Chin. J. Astron. Astrophys. Vol. 6 (2006), No.5, 597 -607Chinese Journal of(nttp://www.chjaa.org)Astronomy andAstrophysicsSpectral Analysis and Atmospheric Models of MicroflaresCheng Fang' , Yu-Hua Tang' and Zhi Xu1,21 Department of Astronomy, Nanjing University, Nanjing 210093; fangc@ nju.edu.cn2 National Astronomical Observatories / Yunnan Observatory, Chinese Academy of Sciences, Kunming65001 1Received 2006 February 7; accepted 2006 February 20Abstract By use of the high-resolution spectral data obtained with THEMIS on 2002September 5, the spectra and characteristics of five well-observed microflares have been an-alyzed. Our results indicate that some of them are located near the longitudinal magneticpolarity inversion lines. All the microflares are accompanied by mass motions. The most ob-vious characteristic of the Ha microflare spectra is the emission at the center of both Haand Call 8542A lines. For the first time both thermal and non-thermal semi-empirical at-mospheric models for the conspicuous and faint microflares are computed. In computing thenon-thermal models, we assume that the electron beam resulting from magnetic reconnectionis produced in the chromosphere, because it requires lower energies for the injected particles.It is found there is obvious heating in the low chromosphere. The temperature enhancementis about 1000- 2200K in the thermal models. If the non-thermal effects are included, then therequired temperature increase can be reduced by 100-150 K. These imply that the Ha mi-crofares can probably be produced by magnetic reconnection in the solar lower atmosphere.The radiative and kinetic energies of the Ha microflares are estimated and the total energy isfound to be 1027 - 4x 1028 erg.Key words: Sun: Microflares - Sun: spectrum - Sun: semi -empirical modelling1 INTRODUCTIONIt is well known that microflares (MFs), or subflares, as they are often called, are small short-lived bright-enings, which have been observed and studied for decades (e.g. Svestka 1976; Tandberg-Hanssen & Emslie1988). In the past, some authors have also called them bright points or minifares, etc. The size of MFs isfrom several arcsec to about 20", their typical lifetime is 10- -30 minutes and their energy has been estimatedto be 1026一1029 erg (Shimizu et al. 2002).The most obvious characteristic of MFs' visible spectra is the weak emission at the center of chromo-spheric lines. The Ha line is thus the most common studied one, and the area on the Ha filtergrams is animportant criterion for MFs (subflares). However, soft X ray (Golub et al. 1974, 1977), hard X-ray (Lin etal. 1984), EUV (Porter et al. 1984; Emslie & Noyes 1978), as well as microwave (e.g. Gary et al. 1988)emissions have also been observed in some MFs. Recently, RHESSI has successively obtained the first hardX-ray image of MFs (Krucker et al. 2002; Benz & Grigis 2002). Some of the observations implied that the\emissions in different wavelengths are coincident . For instance, by use of SMM data, Porter et al. (1987)found that the long lived UV brightenings in the CIV line we n i中國煤化工' MFs. Berghmanset al. (2001) compared the data of Yohkoh/SXT, SOHO/EIT:he strongest EUVbrightenings were counterparts of soft X-ray MFs. Liu et al.|YHC N M H G, RHISSI imagesin 3 to 15 keV and GOES data for 12 MFs, and found all of them are seen in soft X-ray, hard X-ray and Ha* Supported by the National Natural Science Foundation of China.C.Fang,Y.H.Tang&Z.Xuwavelengths. Qiu et al. (2004) found that about 40% of the MFs exhibit hard X-ray emission at over 10keVand microwave emission at around 10 GHz. However, it is obvious that we should not always expect tosee simultaneous emissions in the different wavelengths, for much depends on the heating condition of theparticular MF. However, for MFs with emission at the center of Ha line, which may be called Ha MFs, theheating region should be at least in the solar chromosphere.Mass motion has been observed at or near the location of MFs. Shimizu et al. (2002) found that chro-mospheric ejections are observed in some MFs, and X-ray jets were also observed in some MFs. It was alsofound that some MFs are located close to, or across magnetic polarity inversion lines (Porter et al. 1987;Wang et al. 1999; Shimizu et al. 2002; Liu et al. 2004). Non-thermal properties of MFs are well exploredin the microwave (e.g. Gary & Zirin 1988; White et al. 1995; Nindos et al. 1999) and hard X-ray emissions(e.g., Nitta 1997; Liu et al. 2004; Qiu et al. 2004). Some MFs are even associated with type II bursts (e.g.Liu et al. 2004), which is a clear signature of the presence of non-thermal electrons. Moreover, it was alsofound that in many cases emerging fux occurs about 5- -30 minutes before the MFs (e.g. Tang et al. 2000;Shimizu et al. 2002).All these observations imply that magnetic reconnection in the lower solar atmosphere could be aplausible mechanism for triggering MFs (Tandberg-Hanssen & Emslie 1988; Liu et al. 2004). Chen et al.