Open Access
Issue
A&A
Volume 663, July 2022
Article Number A149
Number of page(s) 8
Section The Sun and the Heliosphere
DOI https://doi.org/10.1051/0004-6361/202243144
Published online 22 July 2022

© A. T. Altyntsev et al. 2022

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

In solar flares, particles are accelerated to energies from a few tens of kilo electron volts to mega electron volts and the ambient plasma is heated. The effectiveness of magnetic energy conversion into plasma heating and particle acceleration strongly depends on the flare configuration. Circular ribbon flares (CRFs) occur in magnetic configurations with a circle-like boundary between magnetic regions of opposite polarity, implying the existence of an overlying dome-shaped fan separatrix (Masson et al. 2009; Sun et al. 2013). The fan-spine magnetic field lines connect this flare kernel with a remote source. The first observational study of CRFs was carried out using the TRACE 1600 Å UV continuum images (Masson et al. 2009). The CRFs form a notable class of solar flares because they imply a three-dimensional magnetic reconnection. In particular, the processes of the flare energy release in the circle domain and brightening in the remote spine are studied using extreme ultraviolet imaging (Sun et al. 2013).

There are only a few studies of CRFs based on microwave imaging (Meshalkina et al. 2009; Kashapova et al. 2020; Lee et al. 2020). The studies used the 17/34 GHz maps from the Nobeyama RadioHeliograph along with (E)UV and magnetic data. Meshalkina et al. (2009) showed that the microwave preflare emission at 17 GHz was mainly thermal during the events SOL2002-06-01T03:57 and SOL2002-06-01T11:47. The ring structure seen in microwaves was similar to the EUV one. During the impulsive phase, the nonthermal electrons appeared due to reconnection between two magnetic ropes. The long spine loop was found in the TRACE 195 Å images. At 17 GHz maps, the flare kernel and the weak remote source with a similar temporal behavior were observed. The spine loop was not detected at 17 GHz maps.

Microwave observations provide a unique possibility for studying variability of parameters of nonthermal electrons down to subsecond timescales. One of the many advantages of the data obtained with the Siberian Solar Radio Telescope (SSRT) and NoRH is their high temporal resolution and possibility to determine positions of the emission sources at discrete frequencies. In the case of rapid variability, it is possible to measure the time profile delay of the remote source relative to the flare kernel one and to determine the velocity of accelerated electron transfer along the spine loop. For comparison, the Reuven Ramaty High Energy Solar Spectroscopic Imager (Lin et al. 2002) provided the imaging spectroscopy capability at a nominal temporal resolution of four seconds; however, in practice, imaging spectroscopy typically needs longer integration times on the order of tens of seconds to minutes. Lee et al. (2020) found the quasi-periodic pulsations (QPPs) with periods of 1–2 min in the flare SOL2014-12-17T04:51, using the 17/34 GHz maps from NoRH. The observed oscillation properties were interpreted in terms of a kink mode and torsional Alfven waves propagating along the spine after the eruption.

Of special interest are the multiperiodic pulsations at lower microwave frequencies from spectropolarimeters, studied by Kashapova et al. (2020). The 150-s period oscillations were seen to coexist in Hα, hard X-rays, and microwave emissions, and their sources were connected with the flare kernel. The authors proposed a modulation of the slipping reconnection rate occurring in the fan as a plausible mechanism. The other oscillation with a period of 125 s can be caused by kink oscillations of the spine loop connecting the primary reconnection site with the remote source (Zhang et al. 2020).

More than a dozen of different QPP mechanisms in solar flares have been proposed (McLaughlin et al. 2018; Kupriyanova et al. 2020; Zimovets et al. 2021). The main problem with mechanism identification is that observations cannot provide the full set of plasma parameters and the proposed models of the QPPs are still rather qualitative than quantitative. Observations show that the amplitude of oscillations in the light curves of flare radiation in hard X-ray and microwave radiation can reach values comparable to the background radiation. In this case, high harmonics can appear in the oscillation spectrum. One of the most striking manifestations of the nonlinearity of oscillations is a two-peak form of pulses (Nakajima et al. 1983; Zimovets & Struminsky 2009; Kumar et al. 2016); various theoretical models have been proposed for the explanation of this (Tajima et al. 1987; Sakai & Ohsawa 1987; Inglis & Dennis 2012; Kolotkov et al. 2016). Observations of the QPPs in circular ribbon flares are of a particular interest since their configuration includes magnetic structures that differ significantly in scales and values of the plasma parameters. The latter significantly broadens the parametric range of QPP research.

This work is devoted to studying the nature of the energy release in the circle ribbon flare that occured on 6 August 2002, in which a sequence of broadband pulses with timescales down to a subsecond were recorded. The sufficiently large intensities of subpeaks and the source imaging allowed for spectra to be measured and the localization of the radio and X-ray sources to be determined.

