Double Plasma Resonance Model Research Articles

Simulations of solar radio zebras

Context.Solar radio zebras are used in diagnostics of solar flare plasmas and it is of great importance to construct accurate models to correctly characterize them.Aims.We simulated two zebras to verify their double-plasma resonance (DPR) model.Methods.In our zebra simulations, we used the DPR model in an expanding and compressing part of the loop as well as with the wave propagating along the loop.Results.Using the DPR model in such a loop, we successfully simulated zebras from the 1 August 2010 and 21 June 2011 flares. We found that increasing the density or decreasing the magnetic field in the part of the loop, where zebra-stripe sources are located, the zebra stripes are shifted to higher frequencies and vice versa. In the case of the 21 June 2011 flare, we confirm that small deviations of zebra-stripe frequencies from their mean values can be explained by waves propagating along the loop. We also confirm high values for the gyro-harmonic number of zebra stripes. We explain an inconsistency in the wave velocities derived from the plasma parameters and from the frequency drift in combination with the density model of the solar atmosphere. Finally, we discuss the high values of the gyro-harmonic number found in the studied zebras.

Alternative Models of Zebra Patterns in the Event on June 21, 2011

The analysis of the spectral characteristics of the burst radio emission on June 21, 2011 was carried out on the basis of an improved methodology for determining harmonic numbers for the corresponding stripes of the zebra structure. By using the parameters of the zebra structure in the time-frequency spectrum and basing on the double-plasma resonance model, the magnetic field and its dynamics, electron density, and the time variation of the distance between the stripes with harmonics \(s = 55\) and 56 and adjacent stripes near the frequency ≈183 MHz have been determined in the burst generation region. The relationships between the scale characteristics of the field and the density along and across the axis of the power tube and their dependence on time have been also determined. The field obtained (1.5 G for the first harmonic and 0.75 G for the second harmonic of the plasma frequency) turned out to be so small that, firstly, it fails to explain the dynamic features of the spectrum based on MHD waves, and secondly, it results in large values for plasma beta (>1). Other possible difficulties of the generation mechanism of bursts with zebra pattern based on the double-plasma resonance are also noted. Another possible mechanism, with whistlers, explains qualitatively the main observational characteristics of this zebra. The magnetic field required in this case is about 4.5 G, and the plasma beta is 0.14, which fully corresponds to the coronal conditions.

Zebra-stripe sources in the double-plasma resonance model of solar radio zebras

Context. Radio bursts with fine structures are used in diagnostics of solar flare plasmas, of which zebra structures are the most important. However, there is still a debate about their origin.Aims. The most probable model of zebras is that based on double-plasma resonance (DPR) instability. The paper wants to contribute to a verification of this model.Methods. We used analytical methods.Results. We studied the DPR model in two scenarios: a model with the zebra-stripe sources in a single loop and a model with the zebra-stripe sources moving through a fan of magnetic field lines. In the first case, we found several new relations among the parameters of zebra stripes and their sources, which can be used to analyze observed zebras and thus to verify if the zebra is generated according to the DPR model. These relations were derived for the zebra-stripe sources distributed along the loop and also for those having some extent in the loop radius. In the scenario with the moving zebra-stripe sources, we determined the parameters of the 14 December 2006 zebra and estimated a change of the ratio of magnetic field and density scales causing the change of zebra-stripe frequencies. In this case we found that this zebra can be also explained in the model with the zebra-stripe sources in a single loop. Both the interpretations are discussed.

Detection of Propagating Fast Sausage Waves through Detailed Analysis of a Zebra-pattern Fine Structure in a Solar Radio Burst

Abstract Various magnetohydrodynamic (MHD) waves have recently been detected in the solar corona and investigated intensively in the context of coronal heating and coronal seismology. In this Letter, we report the first detection of short-period propagating fast sausage mode waves in a metric radio spectral fine structure observed with the Assembly of Metric-band Aperture Telescope and Real-time Analysis System. Analysis of Zebra patterns (ZPs) in a type-IV burst revealed a quasi-periodic modulation in the frequency separation between the adjacent stripes of the ZPs (Δf ). The observed quasi-periodic modulation had a period of 1–2 s and exhibited a characteristic negative frequency drift with a rate of 3–8 MHz s−1. Based on the double plasma resonance model, the most accepted generation model of ZPs, the observed quasi-periodic modulation of the ZP can be interpreted in terms of fast sausage mode waves propagating upward at phase speeds of 3000–8000 km s−1. These results provide us with new insights for probing the fine structure of coronal loops.

