n_{\rm e}^2\mathrm{d}L , \tag{2}\]

\[X_{\rm EUV} = \sqrt{\frac{EM_{\rm D}-EM_{\rm U}}{P_{\rm U}}+1}, \tag{3}\]

where EMU and EMD are the up- and downstream EMs and PU is the contribution to the pre-event EM from the coronal plasma region located in the plasma region being compressed after the transit of the EUV front.

The calculated value XEUV ≈ 1.23 at 13:08:45 UT and for T = 2.5 – 3.0 MK is in good agreement with what estimated from the above type II band-splitting analysis.

From the Differential Emission Measure, $DEM(T)=n_{e}^{2}(\frac{dT}{ds})^{-1}$, we inferred the peak upstream temperature TU ≈ 1.78 MK and, using the results from Mancuso et al. (2019) together with the Rankine-Hugoniot jump conditions,  we estimated the post-shock temperature, TD ≈ 2.75 MK, under the usual hypothesis that the shock was perpendicular.

Conclusions

In this work, we analyzed a peculiar coronal event that occurred on 2014 October 30 in which both a type II radio burst and a CME- driven shock were identified.

The type II emission was observed during the lateral over-expansion phase of the CME bubble; to this respect, the intersection of coronal loops and streamers might be a fundamental factor for the formation and/or enhancement of the shock and the excitation of type II emission (see Mancuso et al. 2019). The presence of the type II radio burst in the low corona at the time and location where the EUV front was identified, together with the comparable values of compression ratios derived from the analysis of both radio and EUV data, concur to indicate that the observed EUV front was, in fact, a CME-driven shock wave.

Additional info

We are grateful to the SDO/AIA teams, the Radio Solar Telescope Network (RSTN), and the e-CALLISTO network for providing open data access.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

References

Frassati, F., Susino, R., Mancuso, S., Bemporad, A.: 2019, Comprehensive Analysis of the Formation of a Shock Wave Associated with a Coronal Mass Ejection. Astrophys. J. 871, 212. DOI. ADS.

Frassati, F., Mancuso, S. & Bemporad, A. Estimate of Plasma Temperatures Across a CME-Driven Shock from a Comparison Between EUV and Radio Data. Sol Phys 295, 124 (2020). https://doi.org/10.1007/s11207-020-01686-0. ADS

Mancuso, S., Frassati, F., Bemporad, A., Barghini, D.: 2019, Three-dimensional reconstruction of CME-driven shock-streamer interaction from radio and EUV observations: a different take on the diagnostics of coronal magnetic fields.Astron. Astrophys.624, L2. DOI. ADS.

Full list of authors: Federica Frassati1, Salvatore Mancuso1 and Alessandro Bemporad1.

1 Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025 Pino Torinese, Italy

Radio bursts in the 2017 September 6, X9.3 flare by M. Karlicky and J. Rybak

Radio bursts and their fine structures are an integral part of solar flares. Although many of them are known as e.g. type II, III, V, J, U, and IV, still some unique bursts and fine structures, not observed so far, can be detected. This is the case of the X9.3 flare observed on September 6, 2017, where we found not only several unique bursts and fine structures, but also their interesting time association with the other flare phenomena observed in extreme ultraviolet (EUV), white-light, X-ray, and γ-ray emissions. Using our new method based on the wavelets we also detected quasi-periodic pulsations (QPPs) in the whole time–frequency domain of the analyzed radio spectrum (11:55–12:07 UT and 22–5000 MHz).

In the pre-impulsive phase of this flare we found a remarkable double drifting pulsation structure (DPS) at high frequencies (2200-4200 MHz) in association with the EUV brightenings caused by the interaction of magnetic ropes, as presented in the paper by Hou at al. (2018).

In the flare impulsive phase, at the time of the hard X-ray and γ-ray peaks and a sunquake start we found strong quasi-periodic pulsations (P in Figure 1). Just after these pulsations an exceptional radio burst drifting from 5000 to 800 MHz (burst B in Figure 1) was detected. Comparing this burst B with time associated EUV phenomena we found that this radio burst was probably generated by a rising magnetic rope. Moreover, in connection with this burst B, we recognized a U burst at about the onset time of an EUV writhed structure and a drifting chain of bursts as a signature of a shock wave at high frequencies (1050–1350 MHz).