(2001) made a 2D numerical MHD simulation, and found that magnetic reconnection in the lower solaratmosphere could explain some characteristics of MFs, such as the temperature enhancement and lifetime,etc.To well explore the nature of MFs, it is very important to know their atmospheric structure. However,spectral observations with high spatial resolution that is essential for constructing accurate atmosphericmodel of MFs have been few up to now. In this paper we use high-resolution spectral data of Ha,Call 8542 A, and FeI 6302.5 A lines obtained with the French-Italian 90 cm vacuum telescope, THEMIS,on 2002 September 5. The characteristics of five well-observed Ha MF's have been analyzed. For two typi-cal MFs, representing bright and faint events, we have computed semi-empirical atmospheric models, withor without considering non- thermal excitation and ionization effects. We have also studied the relationshipbetween MFs and magnetic and velocity fields.Features of the THEMIS observations are described in Section 2. In Section 3 the characteristics ofthe MFs are analyzed, including their relationship with the magnetic and velocity fields. Semi empiricalatmospheric models for the two MFs are given in Section 4. A discussion and conclusions are given inSection 5.2 SPECTROPOLARIMETRIC OBSERVATIONS OF MICROFLARESThe active region 10096 (S16E09) was observed on 2002 September 5 from 08:01 UT to 12:07 UTwith the French-Italian solar telescope, THEMIS, in the MTR multi-line spectropolarimetric mode(www.themisiac.es). In this mode two beams with orthogonal polarization exiting the analyzer are directedinto a single camera. The top part of the camera receives sequentially I+Q, I+U, I+V and I-V, while thebottom part records I-Q, I-U, I-V and I+V. Three cameras record simultaneously the Stokes parameters forHa, CaIl 8542 A and Fel 6302.5 A lines.The active region was scanned several times in 80 steps separated by 1" in space. The spatial samplingalong the slit is 0.42"/pixel. The spectral sampling is 26.1 mA for Ha, 36.3 mA for Call 8542, and 22.4 mAfor FeI 6302.5 A. The seeing condition is better than 1", but the scanning limited the spatial resolution toabout 2”for all 2D maps.After dark current and fiat- field were corrected, the Muller matrix was used to demodulate the Stokesparameters. To remove induced cross-talk and improve the seeing smearing, we sum the top and the bottomspectra. To do so, the two spectra are well aligned in the slit direction (y direction). By use of the Stokes Vprofiles of the Fel 6302.5 A line, the longitudinal magnetic field can be derived. However, due to the lowSN ratio, the transverse magnetic field cannot be convincingly deduced from the Stokes parameters Q andU. The 2D velocity fields were obtained using the bisector m中國煤化工es. Owing to thefact that all lines were observed simultaneously, the 2D interFfields are exactlyCNMHGcoaligned.Spectral Analysis and Atmospheric Models of Microflares5993 CHARACTERISTICS OF THE MICROFLARES3.1 Well. observed MicrofaresBy checking the 2D spectra, we found five well-observed MFs during the observations. Table 1 lists somecharacteristics of the MFs, including the scan time, location, intensity, duration, size and accompanied masscjection. In the column showing the location the (x, y) coordinates of the MF are in pixels, with x alongthe scan direction, and y along the slit direction and the interval between two pixels 0.42". The relationshipof the MF with the longitudinal magnetic field is also given: NN means that the MF is near the magneticpolarity inversion lines (less than 6 "). According to the excess Ha peak intensity△I (MF intensity with thequite-Sun background subtracted), the MFs are classified into bright and faint ones, according as△I≥10or< 10, in units ofergs- 1 cm-2 sr-1 A-1. The duration is estimated by the scanning times during whichthe MF appears. Owing to the low cadence of the scanning, the estimated durations of the MFs may belower