**5.1 Observations and interpretation**

In this subsection, we show how the analysis of long-periodic modulations of solar microwave radiation accompanying the explosive events on the Sun may be used to obtain information on the details of large-scale dynamics of the coronal loops associated with flares and the overall structure of solar active regions. By this, the primary focus here is made on VLF modulations of the radiation, emitted from active regions where TRACE observed in EUV at the same time the large-scale oscillations of coronal loops. Careful check of the solar microwave radio emission records available at Metsähovi revealed several events which coincide in time with the EUV observations of oscillating coronal loops. Below these events are considered in details.

Figure 3c shows the intensity profile and dynamic spectrum of VLF modulations of microwave emission from the active region AR8910 on the limb (see Figure 3a,b) where a group of oscillating loops (Figure 4a) was observed by TRACE after M2.0 flare on 2000-Mar-23, at 11:30-12:00 UT (Aschwanden et al., 2002). These observations were performed at 37 GHz, and the spatial resolution of the Metsähovi radio telescope was sufficient to resolve the radiating source in the active region AR8910.

A remarkable feature of the VLF modulation dynamic spectrum in Fig. 3c,d and the averaged spectral density plot in Fig. 3d consists in the presence of several "modulation pairs". These are the modulations (a) at 1.7 mHz (∼ 10 min) and 3.4 mHz (∼ 4.9 min); (b) at 6.0 mHz (∼ 2.8 min) and 12.0 mHz (∼ 1.4 min), as well as (c) at 7.8 mHz (∼ 2.1 min) and 15.6 mHz (∼ 64 s). According to the considerations in Section 2, these "modulation pairs" could indicate the transverse oscillating loops with the periods, corresponding to the main frequencies of the pairs, i.e. ∼ 10 min; ∼ 2.8 min, and ∼ 2.1 min for the cases (a), (b), and (c), respectively. By this, the first "modulation pair" (case (a)) as a signature of the loop transverse oscillation with a period ∼ 10, fits quite well the results of TRACE observations, which found the oscillating loop with approximately the same period (615 s) (Aschwanden et al., 2002; Schrijver et al., 2002). As it can be seen from the dynamical spectrum in Figure 3c, the spectral resolution of the analysis performed in this particular case was about 0.3 mHz. By this, the frequency 1.62 mHz corresponding to the detected TRACE period of 615 s is definitely within the frequency 12 Will-be-set-by-IN-TECH

and dynamics of coronal loops. At 11.7 GHz the radiation is collected from the whole solar disk and the position of the radiating source cannot be resolved. However, even in this case, by comparison with observations in other wavelengths and timing of the events, it is usually possible to identify the microwave radiation features related to the energy release and

Variations of the background magnetic field in a radiating source may cause not only the amplitude modulation of microwave radio emission from solar active regions (according (1)), but also could result in a certain frequency modulation (due to the dependence of electron gyro-frequency *ν<sup>B</sup>* on the magnetic field). The estimated width of the gyro-frequency variation interval due to this effect is from several tens to several hundreds MHz. At the same time, the bandwidth of the receiver at Metsähovi is much larger than this interval and a possible frequency modulation of the microwave radio emission cannot be resolved. Thus, one can detect only the effects of varying magnetic field, manifested in the intensity modulation of the

In this subsection, we show how the analysis of long-periodic modulations of solar microwave radiation accompanying the explosive events on the Sun may be used to obtain information on the details of large-scale dynamics of the coronal loops associated with flares and the overall structure of solar active regions. By this, the primary focus here is made on VLF modulations of the radiation, emitted from active regions where TRACE observed in EUV at the same time the large-scale oscillations of coronal loops. Careful check of the solar microwave radio emission records available at Metsähovi revealed several events which coincide in time with the EUV observations of oscillating coronal loops. Below these events are considered in

