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ISSN 1063-7737, Astronomy Letters, 2013, Vol. 39, No. 11, pp. 797­807. c Pleiades Publishing, Inc., 2013. Original Russian Text c A.S. Kirichenko, S.A. Bogachev, 2013, published in Pis'ma v Astronomicheski Zhurnal, 2013, Vol. 39, No. 11, pp. 884­896. i

Long-Duration Plasma Heating in Solar Microflares of X-ray Class A1.0 and Lower
A. S. Kirichenko* and S. A. Bogachev
Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia
Received May 14, 2013

Abstract--Three solar microflares of X-ray class A1.0 and lower observed at solar activity minimum in 2009 have been studied: the April 19, 2009 flare (A0.38), the June 24, 2009 flare (A0.47), and the July 18, 2009 flare (A2.2). A distinguishing feature of these events from other microflares of low X-ray classes was the maintenance of a high plasma temperature (T 4 MK) at the decay phase well after the flare peak. The lifetimes of the high-temperature emission source in the corona in all three cases exceed considerably its conductive and radiative cooling times, while the thermal energy released at the decay phase of the flare exceeds the energy liberated during its impulsive phase by an order of magnitude. It is hypothesized that a high plasma temperature in microflares of low X-ray classes can be maintained for a long time through magnetic reconnection associated with mass ejections from the flare region. The lifetime of the hot plasma in the corona in this case can exceed appreciably the plasma cooling time. The study has shown that the eruption of material actually occurred in all three investigated microflares. DOI: 10.1134/S1063773713110042 Keywords: Sun, microflares, high-temperature plasma.

INTRODUCTION Solar microflares are among the smallest-scale energy release processes observed in the solar atmosphere. The emission kernels of microflares are typically no more than 10 arcsec in size, and their lifetimes do not exceed several tens of minutes. The total energy liberated during microflares lies within the range from 1027 to 1030 erg (Christe et al. 2008). Weak flare-like events (subflares) were first discovered on the Sun in the H line (H. Smith and E. Smith 1963). The term "microflare" was introduced in the early 1980s by Schadee et al. (1983) and Lin et al. (1984) for X-ray subflares. Today, emission from microflares is recorded almost at all wavelengths: in the microwave range, in the vacuum ultraviolet, and in the soft and hard X-ray bands. The size of a microflare is usually at a maximum in the H line, while only the individual emission kernels that usually correspond to the brightest knots in the flare's H image (Yokoyama and Shibata 1995) are generally observed X rays. At present, the dominant view is that the physical mechanisms responsible for the formation of microflares coincide with the mechanisms of large flares (with a total energy of 1030 erg and higher). As
*