We analyzed the quasi-periodic pulsations observed at the impulsive flare phase (P in Figure 1) by our new wavelet technique (Karlický, M. et al. (2017)) in detail. We found quasi-periodic pulsations in broad range of periods (1-30 s). Among these QPPs we detected pulsations bi-directionally drifting to higher and lower frequencies (Figure 2). Owing to their low frequency drift they indicate a presence of the magnetosonic waves generated at the primary flare energy-release site and propagating upwards and downwards in the solar atmosphere. The frequency, where the frequency drift changes from the positive to negative value enables us to determine the plasma density in the primary flare energy-release process (magnetic reconnection) as (1.1-1.5) x 1011 cm-3 assuming the emission on the fundamental frequency. Similar drifting phases of pulsations were found in further flare phase, but on lower frequencies. It indicates that the primary flare energy-release process during the flare moved to higher heights in the solar atmosphere.   

 

Figure 1 High-frequency part of the radio spectrum showing an unusual drifting burst B, pulsations P and type IV burst observed by the Ondřejov radiospectrographs on September 6, 2017.

Figure 2 Top panel: Phase map of pulsations P (see Figure 1) in the 2000–5000 MHz range at time of the first the γ-ray peak and at start of the sunquake at 11:55–11:57 UT for periods of 11–30 s. Arrows show the bidirectional drift of the pulsation phase. Bottom panel: The time profiles of the radio flux on 2050, 2500, and 3000 MHz.

Conclusions

The September 6, 2017 X9.3 flare was exceptional not only owing to its γ-ray emission,  sunquake, white light flare and CME, but also by the high-frequency drifting burst, interpreted as the radio emission from the rising filament and by the magnetoacoustic waves propagating upwards and downwards from the primary flare energy-release site in the flare impulsive phase.

Related article: This nugget is based on the paper by Karlický, M. and Rybák, J., 2020, ApJS, 250:31.

References

Hou, Y. J., Zhang, J., Li, T., Yang, S. H., Li, X. H., 2018, A&A, 619, A100

Karlický, M., Rybák, J., Monstein, C., 2017, SoPh, 292, 1

Karlický, M. and Rybák, J. 2020, ApJS, 250:31

                                                           

Magnetic Reconnection during the Post-impulsive Phase of a Long-duration Solar Flare by S. Yu et al.

Magnetic reconnection, a fundamental process in astrophysical environment plasma is believed to facilitate the release of energy stored in the magnetic field. However, where the magnetic reconnections occur, how and where the released magnetic energy is transported, and how it is converted to other forms remain unclear.

Here, we report well-connected observational signatures of magnetic reconnection, plasma heating, and electron acceleration observed during the post-impulsive gradual phase of the X8.2-class eruptive solar flare on 2017 September 10 (see a collection of relevant papers of the celebrated limb flare on ADS). The combined white light and EUV imaging observations allow us to identify the timing and location of multiple intermittent reconnection events by tracking bi-directional plasma outflows in an extremely long plasma sheet. The arrivals of the plasma downflows at the looptop region of the flare arcade correlate with plasma heating events that manifest as impulsive X-ray bursts. In the meantime, nonthermal microwave bursts, obtained by Expanded Owens Valley Solar Array (EOVSA; Gary et al. 2018), are detected in the loopleg region, which have no response in hard X-rays. Such a chain of reconnection-associated observational signatures offers a new view of the energy release and conversion processes with a level of clarity not previously achieved.

Impulsive Microwave/X-Ray Bursts in the Post-impulsive Phase

During the post-impulsive phase of the flare, the EOVSA total-power (full-disk integrated) microwave dynamic spectrum is featured by multiple broadband bursts (Figure 1(b)). These bursts have an impulsive appearance in the dynamic spectrum and light curves. These bursts have an average recurrence period of 5.6 minutes. The individual microwave bursts correlate with weak X-ray bursts at 6–100 keV observed by both RHESSI and Fermi/GBM (Figure 1(c)).

EOVSA multi-frequency images (Figure 1(a)) show that the overall morphology of the evolving microwave source is consistent with the shape and orientation of the EUV flare arcade. There appear to be two distinct sources: one coincides with the looptop HXR source, while the other is in the northern leg of the flare arcade (right side of the diagram). We note that microwave emission is weak or absent in the southern leg of the flare arcade (right side in the diagram).

