MICROWAVE QUASI-PERIODIC PULSATION WITH MILLISECOND BURSTS IN A SOLAR FLARE ON 2011 AUGUST 9

On 2011 August 9, a powerful X6.9 solar flare took place in active region NOAA 11263 near the west limb on the solar disk (left panel of Figure 1, observed at an EUV wavelength of 171 Å by the Atmospheric Imaging Assembly on Solar Dynamics Observatory, AIA/SDO). The X6.9 flare event starts at 08:00 UT, reaches maximum at 08:04 UT, and ends at 08:14 UT (top-right panel in Figure 1). It is the largest flare event in the current solar Schwabe cycle, and it resulted in a coronal mass ejection. A strong microwave burst (right panels of Figure 1) that accompanied this flare was observed at a frequency of 2.60–3.80 GHz by the Chinese Solar Broadband Radio Spectrometer in Huairou (SBRS/Huairou). The microwave burst starts at 08:01 UT and ends at 08:07 UT, lasting only about 6 minutes. For comparison, we know that the microwave burst associated with other X-class flare events always has a long duration of several tens of minutes or 1–2 hr; for example, the X3.4 flare event on 2006 December 13 has a duration of 110 minutes (Tan et al. 2010). In the peculiar short duration of the microwave burst in the X6.9 flare event, the most prominent feature is the quasi-periodic pulsation (QPP) and its accompanied superfine structures of millisecond timescales. The main task of this work is to investigate the peculiar features of the microwave QPP and its related physical processes in detail.

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It is well known that the flare-related QPP, especially at the microwave frequency range, can be a valuable diagnostic tool for in situ conditions in the flaring source region, and the investigations can provide unique insight into coronal plasma dynamic processes. For example, the duration of a QPP can be a measure of the plasma density inhomogeneity in the source region, the periodicity can be a measure of the diameter or the width of the inhomogeneity, and so on (Roberts et al. 1984). Many authors have studied the features and physical mechanisms from observations and theoretical models (Young et al. 1961, Gotwols 1972, Fu et al. 1990, Kliem et al. 2000, Nakariakov et al. 2003, Tan et al. 2007, etc.). Aschwanden (1987) presented an extensive review of QPP models and classified them into three groups: (1) MHD oscillations that modulate the microwave emissivity with standing or propagating waves (Roberts et al. 1984; Nakariakov & Melnikov 2009), (2) periodic self-organizing systems of plasma instability, and (3) the periodic particle accelerations. Different kinds of models can explain different timescales of QPP. Recently, a series of microwave QPPs with multi-timescales forming a broad hierarchy have also been reported; it is proposed that different timescales of QPP may have different generation mechanisms. The broad hierarchy of timescales of QPP that occurred in the same flare event may imply that there is a multi-scale hierarchy of sizes of the magnetic configurations and the timescales of the dynamic magnetic reconnection processes in the flaring region (Tan et al. 2010).

On the spectrogram of broadband microwave observations, the QPP behaves as a train of approximated almost equidistant vertical bright stripes. Each bright stripe is a QPP pulse. Generally, the previous works regarded the pulse as a relatively isolated element. So far, there have been very few works investigating whether there are some further superfine structures in each QPP pulse. Chernov et al. (2008) reported a flare event in which some pulses of the weakly rapid microwave QPP consisted completely of several small-scale narrowband drifting millisecond fibers, and the frequency drift rate of the fibers was in the range of −160 to −270 MHz s⁻¹. In this work, we find that each individual pulse of the rapid microwave QPP is made up of clusters of millisecond spike bursts or narrowband type III bursts with frequency drift rates of about 20 GHz s⁻¹. We will introduce the peculiar features of the superfine structures in the QPP in Section 2 and present a physical analysis in Section 3. Finally, some conclusions are drawn in Section 4.

2.1. Observational Data and Analysis Method

2.2. Observational Results

During the X6.9 flare, SBRS/Huairou obtained high-quality observations at a frequency of 2.60–3.80 GHz. The right panels of Figure 1 present the profiles of the microwave flux at a frequency of 2.80 GHz with left- and right-handed circular polarizations around the flaring event. As a comparison, the profiles of GOES soft X-ray (SXR) intensities at wavelengths of 1–8 Å (GOES8) and 0.5–4 Å (GOES4) are also plotted in Figure 1. Here, we find that the main part of the microwave burst occurred in the flare rising and peak phase, and decays rapidly after the flare peak. The microwave intensity profile has two obvious enhancements; the first one is at about 08:02:04 UT and the second one is at about 08:03:56 UT. An obvious QPP occurred during 08:03:09–08:03:30 UT, in the midst of the two enhancements (marked with a thick bidirectional arrow in the right panel of Figure 1), very close to the maximum of the SXR GOES flare (08:04 UT).