E-mail: kirichenko@lebedev.ru

far as can be judged from observational data, microflares occur in regions of an enhanced magnetic field with a nonpotential magnetic configuration and result from magnetic reconnection (Narain and Ulmschneider 1990). On the whole, the observational manifestations of microflares are the same as those of large flares: plasma heating, particle acceleration, and the formation of thermal and nonthermal radiation (Hannah et al. 2008). The nonthermal component corresponding to the most energetic impulsive phase of the flare is so far recorded only in a relatively small fraction of events. The latter is most likely due to the instrumental limitations when weak X-ray fluxes are recorded. According to the prevalent views, a hot flare plasma in the corona can be formed in two ways (Aschwanden 2004). The first is chromospheric evaporation whereby the accelerated electrons precipitating from the acceleration region into the dense lower layers of the solar atmosphere heat them up and cause their gasdynamic expansion upward into the solar corona (Aschwanden et al. 2007). A hot plasma in the corona appears in this model with some delay after the flare onset and is inside the flare loops. Direct plasma heating in the corona is the second possibility opposite to the first mechanism. A high-temperature plasma in this case appears in the corona during the impulsive phase of the flare and is observed above the flare loops near their tops (Tsuneta et al. 1997).
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The GOES B7.6-class flare on June 7, 2007, is a rare (possibly unique) microevent in which direct plasma heating in the corona was reliably detected. According to the combined RHESSI and Hinode data, a coronal emission source with a temperature of about 15 MK was detected in this flare (Milligan 2008). Chromospheric evaporation in microflares was recorded by several authors, in particular, by Brosius and Holman (2009), Milligan (2008), and Chen and Ding (2010). The latter authors measured the evaporating plasma temperature for the B1.4class flare on December 7, 2007, from 1 to 2.5 MK. In this paper, we provide evidence for direct plasma heating in three solar microflares of record low Xray classes, A1.0 and lower. In all three events, we not just establish the fact of plasma heating in so weak events but show that a high temperature in the microflare region is maintained tens of minutes after the end of the flare impulsive phase, which exceeds considerably the calculated conductive and radiative plasma cooling times. As a possible explanation, we suggest that such long-duration plasma heating can be provided by magnetic reconnection associated with the ejection of plasma from the flare region. We found evidence of eruptions in all three investigated flares. DATA AND THEIR PROCESSING Here, we use the data obtained during the TESIS/CORONAS-Photon experiment from February to November 2009. The satellite operation period coincided with the deep activity minimum between the maxima of solar cycles 23 and 24. The activity level was especially low from February to July 2009. In this time interval, a total of 13 NOAA active regions were observed on the Sun, and the level of ° soft X-ray emission in the 1­8 A band was below the sensitivity threshold of the GOES monitors most of the time. Such conditions turned out to be very favorable for recording microflares, especially the weakest ones, of X-ray class A1.0. For our study, we used data from three instruments of the TESIS scientific instrumentation: (1) the MISH imaging spectroheliometer, which provides monochromatic images of the Sun in the resonance doublet of the hydrogen-like ion Mg XII ° 8.419, 8.425 A with an angular resolution of about 2 per pixel and a 1 15 field of view; (2) the FET telescope to image the full solar disk in the ° Fe IX 171 A line with a spatial resolution of 1.7 per pixel and a 1 field of view; and (3) the SphinX spectrophotometer to measure the soft X-ray flux from the Sun in the energy range from 0.5 to 15 keV (the range was divided into 256 channels). The

° publicly accessible data on the solar flux in the 1­8 A band from GOES satellites (USA) were also invoked. We worked with the data as follows. For the initial search of plasma heating events, we used MISH images in the Mg XII line. This line is a high-temperature one, because any noticeable level of emission in it is observed when the emitting plasma is heated to a temperature of at least 4 MK. The temperature sensitivity is at a maximum in the temperature range 8­10 MK. The instrument as a whole is a very precise indicator of a high-temperature plasma, because the very fact of recording the emission source with it suggests that the temperature here is at least 4­5 MK. The upper boundary of the temperature cannot be determined from MISH data without invoking other data. From the period of the lowest solar activity (from February to July 2009), we excluded the first two months during which the MISH time resolution did not exceed 2 h, and it was impossible to study microflares. From the remaining period (April­ July 2009), we chose single flares (which were not superimposed on the decay phase of another event in the same region) during which at least two images of the high-temperature emission source were recorded. We were interested primarily in weak events in which the high-temperature emission source existed for a long time after the flare peak. The GOES ° observations in the 1­8 A band, which are commonly used to determine the peak time and the X-ray class of a flare, were not particularly useful, because the X-ray flux from the Sun was below the GOES sensitivity threshold most of the time due to the low level of activity. For this reason, we used data from the SphinX/TESIS spectrophotometer with a much higher sensitivity. We constructed the time profiles in ° the 1­8 A band from SphinX data using the software provided by the project team. Based on the results of this analysis, we selected three microflares of X-ray class lower than or A1.0 presented here: the A0.38 event on April 19, 2009, the A0.47 event on June 24, 2009, and the A2.2 event on July 18, 2009. We used telescopic data (FET/TESIS images of ° the full solar disk in the Fe IX 171 A line) to detect the active regions responsible for the microflare formation (the solar disk is absent in the MISH images) and to construct the difference images. The difference images were formed by subtracting the preceding fixed frame with number 0 from a series of successive frames with arbitrary numbers 1, 2,... ,N . Frame 0 corresponded to the time "before the flare onset," i.e., represented the quiet corona, while frames 1,... ,N were recorded during and after the flare. The subtraction was done by taking into account the differential rotation of the Sun: in a spherical coordinate
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Apr. 19, 2009, 01:32:54.350 UT 800 600 400 200 ­ 1000 ­ 800 ­ 600 ­ 400 Apr. 19, 2009, 03:08:37.350 UT 800 600 400 200 ­ 1000 ­ 800 ­ 600 ­ 400 Apr. 19, 2009, 02:02:55.100 UT 800 600 400 200 ­ 1000 ­ 800 ­ 600 ­ 400 Apr. 19, 2009, 02:25:25.100 UT 800 600 400 200 ­ 1000 ­ 800 ­ 600 ­ 400 X, arcsec