The time-series of microwave images reveals that the impulsive component of the microwave emission in each burst is mainly from the loopleg source. In these time-sequence images, the loopleg source shows a large variation in intensity during each burst. In contrast, the looptop source appears relatively stable with more-minor variations in morphology and intensity.

Figure 1 — Microwave bursts observed by EOVSA. (a) Image sequences of the microwave emission at 30 spectral windows overlaid on SDO/AIA 131 Å images around 17:35 UT. The time is indicated by the vertical line in (b-c). (b) EOVSA total-power dynamic spectrum of the post-impulsive phase in 2.5–18 GHz. Overplotted is the EOVSA 5 GHz light curve after removing the slowly varying background. (c) Detrended light curves of RHESSI 6–50 keV and Fermi 25–50 keV X-ray counts, and detrended GOES 1–8 Å flux.

Reconnection in the late phase: bidirectional outflows vs. Microwave/X-Ray Bursts

Shortly after the eruption of the coronal mass ejection, a large-scale reconnection current sheet (RCS; see our other recent paper Chen et al. 2020 and references therein) appeared in white and EUV images (Fig 2(a)-(b)). Multitudes of plasma outflows are present in the RCS during different phases of the event for an extended period of time. We find many recurring pairs of bi-directional plasma outflows that propagate simultaneously along the RCS (Figure 2(d)). The upward-moving EUV outflows extend well into the MLSO/K-cor field of view in white light to at least 1100 Mm (or 1.6 R) above the solar surface (red shaded region in Figure 2(c)). The downward-moving EUV outflows seem to terminate at the looptop region (blue shaded region in Figure 2(c)). Each pair of bi-directional outflows appears to diverge from a discrete site at varying heights in the plasma sheet. We attribute the diverging location of each bi-directional outflow pair as the site of an individual magnetic reconnection event (or reconnection “X” point). Most of these identified reconnection sites are located at d ≈ 50–180 Mm above the limb  (Figure 2(c)), which is only 1%–3% of the total length of the plasma sheet (~10 R) during that period.

The downflows fade away as they merge into the tip of the cusp-shaped flare arcade, where a multitude of slow, downward-contracting loops are present. We illustrate the timing of the impulsive microwave bursts in accordance with the observed EUV plasma downflows in Figure 2(e,f). We overlay the EOVSA 5 GHz microwave light curve (from Figure 1(b)) on the time–distance plots near the separatrix region where the downflow motions appear to “terminate”. The arrival of most EUV plasma downflows at the separatrix region is immediately followed by a microwave burst. This correlation in both space and time is a strong indication for a causal connection between the plasma downflows arriving at the looptop and the appearance of microwave-emitting nonthermal electrons in the flare arcade.

Figure 2 — Magnetic reconnection in the large-scale vertical RCS above the post-flare arcade. (a) Composition of the SDO/AIA 131 Å, MLSO/K-cor, and SOHO/LASCO C2 and C3 white-light images, showing the CME bubble and a long plasma sheet connecting the core of CME and the underlying flare site. (b) Detailed view of the lower portion of the plasma sheet seen in EUV and white light. The green dashed curved is used to derive the time–distance maps shown in panel (c), in which upflows are seen to extend to at least 1200 Mm (or ~1.7 R⊙) above the solar surface. (d) Successive SDO/AIA 131 Å background-detrended images that show bidirectional outflows diverging from a compact region. (e-f) Enlarged view of the time–distance plot for two selected time intervals shown as the orange boxes in panel (c). The tracks of outflows are denoted by blue and red curves. The possible X and Y points are denoted by crosses and circles. The orange solid line is the detrended EOVSA 5 GHz light curve.

Discussion and Conclusion

Our observational results are consistent with the standard CSHKP eruptive flare scenario for the post-impulsive phase. A schematic picture is shown in Figure 3. Sporadic magnetic reconnections occur at localized magnetic null points (or X points) in the RCS, creating pairs of highly bent magnetic flux tubes. Plasma is ejected from the X points both upward and downward along the RCS, resulting in bidirectional plasma outflows.