A careful inspection of the RHESSI HXR observations displays that HXR emission also shows QPP features at an energy of 12–100 keV. The wavelet analysis indicates that evidence of HXR QPP is most obvious at an energy of 25–50 keV. Figure 2 presents the light curve of HXR at an energy of 25–50 keV during the microwave QPP occurrence, which shows that the intensity of HXR emission also has an obvious feature of QPP, and the average period is about 2.46 s, which belongs to short-period pulsation (SPP).

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Figure 3 presents the microwave QPP observed by SBRS/Huairou at a frequency of 2.60–3.80 GHz. The top-left panels show the spectrogram of the QPP at left- and right-handed circular polarizations, and the QPP behaves as a series of bright pulses, which indicates that the QPP can be divided into three different pulse groups: the first pulse group begins at 08:03:09 UT, ends at 08:03:17 UT, and lasts for 8 s (marked as group A); the second begins at 08:03:18, ends at 08:03:22 UT, and lasts for 4 s (marked as group B); and the third begins at 08:03:23, ends at 08:03:29 UT, and lasts for 6 s (marked as group C). The frequency bandwidth of each pulse is in the range of 400–1100 MHz. The comparison between the left- and right-handed circular polarizations shows that the QPP is strongly right-handed circular polarized with a polarization degree of about 70%. The measurement of the time intervals between each adjacent vertical bright stripe indicates that the period of the QPP is about 0.70 s, 0.86 s, and 0.42 s at the first, second, and third pulse groups, respectively. All of them belong to broad bandwidth very short period pulsation (VSP; Wang & Xie 2000; Tan et al. 2007). Comparing the microwave and HXR, we find that the period of the microwave QPP is much shorter than that of the HXR QPP. The top-right panels of Figure 3 show the profiles of the flux intensities of the microwave QPP at left- and right-handed circular polarizations at a frequency of 2.84 GHz (upper and middle panels). This indicates that the emission enhancement at each QPP pulse with respect to the background emission is about 100–250 sfu, which demonstrates that the QPP is very obvious and strong.

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The arranged patterns of microwave QPP pulse groups indicate that there are frequency drifts in each pulse group (GFDR). In order to obtain the frequency drift rate, we define the central frequency of each pulse at its central time as follows:

$$\begin{equation} f_{{\rm cp}}=\frac{\sum (f_{i}\times F_{i})}{\sum F_{i}}. \end{equation} \tag{ 1 }$$

Here, the central time of the pulse is when the flux intensity approaches the maximum around the pulse. f_i is the frequency and F_i is the corresponding flux intensity which subtracts the background emission around the occurrence of the microwave QPP. The bottom of the top-right panel of Figure 3 presents the distribution of the central frequency (f_cp) at each QPP pulse. The dotted lines are fitted by linear least-squares methods. In QPP group A, the central frequency of QPP pulses can be fitted by a single line; the slopes of the fitted lines give an average GFDR of 53.3 MHz s⁻¹. In QPP group B, the central frequency of QPP pulses can also be fitted by a single line with a GFDR of −78.9 MHz s⁻¹. In QPP group C, the central frequency of QPP pulses decreases slowly in the first half with a GFDR of −98.2 MHz s⁻¹, and then increases slowly with a GFDR of 129.5 MHz s⁻¹ in the second half. It seems that some dynamic processes that occurred in the emission source region.