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Fig. 1. Microflare of X-ray class A0.38 on April 19, 2009. The upper panels show the images of the high-temperature ° emission source in the Mg XII 8.42 A line obtained with the MISH spectroheliometer of the TESIS (CORONAS-Photon) ° instrumentation. The lower panels show the difference images of the solar corona in the Fe IX 171 A line constructed from FET/TESIS data. The black areas in the difference images are the dimming regions.

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system, we determined the shift of each pixel in the time elapsed after the zero image had been obtained and then interpolated the frame to the time t = 0. The goal of constructing the difference images was to find coronal dimmings, which generally suggest that some of the material goes away with a mass ejection (Harra et al. 2007). This method allows the fact of coronal material eruption to be established even in the cases where the ejection is not observed directly. The dimming region and its boundaries were determined as follows. We constructed the brightness distribution of pixels whose maximum (the most frequent value) was taken as the background value. Then, we calculated the rms deviation of the signal . We assumed the pixels with a brightness in the range I ± 3 to belong to the quiet corona, the pixels with a brightness I < 3 to belong to the dimming region, and the pixels with I > 3 to belong to the emission kernels of the flare. RESULTS For each of the three microflares, we obtained and present the following results: (1) the images of the high-temperature emission source in the Mg XII ° 8.42 A line (MISH data); (2) the difference images ° of the flare region (FET data in the Fe IX 171 A line); (3) the time profile of the flux from the flare in the ° Mg XII 8.42 A line; (4) the time profile of the flux in ° the Fe IX 171 A line integrated over the dimming region; and (5) the soft X-ray flux from the flare in the ° 1­8 A band (SphinX data).

recorded near 02:10 UT. We estimated the X-ray class of the event from the peak flux to be A0.38. The flare had a rise phase about 10 min in duration and a long decay phase lasted for about 2 h. As applied to large flares, events with such a profile belong to the so-called LDE type,1 which is often accompanied by coronal mass ejections. The first MISH frame with a hot plasma was obtained at the rise phase of the flare, 8 min before its peak. The second frame was recorded already at the decay phase of the flare, 21 min after its peak. The intensity of the high-temperature component reached its maximum at the decay phase of the flare, i.e., in the second frame (Fig. 2a). Figure 1c shows a series of difference images in ° the Fe IX 171 A line. According to them, a coronal dimming was observed in the microflare region, suggesting that some of the material goes away with a mass ejection. The time profile of the emission from the dimming region is shown in Fig. 2b. For comparison, the profiles of the total flux from a randomly chosen area of the quiet corona (dotted line) and an area of a polar coronal hole (dash­dotted line) are shown on the same plot. According to this plot, the onset of dimming formation approximately coincides with the microflare onset, while the dip in its intensity is deepest near the flare peak. The bulk of the hot plasma is formed at the late dimming phase whose time profile has the shape of a plateau.