The plasma outflows carry a significant portion of the total released magnetic energy in the form of electromagnetic Poynting flux, enthalpy flux, and kinetic energy flux of the bulk flows and turbulence (Fletcher & Hudson 2008). Arrival of the downward-propagating plasma outflows at the cusp region dissipates their energy, resulting in plasma heating through thermal conduction and/or adiabatic heating. If a fast-mode termination shock is established in the cusp region (which is perhaps implicated by the presence of the secondary ALT X-ray source near the cusp tip), plasma heating would occur in the shock downstream region (Forbes 1986; Masuda et al. 1994). Such heated plasma is revealed by the thermal X-ray and microwave source observed at the loop top.

The cusp region may serve as the primary plasma heating and electron acceleration site. This argument is supported by the relative timing between the X-ray/microwave bursts and the magnetic reconnection events in the RCS—the occurrence of the X-ray/microwave bursts correlates with the arrival time of the plasma downflows at the cusp, but not the time of the magnetic reconnection events themselves. A straightforward interpretation is that the electrons responsible for the microwave bursts are accelerated locally at the looptop, where freshly injected energy is available from the arrival of the plasma downflows.

 

Figure 3 — Animated schematic diagram of post-impulsive flare arcade and the large-scale RCS (adapted from Forbes & Acton 1996). (b) Schematic diagram of flare arcade and the RCS depicted in 3D. Discrete reconnection events occur at different times and heights within the 3D RCS, visible as the observed scattering of the reconnection sites viewed edge-on. Schematic of the observational signatures including the plasma sheet (with a finite width), EUV flare arcade, and microwave and X-ray sources is shown projected on the plane of sky. The flare arcade is slightly tilted with respect to the line of sight, which may account for the absence of the microwave source in the southern (right) side of the arcade. (c) Composite EOVSA 2.5-18 GHz, RHESSI 6-12 keV and 131 Å image during the post-impulsive phase, showing the MW/X-ray emission in the post-flare arcade.

Based on the recent paper: Sijie Yu, Bin Chen, Katharine K. Reeves, Dale E. Gary, Sophie Musset, Gregory D. Fleishman, Gelu M. Nita, and Lindsay Glesener (2020) “Magnetic Reconnection during the Post-impulsive Phase of a Long-duration Solar Flare: Bidirectional Outflows as a Cause of Microwave and X-Ray Bursts”, 2020, The Astrophysical Journal, 900, 17. DOI:https://doi.org/10.3847/1538-4357/aba8a6; Preprint:https://arxiv.org/abs/2007.10443;  Personal blog: https://web.njit.edu/~sjyu/Res.Blog/20201006.html

References

Chen, B., Shen, C., Gary, D. et al. 2020, Nat. Astron, 10.1038/s41550-020-1147-7

Benz, A. O. 2017, LRSP, 14, 2

Fletcher, L., & Hudson, H. S. 2008, ApJ, 675, 1645

Forbes, T. G. 1986, ApJ, 305, 553

Forbes, T. G., & Acton, L. W. 1996, ApJ, 459, 330

Gary, D., Chen, B., Dennis, B., et al. ApJ, 863, 83

Masuda, S., Kosugi, T., Hara, H., et al. 1994, Natur, 371, 495

Low frequency radio observations of the ‘quiet’ corona during the descending phase of sunspot cycle 24 by R. Ramesh et al.*

The shape, size and electron density (Ne) of the corona varies with the sunspot cycle, which is now very well established by white-light observations. In our study, we investigated the ‘quiet’ solar corona (i.e., the corona distinct from emission due to transient and long-lasting discrete sources) at radio frequencies during the descending phase of sunspot cycle 24. We used the radio images obtained with the Gauribidanur RAdioheliograPH (GRAPH; Ramesh1998) at 80 MHz and 53 MHz at the Gauribidanur observatory in the period of January, 2015 to May, 2019. The GRAPH data were carefully selected such that no H$\alpha$ and/or X-ray flares, coronal mass ejections (CMEs), and short/long duration non-thermal radio burst activities were reported during our observing period as well as for $\approx$30 min before and after the data. Figure 1 shows the GRAPH contours overlapped on LASCO-C2 coronagraph images on January 13, 2016 (a sample day).