The bottom panels of Figure 3 present the expanded spectrograms of QPP pulse groups A (left), B (middle), and C (right) at the left- and right-handed circular polarizations, respectively, which can present the details of the superfine structures on each QPP pulse. With a careful inspection, we find that the frequency drifts also occur at each QPP pulse (SPFDR). We apply a similar method, as described in Tan et al. (2010), to determine the SPFDR. The top-left panel of Figure 4 presents examples of the method; the SPFDR can be calculated by the slope rate of the fitted lines. The top-right panel of Figure 4 plots the calculated results of the SPFDR in the whole QPP. Here, we find that all of the SPFDRs of QPP pulse group A are negative, their absolute values are in the range of 3.51–13.84 GHz s⁻¹, and their average value is 7.73 GHz s⁻¹. However, the SPFDRs in QPP pulse groups B and C change rapidly from negative to positive, the absolute values are from 4.38 GHz s⁻¹ to 14.61 GHz s⁻¹ in group B and 2.91 GHz s⁻¹ to 26.25 GHz s⁻¹ in group C, and their average value is about 7.78 GHz s⁻¹ in group B and 15.88 GHz s⁻¹ in group C. In addition, almost all of the SPFDRs are at least two orders higher than that of GFDR in the QPP pulse groups.

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At the same time, a careful inspection of each individual QPP pulse presents another important feature: each pulse has a superfine structure in shorter timescales. The expanded spectrograms (the bottom panels of Figure 3) present the details of the millisecond superfine structures in each QPP pulse. Here, we find that almost all of the microwave QPP pulses are structured with clusters of millisecond spike bursts. The bandwidth of the spike bursts is in the range of 20–60 MHz, the duration is in the range of 8–24 ms (however, being restricted by the 8 ms cadence of the telescope, we cannot know if there are any spike bursts with durations shorter than 8 ms; in fact, some spike bursts are only observed by a single data point, and this evidence is enough to lead us to believe that some spike bursts may have a lifetime shorter than 8 ms), the flux intensity is in the range of 50–100 sfu, and the polarization degree is close to 100% (bottom-left panel of Figure 4). In addition, part of the millisecond spikes shows obvious evidence of a fast negative frequency drifting rate with values ranging from −18 GHz s⁻¹ to −25 GHz s⁻¹, with an average of −20 GHz s⁻¹.

The bottom-right panel of Figure 4 shows the expanded profile at a frequency of 3.23 GHz of a QPP pulse, which shows that the QPP pulse is structured with a cluster of type III bursts. The type III bursts form a drifting pulsating structure with a local GFDR of about 2.91 GHz s⁻¹ and a pulsating period of about 0.16 s. As for each individual type III burst, the instantaneous duration is about 8–24 ms, the frequency bandwidth is about 500–1000 MHz, the polarization degree is above 85%, the frequency drift rate ranges from −14.58 GHz s⁻¹ to −20 GHz s⁻¹, and the average value is about −17.30 GHz s⁻¹.

From the bottom-right panel of Figure 3, several segments of strong zebra pattern (ZP) structures can be found at a frequency of 2.60–2.75 GHz at 08:03:24–08:03:27 UT accompanying the microwave QPP pulses. Three zebra stripes can be seen in the extended spectrogram in Figure 5 around 08:03:26 UT; the flux intensities on individual stripes are degressive from low frequency to high frequency (about 1100–1300 sfu on the low-frequency stripe, 700–1000 sfu on the middle stripe, and 200–600 sfu on the high-frequency stripe above the adjacent background emission). This shows strong right-handed circular polarization. The frequency separation between the adjacent zebra stripes is about 70–100 MHz. Generally, the ZP structure is always regarded as one of the most important microwave fine structures that can be used to diagnose magnetic field strength in the coronal source regions (Zlotnik 2009; Chernov 2010). Adopting a similar method of magnetic field estimation from ZP structure with a double plasma resonance model in the same frequency range used in the work of Tan et al. (2012), we may obtain that the magnetic field strength in the coronal source region of the ZP structure is about 147–210 G, and the average value is about 178 G.

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In brief, the RHESSI HXR observation at an energy of 25–50 keV implies the existence of an HXR QPP with a period of 2.46 s. At the same time, the microwave observation at a frequency of 2.60–3.80 GHz indicates the occurrence of a much faster QPP with an average period of 0.705 s. Each pulse of the microwave QPP is structured with clusters of spikes or type III bursts in millisecond timescales. All of them are strongly right-handed circular polarizations, and there are three different frequency drifting rates:

• 1.  
  GFDR of the microwave QPP pulse group: in several decades of MHz s⁻¹, positive or negative;
• 2.  
  SPFDR of the microwave QPP pulse: in several or more than 10 GHz s⁻¹, positive or negative; and
• 3.  
  SPFDR of millisecond spike bursts or type III bursts: around 20 GHz s⁻¹, negative.