The paper is organized as follows. Section 2 outlines the observational tools, the results of observations, and the subsequent analysis. The discussion is presented in Sect. 3. Section 4 contains general conclusions.

2. Observations

2.1. Instruments

Microwave data of SSRT at 5.7 GHz were used to find the flare interval with the QPPs. We looked through sequences of a one-dimensional radio brightness distribution of the flare regions, recorded with 14 ms cadence using east-west and north-south antenna arms (Altyntsev et al. 2003; Meshalkina et al. 2004). During observations, the SSRT half beam widths were 27.8 (east-west) and 17.8 (north-south) arcsec. The scanning angles were 9.6 degrees relative to the north-south direction for the east-west array and −61.1 degrees for the north-south array. We also used two-dimensional images of the flare region available every 2–3 min (Grechnev 2003; Kochanov et al. 2013).

To study sources at high frequencies, we used data from the Nobeyama Radio Heliograph (Nakajima et al. 1994) at 17 GHz (intensity and polarization) and 34 GHz (intensity only). The NoRH spatial resolution was 13 arcsec at 17 GHz and 8.5 arcsec at 34 GHz. We used the imaging with a 0.1 s cadence. Microwave spectra were measured using the Nobeyama Radio Polarimeters with a cadence of 0.1 s (NoRP, Torii et al. 1979). We used the data recorded with spectrometers of Learmonth Solar Observatory with a 1 s cadence from the Radio Solar Telescope Network (Guidice et al. 1981).

To analyze the spatial structure of the flare, we also used UV images in 171 Å and 195 Å lines obtained by the Transition Region and Coronal Explorer satellite (Handy et al. 1999), with a spatial resolution of 1 arcsec. The 171 Å channel images the plasma at temperatures of (1.6−20) × 105 K, and the 195 Å channel captures emission from the plasma in the low-temperature range of (5.0−20) × 105 and high-temperature range of (1.1−2.6) × 107 K. The TRACE 195 Å channel is only sensitive to the hotter plasma from Fe XXIV in the case of flares, where the hotter plasma emission measure dominates over the emission measure of the 1.5 MK plasma. The time cadence of the TRACE data in this event is 8 s.

To study hard X-ray spectra and images, we used data from the Reuven Ramaty High-Energy Solar Spectroscopic Imager. The RHESSI data are processed with the software developed by the RHESSI team (Lin et al. 2002) which allowed us to obtain the full-disk flux light curves with a cadence of 0.1 s and the imaging observations with a 4 s cadence. The magnetic field structure was obtained from the line of sight (LOS) magnetic-field magnetograms from the SOHO/Michelson Doppler Imager (MDI: Scherrer et al. 1995).

2.2. Flare overview

The C8.3-class flare occurred in the active region NOAA 10057 in the west part of the solar disk (S07W55). The time profiles of the flare emissions from the beginning to the maximum of the soft X-ray flux are shown in Fig. 1. In the impulsive phase of a flare, two subphases can be distinguished. At the beginning of both subphases (I and II), short peaks at frequencies ≤1.0 GHz are observed (Fig. 1a). It is generally accepted that the appearance of such short decimeter pulses at the beginning of a flare is considered as an indicator of electron acceleration (e.g., Aschwanden & Benz 1997). Beams of the accelerated electrons propagate along high loops toward low density plasma, where they excite the Langmuir oscillations of the background plasma, which are then converted into electromagnetic radiation at the fundamental plasma frequency or its harmonic.

thumbnail Fig. 1.

Flare light curves. From top to bottom: microwave data from the NoRP, RSTN/APL, and hard X-rays from RHESSI in three energy channels. The vertical lines at 01:37:20, 01:38:18, and 01:39:00 mark the beginning of the flare phases.

The first subphase (I) begins abruptly in microwaves at 01:37:20. In hard X-ray emission, a sharp onset is observed for photons with energies above 25 keV (panels g and h); however, at low energies, a gradual increase in the radiation flux is observed. The radiation intensity in the microwave band at 2.0–15.4 GHz and X-ray signals from 25–50 keV channels remains at an approximately constant level. As it can be seen from the amplitudes of the microwave curves at frequencies above 1.0 GHz in Fig. 1, the highest flux was observed at 5 GHz.

The profiles during the second subphase (II) with a sharp rise at 01:38:18 and slow decay are typical for gyrosynchrotron emission at an impulsive phase. The sharp rise of the flux is due to nonthermal electrons rapidly filling flare loops, and then the decay is caused by their gradual precipitating toward the loop footpoints. In the third phase of the flare, the flare flux increases in the channels of soft X-rays and in microwave radiation at high frequencies, which indicates the heating of the plasma emitting due to the bremsstrahlung.