Figure 3c shows the intensity profile and dynamic spectrum of VLF modulations of microwave emission from the active region AR8910 on the limb (see Figure 3a,b) where a group of oscillating loops (Figure 4a) was observed by TRACE after M2.0 flare on 2000-Mar-23, at 11:30-12:00 UT (Aschwanden et al., 2002). These observations were performed at 37 GHz, and the spatial resolution of the Metsähovi radio telescope was sufficient to resolve the

A remarkable feature of the VLF modulation dynamic spectrum in Fig. 3c,d and the averaged spectral density plot in Fig. 3d consists in the presence of several "modulation pairs". These are the modulations (a) at 1.7 mHz (∼ 10 min) and 3.4 mHz (∼ 4.9 min); (b) at 6.0 mHz (∼ 2.8 min) and 12.0 mHz (∼ 1.4 min), as well as (c) at 7.8 mHz (∼ 2.1 min) and 15.6 mHz (∼ 64 s). According to the considerations in Section 2, these "modulation pairs" could indicate the transverse oscillating loops with the periods, corresponding to the main frequencies of the pairs, i.e. ∼ 10 min; ∼ 2.8 min, and ∼ 2.1 min for the cases (a), (b), and (c), respectively. By this, the first "modulation pair" (case (a)) as a signature of the loop transverse oscillation with a period ∼ 10, fits quite well the results of TRACE observations, which found the oscillating loop with approximately the same period (615 s) (Aschwanden et al., 2002; Schrijver et al., 2002). As it can be seen from the dynamical spectrum in Figure 3c, the spectral resolution of the analysis performed in this particular case was about 0.3 mHz. By this, the frequency 1.62 mHz corresponding to the detected TRACE period of 615 s is definitely within the frequency

dynamic phenomena in particular active regions.

microwave signal, due to (1).

details.

**5.1 Observations and interpretation**

radiating source in the active region AR8910.

Fig. 3. (a) SOHO/MDI Magnetogram of the Sun on 2000-Mar-23, white arrow points at the active region AR8910; (b) The Sun image in 304 Å on 2000-Mar-23 from SOHO/EIT, white arrow points at the active region AR8910; (c) Intensity profile and corresponding VLF modulation dynamic spectrum of the microwave radiation, recorded from the active region AR8910 on 2000-Mar-23, at 11:30-12:00; 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.

interval 1.7 ± 0.3 mHz of the modulation feature revealed by the analysis of the microwave radiation.

oscillatory motion of a coronal loop, shown in Fig. 4a, and that it is in very likely related to the motion of the emission diagram pattern, comes from the graphs in Fig. 4b. This figure enables phase comparison for the transverse motion of the loop (observed with TRACE Aschwanden et al. (2002)) and the filtered 1.7 mHz (∼ 10 min) component of the radiation. The last characterizes temporal behaviour of the radio emission received from the oscillating loop. The shifted phase (∼ *π*) means that the maxima and minima of the radiation part controlled by the loop motion correspond to the specific orientations of the loop and are connected with

<sup>157</sup> Analysis of Long-Periodic Fluctuations of Solar

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

The microwave burst on 2001-Sep-07 represents another example of manifestation of the coronal loop transverse oscillations in modulation of solar radio emissions. The burst was produced during M-flare activity at 15:30 UT in the active region AR9601, close to the solar disc center (see Figure 5a,b), where TRACE observed a group of oscillating loops, immediately after the flare (Aschwanden et al., 2002). The corresponding microwave radiation record was made at 11.7 GHz with the Metsähovi radio telescope. At this frequency, the Metsähovi antenna cannot resolve the position of a radiating source, and the emission from the whole solar disk contributed to the analyzed microwave intensity profile. At the same time, as can be seen in Fig. 5c, which presents the analyzed microwave radiation record with the burst and its VLF modulation dynamic spectrum, the spectral features related to the processes in the flaring active region AR9601 can easily be identified by timing of the event. In particular, the dynamic spectrum of VLF modulations of the microwave radiation exhibits several lines, which start simultaneously with the impulsive phase of the flare (at 15:30 UT). These may be the signatures of different oscillating loops excited by the flare. By this, most of the oscillations (e.g. the dynamic spectrum lines) decay at the time intervals > 20 min. Unfortunately for this particular event it is impossible to determine exact duration of each of these decaying modulations because the available microwave radiation record does not cover the end of the event. As it can be seen in Fig. 5c, some of the dynamic spectrum lines continue beyond the