What physical implications are hinted in the millisecond superfine structures of each individual microwave QPP pulse, and how do we understand the three different kinds of frequency drift rates?

First, we need to determine the mechanism of the QPP. Here, we are only interested in the HXR QPP with a period of 2–3 s and the microwave VSP with a period of subseconds. It is well known that propagating MHD oscillation modes or the standing fast sausage modes in dense magnetic traps may produce a QPP with a period of the above values (Roberts et al. 1984; Aschwanden 1987; Tan et al. 2010). Zaitsev et al. (1984) demonstrated that the variation of plasma density in a magnetic loop by fast magnetosonic waves excited by energetic protons in Cherenkov or bounce resonance might produce a QPP with a period of seconds. Zaitsev et al. (1998, 2000) proposed another model in which a current-carrying plasma loop should be an LRC-circuit resonator, which might cause periodic modulation of the loop magnetic field, energy release rate, and energetic electron production; therefore, the microwave emission, and the corresponding period, should be dependent on the longitudinal electric current (P_LRC ∼ 10¹²/I_φ, I_φ is the longitudinal electric current in the loop). In order to produce VSP in this work, the longitudinal electric current in the loop should be in the range of (1.16–2.38) × 10¹² A. Such a value is very popular in a general flaring plasma loop (Gary & Demoulin 1995, Tan 2007, etc.). It seems that the above models are the possible candidates for the QPP with periods as given in this work. However, these models have a bit of difficulty in explaining the frequency drifting rates and the superfine structures with clusters of millisecond spike bursts or type III bursts. Here, we need a model that can explain the properties including the rapid QPP and the superfine spiky structures.

Kliem et al. (2000) and Karlicky (2004) proposed that microwave QPP can be caused by quasi-periodic particle acceleration from a highly dynamic regime of magnetic reconnection in an extended large-scale current sheet above the flaring loop. The reconnection is dominated by repeated formation and subsequent coalescence of magnetic islands, known as secondary tearing modes (TMs). This model can explain the QPP with a period of 0.5–5 s in solar flares. In particular, they may explain the GFDR of QPP as a motion of the plasmoid in the density gradient of the solar atmosphere. Here, particles are accelerated near the magnetic X-points in the DC electric field associated with magnetic reconnection. The strongest electric fields occur at the main magnetic X-points adjacent to the plasmoid, and a large fraction of the accelerated particles may only be temporarily trapped in the plasmoid; the accelerated process itself may form an anisotropic velocity distribution, which may excite the microwave emission. Based on particle-in-cell simulation, Karlicky & Barta (2007) found that electrons are accelerated most efficiently in the region near the X-point of the magnetic configuration at the end of the tearing process and the beginning of plasmoid coalescence. The most energetic electrons are localized mainly along the X-lines of the magnetic configuration. During these processes, plasma emission is generated and propagated.

Tan et al. (2007) proposed that modulations of the resistive TM oscillations in electric current-carrying flaring plasma loops can also produce a VSP with subsecond periods. The duration of the VSP is dominated by the current density distribution, magnetic configuration, and plasma resistivity; the period of VSP is dominated by the total electric current, the loop's geometrical parameters, and the distribution of current density in the cross section of the loop. The pulsating emission is localized in some regions of small size, for example, around magnetic islands in flaring plasma loops. From the bandwidth of the emission we may estimate the perturbation of the plasma density. The frequency drifting rate can reflect the motion of the plasma loop and the energetic particles. Combining all these observable parameters, we may probe many physical conditions and their evolutions.

