SUZAKU/WAM AND RHESSI OBSERVATIONS OF NON-THERMAL ELECTRONS IN SOLAR MICROFLARES

Solar flares are signatures of impulsive releases of magnetic energy in the solar corona. The energy content in the thermal flare loops varies from 10³³ erg in the largest flares down to 10⁻⁶ and 10⁻⁹ times less in microflares and nanoflares, respectively. Hard X-ray (HXR) observations reveal that solar flares also efficiently accelerate electrons (see review by Fletcher et al. 2011). HXRs have also been detected in microflares (Lin et al. 1984). After the first discovery, non-thermal HXR emissions from microflares were observed by the Yohkoh/Hard X-Ray Telescope (Nitta 1997), the Compton Gamma Ray Observatory/BATSE (Lin et al. 2001), and RHESSI (Krucker et al. 2002; Christe et al. 2008; Hannah et al. 2008a). Christe et al. (2008) and Hannah et al. (2008a) performed a statistical study of 25,705 microflare events using RHESSI observations over five years, reporting the statistical properties of non-thermal emissions in microflares. Microflares have non-thermal powers of 10²⁵–10²⁸ erg s⁻¹ (5%–95% range, the median value is 10²⁶ erg s⁻¹) and power-law indices of 4–10 (the median value is 7). The frequency distribution of the RHESSI microflares is similar to that of large flares, suggesting that microflares are qualitatively similar to large flares (Christe et al. 2008). Nanoflares are proposed to contribute to the heating of the corona (e.g., Parker 1988). In particular, the smallest events may play a significant role due to their high frequency of occurrence, even though the energy released in each event is small (Hudson 1991). Although microflares observed with present-day observatories do not have sufficient energy to heat the corona (Hannah et al. 2011), the minimum energy of nanoflares is not yet determined due to limitations in the sensitivity of HXR instruments.

Although not relevant for the total released energy, the maximum energy up to which electrons are accelerated in microflares is not well understood. While microflares frequently show softer/steeper spectra than regular flares (e.g., Battaglia et al. 2005), some also show spectra comparable to the hardest/flattest flare spectra (e.g., Hannah et al. 2008b). Because of the rather short durations of non-thermal HXR microflares (typically <1 minute; see Benz & Grigis 2002), a large effective area is essential for the detection of high-energy photons from microflares. The Wide-band All-sky Monitor (WAM; Yamaoka et al. 2005; Yamaoka et al. 2009), which is a part of the Hard X-Ray Detector (Takahashi et al. 2007; Kokubun et al. 2007) on board the Suzaku satellite (Mitsuda et al. 2007), is an HXR and γ-ray all-sky monitor with the highest effective area among the instruments presently observing the Sun. The WAM detector is a Bi₄Ge₃O₁₂ scintillator with an effective area of ∼800 cm² at 100 keV (∼13 times larger than that of RHESSI) with a 1 s time resolution. The energy range of WAM is from 50 keV up to 5 MeV. The energy bin width is ∼40 keV below 1 MeV (calibration spectra of radioisotope sources including ²⁴¹Am 60 keV and ⁵⁷Co 122 keV lines can be found in Yamaoka et al. 2005). WAM and RHESSI were cross-calibrated using simultaneous flare observations above 50 keV. However, flux uncertainties remain ∼15% above 200 keV and >40% below 200 keV (Endo et al. 2010). WAM has a complex detector response, and the response changes significantly depending on the incident angle. Since Suzaku's pointing changes frequently (every ∼1 day), the angle between the telescope axis and the Sun is different for every flare. Therefore, the detector response matrix must be calculated using Monte Carlo simulations for each event. This makes the conversion from WAM counts to photons labor intensive (see Yamaoka et al. 2009; Ohno et al. 2005).

A statistical survey of 105 solar flares observed by Suzaku/WAM between the Suzaku launch in 2005 July and 2009 November has been reported by Endo et al. (2010). The GOES classes of these flares are from X9.0 down to B2.3 (background not subtracted). Hence, several microflares were found with emissions above >50 keV. In this paper, we present a systematic spectral analysis of non-thermal HXR emissions from microflares (defined here as GOES B-class flares or smaller) using Suzaku/WAM and RHESSI to investigate the question of whether microflares accelerate electrons above 100 keV as observed in regular flares, or if there is a cutoff energy that would indicate a difference in the acceleration process compared to regular flares. The existence or the absence of such a cutoff energy will provide important tests of the proposed acceleration mechanisms.

The data analysis was divided into two tasks: (1) the WAM solar flare list was searched for microflares with simultaneous RHESSI observations and (2) the RHESSI microflare list was searched for events that should be detectable by WAM if the non-thermal power-law spectrum seen by RHESSI extends to above 50 keV.