Three "modulation pairs" can be identified in the dynamic and averaged spectra in Fig. 5c,d: (a) 1.8 mHz (∼ 9.2 min) and 3.6 mHz (∼ 4.6 min); (b) 2.7 mHz (∼ 6.2 min) and 5.4 mHz (∼ 3.1 min); as well as (c) 4.3 mHz (∼ 3.8 min) and 8.6 mHz (∼ 1.9 min), which may be the signatures of transverse oscillating loops with periods ∼ 9.2 min, ∼ 6.2 min, and ∼ 3.8 min, respectively. We note that the loop periods in the cases (a) and (b) are consistent with the 6-10 min oscillating loops observed with TRACE (Aschwanden et al., 2002), whereas the shorter period oscillation (case (c)) cannot be resolved by TRACE because of the relatively long image sampling cadence. The modulation at 5.4 mHz (∼ 3.1 min) may also be a weak third harmonic produced by the 9.2 min oscillating loop. If this is true, then the line at 2.7 mHz (∼ 6.2 min) will have no a pair-companion, and one should exclude the possibility of the ∼ 6.2 min transverse oscillating loop. A "non-paired" weak modulation feature at 6.4 mHz (∼ 2.6 min) may be a signature of an oscillating loop with not resolved second harmonic. At the same time, as for the 2000-Mar-23 event, weak short-period harmonics may be the signatures of oscillatory processes that are unrelated to the transverse motion of a loop, but caused only

The strong modulation line at 0.6 mHz (∼ 27.7 min) should be considered separately from all other modulations mentioned above. The dynamical spectrum in Fig. 5c, as well as a separate study of VLF modulations of the microwave radiation recorded before the faring burst at 15:30 UT, reveal the presence of the ∼ 27.7 min component also before the flare. In view of the fact

a certain direction of the emission diagram relative to the observer.

analyzed record time frame.

by a changing magnetic field in the radiating source.

Fig. 4. (a) Transverse oscillating coronal loops observed by TRACE in the active region AR8910 after an M2.0 flare on 2000-Mar-23 at 11:30-12:00 UT (Aschwanden et al., 2002); (b) Phase comparison of the ∼ 10 min modulation component of the microwave emission on 2000-Mar-23 and the amplitude of the corresponding 615 s oscillation of the TRACE loop.

A higher level of the second harmonic in the modulation pair 1.7 mHz (∼ 10 min) and 3.4 mHz (∼ 4.9 min) is very likely due to the fact that in this particular case two different mechanisms, modulating the microwave emission of the loop, are by chance manifested simultaneously. The first mechanism is that considered in this paper, which is connected with a large-scale transverse oscillation of the loop. The second mechanism is due to the parametric resonance between 5-min velocity oscillations in the solar photosphere and acoustic oscillations of coronal magnetic loop modulating the microwave emission (Zaitsev et al., 2008). The effect consists in simultaneous excitation in the loop, which occasionally appeared to have a resonant frequency close to 10 min, of oscillations with periods ∼5 min, ∼10 min, and ∼3 min, which correspond to the 5-min pumping frequency of the photospheric convection velocity oscillations, subharmonic, and the first upper frequency of the parametric resonance, respectively (Zaitsev et al., 2008; Zaitsev & Kislyakov, 2006).

