Figure - available from: Solar Physics
This content is subject to copyright. Terms and conditions apply.
![The residual value D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D$\end{document}, depending on a fixed value s1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$s1$\end{document}.](profile/L-Yasnov/publication/338735563/figure/fig4/AS:962170984599553@1606410847311/The-residual-value-Ddocumentclass12ptminimal-usepackageamsmath.png)
The residual value D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D$\end{document}, depending on a fixed value s1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$s1$\end{document}.
Source publication
![The residual value D\documentclass[12pt]{minimal} \usepackage{amsmath}...](profile/L-Yasnov/publication/338735563/figure/fig4/AS:962170984599553@1606410847311/The-residual-value-Ddocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The dependence of R=Lbh/Lnh\documentclass[12pt]{minimal}...](profile/L-Yasnov/publication/338735563/figure/fig5/AS:962170984599563@1606410847470/The-dependence-of-RLbh-Lnhdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
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 resonan...
Citations
... Such calculations, made for example by Kuznetsov and Tsap (2007), Yu, Yan, and Tan (2012), Yasnov and Karlický (2020), Yasnov and Chernov (2020), gave the value of the gyro-harmonic number as several tens, and in the case including spatial changes of the magnetic field and density scales this value was even greater than one hundred. Such high values of the gyro-harmonic number give very small values of the magnetic field in zebra sources in comparison with the magnetic field model by Dulk and McLean (1978) at altitudes in the solar atmosphere provided by the density model by Aschwanden and Benz (1995). ...
Using the double-plasma resonance model of solar radio zebras, we analyze five models of the magnetic field and density in the zebra source region. We present analytical relations of zebra-stripe frequencies depending on the gyro-harmonic number. By fitting of observed zebra-stripe frequencies using model frequencies, we find that the determined gyro-harmonic number and corresponding magnetic field depend on the model used. We show that all previously analyzed zebras, where the absolute value of the difference between neighboring zebra-stripe frequencies increases with respect to increasing frequency, can be well fitted by the model with exponential dependencies of the magnetic field and density or by the model with smaller gradients of both of these variables. Although these models give different results, their more sophisticated versions give more similar results. We also present the models that can fit the zebras, if observed, where the absolute value of the difference between neighboring zebra-stripe frequencies decreases with respect to increasing frequency. We check all these models by a fitting of the zebra-stripe frequencies observed in the 21 June 2011 zebra event. In one model, although it reasonably describes the conditions in the atmosphere above the active region, the fit of the observed zebra-stripe frequencies could not be made.
... Based on the DPR mechanism of zebras, physical conditions in a region of the zebra generation are determined, and possible types of waves modulating zebra-stripe frequencies are discussed. Karlický and Yasnov (2015), Yasnov and Chernov (2020), and Karlický and Yasnov (2020) considered the DPR mechanism and the method of determination of the gyro-harmonic number [s] for corresponding zebra stripes was presented. The final version of this method even includes a variation of spatial-density and magnetic-field scales in the zebra source. ...
... An analogous result (or for a very close one) based on wave characteristics would be possible, e.g. a simple approximate function in the form of the polynomial of the third degree. Major problems with DPR models in the interpretation of zebras have been summarized by Chernov (2010), Yu, Yan, and Tan (2012), and Yasnov and Chernov (2020); therefore, here, we do not discuss details of applicability of the DPR model in the interpretation of presented results. Moreover, there are other fully adequate models (see Chernov, 2011) that are used in the interpretation of zebras. ...
... However, it is a necessary condition, but not a sufficient condition in favor of the DPR model. As concerns the model that is connected with whistlers, the present zebra case differs from the one from 21 June 2011 (Yasnov and Chernov, 2020), where the whistler model was fully adequate. In the present zebra case, this whistler model is not appropriate because the magnetic field needs to be sufficiently high (4 -5 G) that does not correspond to the small velocities of waves found in the present case. ...
We analyzed the 17 August 1998 zebra event and showed that some quasi-periodic oscillations modulate the zebra-stripe frequencies. We determined the period of these oscillations as \(P_{n} = 2.01 \pm 0.03\) (in numbers of zebra stripes) and as \(P_{\mathrm{f}} = 11.8 \pm 0.17\) MHz. In the first part of the analyzed zebra, we found a stable density wave that slowly propagated with the frequency drift less than 0.4 MHz s−1. Then, a stationary density wave appeared followed by a transformation of the waves to ones with longer periods. These long-period waves were recorded before and after the time interval when no zebra stripes were observed. We interpreted these density waves as magnetosonic waves. We calculated their wavelength and propagating velocity, considering two types of density models of the solar atmosphere. We also estimated the characteristic density and magnetic-field strength as \(N \approx 9.2\times 10^{8}\) cm−1 and \(B \approx 0.73~\mbox{G}\), respectively. We found similar velocities derived from drifts of the density wave and velocities calculated from the density and magnetic-field strength considering gyro-harmonic numbers of zebra stripes.
