Slowly drifting radio fibres

ABSTRACT

The fine structure in the continuum radiation of type IV solar radio bursts is very rich in various structures (zebra structure, fibres, pulsations, spikes, etc.). So far, however, no attention has been paid to the isolated fibres that occasionally appear in the metre and decimetre ranges. Here we give and discuss examples of the dynamic spectra of such bursts obtained many years ago (in the metre waveband from 1969) as well in recent years (in the decimetre and microwave wavebands from 2003–2013). Isolated fibres are observed mostly in the decimetre range (although there are examples in both the metre and microwave ranges), and they reveal a number of features of classical fibre bursts. As a generation mechanism for such fibres, the process of interaction of whistlers with Langmuir plasmons was suggested. An analysis of conditions for the realization of this process in solar magnetic arch structures and its efficiency was carried out. Estimates of the intensity of low-frequency turbulence (whistlers) and magnetic field strength in the solar corona were obtained using the data of radio fibres.

1 INTRODUCTION

Observations with radio spectrographs in the metre and decimetre ranges began many decades ago (Wild, Smerd & Weiss 1963). Many characteristics of solar radio bursts were obtained, including their fine structure, after the publications of Boischot, Haddock and Maxwell (1960) and Elgarøy (1959). With the development of spectral observations of the continuum emission of type IV radio bursts, broadband pulsations of different periods, the fastest spike-type bursts, and the most mysterious periodic bands in emission and absorption − zebra structure and fibres − in the form of bursts or bursts with intermediate frequency drift were discovered. The development of solar radio astronomy is described in several large monographs, namely Kundu (1965), Zheleznyakov (1964, 1970), and Krüger (1979).

Theoretical models of the origin of the fine structure of type IV continuum radio bursts (zebra structure, fibres, pulsations, spikes, etc.) have been developing for more than 50 years (Chernov 2006, 2011). For zebra structure, the model of double plasma resonance is discussed most often (although a dozen alternative models have been proposed) and for fibres the model of whistlers, although the latter immediately combined an explanation of both zebra stripes (with a variety of frequency drifts) and fibres (usually with a constant negative frequency drift), on the grounds that observations sometimes showed a continuous transition from the spectrum of zebra stripes to fibres and back (Chernov, Korolev & Markeev 1975; Chernov 1976). At the same time, it was scarcely noticed at the beginning that sometimes, instead of numerous zebra stripes or fibres, isolated stripes appeared. Since they were more often observed in events where there were also numerous stripes, this suggested that the models used should allow the formation of unusual isolated fibres as well. All this was considered in the metre wavelength range.

The first spectra of strange isolated slowly drifting fibres in the metre range were shown in Boischot, Haddock and Maxwell (1960) even before the first publication of Elgarøy (1959) about zebra structure. The authors called the unusual intertwined stripes in the event of 1957 November 4 ‘spaghetti’, although no one would doubt now that it was a zebra structure, noting a singularity: the stripes were not regular in frequency but intertwined with each other, and lasted about 4 minutes in the narrow frequency band 160–175 MHz. After about 50 minutes there were single bands, lasting more than a minute with a fluctuating frequency drift, but almost parallel to the time axis. Moreover, the solar origin of the stripes had already been confirmed, as their spectra were identical in two observatories separated by 2000 km.

We are observing the fine structure of solar radio bursts already in the sixth cycle of solar activity (see https://www.izmiran.ru/stp/lars/). In the top ten works, the spectra obtained in remote observatories were compared, and they always coincided in frequency and time, which confirms the solar nature of bursts (Chernov 2011).

Slowly drifting fibres had already been recorded in the first observations with the IZMIRAN high-resolution spectrograph in the range 190–220 MHz in 1969 (see fig. 3 in Markeev and Chernov (1971) and fig. 1 in Chernov (1974); see also the Solar Radio Laboratory (LaRS) website¹ and Gorgutsa et al. (2001)). These first reports show such bursts were observed in groups of fast spike-type bursts during noise storms. The frequency drift of the fibres was on average about 30 MHz s⁻¹ through the entire range 190–220 MHz, although ordinary spikes usually show no frequency drift and occupy a narrow frequency band of 1–10 MHz. In this work, these bursts are referred to as slow drift spikes. In contrast to type III bursts, particle beams must have a non-monotonic distribution of particle velocity (with increasing velocity to the tail of the beam), which neutralizes fast frequency drift. The first report of such bursts was in a work by Markeev and Chernov (1971).

