**6. Discussion, conclusions and perspectives**

18 Will-be-set-by-IN-TECH

c d

Fig. 6. (a) SOHO/MDI Magnetogram of the Sun on 2001-Sep-15, white arrow points at the active region AR9608; (b) The Sun image in 304 Å on 2001-Sep-15 from SOHO/EIT, white arrow points at the active region AR9608; (c) Intensity profile and corresponding VLF modulation dynamic spectrum of the microwave burst on 2001-Sep-15, at 11:23-12:15 associated with an M-flare in the active region AR9608; Color codes the dynamic spectral relative intensity (arbitrary units), more dark features correspond to stronger (better pronounced) modulations; (d) averaged spectral density of the VLF modulation.

It is impossible, using the available data, to perform an exact calculation for the amplitude of magnetic field variations. That is because the analyzed microwave signals were recorded in relative units without calibration to the radiation intensity scale. At the same time, taking into account known values of the maximal intensity measured during the radio

**13:00 14:00**

Solar burst on 15.09.2001 at 11.7 Ghz

Relative spectral density

Frequency, mHz

SOHO/MDI

Magnetogram,

2001-Sep-15

**8 7.5 7**

**6.5 6 5.5** Dynamic spectrum, burst on 2001-Sep-15

**10:00 11:00 12:00**

Time (UT)

**5.2 On the magnetic field variations, estimated from VLF spectra**

Intensity, a.u

**0.002**

a b

SOHO/EIT 304 Å,

2001-Sep-15

**0.0015**

**0.001**

**0.0005**

**0**

**1**

0.7 mHz

1.3 mHz

0.3 mHz

Burst on 15.09.2001 Spectrum averaged on ~ 40 min

**0 2 3 4 5 6 7** Frequency, mHz

2.6 mHz

3.8 mHz

5.2 mHz

at 11.7 Ghz, **0.0025**

The analysis of VLF modulations of solar microwave bursts presented in this work shows good temporal coincidence of the modulations and their oscillatory parameters with the observed decaying large-scale transverse oscillations of the coronal loops triggered by flares. This indicates about a physical link between the oscillatory motion of the loops and variations of the observed radio emission. As a working hypothesis to take this link into account, a loop with the propagating beams of non-thermal particles which produce microwave emission due to the electron gyro-synchrotron mechanism, has been considered. As pointed out by Schrijver et al. (2002), who considered several cases of transverse oscillations of coronal loops observed with TRACE (including the event on 2000-Mar-23 addressed in the present paper), in almost all cases the oscillating loops lie at, or near, the large-scale separatrices, or near the sites involved in reconnection. These regions may be the sources of non-thermal particles injected into the loops and generating microwave emission there. Moreover, in the case on 2000-Mar-23 the loop oscillation happened in response to a flaring event located at the loop base Schrijver et al. (2002). That could provide a direct input of energetic particles into the loop.

In the most general case, thermal bremsstrahlung mechanism of the radiation should be also considered, besides of the gyro-synchrotron, for the analyzed frequency range of the solar microwave emission. If the last mechanism assumes that there are high energy electrons passing through the magnetic loop, the first one is connected with the radiation of hot plasma heated by the electron beams in the chromospheric footpoints of the loop. A comparative study of contribution of the bremsstrahlung and gyro-synchrotron radiation to the microwave emission of a flare, performed in Urpo et al. (1994), shows that thermal bremsstrahlung is more important for the microwave events that have an intensity of the order of or less than 100 SFU, with the exception of cases when the electron spectrum is sufficiently hard. Therefore, correct interpretation of the microwave radiation source requires consideration of both mechanisms, for example by involving of the hybrid thermal/nonthermal model of the solar flare emission (Holman & Benka, 1992). However, looking at a possibility of an oscillatory behaviour of the microwave radiation source which constitutes the primary subject of the present study, we notice that in the case of the bremsstrahlung mechanism it is possible only for a varying energy deposition into the system, i.e. a varying flow of non-thermal particles heating the loop footpoints. In view of the unclearness of how the post-flare transverse oscillating loop may modulate the source of accelerated electrons, we built our analysis with the assumption that the non-thermal particle population remains

in the VLF modulation dynamic spectra, may be either parts of "modulation pairs" in which the second harmonic cannot be resolved because of the strong contamination of the analyzed signal, or be the signatures of other oscillatory processes (MHD modes) in the loops, unrelated