Measurements of the integral flux of the Sun do not contain information about the positions of flare sources. To present the flare configuration, we show the 171 Å images at the first and second subphases in panels a, b and c, d of Fig. 2. The flare microwave source at 17 GHz can be distinguished using a variance map from a set of polarization images recorded during the flare (Grechnev 2003). In our event, two sites of the enhanced variability are revealed which are shown by the green contours (Fig. 2b). These sources are separated in longitude by a distance of about 60 arcsec. The structure of the LOS magnetic field is shown in Fig. 2d by the red (positive field) and blue (negative) contours. The yellow oval marks the Negative Magnetic field Region surrounded by patches of positive polarity. From comparison of panels b and e shows that the NMR is covered by green contours of the western 17 GHz variance emission source.

thumbnail Fig. 2.

Flare configuration. a,c) TRACE images in 171 Å line. b) White contours show 5.7 GHz source (Stokes I) at 01:38 at (4.3, 7.2, 13) MK. The yellow quadrangle indicates the position of the SSP brightness centroids. The dashed lines show the directions of the SSRT east-west and north-south scanning and the sections across the flare kernel (right) and remote source (left). Green contours present levels of variability for 17 GHz polarization maps for time period 01:37–01:40. The cross in the left upper corner shows the SSRT beam widths. d) Blue and red contours (−500, −100, 50, 100, 500 G) show the positive and negative components of the LOS magnetic field, respectively. The white square shows the field of view in image Fig. 3c. The yellow oval marks the negative magnetic region (NMR).

The total flare region is delineated by the white contours of the increase in the brightness temperature of microwave emission at a frequency of 5.7 GHz (b). The shape of the microwave contours resembles a tadpole with a broad head and narrow tail. The tadpole head covers the NMR and the patches of positive polarity. The tail is extended to the east and covers the second (remote) 17 GHz source. The intensity of this remote source is too weak to detect it on the individual 17 GHz maps. We note that the apparent width of the 5.7 GHz tail is comparable with the SSRT beam width. So the real microwave tail could be even narrower.

A bright EUV oval-shaped structure appears during the flare inside the tadpole head, and it consists of the loop bundles which we refer to as ropes hereinafter. We note that there are no obvious signs of large EUV loops along the tail in Fig. 2. During the impulsive phase of the flare, two ropes brighten and the southern footpoints of which are rooted in positive polarity magnetic patches marked by the labels 1 and 2 in Fig. 2d. These patches are close to each other and are located near the southern border of the NMR (Figs. 2d and 3c). Extreme ultraviolet ropes A and B (Fig. 3e) approach each other during the impulsive phase up to a width of 4 arcsec. In the third flare phase, the area of bright EUV structures increases and covers a significant part of the region with a negative magnetic field. In general, the flare configuration in the event under study is similar to the toy model for explosion in fan-spine topology which was presented in Sun et al. (2013) (Fig. 1), and it can be classified as a circular ribbon flare with the spine-shape loops.

thumbnail Fig. 3.

Evolution of flare configuration. The background is the TRACE images in the 171 Å line at the different flare stages. Top row: white and black contours show the 5.7 GHz brightness temperatures in intensity and right polarization, respectively (a and b). Magenta and cyan contours present the 17 GHz and 34 GHz sources in intensity, respectively. The cross in the left upper corner show the SSRT beam widths (a). c) Part of the panel in Fig. 2, bounded by a white square. In the bottom row with extended frames, the color contours show the isolines of the hard X-ray emission at levels (0.5, 0.9): 3–6 keV (black), 6–12 keV (pink), 12–25 keV (green), and 25–50 keV (blue). Arrows mark ropes A and B. The axes show the arcsec from the solar disk center.

The HXR and microwave sources are presented in Fig. 3. The SSRT 2d maps are available before and during the first subphase (panels a and b with a large field of view). The white and black isolines show the 5.7 GHz brightness distribution in intensity and polarization, respectively. In the preflare phase, the brightness centers of the 5.7 GHz source coincide in polarization and intensity; however, during the flare, the centroid of polarized emission is shifted to the tail of the tadpole structure. The sign of polarization is right-handed and the degree can reach ≈40%. At the same time, a compact 17 GHz source is located close to the south footpoints of the bright EUV ropes. It is seen from the EUV images (c, e) that the right bright structure extended about 20 arcsec to the north consists of two ropes (A and B) with the south footpoints rooted in the different magnetic patches of positive polarity (1 and 2).