The June 24, 2009 Microflare
The second high-temperature emission source investigated here was recorded on June 24, 2009, between 08:29 and 09:14 UT in the southern hemisphere of the Sun. The corresponding active region had number 11022 in the NOAA catalog and existed for about 6 days. The maximum number of sunspots in the region was 2; the maximum sunspot area was 20 millionths of a solar hemisphere. A hot plasma was detected in six MISH frames, from 08:29:15 to 09:14:15 UT (Fig. 3, the upper part of the figure), and was observed with a fairly high time resolution, about 9­10 min. The formation time of the high-temperature emission source is determined for this flare very accurately, because there was no hightemperature emission source in the image obtained 9 min before this (08:20:15 UT). According to SphinX data (Fig. 4c), the formation of a hot plasma coincided with a microflare of X-ray class A0.47. The flare peak was recorded at 08:40 UT, the event duration was slightly longer than one hour, and the rise and decay phases of the microflare were
1

The April 19, 2009 Microflare
The high-temperature emission source was recorded by the MISH spectroheliometer on April 19, 2009, in two successive frames (at 02:02:54 and 02:31:34 UT) in the northeastern part of the solar disk (Fig. 1, the upper part of the figure). In two preceding (00:55:51 and 01:32:54 UT) and two succeeding (03:08:37 and 03:38:37 UT) images, no hot plasma was observed. In the photospheric images of the Sun, this area was not highlighted in any way (there were no sunspots and flocculi); for this reason, the corresponding active region was absent in the NOAA catalog. In the images of the corona in the Fe IX ° 171 A line, a structure of small-scale loops with sizes of less than 10 000 km formed approximately two days before the microflare was observed in the flare region. The time profile of the soft X-ray emission from ° the Sun in the 1­8 A band constructed from SphinX data is shown in Fig. 2c. According to these data, the formation of a hot plasma was associated with a microflare of a very low intensity whose peak was

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01:00:00 01:25:00 01:50:00 02:15:00 02:40:00 03:05:00 03:30:00

Time, UT Apr. 19, 2009
Fig. line. total lines time ° 2. Time profiles of the emission for the April 19, 2009 microflare. (a) The total flux from the flare in the Mg XII 8.42 A The measurements are indicated by the dots, and the envelope curve is a polynomial fit for the emission profile. (b) The ° flux in the Fe IX 171 A line summed over the dimming region and normalized to one pixel. The dotted and dash­dotted correspond to the simultaneous flux for the quiet corona and a coronal hole measured at arbitrarily chosen points. (c) The ° profile for the microflare in the 1­8 A band from SphinX/TESIS data.

essentially identical, being 30 and 40 min, respectively. Just as in the April 19, 2009 flare, the first frame with a hot plasma was recorded at the rise phase of the flare, about 10 min before its peak. The intensity of the hot-plasma emission reaches its maximum 2­3 min before the flare peak (the next image from the MISH spectroheliometer). All the succeeding images were recorded at the decay phase of the flare. The intensity ° of the emission in the Mg XII 8.42 A line in these frames decreases monotonically to its original level (Fig. 4a). On the whole, a hot plasma in this event is recorded for almost 45 min, including at least 25 min after the flare peak. The difference images of the flare in the Fe IX ° 171 A line are shown in the lower part of Fig. 3. The dimming formation whose profile is shown in Fig. 4b is observed approximately simultaneously with the flare onset. The dimming profile is relatively monoASTRONOMY LETTERS Vol. 39 No. 11 2013

tonic, the long-duration coronal dimming phase lasts for about an hour; subsequently, the emission profile flattens out. The dimming stayed at this level for several more hours after the flare.

The July 18, 2009 Microflare
A hot plasma was detected on July 18, 2009, from 01:39 to 03:09 UT in the corona above the northwestern solar limb. The corresponding active region was formed three days before this, on July 15, 2009. The MISH instrument recorded a total of seven frames with the high-temperature emission source with a time resolution of about 15 min (Fig. 5, the upper part of the figure). The profile of the soft-X-ray emission from the flare constructed from SphinX data is shown in Fig. 6c. According to these data, the formation of


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Fig. 3. Same as Fig. 1 for the June 24, 2009 microflare of X-ray class A0.47.