Methodology

We determined the one-dimensional (1D) equatorial brightness distribution averaged over an angular width of ${\approx}5^{\prime}$ centered on the solar equator in the 2D images obtained with the GRAPH (Figure 1). The equatorial diameter was particularly chosen for the study due to the comparatively better and declination independent angular resolution of the GRAPH in the east-west direction. Each 1D brightness distribution were reproduced using an iterative multi-Gaussian least squares curve fitting technique as described in Ramesh et. at 2006. The minimum width of each Gaussian profile was limited to $1^{\prime}$, the smallest source size reported at frequencies $<$ 100 MHz in previous studies (see for example, Ramesh et. al. 1999, Mugundhan et. al. 2018, Kundu et. al 1990).  We imposed the following conditions to consider the data obtained at a particular epoch for further analysis: (i) the fits for the 53 MHz and 80 MHz observations must have one Gaussian profile each with width ${>}32^{\prime}$; (ii) the width of the such a profile in the fit for the 53 MHz observations should be larger than the corresponding 80 MHz profile on the same day; (iii) the discrete solar radio sources identified from the fit should be present at both the frequencies; and (iv) the sum of the amplitudes of the Gaussian profiles used to fit the observed 1D brightness distribution at any given position on the latter should be nearly equal to the observed amplitude there. The Gaussian profiles that satisfied these criteria were considered to represent the ‘background’ corona. We also eliminated the GRAPH beam size contribution from the final diameter values. Figure 2 demonstrates the multi Gaussian fit on a sample data on January 16, 2016 after applying all the criteria mentioned above.

Figure 1 – GRAPH images of the solar corona obtained on 2016 January 13 at 53 MHz and 80 MHz superposed on the SOHO/LASCO-C2 whitelight image obtained on the same day around the same time. Solar north is straight up and east is to the left. The ‘white’ colour open circles represent the size of the solar photosphere. The concentric, filled ‘black’ colour circles indicate the occulting disk of the coronagraph. Its radius is ${\approx}2.2\rm R_{\odot}$.

 

Figure 2 – 1D equatorial brightness distribution obtained from the GRAPH radioheliograms at 53 MHz and 80 MHz (see Figure 1) based on the methodology described in Section 3. Two Gaussian profiles, red colour (solid line) and black colour (with dot-dash symbols), were used to match the observations (blue colour profile). The green colour profile (with dash symbols) is the sum of the aforementioned two Gaussian profiles used for the fit. The Chi-square fit errors are $<$1% at both 53 MHz and 80 MHz.

Results and Conclusions

After applying all the criteria on data from January, 2015-May, 2019, we were left with 336 days. Figure 3 shows the monthly minimum values in the equatorial diameters of the solar corona at 53 MHz and 80 MHz during the same period. We chose the monthly minimum values of the diameters since they are more likely to represent the ‘quiet’ solar corona which at low radio frequencies is supposed to be the corona that is nearly free of localized thermal and/or non-thermal sources (Leblanc et. al 1969). The gradual decrease in the equatorial diameters at both 53 MHz and 80 MHz (correlation $\approx$74%) is an indication of the decrease in the heliocentric distances ($r$) of the ‘critical’ plasma levels corresponding to 53 MHz and 80 MHz in the solar atmosphere. We independently estimated $N_{e}$ at the equatorial region of the ‘background’ corona using white-light coronagraph observations and it also suggests a decline ($\approx$1.8 times at $r{\approx}$1.55$\rm R_{\odot}$), consistent with our findings using radio data ($\approx$2.3 times at $r{\approx}$1.16$\rm R_{\odot}$ (80 MHz)). The white-light densities were obtained using the linearly polarized brightness (pB) measurements with STEREO-A/COR1 and the inversion technique based on spherically symmetric polynomial approximation (SSPA; Wang et. al. 2014).

Figure 3 – The data points in red colour are the monthly minimum values in the equatorial diameters of the solar corona at 53 MHz (left panel) and 80 MHz (right panel) during the period 2015 January – 2019 May. The solid lines in red colour are the quadratic least squares fit to the data points. The isolated blue colour data point indicates the monthly maximum value in the equatorial diameter during 2019 January. It is significantly larger than the corresponding monthly minimum value even during the minimum period of sunspot cycle 24 like the aforementioned epoch.

In this work, we investigated the equatorial diameter of ‘quiet’ solar corona at low radio frequencies during the descending phase of sunspot cycle 24. We identified the localized sources of emission in the radioheliograph data at 80 MHz and 53 MHz and removed those using iterative multi-Gaussian curve fitting technique. Our results shows that the minimum radius of the ‘quiet’ solar corona at a typical frequency like 53 MHz/ 80 MHz was found to be ${\approx}1.16/ 1.1 \rm R_{\odot}$.