The bottom panels of Fig. 3 show the hard X-ray source location relative to the EUV loops in a smaller field of view. There are not any HXR source in the remote source. The Pixon algorithm was used for the reconstruction of images from RHESSI data with an integration time of 8–20 s depending on different channels. During the entire impulsive phase, the hard X-ray source is small in comparison with the ropes and its apparent size does not exceed the RHESSI spatial resolution (≈10 arcsec), except for the 3–6 keV source before the start of the flare. The HXR source is located together with the 17 GHz source above the south footpoints of the twinned ropes A and B. In this topology, it is obvious that these sources of nonthermal radiation are close to or coincide with the region of the primary impulsive energy release, that is the flare kernel.

2.3. QPPs in the first impulsive subphase

In this section, we concentrate on studying the nature of quasi-periodic pulses that occurred during subphase I. For this study, we used the temporal profiles recorded with a subsecond cadence (Fig. 4). It is seen that the subpeaks lasting for 0.2–1.8 s are observed in the light curves of the microwave emission at 5.7 GHz (14 ms cadence) and 17 GHz (100 ms), and in hard X-rays at 25–50 keV (100 ms). It can be seen that although the relative amplitudes of the peaks can significantly differ in the presented emission ranges, a high temporal correspondence is observed for a number of peaks.

thumbnail Fig. 4.

Light curves of the first subphase with the QPPs. a) RHESSI channel 25–50 keV. b) SSRT profiles calculated from one-dimension scans in intensity for the total flare source at 5.7 GHz, using the north-south arrays separately, and from the kernel (blue) and remote (red) parts of the east-west scans shown in Fig. 5. The kernel and remote values were multiplied by a factor of 4. c) Same as b), but in circular polarization. d) Profile at 17 GHz calculated from the NoRH images. The vertical lines show the moments before and at the maximum of one of the subpeaks used in Fig. 5. e) Size estimates of the 17 GHz source, smoothed over 0.3 s.

Figures 3b,e show the flare sources during the subphase with the pulses. During this time, the western ropes A and B are brightest in the EUV image and they are extended about 20 arcsec toward the center of the NMR. Accounting for the image alignment accuracy (≈10 arcsec), the compact sources of hard X-ray and 17 GHz microwave radiation coincide and adjoin the southern footpoints 1 and 2 (Fig. 2d). The HXR source size is about spatial resolution (≈10 arcsec). At 17 GHz, the apparent source size is close to the NoRH beam width Δ ≈ 13 arcsec (Fig. 3b). The apparent shape of the source was close to circular with the diameter D. In this case, the true diameter d can be estimated assuming Gaussian distributions of radio brightness over the source and the NoRH diagram as d = (D2 − Δ2)0.5. Changes in size over time are shown in Fig. 4e. It can be seen that the source diameter varies between 10 arcsec and 7 arcsec during the interval for which QPPs are observed. There is a tendency for the microwave source size to decrease at the time of subpeaks’ risings. Observations at 34 GHz were too noisy, but they confirm source size estimates from 17 GHz images on average. At 34 GHz, the apparent source size is about 12 arcsec when the beam width is about 8.5 arcsec, and thus the real source size can be estimated to be 8 arcsec.

At 5.7 GHz, the profiles of intensity (b) and circular polarization (c) are obtained from the one-dimensional observation mode of SSRT for the east-west and north-south arrays separately (Figs. 4b,c). We note that there is the data gap in the east-west profiles. It is important that the scans recorded along the east-west direction (see Fig. 2b) allow us to distinguish between fluxes emitted from the flare kernel and from the remote source. The procedure for selecting these sources is shown in Fig. 5 using the example of a subpeak marked in Fig. 4 by dash-dotted lines before and after the subpeak. The vertical lines correspond to the straight lines in Fig. 2b, that is, the positions of the kernel (right line) and the remote source (left). It can be seen that the subpeak emission (lower solid curves) was emitted from the remote source, and its emission is polarized up to 35% in this pulse. The east-west curves in Figs. 2b,c were obtained by integrating the flux under the fragments of the scans’ sequence marked by the solid sections in the dotted curves in Fig. 5. The profiles in Fig. 2b (red curves) show that the pulses are more prominent in the remote source.

thumbnail Fig. 5.

One-dimensional brightness temperature distributions at 5.7 GHz. East-west scans of the flare region in intensity (top panel) and polarization (bottom) at 01:37:29 (solid curve) and 01:37:34 (dotted). The moments are marked in Fig. 4. The lower solid curves show the short pulse source as the difference between these scans, recorded before and at the maximum of the pulse. The solid sections of the dotted curves correspond to the remote source (left) and the flare kernel (right). The segments’ length corresponds to the SSRT diagram.

The two-dimensional positions of the subpeak sources’ centroids can be determined for the prominent pulses in the remote source from the one-dimensional distributions recorded simultaneously from the both SSRT antenna arrays scanning along the east-west and north-south directions. The localization technique for sources of short pulses relative to the magnetic field structure was described in Meshalkina et al. (2004). The area where the centroids of the all observed pulse sources are located is shown by the yellow rectangle 4  ×  20 arcsec, which is close to the remote source detected from the 17 GHz polarization images (Fig. 2).