a hot plasma is associated with a microflare of Xray class A2.2. The flare peak was recorded near 02:00 UT; its duration is about 3 h. The time profile of this flare is characterized by a fairly long rise phase, 35 min, and a very long decay phase, more than 1 h. The first image with evidence for the existence of a hot plasma was obtained at 01:38:56 UT, which coincides almost exactly with the flare onset (Fig. 6a). The next frame was recorded 6 min before the flare peak (01:53:56 UT); at this time, the intensity of the hot-plasma emission reached its maximum. In the succeeding frames, the intensity of the emission in ° the Mg XII 8.42 A line decreases monotonically to the original level. A series of difference images for the flare is shown in the lower part of Fig. 5. According to them, this flare, just as the previous ones, was accompanied by

the eruption of material that began almost simultaneously with the flare onset. The brightness decline in the dimming region was largest near the flare peak. Subsequently, the time profile of the emission from the dimming region flattens out and, after the end of the flare, returns approximately to the level that it had before the flare. DISCUSSION We analyzed three weak microflares of X-ray class A1.0 and lower whose peculiarity was longduration energy release observed for tens of minutes after the flare peak. For all three events, we selected and analyzed the following experimental data: (1) the ° X-ray fluxes in the 1­8 A band measured by the SphinX instrument onboard the CORONAS-Photon
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TESIS FeIX 171 å, counts/pixel

2000 1500 1000 500
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Fig. 4. Same as Fig. 2 for the June 24, 2009 microflare of X-ray class A0.47.

satellite; (2) the images of the full solar disk obtained by the MISH spectroheliometer of the TESIS instrumentation onboard the CORONAS-Photon satellite; (and 3) the FET/TESIS images of the full solar disk ° in the 171 A line. Observations show that all three events had similar time profiles with a long decay phase, tens of minutes and more. This class of flares is opposite to the so-called impulsive flares with fast rise and decay phases. The increase in the duration of the decay phase in some flares compared to impulsive events is explained by the long existence of a high-temperature plasma in them, for which, as will be shown below, additional energy release is needed. Whereas the detection and study of hightemperature emission sources usually do not present any problems for large flares, in microflares difficulties arise already at the stage of establishing the presence of a hot plasma. Here, for this purpose, we invoked images from the MISH instrument, whose peculiarity is a high temperature sensitivity threshold: the emission sources in the images are formed at a plasma
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temperature of at least 4 MK. Therefore, we believe that the presence of a hot component in all three microflares has been established firmly and focus our attention on another fact: in all three events, a hot plasma was observed for tens of minutes after the flare peak, which exceeds appreciably the expected conductive and radiative cooling times. The cooling times can be calculated from estimates of the plasma temperature and density and the object's sizes. The volume of the high-temperature source as a whole is determined quite accurately from ° its visible image in the Mg XII 8.42 A line. In this case, we should take into account the peculiarities of the instrument: because of the optical scheme used, the apparent sizes of the source in the image are always slightly increased in the direction of the dispersion of the instrument's crystalline mirror. The results of our calculations (the volume of the emission source in cm3 ) are presented in the table. The uncertainty in the volume is due to image dispersion and inaccuracy in determining the source's diameter. We determined the plasma temperature in the isothermal approxima-


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Fig. 5. Same as Fig. 1 for the July 18, 2009 microflare of X-ray class A2.2.

tion by comparing the time profiles of the emission in ° the 1­8 A band measured simultaneously by GOES and SphinX. The plasma density was estimated from the emission measure of the emission source in the ° Mg XII 8.42 A line, which was defined as the ratio of the emission power in this line to the luminosity at the calculated temperature. Since one of the variables in this method of determining the plasma density is the source's volume, inaccuracies in determining the volume lead to an uncertainty in the density, which is also reflected in the table. The most efficient plasma cooling mechanism in the ranges of temperatures 5­10 MK and densities 108 -109 cm-3 is heat conduction along magnetic field lines. The energy loss rate for the cooling of a unit plasma volume through heat conduction can be

calculated from the formula (Aschwanden 2004) d 2 T (t)7/2 [3ne (t)kB T (t)] - , (1) dt 7 L2 where kB is the Boltzmann constant, is the Spitzer thermal conductivity (9.2 â 10-7 erg s-1 cm-1 K-7/2 , T is the temperature, and L is the length scale of the hot region. Pcond = In the case of radiative cooling, Prad = d [3ne (t)kB T (t)] dt -ne (t)2 0 T (t)-2/3 , (2)

where ne is the electron density, 0 = 10-17.73 is the coefficient of the radiative loss function (Rosner 1978). The ratio of the efficiencies of these two
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Fig. 6. Same as Fig. 2 for the July 18, 2009 microflare of X-ray class A2.2.

