Multi-Periodicity of High-Frequency Type III Bursts as a Signature of the Fragmented Magnetic Reconnection

Abstract

Using the radio spectra of the 2 April 2022 eruptive flare, we analyze a group of highfrequency type III bursts by our new wavelet method. In this analysis, we found a multi-periodicity of these bursts that is interpreted by the electron beams accelerated in the fragmented magnetic reconnection in the rising magnetic rope. We propose that each period in these type III bursts is a result of the periodic interaction of sub-ropes formed in the rising magnetic rope. In each interaction, the period depends on the diameter of interacting sub-ropes and local Alfvén velocity. This interpretation is supported by detection of the specific EUV structure which was, according to our knowledge, observed for the first time. All proposed processes occur in the rising magnetic rope. Thus, this flare deviates from the standard flare model, where the main magnetic reconnection is located below the rising magnetic rope.

1. Introduction

Solar flares are the most powerful events in the solar system. The strongest flares are associated with coronal mass ejections and the acceleration of particles into interplanetary space. From the physical point of view, solar flares are explosive phenomena in the solar atmosphere, in which the energy accumulated in the magnetic field and electric currents is rapidly transformed into plasma heating, plasma flows, accelerated particles and emission in a broad range of electromagnetic waves: from radio, through optical, UV, X-rays to gamma-rays. For more details, see the reviews [1,2,3,4,5,6]. The most powerful flares are the eruptive flares that are described by the so-called standard CSHKP flare model [7,8,9,10] or by its generalized three-dimensional version [11,12,13]. In this model, the magnetic rope, carrying the cold and dense filament, is ejected due to toroidal or kink instabilities. Then, below the rising magnetic rope, the narrow current sheet is formed where the main energetic process (magnetic reconnection) occurs. Except for some papers (e.g., [14]), the energetic flare processes in the rising magnetic rope are not considered.

In radio, the eruptive flares are associated with several types of bursts (type II, III, IV, V, J, U) and their fine structures [15]. Among them, there are the high-frequency type III bursts with the normal and reverse frequency drifts that are interpreted as those generated by electron beams with the plasma emission mechanism. While in the normal drifting type III bursts the electron beams are propagating upwards in the solar atmosphere, in the reverse drifting bursts, the beams bombard the dense layers of the solar atmosphere and generate the hard X-ray emission.

In this paper, we analyze an interesting group of the type III bursts observed during the 2 April 2022 flare. Using our new method, we detected multi-periodicity in these bursts. We interpret this multi-periodicity by fragmented reconnection. We support our interpretation with a unique EUV structure. Contrary to the standard flare model, the proposed processes happen inside the rising magnetic rope.

2. Data

We used data from three different radiospectrographs: the ORFEES radiospectrograph working in the 150–1000 MHz range with resolutions of 1.0 s and 0.98 MHz (publicly available data, Observation Radio Frequence pour l’Etude des Eruptions Solaires radiospectrograph, Nancay, France), and the Ondřejov radiospectrographs working in the ranges 800–2000 MHz and 2000–5000 MHz with resolutions of 0.01 s and 4.7 MHz, and 0.01 s and 11.7 MHz [16], respectively. For comparison with radio, we used X-ray and EUV observations from the FERMI [17] and SDO/AIA [18] instruments.

2.1. Data Description

On 2 April 2022, the M3.9 flare occurred in NOAA AR 2975. According to the GOES observation, its start was at 12:56 UT, its maximum was at 13:55 UT and its end was at 14:44 UT. A global overview of this flare in hard X-ray and radio observations is shown in Figure 1 and Figure 2. To see more details, in Figure 3, the 800–5000 MHz spectrum in the 13:22:50–13:25:50 UT time interval is shown. Here, we can see the positively drifting type III bursts (mostly at higher frequencies) as well as the negatively drifting type III bursts (mostly at lower frequencies). The most interesting part of the spectrum is at about 1400 MHz and about 13:25 UT, where type III bursts start to drift to higher and lower frequencies. At this bifurcation region with a frequency of about 1400 MHz, electron beams, generating type III bursts, are accelerated and propagate to lower heights with higher density (positive frequency drift) and to higher heights with a lower density (negative frequency drift). Considering the plasma emission mechanism of the type III burst generation for the emission on the fundamental frequency, the plasma density in the bifurcation (acceleration region) can be estimated as 2.4 × 10${}^{10}$ cm${}^{-3}$. On the other hand, for the emission on the harmonic frequency, this density is 6.0 × 10${}^9$ cm${}^{-3}$. All these bursts were followed in the 1000–4000 MHz range by a broadband continuum that was associated with the hard X-ray flux enhancement (see Figure 1). In the 800–5000 MHz range at times after 13:32 UT until the flare end, only a broadband continuum with decreasing radio flux was observed. On lower radio frequencies (ORFEES spectrum), the type III bursts and pulsations were recorded in the 300–800 MHz range at 13:21–13:29 UT.

2.2. Method of Radio Data Analysis

Before calculations, the Ondřejov radiospectrum data were resampled to 0.1 s temporal resolution. In our analysis, we searched for quasi-periodic variations of radio fluxes in these radio spectra. For this purpose, we used our new method as described in [19,20]. It is based on the wavelet transform (WT) [21] providing a clear detection of the time-frequency evolution of the strong radio wave patterns. The Morlet mother wavelet, consisting of a complex sine wave modulated by a Gaussian, was used to search for radio signal variability, with the non-dimensional frequency ${\omega }_0$ satisfying the admissibility condition [22]. The WT was calculated for the period range starting from 4 time steps with scales sampled as a fractional power of two with $\delta j=0.4$. Both the calculated significance of the derived WT periodicities and the cone-of-influence are taken into account as described in [19]. For analysis, the value of the significance level was set to 95%. However, for verification of results, we increased the significance level to 99%. Examples of the WT spectra, calculated using the above-mentioned mother wavelet with the specified values of the WT parameters, are shown in Figure 4 and Figure 5 with two different significance levels of 95% and 99% overplotted on the radio spectrum.