To determine the agent that synchronizes the pulses in the flare kernel and remote source, a cross-correlation analysis of the SSRT and Nobeyama time profiles was carried out during the first subphase. To highlight subpeaks, trends with a window of 5 s were removed from profiles. In the interval before the east-west gap in the data (Fig. 4), the correlation coefficient is 0.75, and the subpeaks in the remote source are delayed by 0.2 s. For the interval after the gap, the correlation coefficient is 0.6 and the delay increases up to 0.3 s.

On the other hand, the sequence of subpeaks can be analyzed as a sequence of quasi-periodic pulses. For the spectral analysis of the periodicity, we used the wavelet transform (Torrence & Compo 1998; Karlický et al. 2020). The results are shown in Fig. 6 where the rows of panels correspond to 5.7 GHz, 17 GHz, and 25–50 keV emission bands. In all emission bands, the main period of 8.1 s is clearly seen in the global wavelet power spectrum. There is also the peak of a 3 s period which is most prominent in hard X-rays. The red and blue curves in the left panel present the sums of wavelet harmonics with periods of 6.5–10 s and 2.4–3.7 s, respectively. In hard X-rays, the amplitudes of pulses exceed the background level and the 3 s harmonic reflects the nonlinear double-peak structure of the pulses with an 8 s periodicity. The double structure is clearly visible from the comparison of the red and blue dotted curves after 01:37:28 in the RHESSI row in Fig. 6. We note that in the previous 8 s interval, two peaks are also observed, but they are spaced by about 5 c. The 3 s harmonic is present in the flux intensity of the flare microwave burst, but its relative power is much weaker, and it is only visible in some oscillation cycles.

thumbnail Fig. 6.

Results of the wavelet analyses of the emission at 5.7 GHz (SSRT/NS), 17 GHz (NoRH), and 25–50 keV (RHESSI). Left panels: normalized time profiles of signals (black) and sums of harmonics in 2.4–3.7 s (blue) and 6.5–10 s (red) period ranges. Middle panels: wavelet Morlet power spectra. Right panels: global wavelet spectra.

The wavelet cross-correlation between pairs of the flux profiles recorded with SSRT at 5.7 GHz, NoRH at 17 GHz, and RHESSI at 25–50 keV are shown in Fig. 7. The phase shifts between radio at 5.7 GHz and HXR oscillations for both periods correspond to a temporal shift of 0.4 s, which is slightly higher than the abovementioned estimate of 0.2–0.3 s. At 17 GHz, the phase shift of the oscillations depends on the oscillation mode, that is to say the period. In oscillations with a period of 8 s, the flux varies synchronously with the hard X-ray radiation. In the 3-s mode, the in-phase behavior is observed with the flux variations at 5.7 GHz.

thumbnail Fig. 7.

Wavelet cross-correlation of the light curves, shown in Fig. 6 for SSRT-NoRH, SSRT-RHESSI, and NoRH-RHESSI (top panels, from left to right), and the phase relations (bottom panels).

The composite integral spectrum of the microwave emission in the first subphase is presented in Fig. 8a. The spectrum shape is typical for the gyrosynchrotron emission of nonthermal electrons with the power law energy distribution. However, from the SSRT and NoRP images it is seen that the 5.7 GHz source is more powerful than the 17 GHz source. So, we can suggest that the presented spectrum contains a large contribution from the extended source at frequencies below the maximum of the spectrum. The compact source provides the main contribution to the spectrum at higher frequencies, that is above 5 GHz. For this compact source, we can estimate the power law index of emitting electrons as δ = (γ − 1.22)/0.9 (Dulk 1985), where the index γ can be found from the ratio of fluxes at two frequencies γ = lg(F1/F2)/lg(f2/f1). We note that Fi is the flux at frequency fi.

thumbnail Fig. 8.

Spectra in microwaves and hard X-ray. a) Composite microwave spectrum at 01:37:41. Diamonds show observations with RSTN, and the cross corresponds to NoRP. The spectrum fitting is shown by the solid line. b) and c) HXR spectra. The photon accumulation intervals are 4 s. The thick line is a function approximation (vth+bpow). The dotted lines show the background levels. The bpow function is shown by the dashed line, and the thermal function is shown by the dash-dotted line.

The temporal dependence of electron hardness can be obtained with higher temporal resolution using the ratio of microwave fluxes F15/F9 at 8.8 and 15.4 GHz, recorded with the Learmonth spectrometer (Fig. 9). The ratio F15/F9 reflecting the hardness of the emitting electrons oscillates with a period of about 8 s and the amplitude increasing in time up to the impulsive flare stage. The power law index of nonthermal electrons varies within δ ≈ 3 ± 1. According to the global wavelet power spectrum (Fig. 9, right), the contribution of oscillations with a 3 s period is weak.

thumbnail Fig. 9.