As for the mechanism of the millisecond spike bursts or narrowband type III bursts, Benz (1986) proposed that decimeter narrowband millisecond spikes are coherent emission as a signature of electron acceleration in the flare, and that flare energy release must be fragmented with each spike indicating a single energy release episode in the shortest time and space scale originating from magnetic reconnection sites (Huang & Nakajima 2005; Wang et al. 2008). Fleishman & Melnikov (1999) made a detailed comparison of the observed spike properties with various theoretical models and found that the electron cyclotron maser emission (ECME) driven by nonthermal electrons can explain almost all the observed properties. Fleishman et al. (2003) proposed that the source of the spike cluster should be a coronal loop filled by fast electrons and relatively tenuous background plasma. Each spike is generated by ECME in a local small source inside the loop. ECME takes place only when the following conditions are satisfied (Melrose & Dulk 1982):

$$\begin{equation} \omega -\frac{s\omega _{{\rm ce}}}{\gamma }-k_{\parallel }v_{\parallel }=0 \end{equation} \tag{ 2 }$$

and

$$\begin{equation} \omega _{{\rm ce}}\gg \omega _{{\rm pe}}. \end{equation} \tag{ 3 }$$

Here, ω is the emission frequency, ω_ce is the electron gyrofrequency, ω_pe is the electron plasma frequency, s is the harmonic number, γ is the Lorentz factor of the energetic electrons, and k_∥ and v_∥ are the parallel components of the wave number and particle velocity, respectively. Equation (3) implies that the source region of ECME must have a relatively strong magnetic field. Because of the accompanying ZP and microwave QPP structures, we may suppose that their source regions are close to each other, and the magnetic field strengths are also similar to each other. However, the estimation of ZP structures indicates that the magnetic field strength is about 147–210 G, and the corresponding gyrofrequency f_ce is about 412–588 MHz, which is much lower than the observed frequency (∼ 3.00 GHz). This fact implies that ECME seems not to be the formation mechanism of the millisecond spiky bursts observed in this work.

It is well known that there is another kind of coherent emission: plasma emission, which is always generated from the coupling of two excited plasma waves with frequency of about 2f_pe and weak polarizations, or the coupling of an excited plasma wave and a low-frequency electrostatic wave with frequency of about f_pe and strong polarizations (Zheleznyakov & Zlotnik 1975; Chernov et al. 2003). Generally, the plasma emission is triggered by some Langmuir turbulence produced from nonthermal energetic electrons.

Combining the above analysis, we may qualitatively plot the physical processes associated with the QPP as in Figure 6:

• 1.  
  From the idea of Kliem et al. (2000), we may propose that the energetic electrons accelerating from a highly dynamic magnetic reconnection in an extended large-scale current sheet above the flaring loop propagate downward, interact with the plasma in the flaring loop, and produce HXR bursts by the bremsstrahlung mechanism. The TM oscillation in the current sheet may modulate the HXR emission and form the HXR QPP (the big red arrow in Figure 6).
• 2.  
  The energetic electrons propagating downward may impact the flaring loop and trigger the Langmuir turbulence and plasma waves in the loop. The coupling between the plasma wave and the low-frequency electrostatic wave emits microwave radiation by the mechanism of plasma emission. From the idea of Tan et al. (2007), the modulation of the TM oscillation in the current-carrying plasma loop may lead to the formation of microwave QPP. As the frequency of plasma emission depends on the plasma density, the motion of the flaring loop with respect to the background may change the plasma density and result in the frequency drifting rate of the microwave QPP pulse groups. The motion of the energetic electron beam with respect to the background results in the frequency drifting rate of the QPP pulses. From the mechanism of plasma emission, the GFDR of the QPP pulse group is due to the motion of the plasma loop (Aschwanden & Benz 1986):

  $$\begin{equation} \frac{\partial \omega }{\partial t}=-\frac{\omega }{2H_{n}}v_{{\rm loop}}\cos \theta. \end{equation} \tag{ 4 }$$