<sup>163</sup> Analysis of Long-Periodic Fluctuations of Solar

The presence of "modulation pairs" in the VLF spectra of solar microwave radiation is considered here as an indication of the transverse oscillating coronal loops. However, the exact characterization of the transverse motion of radiating loops by the dynamical spectra of microwave emission needs a quantitative analysis of the measured radio signal and superimposing these results with a precise calculation of the radiation from the loop, taking into account the loop position relative observer. This topic requires a dedicated study. It outlines the general direction for further development of the ideas expressed in the paper. Besides of that, of certain interest appear the long lasting ULF modulations of solar microwave radiation detected at < 0.6 mHz (> 30 min) in the absence of bursts, i.e. during the periods of quiet Sun. It is remarkable that these modulations are not visible in the emissions from separate active regions, recorded in particular at 37 GHz with Metsähovi radio telescope. But they appear in the integrated radiation received from the whole solar disk at 11.7 GHz. This fact may be considered as an argument in support of the global helioseismic nature of these

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

Allen, R.L. & Mills, D.W. (2004). *Signal analysis: time, frequency, scale, and structure*. IEEE Press,

Aschwanden, M.J.; Fletcher, L.; Schrijver, C.J.; Alexander, D. (1999). Coronal Loop Oscillations

Aschwanden, M.J. (2002). Particle acceleration and kinematics in solar flares - A Synthesis

Aschwanden, M.J.; DePontieu, B.; Schrijver, C.J.; Title, A. (2002). Transverse Oscillations in

Cohen, L. (1989). Time-frequency distributions - A review. *IEEE Proc.*, Vol. 77, July-1989,

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Coronal Loops Observed with TRACE II. Measurements of Geometric and Physical Parameters. *Solar Physics*, Vol. 206, No. 1, 99–132, (DOI:10.1023/A:1014916701283). Cargill, P.J.; Goodrich, C.C.; Vlahos, L. (1988). Collisionless shock formation and the prompt

acceleration of solar flare ions. *Astronomy and Astrophysics*, Vol. 189, No. 1-2, Jan.,

to their large-scale transverse motion, e.g., sausage-type MHD waves.

Microwave Radiation, as a Way for Diagnostics of Coronal Magnetic Loops Dynamics

ULF modulations, which also require further more detailed study.

and the data regarding the transverse large-scale dynamics of coronal loops.

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**7. Acknowledgements**

**8. References**

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 provided by the gyro-synchrotron mechanism.

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)

$$
\eta\_{\nu} \approx 3.3 \times 10^{-24} 10^{-0.52\delta} N B (\sin \theta)^{-0.43 + 0.65\delta} \left(\frac{\nu}{\nu\_B}\right)^{1.22 - 0.9\delta} \tag{9}
$$

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 expression:

$$\kappa\_{\nu} \approx 1.4 \times 10^{-9} 10^{-0.22\delta} (N/B) (\sin \theta)^{-0.09 + 0.72\delta} \left(\frac{\nu}{\nu\_B}\right)^{-1.3 - 0.98\delta} . \tag{10}$$

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 thick source.

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 in the VLF modulation dynamic spectra, may be either parts of "modulation pairs" in which the second harmonic cannot be resolved because of the strong contamination of the analyzed signal, or be the signatures of other oscillatory processes (MHD modes) in the loops, unrelated to their large-scale transverse motion, e.g., sausage-type MHD waves.

The presence of "modulation pairs" in the VLF spectra of solar microwave radiation is considered here as an indication of the transverse oscillating coronal loops. However, the exact characterization of the transverse motion of radiating loops by the dynamical spectra of microwave emission needs a quantitative analysis of the measured radio signal and superimposing these results with a precise calculation of the radiation from the loop, taking into account the loop position relative observer. This topic requires a dedicated study. It outlines the general direction for further development of the ideas expressed in the paper.

Besides of that, of certain interest appear the long lasting ULF modulations of solar microwave radiation detected at < 0.6 mHz (> 30 min) in the absence of bursts, i.e. during the periods of quiet Sun. It is remarkable that these modulations are not visible in the emissions from separate active regions, recorded in particular at 37 GHz with Metsähovi radio telescope. But they appear in the integrated radiation received from the whole solar disk at 11.7 GHz. This fact may be considered as an argument in support of the global helioseismic nature of these ULF modulations, which also require further more detailed study.