It makes no sense to search in TRACE data for the signatures of other oscillating loops (cases (b) and (c)), indicated by the VLF modulations of the microwave radiation during the 2000-Mar-23 event, since with the usual 40 s image sampling cadence of TRACE and the 4-point resolution limit of the instrument (Aschwanden et al., 2002) the fastest detectable by TRACE period is about 3 min. The remaining short-periodic "non-paired" modulation feature at 8.4 mHz (∼ 1.9 min) may also be a part of a "modulation pair", of which the second harmonic counterpart could not be resolved in the VLF spectrum due to the strong contamination of the analyzed microwave signal. Such weak higher harmonic components may be as well a signature of another oscillatory process, which is unrelated to the large-scale transverse motion of loops, e.g., a sausage-type MHD wave excited in a loop. Detailed analysis of this special case remains however beyond the scope of the present study.

An additional confirmation of the fact that ∼ 10 min modulation of the microwave radiation emitted from the active region AR8910 on 2000-Mar-23, is connected with the transverse 14 Will-be-set-by-IN-TECH

Fig. 4. (a) Transverse oscillating coronal loops observed by TRACE in the active region AR8910 after an M2.0 flare on 2000-Mar-23 at 11:30-12:00 UT (Aschwanden et al., 2002); (b) Phase comparison of the ∼ 10 min modulation component of the microwave emission on 2000-Mar-23 and the amplitude of the corresponding 615 s oscillation of the TRACE loop.

resonance, respectively (Zaitsev et al., 2008; Zaitsev & Kislyakov, 2006).

A higher level of the second harmonic in the modulation pair 1.7 mHz (∼ 10 min) and 3.4 mHz (∼ 4.9 min) is very likely due to the fact that in this particular case two different mechanisms, modulating the microwave emission of the loop, are by chance manifested simultaneously. The first mechanism is that considered in this paper, which is connected with a large-scale transverse oscillation of the loop. The second mechanism is due to the parametric resonance between 5-min velocity oscillations in the solar photosphere and acoustic oscillations of coronal magnetic loop modulating the microwave emission (Zaitsev et al., 2008). The effect consists in simultaneous excitation in the loop, which occasionally appeared to have a resonant frequency close to 10 min, of oscillations with periods ∼5 min, ∼10 min, and ∼3 min, which correspond to the 5-min pumping frequency of the photospheric convection velocity oscillations, subharmonic, and the first upper frequency of the parametric

It makes no sense to search in TRACE data for the signatures of other oscillating loops (cases (b) and (c)), indicated by the VLF modulations of the microwave radiation during the 2000-Mar-23 event, since with the usual 40 s image sampling cadence of TRACE and the 4-point resolution limit of the instrument (Aschwanden et al., 2002) the fastest detectable by TRACE period is about 3 min. The remaining short-periodic "non-paired" modulation feature at 8.4 mHz (∼ 1.9 min) may also be a part of a "modulation pair", of which the second harmonic counterpart could not be resolved in the VLF spectrum due to the strong contamination of the analyzed microwave signal. Such weak higher harmonic components may be as well a signature of another oscillatory process, which is unrelated to the large-scale transverse motion of loops, e.g., a sausage-type MHD wave excited in a loop. Detailed

analysis of this special case remains however beyond the scope of the present study.

An additional confirmation of the fact that ∼ 10 min modulation of the microwave radiation emitted from the active region AR8910 on 2000-Mar-23, is connected with the transverse oscillatory motion of a coronal loop, shown in Fig. 4a, and that it is in very likely related to the motion of the emission diagram pattern, comes from the graphs in Fig. 4b. This figure enables phase comparison for the transverse motion of the loop (observed with TRACE Aschwanden et al. (2002)) and the filtered 1.7 mHz (∼ 10 min) component of the radiation. The last characterizes temporal behaviour of the radio emission received from the oscillating loop. The shifted phase (∼ *π*) means that the maxima and minima of the radiation part controlled by the loop motion correspond to the specific orientations of the loop and are connected with a certain direction of the emission diagram relative to the observer.