Brightness Temperature of Radio Zebras and Wave Energy Densities in Their Sources

We estimated the brightness temperature of radio zebras (zebra pattern -- ZP), considering that ZPs are generated in loops having an exponential density profile in their cross-section. We took into account that when in plasma there is a source emitting in all directions, then in the escape process from the plasma the emission obtains a directional character nearly perpendicular to the constant-density profile. Owing to the high directivity of the plasma emission the region from which the emission escapes can be very small. We estimated the brightness temperature of three observed ZPs for two values of the density scale height (1 and 0.21 Mm) and two values of the loop width (1 and 2 arcsec). In all cases high brightness temperatures were obtained. For the higher value of the density scale height, the brightness temperature was estimated as 1.1 $\times$ 10$^{15}$ - 1.3 $\times$ 10$^{17}$ K, and for the lower value as 4.7 $\times$ 10$^{13}$ - 5.6 $\times$ 10$^{15}$ K. We also computed the saturation energy density of the upper-hybrid waves (which according to the double plasma resonance model are generated in the zebra source) using a 3D particle-in-cell model with the loss-cone type of distribution of hot electrons. We found that this saturated energy is proportional to the ratio of hot electron and background plasma densities. Thus, comparing the growth rate and collisional damping of the upper-hybrid waves, we estimated minimal densities of hot electrons as well as the minimal value of the saturation energy density of the upper-hybrid waves. Finally, we compared the computed energy density of the upper-hybrid waves with the energy density of the electromagnetic waves in the zebra source and thus estimated the efficiency of the wave transformation.

Determination of plasma parameters in solar zebra radio sources

Aims. We present a new method for determining the magnetic field strength and plasma density in the solar zebra radio sources. Methods. Using the double plasma resonance (DPR) model of the zebra emission, we analytically derived the equations for computing the gyroharmonic number s of selected zebra lines and then solved these equations numerically. Results. The method was successfully tested on artificially generated zebras and then applied to observed ones. The magnetic field strength and plasma density in the radio sources were determined. Simultaneously, we evaluated the parameter Lnb = 2Lb/(2Ln − Lb), where Ln and Lb are the characteristic scale-heights of the plasma density and magnetic field strength in the zebra source, respectively. Computations show that the maximum frequency of the low-polarized zebras is about 8 GHz, in very good agreement with observations. For the high-polarized zebras, this limit is about four times lower. Microwave zebras are preferentially generated in the regions with steep gradients of the plasma density, such as in the transition region. In models with smaller density gradients, such as those with a barometric density profile, the microwave zebras cannot be produced owing to the strong bremsstrahlung and cyclotron absorptions. We also show that our DPR model is able to explain the zebras with frequency-equidistant zebra lines.

The importance of source positions during radio fine structure observations

The measurement of positions and sizes of radio sources in the observations of the fine structure of solar radio bursts is a determining factor for the selection of the radio emission mechanism. The identical parameters describing the radio sources for zebra structures (ZSs) and fiber bursts confirm there is a common mechanism for both structures. It is very important to measure the size of the source in the corona to determine if it is distributed along the height or if it is point-like. In both models of ZSs (the double plasma resonance (DPR) and the whistler model) the source must be distributed along the height, but by contrast to the stationary source in the DPR model, in the whistler model the source should be moving. Moreover, the direction of the space drift of the radio source must correlate with the frequency drift of stripes in the dynamic spectrum. Some models of ZSs require a local source, for example, the models based on the Bernstein modes, or on explosive instability. The selection of the radio emission mechanism for fast broadband pulsations with millisecond duration also depends on the parameters of their radio sources.

STATISTICS AND CLASSIFICATION OF THE MICROWAVE ZEBRA PATTERNS ASSOCIATED WITH SOLAR FLARES

The microwave zebra pattern (ZP) is the most interesting, intriguing, and complex spectral structure frequently observed in solar flares. A comprehensive statistical study will certainly help us to understand the formation mechanism, which is not exactly clear now. This work presents a comprehensive statistical analysis on a big sample with 202 ZP events collected from observations at the Chinese Solar Broadband Radio Spectrometer at Huairou and the Ondrejov Radiospectrograph in Czech Republic at frequencies of 1.00 - 7.60 GHz during 2000 - 2013. After investigating the parameter properties of ZPs, such as the occurrence in flare phase, frequency range, polarization degree, duration, etc., we find that the variation of zebra stripe frequency separation with respect to frequency is the best indicator for a physical classification of ZPs. Microwave ZPs can be classified into 3 types: equidistant ZP, variable-distant ZP, and growing-distant ZP, possibly corresponding to mechanisms of Bernstein wave model, whistler wave model, and double plasma resonance model, respectively. This statistical classification may help us to clarify the controversies between the existing various theoretical models, and understand the physical processes in the source regions.

