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

Abstract

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.

14 pages, 6 figures, 3 tables

References in corpus (4)

• The Magnetic Field in the Solar Atmosphere
• Spatially-resolved Energetic Electron Properties for the 21 May 2004 Flare from Radio Observations and 3D Simulations
• Temperature dependent growth rates of the upper-hybrid waves and solar radio zebra patterns
• A Very Small and Super Strong Zebra Pattern Burst at the Beginning of a Solar Flare

Cited by in corpus (4)

• Growth rates of the electrostatic waves in radio zebra models
• Alternative Models of Zebra Patterns in the Event on June 21, 2011
• Particle-in-cell simulations of electron-positron cyclotron maser forming pulsar radio zebras
• Growth Rates of the Upper-hybrid Waves for Power-law and Kappa Distributions with a Loss-cone Anisotropy