The microwave burst on 2001-Sep-07 represents another example of manifestation of the coronal loop transverse oscillations in modulation of solar radio emissions. The burst was produced during M-flare activity at 15:30 UT in the active region AR9601, close to the solar disc center (see Figure 5a,b), where TRACE observed a group of oscillating loops, immediately after the flare (Aschwanden et al., 2002). The corresponding microwave radiation record was made at 11.7 GHz with the Metsähovi radio telescope. At this frequency, the Metsähovi antenna cannot resolve the position of a radiating source, and the emission from the whole solar disk contributed to the analyzed microwave intensity profile. At the same time, as can be seen in Fig. 5c, which presents the analyzed microwave radiation record with the burst and its VLF modulation dynamic spectrum, the spectral features related to the processes in the flaring active region AR9601 can easily be identified by timing of the event. In particular, the dynamic spectrum of VLF modulations of the microwave radiation exhibits several lines, which start simultaneously with the impulsive phase of the flare (at 15:30 UT). These may be the signatures of different oscillating loops excited by the flare. By this, most of the oscillations (e.g. the dynamic spectrum lines) decay at the time intervals > 20 min. Unfortunately for this particular event it is impossible to determine exact duration of each of these decaying modulations because the available microwave radiation record does not cover the end of the event. As it can be seen in Fig. 5c, some of the dynamic spectrum lines continue beyond the analyzed record time frame.

Three "modulation pairs" can be identified in the dynamic and averaged spectra in Fig. 5c,d: (a) 1.8 mHz (∼ 9.2 min) and 3.6 mHz (∼ 4.6 min); (b) 2.7 mHz (∼ 6.2 min) and 5.4 mHz (∼ 3.1 min); as well as (c) 4.3 mHz (∼ 3.8 min) and 8.6 mHz (∼ 1.9 min), which may be the signatures of transverse oscillating loops with periods ∼ 9.2 min, ∼ 6.2 min, and ∼ 3.8 min, respectively. We note that the loop periods in the cases (a) and (b) are consistent with the 6-10 min oscillating loops observed with TRACE (Aschwanden et al., 2002), whereas the shorter period oscillation (case (c)) cannot be resolved by TRACE because of the relatively long image sampling cadence. The modulation at 5.4 mHz (∼ 3.1 min) may also be a weak third harmonic produced by the 9.2 min oscillating loop. If this is true, then the line at 2.7 mHz (∼ 6.2 min) will have no a pair-companion, and one should exclude the possibility of the ∼ 6.2 min transverse oscillating loop. A "non-paired" weak modulation feature at 6.4 mHz (∼ 2.6 min) may be a signature of an oscillating loop with not resolved second harmonic. At the same time, as for the 2000-Mar-23 event, weak short-period harmonics may be the signatures of oscillatory processes that are unrelated to the transverse motion of a loop, but caused only by a changing magnetic field in the radiating source.

The strong modulation line at 0.6 mHz (∼ 27.7 min) should be considered separately from all other modulations mentioned above. The dynamical spectrum in Fig. 5c, as well as a separate study of VLF modulations of the microwave radiation recorded before the faring burst at 15:30 UT, reveal the presence of the ∼ 27.7 min component also before the flare. In view of the fact

The last example of possible manifestation of transverse oscillations of coronal loops in microwaves which we present here, is the event on 2001-Sep-15, when TRACE observed oscillating loops, associated with M flare at 11:23 UT in the active region AR9608, close to the limb (see Figure 6a,b). Similar to the case of the microwave burst on 2001-Sep-07, the event on 2001-Sep-15 was observed at 11.7 GHz, and the microwave radiation source in AR9608 was not resolved by the Metsähovi antenna. Thus, the emission from the whole solar disk contributed to the analyzed microwave intensity profile. However, as for the burst on 2001-Sep-07, all the spectral features related to the flaring active region AR9608 can be identified by event timing. As it can be seen in Fig. 6c, the dynamic spectrum of VLF modulations of the microwave radiation consists of several lines, most of which begin simultaneously with the impulsive phase of the flare at 11:23 UT. These lines may be associated with oscillatory processes in the active region loops triggered by the flare. All the

<sup>159</sup> Analysis of Long-Periodic Fluctuations of Solar

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

post-flare oscillations decay at the time intervals from ∼ 20 min up to ∼ 1 hour.

the active region AR9608.