Further, in several events we observed unusual long fibres (0.5–2 min) that were non-drifting (almost parallel to the time axis), which are close in parameters to the fibres in Boischot, Haddock and Maxwell (1960). Here, we show in Fig 1 a remarkable example of such fibres from IZMIRAN's archive of spectra of 1981 October 12. This phenomenon has been discussed in various aspects in the works of Aurass and Chernov (1983) and Chernov (1997).

A large radio burst in a wide band was associated with a large Hα flare of magnitude 3B with coordinates S15, E09. Fibres appeared at the very beginning of the phenomenon at 06:26 ut, with the maximum radio burst in the metre band (3000 s.f.u. at 204 MHz) occurring 7 min earlier than the maximum in the microwave band (about 2300 s.f.u. at 3000 MHz), i.e. the flare energy release began high in the corona. In the descending phase of the burst, the fibres were accompanied by a zebra structure (Fig. 1) for ∼15 minutes in the metre range (Aurass and Chernov 1983).

Subsequently, suggestions have been made to use just strange isolated fibres as important signs of other connections. For example, in the events of 1981 October 12 (fig. 3 in Aurass and Chernov, 1983) and 1983 February 3 (fig. 12 in Bakunin et al. 1991), the unusual long (0.5–2 min), almost non-drifting, solitary fibres at the maximum phase of radio bursts in the metre range are recognized as signs of fast coronal mass ejections (CMEs) in large events. Analysis of the 3.02.1983 event in Bakunin et al. (1991) showed that the radio emission of fibres was associated with the capture of a whistler packet between the shock front and tangential rupture before the reverse shock wave.

With the development of radio spectral observations at decimetre and microwave wavelengths, it became clear that slowly drifting fibres were observed there as well.

2 NEW OBSERVATIONS

New observations do not necessarily correspond to the most recent by date. Basically, they include the registration of similar slow-drifting fibres observed in the last 20 years, but barely discussed in publications. Most of these bursts have been observed in the decimetre band, thanks to observations at station Huairou (National Astronomical Observatories of China (NAOC): Fu et al. 2004).

One of the most evident examples of strange slow-drifting fibres is the event on 2004 November 30 (Fig. 2), associated with a small C5 (GOES X ray) outburst.

The maximum radio emission was in the decimetre band (100 s.f.u. at 1415 MHz, where 1 solar flux unit = 10⁻²² W m⁻²Hz⁻¹). The flare of C4.8 (GOES 1–8 Å) occurred in the active region (AR) of NOAA 10708 (N09 E33) between 06:32 and 07:22 ut.²

The SXR (GOES) and 1415-MHz radio burst maxima coincided in time at around 06:58 ut. A small-intensity radio burst turned out to be rich in fine structure in the decimetre range 1–2 GHz. Almost from the beginning of the phenomenon, fibre bursts were observed, especially after 06:38 ut. Then a zebra structure, mainly in the cloud of spike bursts, and, after 06:46 ut, groups of fibres with different frequency drift and emission bandwidths dominated. Occasionally, fibres consisting of spike-like bursts appeared, all the way up to our fibre at 06:59:52 ut. Such a complex set of almost simultaneous fine structures is difficult to analyse, so let us first consider our individual isolated fibre.

This is an isolated fibre in a low continuum with sawtooth changes of frequency drift in the range 1.34–1.1 GHz for 2.5 s, at some moments similar to a fibre burst (but without obvious absorption from the low-frequency (LF) edge), and without zebra elements in the immediate surroundings. The origin of such a fibre remains unknown, although sawtooth drift is often observed in zebra stripes. The radiation is strongly polarized, and one can only observe that the fibre appeared to be some sort of high-frequency (HF) boundary of a weak continuum. All of the signs noted do not give clear preference to any model of zebra formation or fibre bursts. The latter also appear in groups and with a constant drift, most often to low frequencies.

