Estimating density and magnetic field turbulence in solar flares using radio zebra observations

Abstract

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 = Lb/Ln (Ln and Lb 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) × 1010 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 |Δn/n|t = 0.0112–0.0149 and |ΔB/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 |Δn/n|s = 0.0047 and |ΔB/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.