Based on the recent paper: Ramesh, R., Kumari, A., et. al.: Low frequency radio observations of the ‘quiet’ corona during the descending phase of sunspot cycle 24. Geophysical Research Letters, e2020GL090426. DOI: https://doi.org/10.1029/2020GL090426

References

R. M. MacQueen, J. T. Burkepile, T. E. Holzer, A. E. Stanger and K. E. Spence (2001). The Astrophysical Journal  549, 1175

R. Ramesh, H. S. Nataraj, C. Kathiravan, and Ch. V. Sastry (2006). The Astrophysical Journal 648, 707

*Full list of Authors:  R. Ramesh, Anshu Kumari, C. Kathiravan, D. Ketaki, M. Rajesh, M. Vrunda

Microwave Spectral Imaging of an Erupting Magnetic Flux Rope During a Large Solar Flare by B. Chen et al.*

Magnetic flux ropes are believed to be the centerpiece of the three-part structure of coronal mass ejections. In the standard model of eruptive solar flares, flux rope eruption also induces the impulsive flare energy release through magnetic reconnection. Signatures of flare-associated flux ropes in the low solar corona have been frequently reported in extreme ultraviolet (EUV) wavelengths, particularly the so-called EUV “hot channel” structures (see, e.g., Cheng et al. 2017 for a review). However, reports of the nonthermal counterpart of the erupting flux ropes in the low solar corona are relatively rare. 

Here we report microwave spectral imaging of a flux rope eruption associated with the celebrated X8.2 limb flare event on 2017 September 10 (see a collection of relevant papers on ADS) based on data from the Expanded Owens Valley Solar Array (EOVSA). Complemented by EUV and X-ray data, our observations reveal a detailed picture of the flux rope illuminated by flare-accelerated nonthermal electrons. These data also allow us to diagnose the magnetic properties of the flux rope and the nonthermal electrons in a broad flare region.

The Preexisting Filament

Figure 1 – Preexisting filament that led to the SOL2017-09-10 GOES X8.2-class eruptive flare. (a) Photospheric magnetogram on 2017 September 7. (b) A filament is seen as a reverse S-shaped dark structure in H-alpha image close to the polarity inversion line. (c)–(f) SDO/AIA 171 Å images of the dark filament seen against the disk (c), ∼5 hr prior to the X8.2 event (d), during the eruption (e), and after the flare peak (f). Symbol “X” marks the center of the filament. Circles marked with “N” and “S” denote the northern and southern footpoints of the filament/flux rope, respectively. 

Three days prior to the event when the active region was viewed against the disk, a reverse S-shaped filament was seen in both the H-α and SDO/AIA 171 Å images (Figure 1). The filament was located along the polarity inversion line (PIL) of the main sunspot groups. The northern and southern ends of the filament were anchored near the edge of the sunspot group (marked by circles). Near the central active region (marked by a symbol “X”), the filament and the PIL display a sharp turn from a north–south orientation toward the east–west orientation. When the filament rotated to the west limb on 2017 September 10, the central part of the filament was then aligned nearly along the line of sight. When the eruption occurred, this location was directly below the erupting dark cavity. The latter implicates that the erupting flux rope at this central location was viewed along its axis, consistent with the geometry of the preexisting filament.

Flux Rope Eruption: EUV Hot Channel and Microwave Counterpart

When the filament erupted early in the SOL2017-09-10 X8.2 flare event (at ~15:46 UT), it was visible as a hot channel structure in AIA 131 Å images (Figure 2(a)–(d)). The hot channel structure was nearly parallel to the limb, consistent with the overall north–south geometry of the reverse S-shaped filament when viewed against the disk. At the center of the hot channel structure, a bright core was present, connected by strands linking to the footpoints identified from the preexisting filament (circles, same as those in Figure 1). Soon the central core developed into a teardrop-shaped cavity. A long and thin plasma sheet appeared below the cavity, which is the signature of a large-scale reconnection current sheet (see our other recent paper Chen et al. 2020 and references therein).