... To determine the physical conditions in the burst generation regions with ZP, it is necessary to determine the value of s that corresponds to a given stripe in the time-frequency spectrum. In the articles by Karlický and Yasnov (2015), Yasnov and Chernov (2020), and Karlický and Yasnov (2020), based on the DPR mechanism, a corresponding method was developed and improved, including the case of spatial variability of both the density and magnetic-field scales. ...
... Considering the above, let us analyze the dynamics of density variation in the region of generation of a burst with ZP recorded on 21 June 2011 (Kaneda et al., 2018) and determine the parameters of this region, assuming, as in the cited article, that the emission is related to DPR and occurs at the first harmonic of the plasma frequency. Earlier, the calculation of harmonic numbers without taking into account the variability of the parameter R was carried out by Yasnov and Chernov (2020). Table 1 shows the parameters derived by the analysis of zebra stripes. ...
... Note that earlier Yasnov and Chernov (2020), when determining the values of s1 for this ZP, the variability of the magnetic-field and plasma-density scales in the emission region was not taken into account, and s1 was found to be close to 60. In this case, the magneticfield strength is close to 1 G, and the speed of the sausage wave is about 370 km s −1 , that is, it is still 3.6 times less than the observed wave speed for the power-law density model and 12 times less than the observed speed for the barometric density model. ...
Analysis of the solar radio zebra-pattern (ZP) spectrum for the burst on 21 June 2011 has shown that the frequencies corresponding to the stripes of this ZP experience quasiperiodic oscillations relative to some average values. The period of such oscillations, expressed in the number of the ZP stripes, is \(2.41\pm0.21\), and expressed in frequencies, it is (\(5.00\pm0.68\)) MHz. The change in the period of oscillations with time anticorrelates with the amplitude of the oscillations. The values of the harmonic numbers for the corresponding bands are given, and thus the magnetic-field strength is also estimated on the basis of the theory of double plasma resonance (DPR). In addition, a possible change in the \(L_{\mathrm{bh}}/L_{\mathrm{nh}}\) parameter in the ZP-generation region is taken into account (\(L_{\mathrm{bh}}\) and \(L_{\mathrm{nh}}\) respectively are the magnetic-field and density scales). Calculations of the frequency-drift rate, carried out using an improved method for its determination, have shown that the drift values (\(3\,\text{--}\,8~\text{MHz}\,\text{s}^{-1}\)) are in accordance with Kaneda et al. (Astrophys. J. Lett. 855, L29, 2018). By using two density models of the solar atmosphere, the wavelength of these oscillations has also been determined. For the model presented by Aschwanden (Space Sci. Rev. 101, 1, 2002), the wavelength is about 1370 km while for the barometric density model, the wavelength is about 4650 km. The wavelength increases with time; for example, in the first model, the wavelength increases with time from 1200 to 1490 km. The calculated kink and sausage wave velocities turned out to be significantly lower than the observed ones. The reason for this discrepancy requires additional analysis.
... A third model attributes zebra patterns to whistler waves (for details see Chernov, 2006Chernov, , 2011; in this case a magnetic trap is filled with periodic whistler emission zones separated by their absorption zones. Yasnov and Chernov (2020) noted that this model gave a reasonable magnetic field of 4.5 G, whereas the double plasma resonance model gave only 1-1.5 G together with plasma β > 1, for an event at 183 MHz that they analyzed. ...
The structure of the upper solar atmosphere, on all observable scales, is intimately governed by the magnetic field. The same holds for a variety of solar phenomena that constitute solar activity, from tiny transient brightening to huge Coronal Mass Ejections. Due to inherent difficulties in measuring magnetic field effects on atoms (Zeeman and Hanle effects) in the corona, radio methods sensitive to electrons are of primary importance in obtaining quantitative information about its magnetic field. In this review we explore these methods and point out their advantages and limitations. After a brief presentation of the magneto-ionic theory of wave propagation in cold, collisionless plasmas, we discuss how the magnetic field affects the radio emission produced by incoherent emission mechanisms (free-free, gyroresonance, and gyrosynchrotron processes) and give examples of measurements of magnetic filed parameters in the quiet sun, active regions and radio CMEs. We proceed by discussing how the inversion of the sense of circular polarization can be used to measure the field above active regions. Subsequently we pass to coherent emission mechanisms and present results of measurements from fiber bursts, zebra patterns, and type II burst emission. We close this review with a discussion of the variation of the magnetic field, deduced by radio measurements, from the low corona up to ~ 10 solar radii and with some thoughts about future work.