MICROWAVE BURSTS WITH FINE STRUCTURES IN THE DECAY PHASE OF A SOLAR FLARE

This paper presents the microwave bursts with fine structures (FSs) at 1.10-1.34 GHz in the decay phase of a solar flare observed by the Chinese Solar Broadband Radio Spectrometer in Huairou, which show a peak-to-peak correlation with 25-50 keV hard X-ray (HXR) bursts observed by RHESSI. In the microwave spectra, we have identified stripe-like bursts such as lace bursts, fiber structures, zebra patterns (ZPs), and quasi-periodic pulsations. We also have detected short narrowband bursts such as dots, type III, and spikes. The lace bursts had rarely been reported, but in this event they are observed to occur frequently in the decay phase of the flare. The similarity between 25 and 50 keV HXR light curve and microwave time profiles at 1.10-1.34 GHz suggests that these microwave FSs are related to the properties of electron acceleration. The electron velocity inferred from the frequency drift rates in short narrowband bursts is in the range of 0.13c-0.53c and the corresponding energy is about 10-85 keV, which is close to the energy of HXR-emitting electrons. From the Alfven soliton model of fiber structures, the double plasma resonance model of ZPs, and the Bernstein model of the lace bursts, we derived a similar magnetic fieldmore » strength in the range of 60-70 G. Additionally, the physical conditions of the source regions such as height, width, and velocity are estimated.« less

MICROWAVE ZEBRA PATTERN STRUCTURES IN THE X2.2 SOLAR FLARE ON 2011 FEBRUARY 15

Zebra pattern structure (ZP) is the most intriguing fine structure on the dynamic spectrograph of solar microwave burst. On 15 February 2011, there erupts an X2.2 flare event on the solar disk, it is the first X-class flare since the solar Schwabe cycle 24. It is interesting that there are several microwave ZPs observed by the Chinese Solar Broadband Radiospectrometer (SBRS/Huairou) at frequency of 6.40 ~ 7.00 GHz (ZP1), 2.60 ~ 2.75 GHz (ZP2), and the Yunnan Solar Broadband Radio Spectrometer (SBRS/Yunnan) at frequency of 1.04 ~ 1.13 GHz (ZP3). The most important phenomena is the unusual high-frequency ZP structure (ZP1, up to 7.00 GHz) occurred in the early rising phase of the flare, and there are two ZP structure (ZP2, ZP3) with relative low frequencies occurred in the decay phase of the flare. By scrutinizing the current prevalent theoretical models of ZP structure generations, and comparing their estimated magnetic field strengths in the corresponding source regions, we suggest that the double plasma resonance model should be the most possible one for explaining the formation of microwave ZPs, which may derive the magnetic field strengths as about 230 - 345 G, 126 - 147 G, and 23 - 26 G in the source regions of ZP1, ZP2, and ZP3, respectively.

Recent results of zebra patterns in solar radio bursts

This review covers the most recent experimental results and theoretical research on zebra patterns (ZPs) in solar radio bursts. The basic attention is given to events with new peculiar elements of zebra patterns received over the last few years. All new properties are considered in light of both what was known earlier and new theoretical models. Large-scale ZPs consisting of small-scale fiber bursts could be explained by simultaneous inclusion of two mechanisms when whistler waves “highlight" the levels of double plasma resonance (DPR). A unique fine structure was observed in the event on 2006 December 13: spikes in absorption formed dark ZP stripes against the absorptive type III-like bursts. The spikes in absorption can appear in accordance with well known mechanisms of absorptive bursts. The additional injection of fast particles filled the loss-cone (breaking the loss-cone distribution), and the generation of the continuum was quenched at these moments. The maximum absorptive effect occurs at the DPR levels. The parameters of millisecond spikes are determined by small dimensions of the particle beams and local scale heights in the radio source. Thus, the DPR model helps to understand several aspects of unusual elements of ZPs. However, the simultaneous existence of several tens of the DPR levels in the corona is impossible for any realistic profile of the plasma density and magnetic field. Three new theories of ZPs are examined. The formation of eigenmodes of transparency and opacity during the propagation of radio waves through regular coronal inhomogeneities is the most natural and promising mechanism. Two other models (nonlinear periodic space – charge waves and scattering of fast protons on ion-sound harmonics) could happen in large radio bursts.

