**7. Acknowledgements**

20 Will-be-set-by-IN-TECH

more-or-less stable, and all the variations of the observed microwave radiation are connected with the non-thermal gyro-synchrotron part of the radiation, modulated by the large-scale oscillatory motion of the loop. The bremsstrahlung component, even being present in the microwave radiation, does not contribute to the analyzed oscillating part of the emission

Our analysis here is based on the assumption of an optically thin microwave source. In this case the radiation intensity is proportional to emissivity *ην*, given by equation (Dulk, 1985)

where *ν* is radiation frequency, *N* is the number of electrons per cubic centimeter with energy higher than 10 keV, *B* is magnetic field, *ν<sup>B</sup>* = *eB*/(2*πmec*), is the electron-cyclotron frequency, and *δ* is the electron energy spectrum index. This fact has been used for obtaining our basic equation (1) in Section 1. In the opposite case of an optically thick source, the intensity of microwave radiation is proportional to the effective temperature *Teff* , i.e., to the ratio of emissivity *ην* and absorption coefficient *κν*. For the last, Dulk (1985) provides the following

Therefore, in the case of an optically thick source the dependence of radiation intensity on the varying magnetic field *B*(*t*) and direction to the observer Θ(*t*) will be different than that given by the equation (1). However, the character of this dependence, i.e. *I<sup>ν</sup>* ∝ (sin(Θ(*t*)))*kB*(*t*)*<sup>l</sup>*

where *k* and *l* are the numbers depending on the non-thermal electron spectral index *δ*, will remain the same. Therefore, one may expect similar manifestation of the varying *B*(*t*) and Θ(*t*) in the modulation of the received microwave emission also in the case of an optically

Analysis of LF and VLF modulations of solar microwave radiation is a relatively new direction in solar radio astronomy which appears nowadays a subject of a certain interest. VLF variations of solar microwave radiation intensity may be related to slow variations of magnetic field in a radiating source, as well as to large-scale motions of coronal structures containing the radiating source. Joint action of two radiation modulating factors: (i) the quasi-periodic fluctuation of magnetic field and (ii) motion of the radio emission diagram, in the case of a transverse oscillating coronal loop results in essentially non-sinusoidal (non-harmonic) character of the signal received by a remote observer, with strongly pronounced two first harmonics (at the main and double frequency of the oscillation), called here as "modulation pairs". Such specifics of the VLF spectrum has been used for the identification of transverse oscillating loops triggered by flares. The analysis of solar microwave records has been performed with an algorithm based on Sliding Window Fourier transform and Wigner-Ville techniques. This high sensitive algorithm provides, significant spectral and temporal resolution which enable clear detection of VLF "modulation pairs" in the solar flaring microwave radiation (microwave bursts). Comparison of parameters of these "modulation pairs" with the simultaneous TRACE observations in EUV of the corresponding solar active regions enabled to associate some of the paired VLF modulation features with the large-scale transverse oscillations of coronal loops. The "non-paired" features also detected

 *ν νB*

> *ν νB*

1.22−0.9*<sup>δ</sup>*

−1.3−0.98*<sup>δ</sup>*

, (9)

. (10)

,

*ην* <sup>≈</sup> 3.3 <sup>×</sup> <sup>10</sup><sup>−</sup>2410 <sup>−</sup>0.52*δNB*(sin *<sup>θ</sup>*) <sup>−</sup>0.43+0.65*<sup>δ</sup>*

*κν* <sup>≈</sup> 1.4 <sup>×</sup> <sup>10</sup><sup>−</sup>910 <sup>−</sup>0.22*δ*(*N*/*B*)(sin *<sup>θ</sup>*) <sup>−</sup>0.09+0.72*<sup>δ</sup>*

provided by the gyro-synchrotron mechanism.

expression:

thick source.

This work was supported by the Austrian Fond zur Förderung der wissenschaftlichen Forschung (project P21197-N16). The authors are thankful to the JRA3/EMDAF (European Modelling and Data Analysis Facility; http://europlanet-jra3.oeaw.ac.at) – a subdivision of the European research infrastructure EUROPLANET-RI and EU FP7 project IMPEx (http://impex-fp7.oeaw.ac.at) for the support of their research communication and collaboration visits. The authors would like to thank M.Aschwanden for useful discussions and the data regarding the transverse large-scale dynamics of coronal loops.