mechanisms is Pcond 103 , Prad (3)

which is the lower boundary of the MISH temperature sensitivity. We applied the formula T (t) = T1 whence we obtain
cond

i.e., the energy loss rate for conductive cooling exceeds the energy loss rate for radiative cooling by three orders of magnitude. As the actual cooling time of the high-temperature emission source, we used the time interval between the flare peak (i.e., the end of its impulsive phase) and the time of the last observation of the emission source in the Mg XII line by the MISH spectroheliometer. In fact, this time is a lower limit: the source could not exist for a shorter time than we actually observed it but could exist for a longer time. Since the time resolution of the MISH observations in this period lay in the range from 5 to 20 min, the upper limit for thecooling timecannot exceed the lower onebymore than 20 min. The theoretical plasma cooling time was calculated as the time of its temperature decrease from the initial value from the table to a temperature of 4 MK,
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t - t1 1- cond

-2/5

,

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=

21 ne kB L2 . 5 T 5/2 1

(5)

The results of our calculations are presented in the table. The total energy that was "put" into the source to maintain its existence can be determined by comparing the actual lifetime of the source with the rate of its conductive cooling. For the April 19, June 24, and July 18, 2009 flares, this energy was (8.0 ± 3.5) â 1029 , (2.4 ± 0.7) â 1030 , and (3.6 ± 0.5) â 1030 erg, respectively. The initial formation of the emission sources with the observed temperatures requires expending from 2.1 â 1028 to 1.5 â 1029 erg. Thus, the energy balance in all the investigated microflares was not quite ordinary. Only about 5-10% of the


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Basic characteristics of the investigated microflares Date Volume, 1027 cm3 Electron temperature Te ,MK Electron density Ne , 109 cm-3 Thermal energy Et , 1028 erg Emission measure, 1046 cm-3 Calculated source cooling time Actual source cooling time Apr. 19, 2009 4­52 5.3 0.6 ± 0.3 4.1 ± 1.9 0.9 30 ± 5 s 22­59 min June 24, 2009 5­52 6.3 1 ± 0.5 4.2 ± 2.2 1.2 40 ± 10 s 34­76 min July 18, 2009 12­84 7.4 2±1 9.6 ± 5.2 4.6 80 ± 15 s 69­84 min

total thermal energy was directly liberated at the flare time, while the remaining 90-95% came into the region already after the end of the impulsive phase of the event during several tens of minutes. It may well be that all microflares in which large volumes of high-temperature plasma are recorded have such a peculiarity. On the whole, the possibility of maintaining longduration energy release at late stages of flares through

(a)

(b)

(c)

Fig. 7. Reconnection scheme during an eruptive process for a quadrupole field configuration. The crosses indicate the reconnection sites. The solid lines correspond to the field lines that are not involved in reconnection. The dotted lines correspond to the field lines heated through reconnection.

eruption is consistent with the data known from the physics of large flares. It is widely believed that all (or almost all) flares in which a long decay phase is observed are accompanied by ejections (Sheeley et al. 1983; Kay et al. 2003). In this case, magnetic reconnection associated with a rearrangement of the magnetic configuration during the rise of a plasmoid is considered as an energy release mechanism. As an example, we may consider the case described by Moore et al. (2011) and shown in Fig. 7. This scheme of magnetic reconnection corresponds to the development of an eruption in a quadrupole magnetic configuration. Figure 7a schematically shows the initial magnetic configuration with the formed plasmoid. Figure 7b shows the onset of reconnection associated with the plasmoid rise. The cross indicates the reconnection site, and the dotted line corresponds to the field line involved in reconnection. Figure 7b demonstrates the consequences of the further plasmoid rise. The plasmoid not only breaks the lines located at the top but also separates from the field lines holding it at the bottom. The crosses indicate two reconnection regions, one of which (more compact) is located in the lower corona and may correspond to the bright high-temperature emission source observed in the investigated microflares. The upper reconnection region is not observed at high temperatures (probably because the energy liberated here is distributed over a much larger volume). The solid lines in the figure correspond to the field lines that are not involved in reconnection; the dotted lines correspond to the field lines heated through reconnection. The energy release arising in twisted magnetic configurations when a critical electric current is reached in them can be an alternative to this mechanism. According to calculations, the energy release in this case can last up to several hours (Solov'ev 2012). In conclusion, note that CMEs are generally believed to be an attribute of fairly powerful flares. For example, Yashiro et al. (2006) demonstrated the existence of a relationship between the flare power and the probability of occurrence of an accompanying CME and showed that CMEs are observed almost always in flares of high X-ray classes (Fig. 8). At the same
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LONG-DURATION PLASMA HEATING