The Suzaku/WAM team released the list of detected solar flare events observed by WAM: 17 B-class flares were reported between the Suzaku launch (2005 July) and 2010 February. Simultaneous RHESSI observations exist for 7 of these 17 microflares. Before the observation of the WAM event of 2006 November 20, an unusual behavior on the Suzaku spacecraft was detected and the spacecraft's mode was changed to the safehold mode, which is an emergency low-power operation mode. While WAM continues to observe in safehold mode, the effect of the mode on WAM observations is not well known. We regard the data of that event as unreliable, and thus we only analyzed the other six events. The background-subtracted GOES classes of the remaining six events are between B1.3 and B9.5.

X-ray light curves of the six Suzaku/WAM and RHESSI microflares are shown in Figure 1. Thermal soft X-ray emissions from GOES and the non-thermal HXRs from RHESSI and WAM are plotted in the time ranges including the start of the event and the GOES peak time. Durations of the HXR events at 20–30 keV are a few tens of seconds. Three time bins (3 s) of WAM's first energy bins and 10 time bins (10 s) of the second energy bins are averaged to produce the light curves shown. HXRs are clearly detected by the WAM first energy bin in all the flares. Although the emissions are not as clearly detected by the second energy bin compared to the first energy bin, peaks in the second bin corresponding to the HXR peaks are seen in all events. In all six events, the RHESSI and WAM light curves show a close temporal agreement. For four out of six events, NoRH microwave observations are available. No significant radio emission from the 2006 November 10 event is seen. In the three other events with radio observations, the radio light curves also agree with the time evolution of the HXR light curves. The lack of magnetic field estimates, however, makes it difficult to get any quantitative estimates for the typical energy of the synchrotron-producing electrons. However, the radio observations indicate that in at least three out of four events, electrons with energies of at least several hundred keV are present as well.

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Figure 2 shows combined spectra of RHESSI and WAM for the six microflares integrated over the HXR peaks. The black lines with the error bars are RHESSI data, and the gray curves are RHESSI background spectra, which are determined by interpolating the fluxes from before and after each HXR peak with a polynomial function (the same method is used by Endo et al. 2010 and Sugita et al. 2009 for WAM data). Although WAM data are about 20 times smaller than RHESSI background around 100 keV, >50 keV emissions are clearly detected. We fitted the RHESSI data with a thermal bremsstrahlung model (red curve) and a power law (blue line) for the non-thermal emissions. In each plot, we give the numbers of the RHESSI detectors used in the spectral fit. If the counting rate was high enough, we only used detector 1, which appears to have the least degradation due to radiation damage, to determine the thermal components. For the three events (2005 November 17, 2007 May 19, and 2010 February 12), the non-thermal parameters were obtained using all the detectors except for 2 and 8.

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The WAM backgrounds are also determined by fittings with a polynomial function, and are shown by the brown lines in Figure 2. The error estimates consider two components: a statistical error

$$\begin{equation} \sigma _{{\rm st}} = \sqrt{S+B}, \end{equation} \tag{ 1 }$$

where S is the signal count and B is the background count, and a systematic error

$$\begin{equation} \sigma _{{\rm sy}} = \alpha S, \end{equation} \tag{ 2 }$$

where α is a constant. By comparing Wind/Konus and Swift/BAT data, Sakamoto et al. (2011) derived α < 0.2 for >200 keV. However, as mentioned by Endo et al. (2010), α is larger than 0.4 for the < 200 keV energy bins mainly because it contains the digitization errors of the analog-to-digital converter due to the wide energy bin width. We assumed and used α = 0.5 for the analysis here. The total uncertainty σ becomes

$$\begin{eqnarray} \sigma &=& \sqrt{\sigma _{{\rm st}} ^2 + \sigma _{{\rm sy}} ^2} \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} \qquad \quad &=& \sqrt{0.25S^2+S+B}. \end{eqnarray} \tag{ 4 }$$

For the first energy bin of WAM, the systematic errors σ_sy are dominant for all the events due to large enough statistics. On the other hand, the statistic errors σ_st are dominant in the second and third energy bins. The conversion of the WAM count rate to photon fluxes has a slight (lower than ∼20% at most) dependence on the spectral shape. Since the error estimates are dominated by systematic and statistical errors, the dependence on the spectral shape does not influence the results shown here. For the conversion, we assume that the power-law indices obtained by RHESSI fittings are the same in the WAM energy band. The estimated photon fluxes of the WAM bands are given as magenta points in Figure 2.

The power laws obtained by RHESSI non-thermal emissions of all flare events have good agreement with the WAM data within the errors. We did not find any significant cutoff of the power-law spectra below the third energy bin of WAM. This suggests that electrons are accelerated with single power-law distributions up to at least ∼100 keV for all events.

