Inference of Magnetic Fields from Solar Flares

Abstract

The magnetic field induction present in the flare region can be inferred from the observed spectrum peak by the gyro synchrotron theory. For homogeneous magnetic field the spectrum peak is well defined and may be used for the inference of the field induction whenever we know the other important source parameters. The magnetic induction is the strongest dependence of the peak frequency and has been widely inferred from these spectra peak in solar flare analysis. The non homogeneous magnetic field may modify the spectrum width and peak mainly due to changes in the optically thick spectral index. Thus, for non homogeneous magnetic field the inferred induction may be interpreted as an effective value when the observation is fit, for example, by the four parameter fit‐function given by most of solar flare analysis in the literature. Simple formulas are given for the gyro‐synchrotron spectra peak in the literature where the peak is derived for the opacity equal one. This simplification causes the peak to be uncertain mostly for the cases where the optically thin spectral index is low. Besides, these simple equations are not applicable for spectra peak occurring below the tenth harmonic number of the electron gyro‐frequency which excludes most of the observed flares. We present a simple expression for the magnetic induction in a self‐absorbed gyro‐synchrotron emission to infer it from the spectrum peak frequency as given by the spectrum least square fit instead of opacity equal one. Our equation is valid for a large range of parameters generally accepted for solar flare conditions including peak frequency below the tenth harmonic of the gyro‐frequency.