Fig. 6d shows the averaged spectral density of the VLF modulations of the microwave burst on 2001-Sep-15. At least one "modulation pair": 1.3 mHz (∼ 12.8 min) and 2.6 mHz (∼ 6.4 min) can be identified among the detected modulation lines. It is very likely connected with a transverse oscillating loop having the period ∼ 12.8 min. This result agrees with the reported TRACE observations of the oscillating loop in the active region AR9608 with a period ∼ 12 − 15 min. Other detected in the microwave record on 2001-Sep-15 (see Fig. 6c,d), more short-periodic modulations at 3.8 mHz (∼ 4.4 min) and 5.2 mHz (∼ 3.2 min) could be higher-order harmonics produced by the 12.8 min oscillating loop, or the modulations associated with oscillatory processes not connected with the transverse motion of loops. They may also be the signatures of oscillatory processes in small loops, which cannot be seen in the TRACE EUV movies due to the limitations of the operated observing mode. Additionally should be mentioned a relatively weak line at 0.7 mHz (∼ 23.8 min). Its possible second harmonic could contribute to the broad line near 1.3 mHz, which is identified as a main frequency line in another modulation pair. If that is the case, then this may be a signature of another transverse oscillating loop with the period ∼ 23.8 min. Verwichte et al. (2010) reported recently detection of such an oscillating loop related with the considered flaring event in the

A special remark deserves also the long lasting ultra-low-frequency (ULF) modulation at 0.3 mHz (∼ 56 min), clearly visible in both, the dynamic and averaged, spectra of the long-periodic modulations of solar microwave radiation on 2001-Sep-15 in Figs. 6c,d. Similarly to the 27 min line in the case of the 2001-Sep-07 burst, this ULF modulation appears before the flaring burst and lasts much longer than all other modulation lines in the spectrum (Fig. 6c). Therefore, it cannot be related to the flare in the active region AR9608 and consequent post-flare dynamics of coronal loops. This modulation feature is probably connected with the solar seismology processes, or a slow dynamics of another active region. As an additional argument in support of the solar global i.e., helioseismic nature of the ULF (*ν*<sup>0</sup> < 0.6 mHz, i.e. *τ* > 30 min) modulations may be the fact that these modulations are usually detected in the radiation records made at 11.7 GHz when the radio emission from the whole solar disk contributes to the analyzed microwave intensity profile. The radiation emitted from the spatially resolved separate active regions, for example, at 37 GHz with Metsähovi radio telescope, does not exhibit any ULF modulation features. In more details the ULF modulations

of solar microwave radiation are considered in Kislyakova et al. (2011).

Fig. 5. (a) SOHO/MDI Magnetogram of the Sun on 2001-Sep-07, white arrow points at the active region AR9601; (b) The Sun image in 304 Å on 2001-Sep-07 from SOHO/EIT, white arrow points at the active region AR9601; (c) Intensity profile and corresponding VLF modulation dynamic spectrum of the microwave burst on 2001-Sep-07, at 15:30-15:50 associated with an M-flare in the active region AR9601; 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.

that the analyzed microwave emission (at 11.7 GHz) was received from the whole solar disk, the ∼ 27.7 min modulated part of radiation very likely originates in another active region. It may also be connected with a kind of global solar seismology process.

16 Will-be-set-by-IN-TECH

Fig. 5. (a) SOHO/MDI Magnetogram of the Sun on 2001-Sep-07, white arrow points at the active region AR9601; (b) The Sun image in 304 Å on 2001-Sep-07 from SOHO/EIT, white arrow points at the active region AR9601; (c) Intensity profile and corresponding VLF modulation dynamic spectrum of the microwave burst on 2001-Sep-07, at 15:30-15:50 associated with an M-flare in the active region AR9601; 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.

that the analyzed microwave emission (at 11.7 GHz) was received from the whole solar disk, the ∼ 27.7 min modulated part of radiation very likely originates in another active region. It

may also be connected with a kind of global solar seismology process.