807

120

100

CME detection probability

80

60

40

20

0 10

­6

10­4 10­3 10­5 X-ray flux in flare, W m­2

10­2

Fig. 8. CME detection probability in a flare versus its X-ray class.

time, according to the derived relationship in flares of X-ray class lower than B5 according to the GOES classification, there should be no CMEs. Here, we showed that although there are no direct observations of CMEs in the investigated events, plasma eruption is observed in them, which we consider as circumstantial evidence of CME. Yashiro et al. (2006) also concluded that the absence of CME in weak flares could be related to an insufficient sensitivity of present-day coronagraphs. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research (project no. 11-02-01079), Basic Research Program no. 22 of the Presidium of the Russian Academy of Sciences (Section 2 "the Sun and the Heliosphere") and an eHEROES grant of the 7th Framework Program of the European Commission (2007­2013, project no. 284461, www.eheroes.eu). REFERENCES
1. M. J. Aschwanden, Physics of the Solar Corona. An Introduction (Praxis, Chichester, UK, 2004). 2. M. J. Aschwanden, A. Winebarger, D. Tsiklauri, et al., Astrophys. J. 659, 1673 (2007). 3. J. W. Brosius and G. D. Holman, Astrophys. J. 692, 492 (2009). 4. F. Chen and M. D. Ding, Astrophys. J. 724, 640 (2010). 5. S. Christe, I. G. Hannah, S. Krucker, et al., Astrophys. J. 677, 1385 (2008).
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6. I. G. Hannah, S. Christe, S. Krucker, et al., Astrophys. J. 677, 704 (2008). 7. L. K. Harra, H. Hara, S. Imada, et al., Publ. Astron. Soc. Jpn. 59, 801 (2007). 8. H. R. M. Kay, L. K. Harra, S. A. Matthews, et al., Astron. Astrophys. 400, 779 (2003). 9. R. P. Lin, R. A. Schwartz, S. R. Kane, et al., Astrophys. J. 283, 421 (1984). 10. R. O. Milligan, Astrophys. J. Lett. 680, L157 (2008). 11. R. L. Moore, A. C. Sterling, G. A. Gary, et al., Space Sci. Rev. 160, 73 (2011). 12. U. Narain and P. Ulmschneider, Space Sci. Rev. 54, 377 (1990). 13. R. Rosner, W. H. Tucker, and G. S. Vaiana, Astrophys. J. 220, 643 (1978). 14. A. Schadee, C. de Jager, and Z. Svestka, Solar Phys. 89, 287 (1983). 15. N. R. Sheeley, Jr., R. A. Howard, M. J. Koomen, et al., Astrophys. J. 272, 349 (1983). 16. H. J. Smith and E. V. P. Smith, Solar Flares (Macmillan, New York, 1963). 17. A. A. Solov'ev, Geomagn. Aeron. 52, 1062 (2012). 18. S. Tsuneta, S. Masuda, T. Kosugi, et al., Astrophys. J. 478, 787 (1997). 19. S. Yashiro, S. Akiyama, N. Gopalswamy, et al., Astrophys. J. Lett. 650, L143 (2006), arXiv:astroph/0609197. 20. T. Yokoyama and K. Shibata, Nature 375, 42 (1995).

Translated by V. Astakhov