Similarly as in papers by [19,20,23], at first, we computed the histogram of the detected periods in the whole time-frequency domain of the radio spectra. Each peak in this histogram represents a group of significant periodic signals of a roughly similar period without the location of the periodic signal in the time-frequency domain of the radio spectra.

To show the temporal and frequency location of these periods, for each peak in the period histograms, we made maps of the period phases which we overplotted on the radio spectra. The phases are drawn only in these radiospectrogram time-frequency locations where the periodicities were detected at least with the specified significance. The values of the phases are displayed using their angular values (0–360${}^{\circ }$).

3. Results

Analyzing radio spectra, we found the most interesting example of the radio flux variations for the group of type III bursts at 13:22–13:27 UT in the 2000–5000 MHz range, where most of them were of the reverse type III bursts. This part of the spectrum together with the histogram of detected periods and four examples of phase maps (for 7.6–11.3, 5.2–7.5, 3.4–5.1 and 1.9–3.3 s quasi-periods given by peaks in the histogram), overplotted on the radio spectrum, are shown in Figure 4.

The histogram of periods and phase maps in Figure 4 show several quasi-periodic processes (for 7.6–11.3, 5.2–7.5, 3.4–5.1 and 1.9–3.3 s quasi-periods) around 13:24 UT, which are especially close to 3 GHz. To verify these results, we increased the significance level from 95% to 99% (Figure 5). As seen by the comparison of Figure 4 and Figure 5, the peaks in histograms and forms of phase maps are nearly the same. To see more details, we made the wavelet analysis of the radio flux at 3 GHz in the 13:22–13:27 UT time interval with the significance levels set to 95% and 99%; see Figure 6. As expected, the area specified by the significance level with 99% is smaller than the area for level 95%. Both these wavelet spectra show a broad interval of periods (0.2–∼10 s) around 13:24 UT.

At the time interval of the analyzed radio spectra, i.e., at the time of the type III bursts, AIA/SDO observations show a huge rising magnetic rope (Figure 7). Three bright features, distributed along the magnetic rope and designated in this figure as HS, indicate a helical magnetic field structure. Most of the flare EUV brightenings (B) are located near the magnetic rope footpoint. Furthermore, during the time interval with type III bursts, we observed a very unique EUV structure in the cross-section of the magnetic rope; see the structure shown by the arrow in Figure 8. This structure has a semi-circular form with four blobs located around a circle. According to our knowledge, such a structure is observed for the first time. Observations in other AIA/SDO EUV lines confirm its reality.

4. Discussion and Conclusions

According to the previous findings (e.g., [15]), the type III bursts with normal (negative) frequency drift are generated by the electron beams propagating upwards in the solar atmosphere and the reverse (positively) drifting type III bursts by beams propagating downwards. In our case, the type III bursts were generated by beams that were accelerated multi-periodically with the quasi-periods in the period ranges 7.6–11.3, 5.2–7.5 and 1.1–1.7 s.

Most of the flare AIA/SDO EUV 304 Å brightenings at the time of the analyzed type III bursts were located near the magnetic rope footpoint. Because the electron beams, generating the type III bursts, propagate along the magnetic field lines, these beams need to be accelerated and propagating inside the magnetic rope.

We interpret the found multi-periodicity of the type III bursts as follows (see also the scenario of processes in Figure 9): the magnetic rope, as shown by its helical structure, carries the electric current. The unique structure, presented in Figure 8, shows that the magnetic rope is not homogeneous in its cross-section. It is structured; it consists of sub-ropes. These sub-ropes can be a result of the rope formation before its rising or they are generated during the rising of the magnetic rope. Some sub-ropes can mutually interact. When the electric current in interacting sub-ropes is oriented in the same direction, then between them in their interaction region, the current sheet is formed. Such a current sheet can be unstable owing to the tearing mode instability [24,25]. As shown by [26,27], this instability can produce a fragmented current sheet, consisting of sub-ropes with different cross-section diameters. Some of these sub-ropes interact. As presented by [28,29], the process of interaction between two sub-rope is periodic. Its period depends on the diameter of cross-sections of the interacting sub-ropes and local Alfvén velocity. Because in our case, the interacting sub-ropes have different cross-sections, the interaction between different sub-ropes has a different period. Each sub-rope interaction periodically accelerates electron beams, and thus, the type III bursts are generated periodically. The beams generating the reverse type III bursts bombard the chromosphere and cause the EUV brightenings there.

The type III bursts analyzed here indicate that they were generated by the fragmented magnetic reconnection inside the rising and unstable magnetic rope. It means that this flare deviates from the standard CSHKP flare model, where the main magnetic reconnection is located below the rising magnetic rope and reconnection processes inside the magnetic rope are not considered. On the other hand, it does not mean that energy release processes according to the standard flare model do not work in later phases of this flare. In future works, it would be interesting to compare the released energy in the rising magnetic rope with that released in the whole flare.

Remark 1. 

From a global point of view, the magnetic rope can be considered as half of the toroidal plasma in laboratory systems. Although phenomena in both cases cannot be directly compared, owing to different conditions, the processes such as magnetic islands, local 2D magnetic reconnection and particle acceleration found in the unstable toroidal plasma support our interpretation; see Figure 9, 11, 18–22 and chapter 4.5 in [30].