The last example of possible manifestation of transverse oscillations of coronal loops in microwaves which we present here, is the event on 2001-Sep-15, when TRACE observed oscillating loops, associated with M flare at 11:23 UT in the active region AR9608, close to the limb (see Figure 6a,b). Similar to the case of the microwave burst on 2001-Sep-07, the event on 2001-Sep-15 was observed at 11.7 GHz, and the microwave radiation source in AR9608 was not resolved by the Metsähovi antenna. Thus, the emission from the whole solar disk contributed to the analyzed microwave intensity profile. However, as for the burst on 2001-Sep-07, all the spectral features related to the flaring active region AR9608 can be identified by event timing. As it can be seen in Fig. 6c, the dynamic spectrum of VLF modulations of the microwave radiation consists of several lines, most of which begin simultaneously with the impulsive phase of the flare at 11:23 UT. These lines may be associated with oscillatory processes in the active region loops triggered by the flare. All the post-flare oscillations decay at the time intervals from ∼ 20 min up to ∼ 1 hour.

Fig. 6d shows the averaged spectral density of the VLF modulations of the microwave burst on 2001-Sep-15. At least one "modulation pair": 1.3 mHz (∼ 12.8 min) and 2.6 mHz (∼ 6.4 min) can be identified among the detected modulation lines. It is very likely connected with a transverse oscillating loop having the period ∼ 12.8 min. This result agrees with the reported TRACE observations of the oscillating loop in the active region AR9608 with a period ∼ 12 − 15 min. Other detected in the microwave record on 2001-Sep-15 (see Fig. 6c,d), more short-periodic modulations at 3.8 mHz (∼ 4.4 min) and 5.2 mHz (∼ 3.2 min) could be higher-order harmonics produced by the 12.8 min oscillating loop, or the modulations associated with oscillatory processes not connected with the transverse motion of loops. They may also be the signatures of oscillatory processes in small loops, which cannot be seen in the TRACE EUV movies due to the limitations of the operated observing mode. Additionally should be mentioned a relatively weak line at 0.7 mHz (∼ 23.8 min). Its possible second harmonic could contribute to the broad line near 1.3 mHz, which is identified as a main frequency line in another modulation pair. If that is the case, then this may be a signature of another transverse oscillating loop with the period ∼ 23.8 min. Verwichte et al. (2010) reported recently detection of such an oscillating loop related with the considered flaring event in the the active region AR9608.

A special remark deserves also the long lasting ultra-low-frequency (ULF) modulation at 0.3 mHz (∼ 56 min), clearly visible in both, the dynamic and averaged, spectra of the long-periodic modulations of solar microwave radiation on 2001-Sep-15 in Figs. 6c,d. Similarly to the 27 min line in the case of the 2001-Sep-07 burst, this ULF modulation appears before the flaring burst and lasts much longer than all other modulation lines in the spectrum (Fig. 6c). Therefore, it cannot be related to the flare in the active region AR9608 and consequent post-flare dynamics of coronal loops. This modulation feature is probably connected with the solar seismology processes, or a slow dynamics of another active region. As an additional argument in support of the solar global i.e., helioseismic nature of the ULF (*ν*<sup>0</sup> < 0.6 mHz, i.e. *τ* > 30 min) modulations may be the fact that these modulations are usually detected in the radiation records made at 11.7 GHz when the radio emission from the whole solar disk contributes to the analyzed microwave intensity profile. The radiation emitted from the spatially resolved separate active regions, for example, at 37 GHz with Metsähovi radio telescope, does not exhibit any ULF modulation features. In more details the ULF modulations of solar microwave radiation are considered in Kislyakova et al. (2011).

