Millisecond Microwave Spikes: Statistical Study and Application for Plasma Diagnostics

I.V. Rozhansky$^1$, G.D. Fleishman$^1$, G.-L. Huang$^2$

$^1$A. F. Ioffe Physico-Technical Institute, 194021 St.Petersburg, Russia
$^2$Purple Mountain Observatory, National Astronomical Observatories,Nanjing 210008, People's Republic of China

We analyze a dense cluster of solar radio spikes registered at $\sim$ 4.5-6 GHz by the Purple Mountain Observatory spectrometer (Nanjing, China) operating in the 4.5-7.5 GHz range with the sampling time of 5 ms. The cluster occurred during a X2.3 flare on April 10, 2001, NOAA region 9415, located close to the center of the solar disk (S23W06-08). The flare was associated with a halo CME, meter-wavelength types II and IV bursts, and strong microwave continuum burst.

To handle with the data from the spectrometer we developed a new technique utilizing a nonlinear multi-gaussian spectral fit based on chi-squared criteria to extract individual spikes from the originally recorded spectra. The proposed procedure yields statistically significant series of the spikes with the gaussian spectral shape even in the case of overlapping spikes. Applying this method to the experimental raw data we eventually identified more than 5000 spikes for this event, which allows for a detailed statistical analysis. Various statistical characteristics of the spikes have been evaluated, including intensity distributions, spectral bandwidth distributions and distribution of the spike mean frequencies. The most striking finding of this analysis is distributions of the spike bandwidth, which are remarkably asymmetric. The overall bandwidth distribution has a skew shape with rapid increase at low values of the relative bandwidth followed by maximum at 0.6% and smooth tail approaching zero at approximately 3%, the overall skewness is about 1.5.

This puzzling shape of the distribution is clearly a manifestation of some microphysics hidden in the data. To reveal this microphysics we explore the local trap model, which is known to be capable of reproducing many of the observed spike properties. In order to account for the essential features of the bandwidth distributions we explicitly use the renormalized theory of spectral profile of the electron cyclotron maser emission line. The theory accurately takes into account the fluctuations of the magnetic field in the spike source. It shows that even rather small fluctuations of the magnetic field can provide a substantial broadening of the radiation line bandwidth. The distribution of the solar spikes relative bandwidth calculated so within the local trap model represents an excellent fit to the experimental data. Thus the developed theory adequately describes the spike emission spectra and the suggested model does pick up essential physical properties of the spike sources. Complimentary, the remarkable agreement between the model and the observations enhances substantially our ability to remotely diagnose the solar plasma, providing us, in particular, with the natural bandwidth of the responsible emission mechanism and the level of magnetic turbulence in the spikes cluster source.