Temporal variation of the ratio F15/F9 obtained from the flux profiles at 15.4 and 8.8 GHz (left) and the global wavelet power spectrum (right).

In Fig. 8b,c the HXR spectra are shown for the two instants of time: in the beginning and the end of the interval with pulses (impulsive subphase I). The sensitivity of the RHESSI telescope was sufficient to identify the hard X-ray emission exceeding the background one at energies up to 50 keV. The OSPEX fitting shows the nonthermal electron component with a power law index changing during the first stage as 4.3–5.4. It is in accordance with gradually decreasing HXR flux in the 25–50 keV channel (Fig. 4). We note that the photon accumulation time is 4 c and it is not sufficient to study rapid pulses.

3. Discussion

We believe that the analyzed flare can be classified as a circular ribbon flare, similarly to those considered in earlier works (e.g., Shibata et al. 1994; Masson et al. 2009; Sun et al. 2013; Devi et al. 2020). This conclusion is based on the following: first, the features of the magnetic field configuration in the flare region, where dispersed negative polarity regions are surrounded by patches of positive polarity; second, the large-scale oval-shaped structure of UV brightenings adjacent to the boundary of this NMR; and third, the presence of a remote flare source connected with the flare kernel by electron fluxes emitting in the microwave range.

In our event, the impulsive phase of the flare is associated with two neighboring ropes extending toward the center of the NMR from the different south patches of positive polarity. We note that the CFRs caused by an interaction of two ropes were studied by Meshalkina et al. (2009). The authors concluded that the major drivers of these flares were eruptions of magnetic flux ropes. In their events, the rise and eruption of ropes preceded the onset of the event in microwaves and HXR. Neither the triggering of the events nor their evolution appear to be controlled by processes at the coronal null point.

In our case, the rope eruption was not observed before the onset of the impulsive phase of the flare. A compact source of nonthermal radiation is located at the periphery of the NMR near the south footpoints of the two ropes (seen in the EUV images) approaching each other, with a length of 20 arcsec. These properties are inconsistent with the assumption that the nonthermal energy release is driven by either the slipping magnetic reconnection or null-point reconnection in fan-spine topology considered by Masson et al. (2009), Sun et al. (2013), Devi et al. (2020), Liu et al. (2020), Lee et al. (2020), Joshi et al. (2021), Mitra & Joshi (2021). The null-point reconnection can be responsible for the oval-shape EUV brightening observed during the flare.

The main purpose of this study is to elucidate the nature of short-term synchronous intensity fluctuations in a wide range of electromagnetic radiation from centimeter radio waves to hard X-rays. The properties of the broadband QPPs observed during the first subphase of the CRF can be summarized as follows:

First, The notable QPPs of the hard X-ray and microwave emission with a periodicity of 8 s are observed during a one minute interval. These oscillations are accompanied by the modulation of the hardness of the nonthermal electron energy distribution with the same periodicity and the amplitude increasing in time.

Secondly, The double-peak shape of the QPPs results in a 3 s harmonic in the wavelet power spectrum. There is a tendency of increasing amplitude for this harmonic near maxima of the 8-s oscillation. The two-peak shape is more pronounced in hard X-rays.

Thirdly, The QPPs are found to originate from the flare kernel, that is to say compact sources of HXR and 17 GHz emission, where the two positive-field patches adjoin the NFR boundary (Fig. 2d). The HXR and high frequency microwave sources are located close to each other and have sizes of 7–11 arcsec.

In their fourth, The remote source is shifted eastward toward the sunspots with a positive polarity at a distance of about 60 arcsec, detected on 5.7 GHz and 17 GHz variation maps. Elongated in the latitudinal direction, the 5.7 GHz emission belt connects both flare sites: the kernel and remote sources. At 5.7 GHz, the short-period pulsations are clearly seen in the remote source and they are delayed by 0.2–0.3 s relative to 25–50 keV pulsations in the flare kernel. A high degree of polarization observed in the remote source indicates their nonthermal nature.

The SSRT imaging at 5.7 GHz directly shows, for the first time, the elongated microwave structure linking the remote source with the flare kernel. The spine-loop structure formed before the flare. The measured pulsation delays of 0.2 s–0.3 s allow us to estimate the speed of the agent synchronizing pulsations in the kernel and the remote source. With a distance between the sources of about 60 arcsec, we obtain the apparent propagation speed of (1.5−2) × 1010 cm s−1. Thus, between the flare kernel and the remote source, there is a magnetic channel through which electrons with energies above 100 keV propagate and generate radiation in the remote source.