Another unknown fibre in the same range was obtained on 2003 October 26 (Fig. 3), but in the course of a powerful X1.2 (GOES) in AR 10486 (S15 E31) flare and a large type II + IV radio burst with a maximum in the decimetre range of 650 000 s.f.u. at 606 MHz.³

About 20 short zebra-structure series and fibre bursts against a background of fast decimetre pulsations were observed in the range 1–2 GHz during more than 2 hours (06:13–08:40 ut). The parameters of the fine structure changed in a complex way. In the beginning, the emission was almost unpolarized, which is unusual for the decimetre range. The main property of the zebra stripes was that they drifted rapidly in frequency and changed sign when crossing regions with pulsations. After about 06:25 ut, however, the polarization became strong right-hand, indicating the dynamics of the radio sources.

An isolated fibre changes its direction of frequency drift sharply twice in 1.9 s in the range 1.1–1.214 MHz. There are no zebra stripes in the nearest spectrum bands and at the beginning and end of the fibre it is more like a fibre burst, only with the opposite frequency drift and no absorption from the LF edge of the fibre. This appeared at the time of the X-ray burst maximum and on a growing high type IV continuum, so it can be assumed that the source may have been magnetically trapped, but the absence of zebra and fibre bursts at this time complicates the choice of an unambiguous emission mechanism. The general appearance of fibres is more characteristic of fibre bursts, but with the source trapped between the leading-edge fronts of the CME and the shock wave.

Another example of an isolated fibre in the decimetre range is shown in Fig. 4.

This isolated fibre with a constant positive drift reveals that absorption from the LF edge can almost definitely be considered as fibre-burst type.

The event was rather complicated: after a moderate flare of M1.1 in the western region 10786, N11 W82, the continuum burst in the decimetre band lasted almost 2 hours. None of the observers recorded the II + IV burst, although there was rich fine structure in the decimetre continuum: zebra, pulsations, fibres, spikes.⁴

Moreover, our fibre appeared at the end of another continuum burst (Fig. 5).

One minute before our burst, almost the same fibre was observed, but against a background of fast pulsations in emission and absorption, with the fibre reacting only to absorption (dips in the intensity profile shown above the spectrum in Fig. 6). Further, for almost 20 minutes, spikes appeared in the background of fast pulsations, zebra structure, and fibres (fibre bursts).

In the microwave range, slow-drifting fibres have also been observed, mostly during large radio bursts (Figs 7 and 8). One may also note the isolated fibre in fig. 3 in Fomichev & Chernov (2020) observed during a large radio burst on 2003 November 18, at 08:25:12–08:25:15 ut. It looks identical to the spectra from two observatories separated by nearly 7000 km, confirming the solar nature of the event, although all three cases can be recognized as off-spurs of a zebra structure with one or two stripes.

3 DISCUSSION

3.1 Mechanism of generation of the fibre bursts

Isolated slow-drifting fibres have been observed mainly in the decimetre range, although there are examples in both the metre and microwave ranges. They exhibit a number of features of classic fibre bursts. However, they are isolated, whereas fibre bursts tend to appear in large groups, which are naturally associated with the whistler model, the excitation of which is characterized by periodicity and related both to non-linear instability processes (whistler scattering on fast particles, interaction with ion–sonic waves) and the bounce period of the particle beam trapped in the magnetic trap (Chernov 2006). The frequency drift differs sharply from that of a fibre burst: sometimes it is almost absent (long fibres in the metre range, noted in the Introduction) or has a sawtooth character (Fig. 3).

All the slow-drifting bursts (examples of dynamic spectra of some bursts are shown above) have been observed within the background of wide-band continua named as type IV radio bursts.

Sources of this continuum radio emission are coronal magnetic loops in the solar atmosphere (Stepanov and Zaitsev 2018). In such magnetic arc structures, loss-cone distributions of fast electrons superimposed upon a thermal background are formed, which are unstable for plasma waves (ω_l, k_l) and whistlers (ω_w, k_w). A coupling process of whistlers with plasma waves (ω + l → t) can lead to generation of electromagnetic (t) waves, in our case radio fibres. Such a mechanism was used to explain the generation of fibres with intermediate drift (Kuipers 1975); later an analysis of the conditions for realization of this process and its efficiency in the solar corona was given in Fomichev and Fainshtein (1988). As is well known, the conditions of spatio-temporal synchronization (or the conservation laws for energy and moment) must be satisfied in such an interaction:

The frequencies and wave numbers appearing in these relations must satisfy the dispersion relations for the corresponding branch of oscillations in a plasma:

Here V_Те = (k_BT/m_e)^1/2is the electron thermal velocity, k_B is the Boltzmann constant, ω_H = еН/m_eсis the electron gyrofrequency, ω_L = (4πe²N/m_e)^1/2 is the electron Langmuir frequency, N is the electron density, and His the constant magnetic field strength.