HXR imaging of these events is not the focus of this paper. In any case, it is difficult to create an image of each WAM/RHESSI microflare event because of the poor statistics, particularly in the non-thermal range. For the 2007 May 19 event, RHESSI HXR imaging results are reported by Hara et al. (2011) finding systematic HXR source motion at 15–40 keV. These observations, as well as the statistical analysis of microflare imaging by Hannah et al. (2008a), suggest that this flare can be explained by the standard scenario with magnetic reconnection near the loop-top.

The non-thermal parameters of the Suzaku/WAM and RHESSI microflare events are summarized in Table 1. The photon indices are between 3.3 and 4.5, which are rather hard compared to statistical studies of microflares that show values between 4 and 10 (Christe et al. 2008; Hannah et al. 2008a). This is a natural result considering the sensitivity limit of WAM. In addition, the non-thermal powers are large compared to the RHESSI microflare statistics. This can also be explained by the sensitivity limit of WAM, because detectable microflares must have hard power-law indices and high fluxes.

The distribution of fluxes and photon indices of the RHESSI microflares observed between 2002 February and 2007 February appearing in Christe et al. (2008) and Hannah et al. (2008a) are plotted in Figure 3. In case a low-energy break of a non-thermal component is low, the estimated non-thermal spectra is not reliable because it is difficult to distinguish thermal and non-thermal components. We plotted the events with the low-energy break of >7 keV following Hannah et al. (2008a), at the 3σ confidence level. This criterion eliminates about 80% of events, with 4401 events remaining out of 25,705. The six Suzaku/WAM and RHESSI microflare events noted in the previous section are plotted in red in Figure 3. The black solid curve shows the estimated detection limit of microflares in the first energy bin of WAM (∼60–100 keV) by assuming that the power-law spectra extend up to 100 keV. This limit corresponds to counts from a flare that is 3σ larger than the background in that energy bin. A typical response of WAM is used for this estimation together with a duration of 20 s and typical background count rate of 500 counts s⁻¹. The limit of a flux changes up to ∼50% due to differences in the WAM response and background and flare duration, and the dashed curves show ±50% of the black curve for a flux. Only 2.8% of the RHESSI microflares are above this limit (the upper left side of the solid curve). These events have relatively high fluxes and hard indices.

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According to the RHESSI microflare list (Christe et al. 2008), 15 RHESSI microflares should have been detected by WAM (i.e., 15 microflares are above the curve in Figure 3 during the time WAM was operating, excluding times when Suzaku was in the South Atlantic Anomaly or otherwise not ready for observations) between 2005 July and 2007 February. After closer inspection, it turns out that three of these automatically fitted RHESSI events are due to instrumental artifacts: in the 2006 December 14 event around 08:53 UT, the RHESSI peak is seen only by detector 4, up to >100 keV with a flat count rate spectrum indicating an instrumental origin. Two events were wrongly fitted due to incorrect subtraction of the pre-event background (2006 November 6 around 03:57 UT and 2006 November 11 around 22:49 UT). This leaves a total of 12 detectable events, 4 of which were microflares shown in Figure 1 from the original WAM solar flare list (note that the remaining two events from Table 1 occur after the end of the RHESSI microflare list from Christe et al. 2008). The eight new events are listed in Table 2, and shown in Figure 3 by the orange data points. We checked WAM light curves for all of these events, and found significant emission at the lowest energy bin in seven events. The only event not detected by WAM is the smallest event in the sample (2005 December 12 at 03:06 UT). Hence, by slightly changing the input to the WAM sensitivity estimates, we could in principle exclude this event (see the dashed curves in Figure 3). In summary, 11 out of 12 (92%) RHESSI microflares are detected by Suzaku/WAM.

We analyzed six events that were simultaneously observed by both Suzaku/WAM and RHESSI, and compared light curves and spectra. Non-thermal spectra of all six events are well represented by the single power-law model. We also searched WAM-detectable microflares using the RHESSI statistical data, and we found that 11 out of 12 events expected to be detectable by WAM were indeed observed, with the only non-detection corresponding to the smallest event. These findings indicate that microflares can accelerate electrons to energies up to at least 100 keV. Hence, this corroborates the finding that microflares are similar to large flares, and it suggests that the same acceleration mechanism could be operating for regular flares and microflares.

We thank Dr. Teruaki Enoto for his comments on the Suzaku data. We thank the anonymous referees for detailed comments. This work was supported through NASA contract NAS 5-98033 for RHESSI. S. Ishikawa was supported by the Japan Society for Promotion of Science. R. P. Lin was supported in part by the WCU grant No. R31-10016 funded by the Korean Ministry of Education, Sciences, and Technology.