Figure 2 – (a)–(d) Erupting magnetic flux rope seen as a hot channel structure in SDO/AIA 131 Å passband sensitive to ∼10 MK plasma (shown in reverse grayscale). (e)–(h) EOVSA 4.2 GHz microwave sources superposed on SDO/AIA 131 Å.

EOVSA observed the event from ∼14:30 UT to 01:10 UT of the next day (Gary et al. 2018). We adopted a multifrequency synthesis imaging technique to increase the dynamic range of the images. The results are shown in Figure 2(e)–(h). The microwave images at 4.2 GHz showed a striking similarity in morphology to the EUV hot channel structure. In particular, at ~15:54 UT during the early impulsive phase, the image showed a faint cavity-shaped structure encompassing the hot channel cavity. Moreover, both the northern and southern microwave sources showed a clear extension from the flux rope footpoints toward higher heights, which also appeared to follow the hot channel strands connecting to the cavity.

We also derive spatially-resolved microwave light curves and spectra for the central source and the double flux rope footpoints sources. The light curves display very similar temporal evolution since the onset of the flare. The spectra of the three sources show that they are due to gyrosynchrotron radiation from nonthermal electrons, which have similar spectral indices (see Figure 4 of the paper). Both phenomena suggest that the central and side sources are physically connected, probably by nonthermal electrons propagating along magnetic field lines of the erupting flux rope.

Discussion and Conclusion

Our observational results are broadly consistent with the magnetic topology and the associated energy release scenario suggested in the 3D standard model for eruptive flares (Aulanier et al. 2012, 2013; Janvier et al. 2013, 2014). A schematic picture is shown in Figure 3.  During the early eruption phase, the pre-reconnection field lines are highly sheared. While the inner ends of these field lines are rooted close to the polarity inversion line and reconnect at the central current sheet, their far ends are rooted near the legs of the flux rope. After the reconnection, the newly reconnected field lines above the primary reconnection X point join the flux rope and add to its magnetic flux. The other set of the reconnected field lines below the X point, in turn, form the main flare arcade. The majority of nonthermal electrons are presumably accelerated at or below the central current sheet and escape along the newly reconnected field lines. Those traveling upward can gain access to the outer shell of the flux rope and propagate back to the solar surface near the flux rope footpoints. Hence, microwave sources can be detected at both the central current sheet region, near the flux rope cavity, and near the flux rope footpoints, all of which are vividly shown in the EOVSA images. 

We note that double nonthermal side sources near the flux rope footpoints were previously depicted in the celebrated semi-3D standard flare cartoon by Shibata et al. (1995), and more recently, in the double-arc instability scenario proposed by Kusano et al. (2020). However, to our knowledge, reports of these remote side sources have been elusive. In this event, no HXR counterpart is found at the flux rope footpoints, which is possibly due to 1) the limited dynamic range of RHESSI, and 2) the relatively shorter propagation distance of the X-ray emitting electrons due to Coulomb collision losses. Our observations demonstrate the unique power of microwave spectral imaging in exploring the energy release, electron acceleration, and electron transport processes throughout the flaring region.

Figure 3 – Schematic of the observations within the context of the 3D standard model for eruptive solar flares. (a) SDO/AIA 171 Å image just before the flare impulsive phase, showing pre-reconnection loops surrounding the flux rope cavity. (b) Composite EOVSA 4.2 GHz and 131 Å image during the impulsive phase (same as Figure 3(d)). (c) and (d) Schematic for the pre-impulsive and post-reconnection scenario adapted from Janvier et al. 2014. (e) Schematic of the standard model adapted from Shibata et al. 1995 (and Holman 2012).

*Based on the recent paper: Bin Chen, Sijie Yu, Katharine K. Reeves, Dale E. Gary (2020) “Microwave Spectral Imaging of an Erupting Magnetic Flux Rope: Implications for the Standard Solar Flare Model in Three Dimensions”, 2020, The Astrophysical Journal Letters, 895, L50. DOI: https://doi.org/10.3847/2041-8213/ab901a; Preprint: https://arxiv.org/abs/2005.01900

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Chen, B., Shen, C., Gary, D. et al. 2020, Nature Astronomy, 10.1038/s41550-020-1147-7

Cheng, X., Guo, Y., Ding M. 2017, ScChD, 60, 1383

Gary, D., Chen, B., Dennis, B., et al. 2018, ApJ, 863, 83

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