The solar radio zebra patterns, or zebras, provide comprehensive diagnostics of plasma density and magnetic field in the corona. The zebras appear in radiograms during Type IV solar radio bursts as a series of parallel stripes that are narrow in frequency.
The primary emission model of radio zebras depends on a double plasma resonance, a resonance in between the plasma frequency, gyro-harmonic of the cyclotron frequency, and the frequency of unsteady upper-hybrid (UH) electrostatic waves (Zhelezniakov & & Zlotnik 1975, Chen et al. 2011). The motorist of the instability are superthermal electrons which are caught in a flare loop and form a loss-cone distribution. During the instability, the UH waves grow and fill. The electrostatic waves are then subsequently converted to the observed electro-magnetic waves by merging with low-frequency waves or scattering on plasma particles.
Assuming that private stripes are produced at gyro-harmonics of the cyclotron frequency, extremely high gyro-harmonic numbers s are typically found, s ~ 50– 150 (Karlický & & Yasnov, 2021). In contrast, the theoretical designs anticipate that the greatest development rates are obtained for relatively low gyro-harmonic numbers, s<< 10 (Benáček & & Karlický, 2018)
. Results and techniques
We think about a plasma consisting of two components: 1) thick thermal background plasma and 2) low-density loss-cone superthermal electrons defined by their thermal criterion vκ and Kappa loss-cone distribution with a loss-cone angle θc. We numerically computed the development rates of the UH waves as a weighted averages over the entire UH branch. When the growth rates form peaks, we assumed that zebra stripes are formed.
Figure 1 provides the growth rates as functions of gyro-harmonic number for loss-cone angles θc = 30 °-- 80 °. For little angles θc = 30 °-- 50 °, the development rates smooth with increasing gyro-harmonic number. However, for a big angle θc = 80 °, the growth rates increase.
In addition, comparable development rate habits likewise takes place when differing the thermal specification of the loss-cone circulation vκ (Figure 2), assuming θc = 80 ° is constant. For vκ = 0.3 c, the values of growth rate peaks are around constant for all gyro-harmonic numbers, and the peaks smooth out. Nevertheless, for smaller sized thermal specifications vκ = 0.15-- 0.25 c, the development rates increase with increasing gyro-harmonic numbers, and the peaks, essential for the development of the Zebra pattern, are still formed.
Figure 1: Average growth rates of the UH waves as a function of the loss cone angle θc for intervals: a) s = 7-- 10, b) s = 20-- 23, c) s = 50-- 53, and d) s = 100-- 103. Compare the red and blue lines for different s.
Figure 2: Similar as Figure 1, but for a dependence on the loss-cone thermal specification vκ. Compare the red and black lines for different s.
Conclusions
We found that the zebras with really high gyro-harmonic numbers, s ~ 100, can be just formed for particular homes of the superthermal electrons-- really high loss-cone angles θc = 80 ° and reasonably low thermal parameters vκ << 0.3 c. Moreover, to satisfy the double-plasma resonance condition for high gyro-harmonic numbers, the plasma density in the zebra source requires to be high and the magnetic field strength reasonably low.
Thus, we propose that zebras with high gyro-harmonic numbers might be produced in two areas:
In the area below the X-point of the magnetic reconnection in the standard flare model. Namely, it is expected that there is a plasma with high density and low magnetic field strength. For the zebra generation, the electron acceleration processes at the X-point and in collapsing magnetic trap in the plasma reconnection outflow need to produce the loss-cone distribution with a pitch angle of about 80 °.
Based upon a recent paper by Benacek & & Karlicky, Zebra Stripes with High Gyro-Harmonic Numbers, Solar Physics 297:103 (2022 ), DOI: 10.1007/ s11207-022-02036-y, ADS: 2022SoPh..297..103 B.
References:.
Benáček, J. and Karlický, M. 2018, A&A, 611, A60.
Chen, B., Bastian, T. S., Gary, D. E., and Jing, J., 2011, ApJ, 736, 64.
Krucker, S., Masuda, S., White, S. M., 2020, ApJ, 894, 158.
Zhelezniakov, V.V. and Zlotnik, E.Ya., 1975, Sol. Phys., 44, 2, p.461-470.
In magnetic loops that are only slightly wider at their midpoints than at their footpoints. In such loops, only superthermal electrons with high pitch angles can be caught (Krucker et al. 2020). The plasma density in these loops needs to be high and the magnetic field strength reasonably low.
Particularly, it is expected that there is a plasma with high density and low magnetic field strength.
We consider a plasma consisting of 2 elements: 1) thick thermal background plasma and 2) low-density loss-cone superthermal electrons identified by their thermal parameter vκ and Kappa loss-cone circulation with a loss-cone angle θc. We presumed that zebra stripes are formed when the development rates form peaks.
Figure 1: Average growth rates of the UH waves as a function of the loss cone angle θc for periods: a) s = 7-- 10, b) s = 20-- 23, c) s = 50-- 53, and d) s = 100-- 103. The plasma density in these loops requires to be high and the magnetic field strength fairly low.