On the Origin of the Zebra Pattern with Pulsating Superfine Structures on 21 April 2002

Through the data around 3 GHz from the Radio Spectrometer in Huairou, Beijing, zebra-pattern structures from the 21 April 2002 event have been studied. Zebra stripes consist of periodically pulsating superfine structures in this event. An analysis of temporal profiles of intensities at multiple frequency channels shows that the Gaussian temporal profiles of pulse groups on zebra stripes are caused by drifting zebra stripes with Gaussian spectral profiles. The observed quasiperiodic pulsations with about 30 ms period have a peculiar feature of oscillation near a steady state, probably resulting from relaxation oscillations, which modulate the electron cyclotron maser emission that forms the zebra stripes during the process of wave – particle interactions. All the main properties of the zebra stripes with pulsating superfine structures indicate that the double plasma resonance model might be the most suitable one, with the relaxation oscillations, to form the superfine structures. The model of LaBelle et al. (Astrophys. J.593, 1195, 2003) could not account for the observed properties of zebra-pattern structures in this event nor for most zebra-pattern structures occupying a wide frequency range, mainly because the allowable frequency range of the zebra-pattern structures in their model is too narrow to reproduce the observed zebras.

Recent data on zebra patterns

A comparative analysis of two recent solar radio outbursts around 3 GHz with zebra structures and fiber bursts in their dynamical radio spectra is carried out using all available ground-based and satellite data (SOHO, TRACE, RHESSI). The latest theoretical models of the zebra pattern are critically discussed . New data on microwave zebra structures and fiber bursts suggests that they are analogous to similar structures observed at meter wavelengths. It was discovered that in the 2,6-3,8 GHz frequency band more than 34 zebra stripes can appear simultaneously, and some isolated fiber bursts can continuously be transformed into zebra stripes. This fact indicates a single origin for both structures. The zebra pattern was observed when the signs of magnetic reconnections were revealed in images of 195 ˚ lines, and radio sources coincided with positions of some new sources in hard X-rays. All the main properties of the stripes in emission and absorption can be explained if they are associated with interactions between electrostatic plasma waves and whistlers, taking into account the quasi-linear diusion of fast particles with the loss-cone distribution on whistlers. In this model it is possible to obtain realistic values for the magnetic field strength of B … 160G at the plasma level of about 3 GHz. The double plasma resonance model for the zebra pattern based on the known realistic dependences of electron density and magnetic field yields a frequency dependence for the frequency separation between stripes that does not agree with the observations.

Manifestation of quasilinear diffusion on whistlers in the fine-structure radio sources of solar radio bursts

The zebra structure and fiber bursts in the dynamic spectra of the solar type IV radio burst recorded on October 25, 1994, are analyzed using observational data from ground-based stations and Earth-orbiting satellites. The fine structure is observed when new hot magnetic loops, in which high-and low-frequency plasma instabilities develop, ascend to the solar corona. The frequency range of the fine structure is determined by the dimensions of these loops. The main features of the zebra structure are analyzed in terms of the interaction of plasma waves with whistlers. The results obtained are compared to the predictions from the double plasma resonance model.

Solar type IV burst spectral fine structures

We discuss a source model for the origin of solar type IV burst fine structures (FS) using the data of an event in AR 7792 on 25 October 1994. After giving a comprehensive observational treatment of FS (Paper I), here we repeat the main observed facts to construct a simplified radio source model. It consists of two interacting loops (named LS1 and EL) with one spatial order of magnitude scale difference (turning heights 70 and 7 Mm). We consider the implications of this model for physical mechanisms of broad band pulsations (BBP) and zebra patterns (ZP). Our analysis leads to the conclusion that meter wave BBP and ZP originate from a common magnetic source structure – a large asymmetric coronal loop. It is shown that the BBP result from periodically repeated injections of fast electrons into the asymmetric magnetic trap. The excitation of plasma waves is due to the stream instability when these electrons are propagating along the loop. We demonstrate that a two percent quasi-periodic modulation of a magnetic field component in EL is sufficient for it to act as a periodic electron accelerator. The ZP is due to a plasma wave instability at the levels of double plasma resonance (DPR) in an inhomogeneous source distributed along the loop axis of LS1. The DPR frequencies appear at those height levels where the upper hybrid frequency is equal to a harmonic of the gyrofrequency. Two Appendices review theoretical details needed to understand the given ZP interpretation. The gyrofrequency as a function of height was derived from a force-free extrapolated field line that passes the coronal radio source. After knowing the loop turning height and the magnetic field strength we identified for a fixed observing time the harmonic number of each zebra stripe. The comparison of the calculated DPR levels with the observed zebra stripe peak frequencies yields a density law for the ZP source volume. It turns out that this is a barometric law with a temperature near 106 K. We demonstrate that the drift of the whole ZP to higher frequencies can be explained as a signature of magnetic field decrease and/or plasma cooling in the ZP source. The time delay between BBP and ZP was found to be due to the higher fast particle threshold of the DPR versus the beam instability. The present analysis confirms the double plasma resonance model for the ZP fine structure, and underlines the significance of force-free extrapolated photospheric fields for coronal magnetic field modelling.