We can distinguish the microwave emission from the remote source using only imaging at 5.7 GHz. It can be assumed that short radiation pulses from a remote source are generated by electron pulses with a beam-like distribution over pitch angles. Based on the absence of significant HXR and 17 GHz radiation, it can be assumed that the electron flux in the remote source is less intense and with lower energies than in the flare kernel. Taking the high degree of polarization into account, we can assume a plasma emission mechanism for the QPPs’ emission. However, in this case, there should be a large plasma density of about 1011 cm−3 in the remote source. In the case of gyrosynchrotron emission, the high degree of circular polarization can be observed due to beam-like electron fluxes (Fleishman & Kuznetsov 2010). It should be noted that a high polarization degree of radiation from the footpoints of large loops that are remote from the region of electron acceleration was detected by Nakajima et al. (1985) and Gary & Hurford (1990). Radiation from the loop connecting the kernel to the remote source is generated by the nonthermal electrons with large pitch angles trapped in the loop.

The generation of nonthermal electrons of high energies is evident by the emission spectra of flare sources of hard X-ray and microwave radiation, located at the flare kernel. The sensitivity of the RHESSI telescope permits us to detect electrons with energies up to 50 keV (Figs. 8b,c). Observations with the large radioheliographs makes it possible to detect the electrons in the same event with energies that are an order of magnitude higher. In Fig. 8a the solid curve shows the results of fitting the observed spectrum of the compact kernel source at frequencies above 5 GHz with the gyrosynchrotron spectrum model. We assume that the kernel source contribution is half of the total emission at 5 GHz and that it does not fit the model spectrum at lower frequencies because there is large emission contribution from the elongated spine-related sources. For fitting, we used the fast GS code developed by Fleishman & Kuznetsov (2010) to compute the microwave emission from a uniform source with a size of 8 arcsec determined from the NoRH mapping.

The best fitting is provided by the following parameters of the source: the magnetic field value is 70 G, and the power index and density of nonthermal electrons are 2.3 and 8 × 106 cm−3, respectively. Here, the magnetic field was determined by a turnover frequency, and the hardness index of the electronic spectrum was determined by a slope of the microwave spectrum. The dependence on a number of accelerated particles is relatively weak. The highest energy of emitting electrons should reach 2.2 MeV. The results of fitting the high-frequency part of the spectrum are practically not affected by the parameters of the plasma in the source.

We used the IDL software routine goes_tem.pro distributed in SolarSoft to estimate the temperature and emission measure of the flare plasma. During the first impulsive subphase, a temperature and an emission measure were 4–6 MK and 2.5 × 1047 cm−5, respectively. Assuming the sizes of the EUV source at this time to be 20 × 4 × 4 arcsec, we get the plasma density estimate of 4.5 × 1010 cm−3.

Using the above estimations of the flare plasma density and magnetic field, we get the Alfven velocity in the HXR source equal to 7.2 × 107 cm s−1. Consequently, the characteristic transit time τA across the flare core is about 8 s, which is close to the observed period. In general, the observational results agree with the loop coalescence model which suggests the presence of the QPPs with a double peak structure. According to Tajima et al. (1987), the period of oscillations of the current sheet that formed during the coalescence is determined as 2πβ1.5τA, where β is the ratio of the gas to magnetic pressures. In our case, β ≈ 0.4 gives a period of about 12 s, which is close to the observed value.

4. Conclusion

We analyze a GOES C8.3 class flare exhibiting pronounced QPPs across a broad band of wavelengths using imaging and time series analysis. We identify QPPs in the time series of X-ray and microwave fluxes using the wavelet analysis, and localize the region of the flare site from which the QPPs originate via microwave and X-ray imaging. It was found that the pulsations in the hard X-ray and microwave light curves yielded similar periods of 3 s and 8 s, indicating a common origin. The main tone with a period of 8 s is also seen in the temporal evolution of the hardness of nonthermal electrons, that is, it is modulated by the efficiency of their acceleration mechanism. The appearance of a harmonic with a period of 3 s is associated with a two-peak structure of pulsations and it could indicate a nonlinear nature for the observed QPPs. Imaging analysis indicates that the pulsations originate from the footpoint linked to the system of EUV loops. Our results suggest that intermittent particle acceleration, due to the oscillatory regime of the coalescence of current carrying ropes, is responsible for the QPPs. The precipitating electrons accelerated toward the chromosphere produce X-ray pulsations, while the electrons escaping along the spine-loop structure result in the short microwave pulses from the remote source.