... Karlický and Yasnov (2015) proposed a technique to determine the numbers s of zebra stripes in ZP events. A new version of the method for calculating the harmonic number (s1) for a given stripe and with the definition of R = L bh /L nh is given in Yasnov and Chernov (2020). This method is based on approximating data by polynomials of 2-4 orders and using the 3-4 zebra-stripe frequencies. ...
... Note that at higher frequencies (> 1500 MHz) the values of s1 are noticeably lower than at lower frequencies. In Yasnov and Chernov (2020), it was shown that, if R is assumed to be constant in the ZP emission region, then, for the 21 June 2011 zebra event, the value s1 obtained at lower frequencies is of about 75. Thus, taking into account the variability of the scales this value increases significantly (up to 115). ...
Zebra patterns (zebras) play an important role in the plasma diagnostics during solar flares. Considering their double plasma resonance (DPR) model, we present an improved method for the determination of the gyro-harmonic numbers of the zebra stripes that are essential in determining the electron density and magnetic field strength in zebra sources. Furthermore, we present the magnetic field and density spatial scales in zebra sources. Compared to the previous method, we change the basic assumption of the method. Namely, the assumption that the ratio \(R={L_{\mathrm{bh}}} / {L_{\mathrm{nh}}}\) (\(L_{\mathrm{bh}}\) and \(L_{\mathrm{nh}}\) are the magnetic field and density scales) is constant in the whole zebra source is changed to its more generalized form, where the ratio \(R\) is a linear function. Using this improved method, first, we determine the gyro-harmonic numbers of several observed zebras and variations of the spatial scales. Then, knowing the gyro-harmonic numbers of zebra stripes, we compute the electron plasma density and magnetic field strength in zebra sources. It is shown that in all cases the gyro-harmonic numbers of zebra stripes are quite high (> ≈50). This significantly reduces the magnetic field strength and thus increases the plasma beta parameter in zebra sources. The change in the ratio of the magnetic field and density scales along the axis of the radiating tube for the studied zebras is within ± 5 percent. For zebras at high frequencies, this ratio increases with the height, and for zebras at lower frequencies it decreases. The ratio of the magnetic field and density scales across the radiating tube is close to 1 and varies in the range 0.87–1.20.
... The spatially varying turbulence between zebra-stripe sources is a new aspect in the zebra-stripe analysis. Moreover, it removes some problems with the DPR zebra model recently discussed in the paper by Yasnov & Chernov (2020). The authors calculated a sequence of the gyroharmonic numbers of zebra stripes in the whole zebra from the zebra-stripe frequencies at the high-and low-frequency parts of the zebras. ...
Context. In solar flares the presence of magnetohydrodynamic turbulence is highly probable. However, information about this turbulence, especially the magnetic field turbulence, is still very limited.
Aims. In this paper we present a new method for estimating levels of the density and magnetic field turbulence in time and space during solar flares at positions of radio zebra sources.
Methods. First, considering the double-plasma resonance model of zebras, we describe a new method for determining the gyro-harmonic numbers of zebra stripes based on the assumption that the ratio R = L b / L n ( L n and L b are the density and magnetic field scales) is constant in the whole zebra source.
Results. Applying both the method proposed in this work and one from a previous paper for comparison, in the 14 February 1999 zebra event we determined the gyro-harmonic numbers of zebra stripes. Then, using the zebra-stripe frequencies with these gyro-harmonic numbers, we estimated the density and magnetic field in the zebra-stripe sources as n = (2.95−4.35) × 10 ¹⁰ cm ⁻³ and B = 17.2−31.9 G, respectively. Subsequently, assuming that the time variation of the zebra-stripe frequencies is caused by the plasma turbulence, we determined the level of the time varying density and magnetic field turbulence in zebra-stripe sources as |Δ n / n | t = 0.0112–0.0149 and |Δ B / B | t = 0.0056–0.0074, respectively. The new method also shows deviations in the observed zebra-stripe frequencies from those in the model. We interpret these deviations as being caused by the spatially varying turbulence among zebra-stripe sources; i.e., they depend on their gyro-harmonic numbers. Comparing the observed and model zebra-stripe frequencies at a given time, we estimated the level of this turbulence in the density and magnetic field as |Δ n / n | s = 0.0047 and |Δ B / B | s = 0.0024. We found that the turbulence levels depending on time and space in the 14 February 1999 zebra event are different. This indicates some anisotropy of the turbulence, probably caused by the magnetic field structure in the zebra source.