Equation (4) is written for the case of longitudinal propagation of a whistler and ω_w<< ω_H. The basis for such an assumption is the fact that, for frequencies close to ω_H, resonant cyclotron absorption at the fundamental resonance frequency (ω ≈ ω_H) becomes important. According to Ginzburg (1967), the half-width of the resonance line ∆ω/ω = √2V_Теn/с (n = ω_L/(ω ω_H)^½ >> 1 is the index of refraction for whistlers. For ω_H/ω_L ∼ 0.1, V_Те/с ∼ 1.5 ×10⁻² (T ≈ 10⁶ К), we obtain ∆ω/ω ∼ 02–0.4. Numerical calculations of the cyclotron absorption coefficient in coronal plasma have also shown that whistlers are strongly damped at frequencies ω > ω_H/2.

For ω_l≈ ω_L, ω_t ≥ ω_L,and ω_L >> ω_H, the case of interest for us, and also using the relation k²_t = k_l² + k_w² + 2k_l·k_w·cos θ (where θ is the angle between the directions of propagation of the whistler and the plasmon) that follows from k_l+ k_w= k_t,we can obtain from equations (1)–(4) the frequencies and wave numbers of interacting waves. For the conditions in the sources of type IV bursts, we obtain k_l ≈ k_w and k_l ≈ −k_w, i.e. plasmons and whistlers with approximately equal and oppositely directed wave vectors take part in the interaction. Also, we can obtain the estimates for the frequencies and the wave numbers of interacting waves:

It should be noted that all the conclusions and estimates given above are under the assumption that HF electromagnetic waves are the ordinary mode. Analysis for extraordinary modes showed that the synchronization conditions (1) are not satisfied for any values of k_l/k_w and ω_H/ω_L, and hence the generation of an extraordinary wave through the interaction of plasma waves and whistlers is impossible. Therefore, the polarization of the radio emission in this case will correspond to the ordinary wave, which agrees with observations.

In the frames of this model, the generation of whistlers occurs in the low part of the coronal magnetic loop, and, on propagating towards higher levels of the solar atmosphere with decreasing magnetic fields, whistlers will approach and reach levels where strong resonance cyclotron absorption takes place because of an increase in the parameter ω_w/ω_H. This effect can explain the rarer registration of such fibres in the metre-wave range in comparison with the decimetre-wave range.

3.2 Estimates of the parameters of the radio sources

Let us use the relations obtained above to estimate the parameters of the sources of type IV radio bursts. First of all, let us estimate one important parameter, the turbulence level of whistlers in the source. To do so, we use the data on the observed radio flux S and the brightness temperature T_eff of the emission in fibres. For frequency f ≈ 0.3 GHz, the observed values of S ≈ 10²–10³ W m⁻² Hz⁻¹ correspond to T_eff << 10¹⁴ K. The brightness temperature T_eff of the emission is determined by the formula

where W_k= W_t/∆k_t is spectral energy density. Substituting the expressions for k_t= (ω_L/с)·(2ω_w/ω_L)^1/2 and ∆k_t= (ω_L/с)·(ω_w/2ω_L)^1/2 here and adopting the values ω_w/ω_H = 0.25, ω_Н/ω_L = 0.1, we obtain W_t≈ 10⁻⁹erg сm⁻³. Then, taking a value of W_l= 10⁻⁵–10⁻⁶ erg cm⁻³ for the level of plasma turbulence in the sources of type IV bursts (Stepanov 1973), we obtain the result W_w= 2 × 10⁻¹⁰ erg cm⁻³ for the level of low-frequency turbulence of whistler type in a coronal arch.