bursts and the lower limit of sensitivity of the Metsähovi receiver, the intensity modulation amplitude Δ*I<sup>ν</sup>* can be estimated roughly from the obtained VLF spectra, by their comparison with the spectra of specially created modelling signals (Khodachenko et al., 2005). For the considered in the paper events this estimation gives the value of the relative variation of

<sup>161</sup> Analysis of Long-Periodic Fluctuations of Solar

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

intensity is connected only with the varying magnetic field, we come to a relation Δ*Iν*/*I* <sup>0</sup>

(*B*/*B*0)*<sup>γ</sup>* <sup>−</sup> <sup>1</sup> = ((Δ*B*/*B*<sup>0</sup> <sup>+</sup> <sup>1</sup>)*<sup>γ</sup>* <sup>−</sup> <sup>1</sup>), where <sup>Δ</sup>*B*/*B*<sup>0</sup> is the relative variation of magnetic field, and *γ* = −0.22 + 0.9*δ* is the power index of magnetic field in the equation (1). For 2 < *δ* < 7 one gets that *γ* = 1.58 ÷ 6.08. For the case of small relative variations of the magnetic field we

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

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

*<sup>ν</sup>* <sup>∼</sup> <sup>10</sup>−<sup>2</sup> <sup>÷</sup> <sup>10</sup>−1. Assuming, as an upper rough limit, that this variation of

*<sup>ν</sup>* <sup>≈</sup> *<sup>γ</sup>*Δ*B*/*B*<sup>0</sup> <sup>=</sup> <sup>10</sup>−<sup>2</sup> <sup>÷</sup> <sup>10</sup>−1, which for *<sup>B</sup>*<sup>0</sup> <sup>=</sup> 100G gives the amplitude

*<sup>ν</sup>* =

intensity Δ*Iν*/*I* <sup>0</sup>

finally obtain Δ*Iν*/*I* <sup>0</sup>

Δ*B* = (0.16 ÷ 6.3) G.

loop.

**6. Discussion, conclusions and perspectives**

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.

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

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 bursts and the lower limit of sensitivity of the Metsähovi receiver, the intensity modulation amplitude Δ*I<sup>ν</sup>* can be estimated roughly from the obtained VLF spectra, by their comparison with the spectra of specially created modelling signals (Khodachenko et al., 2005). For the considered in the paper events this estimation gives the value of the relative variation of intensity Δ*Iν*/*I* <sup>0</sup> *<sup>ν</sup>* <sup>∼</sup> <sup>10</sup>−<sup>2</sup> <sup>÷</sup> <sup>10</sup>−1. Assuming, as an upper rough limit, that this variation of intensity is connected only with the varying magnetic field, we come to a relation Δ*Iν*/*I* <sup>0</sup> *<sup>ν</sup>* = (*B*/*B*0)*<sup>γ</sup>* <sup>−</sup> <sup>1</sup> = ((Δ*B*/*B*<sup>0</sup> <sup>+</sup> <sup>1</sup>)*<sup>γ</sup>* <sup>−</sup> <sup>1</sup>), where <sup>Δ</sup>*B*/*B*<sup>0</sup> is the relative variation of magnetic field, and *γ* = −0.22 + 0.9*δ* is the power index of magnetic field in the equation (1). For 2 < *δ* < 7 one gets that *γ* = 1.58 ÷ 6.08. For the case of small relative variations of the magnetic field we finally obtain Δ*Iν*/*I* <sup>0</sup> *<sup>ν</sup>* <sup>≈</sup> *<sup>γ</sup>*Δ*B*/*B*<sup>0</sup> <sup>=</sup> <sup>10</sup>−<sup>2</sup> <sup>÷</sup> <sup>10</sup>−1, which for *<sup>B</sup>*<sup>0</sup> <sup>=</sup> 100G gives the amplitude Δ*B* = (0.16 ÷ 6.3) G.