Acknowledgments

We thank the reviewer for useful remarks. We are grateful to the teams of the Siberian Solar Radio Telescope, Nobeyama Radio Observatory, Radio Solar Telescope Network (RSTN), The Transition Region and Coronal Explorer and RHESSI, who have provided open access to their data. The experimental data were obtained using the Unique Research Facility Siberian Solar Radio Telescope, the equipment of Center for Common Use “Angara”. The development of the methods used in Sect. 2 was supported by the budgetary funding of Basic Research program No. II.16. This work was supported by the Ministry of Education and Science of the Russian Federation, and the Russian Science Foundation (Grant No. 21-12-00195).

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All Figures

thumbnail Fig. 1.

Flare light curves. From top to bottom: microwave data from the NoRP, RSTN/APL, and hard X-rays from RHESSI in three energy channels. The vertical lines at 01:37:20, 01:38:18, and 01:39:00 mark the beginning of the flare phases.

In the text
thumbnail Fig. 2.

Flare configuration. a,c) TRACE images in 171 Å line. b) White contours show 5.7 GHz source (Stokes I) at 01:38 at (4.3, 7.2, 13) MK. The yellow quadrangle indicates the position of the SSP brightness centroids. The dashed lines show the directions of the SSRT east-west and north-south scanning and the sections across the flare kernel (right) and remote source (left). Green contours present levels of variability for 17 GHz polarization maps for time period 01:37–01:40. The cross in the left upper corner shows the SSRT beam widths. d) Blue and red contours (−500, −100, 50, 100, 500 G) show the positive and negative components of the LOS magnetic field, respectively. The white square shows the field of view in image Fig. 3c. The yellow oval marks the negative magnetic region (NMR).

In the text
thumbnail Fig. 3.

Evolution of flare configuration. The background is the TRACE images in the 171 Å line at the different flare stages. Top row: white and black contours show the 5.7 GHz brightness temperatures in intensity and right polarization, respectively (a and b). Magenta and cyan contours present the 17 GHz and 34 GHz sources in intensity, respectively. The cross in the left upper corner show the SSRT beam widths (a). c) Part of the panel in Fig. 2, bounded by a white square. In the bottom row with extended frames, the color contours show the isolines of the hard X-ray emission at levels (0.5, 0.9): 3–6 keV (black), 6–12 keV (pink), 12–25 keV (green), and 25–50 keV (blue). Arrows mark ropes A and B. The axes show the arcsec from the solar disk center.

In the text
thumbnail Fig. 4.

Light curves of the first subphase with the QPPs. a) RHESSI channel 25–50 keV. b) SSRT profiles calculated from one-dimension scans in intensity for the total flare source at 5.7 GHz, using the north-south arrays separately, and from the kernel (blue) and remote (red) parts of the east-west scans shown in Fig. 5. The kernel and remote values were multiplied by a factor of 4. c) Same as b), but in circular polarization. d) Profile at 17 GHz calculated from the NoRH images. The vertical lines show the moments before and at the maximum of one of the subpeaks used in Fig. 5. e) Size estimates of the 17 GHz source, smoothed over 0.3 s.

In the text
thumbnail Fig. 5.

One-dimensional brightness temperature distributions at 5.7 GHz. East-west scans of the flare region in intensity (top panel) and polarization (bottom) at 01:37:29 (solid curve) and 01:37:34 (dotted). The moments are marked in Fig. 4. The lower solid curves show the short pulse source as the difference between these scans, recorded before and at the maximum of the pulse. The solid sections of the dotted curves correspond to the remote source (left) and the flare kernel (right). The segments’ length corresponds to the SSRT diagram.

In the text
thumbnail Fig. 6.

Results of the wavelet analyses of the emission at 5.7 GHz (SSRT/NS), 17 GHz (NoRH), and 25–50 keV (RHESSI). Left panels: normalized time profiles of signals (black) and sums of harmonics in 2.4–3.7 s (blue) and 6.5–10 s (red) period ranges. Middle panels: wavelet Morlet power spectra. Right panels: global wavelet spectra.

In the text
thumbnail Fig. 7.

Wavelet cross-correlation of the light curves, shown in Fig. 6 for SSRT-NoRH, SSRT-RHESSI, and NoRH-RHESSI (top panels, from left to right), and the phase relations (bottom panels).

In the text
thumbnail Fig. 8.

Spectra in microwaves and hard X-ray. a) Composite microwave spectrum at 01:37:41. Diamonds show observations with RSTN, and the cross corresponds to NoRP. The spectrum fitting is shown by the solid line. b) and c) HXR spectra. The photon accumulation intervals are 4 s. The thick line is a function approximation (vth+bpow). The dotted lines show the background levels. The bpow function is shown by the dashed line, and the thermal function is shown by the dash-dotted line.

In the text
thumbnail Fig. 9.

Temporal variation of the ratio F15/F9 obtained from the flux profiles at 15.4 and 8.8 GHz (left) and the global wavelet power spectrum (right).

In the text

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