Another important parameter that can be estimated from the characteristics of filamentary bursts is the magnetic field H. To find the magnetic field, we use the value of the frequency drift of bursts, which within the framework of our model is determined by the group velocity of propagation of whistlers, and we can write

where L_N= N(dN/dr)⁻¹ is the scale of electron density inhomogeneity in the solar corona. On the other hand, from equations (1)–(4) it follows that ∆ω_t= ∆ω_l+ ∆ω_w, ∆ω_l= ½·β_T²·ω_L/ω_H·∆ω_w, and ∆ω_t ≈ ∆ω_l. On this basis we may adopt the emission and absorption bandwidth frequencies as approximately equal, and write

where ∆f_b is the observed frequency bandwidth of brightening. Using the data on the frequency drift df/dt and ∆f_b (Elgaroy 1982; Chernov 2011) as well the model of the height distribution of electron density in the corona, we can obtain estimates of the magnetic field in the emission source from equations (7) and (8). Thus, using the doubled model of Newkirk for the density distribution, usual for the metre range, and values df/dt = 7.4 МHz s⁻¹, ∆f_b= 2.1 MHz for a source at frequency f = 300 МHz, we obtain the estimate H ≈ 5 G, and for a source at frequency f = 150 МHz with df/dt = 3.1 МHz s⁻¹, ∆f_b = 11 MHz, we obtain H ≈ 1.4 G.

The Newkirk model predicts a variation of electron density, Ne, with distance, r, from the centre of the Sun, which has the form

where |$\mathrm{ R}_\odot $| is the solar radius (Newkirk 1961).

Other peculiarities of the dynamic spectra of radio fibres (low frequency drift, irregular changes of frequency drift, including changes of sign of drift, etc.) may be connected with features of non-linear processes involved in the generation of whistlers and their interaction with fast electrons in arch-like magnetic structures in the solar atmosphere.

An isolated fibre means no bounce period and non-linear processes cause only a sawtooth-like nature of frequency drift. In principle, both of these cases are perfectly acceptable – for example, in open magnetic field configurations. Interactions with fast particles are still possible, at least once. Multiple new injections of fast particles, leading to a change in the whistler instability from normal to anomalous resonance, are also possible (Chernov 1990, 1996). The latter process causes an abrupt change in the direction of the whistler group velocity, which determines the frequency drift, which explains the sawtooth character of the fibre. However, in the fibre in Fig. 6 the background pulsation is surprising in the absence of a sawtooth frequency drift, although new beams of fast particles clearly occurred, according to the pulsation model in emission and absorption.

The absence of fibre frequency drift in the metre range can probably be explained by the advance of the whistler wave packet almost across the plasma frequency gradient (along the plasma levels). In addition, there is still the effect of some compensation of the whistler group velocity when its direction is changed. In this case, a wave-like frequency drift should appear instead. When the whistler instability switches from a normal Doppler effect to an anomalous one, the whistler group velocity reverses (Chernov 1996). If this process is slowed down (e.g. by additional particle injection), the fibres can remain almost parallel to the time axis on the spectrum.

4 CONCLUSIONS

The isolated radio fibre bursts observed mainly in the decimetre range and considered in this work display a number of features of classical fibre bursts. The process of interaction of whistlers with Langmuir plasmons was suggested as a mechanism of generation for such radio fibres. Analysis of the conditions for realization of this process in coronal magnetic arch structures, with formation of a distribution function of fast electrons of loss-cone type, and its efficiency was carried out. Unusual peculiarities of the dynamic spectra of such fibres (irregular frequency drift including a change of sign of frequency drift, etc.) can be connected with features of the non-linear processes involved in the generation of whistlers and their interaction with fast electrons in arch-like magnetic structures in the solar atmosphere. Estimates of the intensity of low-frequency turbulence of whistler type and magnetic field strength in sources of radio emission were obtained from data on radio fibres.

ACKNOWLEDGEMENTS

The authors are grateful to Chinese colleagues for the kindly opportunity to work with the radio spectral data of the Huairou Station of the National Astronomical Observatory of China (NAOC) in the frames of grant No. 2011T1J20. The authors are grateful to the RHESSI, GOES, and LASCO teams for open access to their data and also the reviewers for their remarks and comments. This work was also supported by the Ministry of Education and Science Project KP19-270.

DATA AVAILABILITY

The dynamic spectra given in Figs 2–8 were produced by one of the authors (GPCh) and now they are part of his own archive. The data underlying this article are available on request to the corresponding author (GPCh).

Conflict of Interest

We have not any conflict of interest.

Footnotes

References