  Here, H_n is the scale length of the density inhomogeneity in the ambient plasma of the loop, v_loop is the velocity of the loop's motion, and θ is the angle between the line-of-sight and the magnetic field line. Generally, we may assume H_n ∼ 10⁴ km and θ ∼ 0. Substituting the GFDR of the QPP group into Equation (4), we may obtain that the velocity of the loop is about 550 km s⁻¹ upward in group A, 526 km s⁻¹ downward in group B, and from 655 km s⁻¹ downward to 863 km s⁻¹ upward in group C.In Equation (4), if we replace v_loop with the velocity of the energetic electron beams (v_beam), then we may obtain the SPFDR of the QPP pulse. Substituting the values of SPFDR of QPP pulses into Equation (4), we obtain that the velocity of the energetic electron beams is about 1.94 × 10⁴–1.75 × 10⁵ km s⁻¹, and the corresponding kinetic energy of the energetic electrons is about 1.07–86.7 keV.
• 3.  
  The TM instability causes the formation of many magnetic islands in the current-carrying plasma loop. Each X-point between the adjacent magnetic islands will be a small reconnection site and will make a secondary acceleration on the ambient electrons (Drake et al. 2006). These accelerated electrons impact the adjacent plasmas around the X-point, trigger the Langmuir turbulence and plasma waves, and produce microwave bursts by plasma mechanism. Such microwave bursts are just the spikes or type III bursts. As there are many magnetic X-points in the current-carrying plasma loop, each X-point will be a small reconnection site, and the region around each X-point will be a source of a spike burst or type III burst. As a result, the spike bursts or the type III bursts can arise in huge clusters. Because the plasma density always has a negative gradient from the X-point to the space between two adjacent rational surfaces (Furth et al. 1973; Drake et al. 2006), the frequency drifting rates of spike bursts or type III bursts are negative. Because the scale length of the density inhomogeneity (H_n) around the X-point is shorter than that in the ambient plasma of the loop, from Equation (4) we may conclude that the frequency drifting rates of spike bursts or type III bursts are higher than those of the microwave QPP pulses.

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Based on the above observations and physical analysis, we derive the following conclusions:

• 1.  
  Just before the flare maximum, there are HXR QPPs and microwave QPPs with durations of about 20 s. The HXR QPP belongs to an SPP, and the microwave QPP belongs to a VSP. Each individual microwave QPP pulse is structured with clusters of millisecond bursts; most of the millisecond bursts are clusters of spike bursts, and the rest are type III bursts. There are three different frequency drifting rates: GFDR of the microwave QPP pulse group, SPFDR of the microwave QPP pulse, and SPFDR of millisecond spike bursts or narrowband type III bursts.
• 2.  
  The physical processes associated with the QPP can be described as follows: the energetic electrons accelerating from a highly dynamic magnetic reconnection in an extended large-scale current sheet above the flaring loop propagate downward, interact with the plasma of the flaring loop, and produce HXR bursts by bremsstrahlung mechanism. The TM oscillation in the current sheet may modulate the HXR emission and form HXR QPP; the energetic electrons propagating downward may produce the Langmuir turbulence and plasma waves in the loop and trigger the plasma emission. The modulation of the TM oscillations in the current-carrying plasma loop may lead to the formation of microwave QPP. The TM instability causes the formation of magnetic islands in the current-carrying plasma loop. Each magnetic X-point between the adjacent two magnetic islands will be a small reconnection site and will make a secondary acceleration on the ambient electrons. These accelerated electrons may impact the ambient plasma and trigger the millisecond spike clusters or the group of type III bursts by plasma mechanism.
• 3.  
  Each magnetic X-point is an energy releasing site in the current-carrying plasma loop, and each millisecond spike burst or type III burst is possibly one of the elementary bursts (EBs). A large number of EB clusters form an intense flaring microwave burst.
• 4.  
  We may apply the above conclusions to analyze the conditions of the source regions, e.g., the GFDR of the microwave QPP pulse group can be adopted to estimate the motion of the flaring loop, the SPFDR of the microwave QPP pulse can be adopted to estimate the velocity of the energetic electrons and the corresponding energies, and the SPFDR of millisecond spike bursts or type III bursts can be applied to estimate the density inhomogeneity (H_n) around the X-point in the flaring plasma loops.

However, as we lack imaging observations with spatial resolutions in the corresponding frequency range, there are many unresolved problems of the QPPs, for example, the spatial behaviors, the spatial scales of the source region, etc. To overcome these problems, some new instruments are needed, for example, the Chinese Spectral Radioheliograph (0.4–15 GHz) in the decimeter- to centimeter-wave range, currently being constructed (Yan et al. 2009), and the proposed American Frequency Agile Solar Radiotelescope (50 MHz–20 GHz; Bastian 2003). Perhaps, when these instruments begin to work, we will obtain further cognitions of the solar activities.

The authors thank the referee for helpful and valuable comments on this paper. Thanks are also due to the GOES, RHESSI, SDO/AIA, and SBRS/Huairou teams for the observational data. This work is mainly supported by NSFC grant nos. 11103044 and 10921303, MOST grant no. 2011CB811401, and the National Major Scientific Equipment R&D Project ZDYZ2009-3.