limits. If the MF appears only in one scan then the duration should be less than the period betweenthe previous and following scan, which is an upper limit for the lifetime of the MF. The average sizes areestimated by counting how many pixels on the spectra along the slit and how many steps along the scandirection that the MF can be still identified.Table 1 Characteristics of the Observed MFsNo. Time LocationIntensityDurationSizeMass ejection(x,y)(min)(arcsec)0812 93.65 NN bright≥40yes0812124, 48faint0947 98, 77 NN< 200959 121, 68ye114917, 11 NNbngntbnightFrom Table 1 it can be seen that the sizes of the MFs are about 4"-9", and generally the fainter MFsare smaller than the brighter MFs. Moreover, three MFs are located near the magnetic polarity inversionlines, and all the MFs are accompanied by downward and/or upward flows, although some of the ejectionsare not strong.3.2 Spectral CharacteristicsFigures 1-2 show the Ha and Call 8542 spectral profiles for one bright (No.1) and one faint (No.3) MF,respectively. The line intensities of the MFs with the quiet- Sun background subtracted (MF-Q) are alsoshown. It is seen that all the MF-Q profiles show excess emission around the line center. It implies thatcompared to the quiet-Sun region, the heating of the Ha MFs is significant in the chromosphere. This canbe clearly seen in the semi empirical atmospheric models which will be presented in Section 4.3.3 Locations of the MFs on 2D Magnetic and Velocity MapsFigure 3 gives the locations of the four MFs on the 2D Ha images at 08:12 UT (left) and 09:59 UT (right).The crosses mark the positions of the MFs. We do not give the position of the No.5 MF, because it wasobserved at a much later time when the image had changed. Also shown are longitudinal magnetic fieldcontours at levels - -800, - -300, - 50, -5, 4, 40, 200 and 500 G, in green (purple) for negative (positive)polarity. Figure 3 shows clearly that three of the MFs appear close to the magnetic polarity inversion lines.Moreover, there is a two-ribbon brightening in the lower-left part of this figure. It is an interesting two-ribbon small flare, which we will analyze in another paper. Figure 4 shows the velocity distribution at08:12UT and 09:59 UT, and the size of the Doppler velocity is color-coded. Owing to the rapid changes ofthe velocity field, only the MFs appearing around the given中國煤化工s.1 and 2) around08:12UT and the two MFs (Nos. 3 and 4) at or near 09:59LCHCNMHG; can be seen fromthe figure that the MFs are closely related to mass motions,2even have upwardand downward motions of different velocities on either side. It implies that the MFs are accompanied byplasma ejections, which provide evidence for magnetic reconnection.600C.Fang,Y.H.Tang&Z.Xu30會20。20器150E; 15a\ (A)A(A).(A)Q\ (A)Fig.1 Ha and Call 8542 A line profiles of a brightFig2 Same as Fig. I, but for a faint MF (No.3).MF (No.l). Panel (a) shows the Ha profile (solid)and the quite Sun background (dashed), and Panel (b)shows the“net" profile (Ha - Q); Panels (C) and (d)do the same for the Call 8542 A line.120101005060400202O人80160Fig.3 Locations for two well- observed MFs (Nos. 1 and 2) on the 2D images of the Ha center at 08:12UT(eft), and for two other MFs (Nos. 3 and 4) at 09:59 UT (right). The contour levels of the longitudinalmagnetic field are -800, -300, -50,-5, 4, 40, 200 and 500 G, green for ncgative polarity, purple for positivepolarity.Doppler velocity (km/s)1C12-230 I620 160中國煤化工Fig. 4 Color- coded velocity distributions at 08: 12 UT (ef)MTHCNMHGossesmarkthe.locations of MFs (Nos. I and 2) in the left panel and of MFs (Nos. 3 and 4) in the right panel.Spectral Analysis and Atmospheric Models of Microflares6010上MF二evuLCLOG M? 2.taCall 8542-2020\ (&) .A\ (A)Fig.5 Upper panel shows the temperature distributions in the thermal semi- empirical model for the brightMF No.i) (solid line), compared to those for the plage model (P) (dotted-dashed line) given by Fang et al.(2001), the quiet-Sun model (VALC) (dotted line) given by Vermazza et al. (1981), and the fare model F1(dashed line) given by Machado et al. (1980). The lower panels compare the computed line profiles (solidlines) with the observed ones (dotted lines) for Ha (lower left penal) and Call 8542 A (lower right penal). AGaussian macroturbulence velocity of 10 kms' - 1 for the Ha line and 6 km s -1 for the Call line is adoptedto convolve the computed line profiles.4 SEMIEMPIRICAL ATMOSPHERIC MODELS OF THE MFS .4.1 Computation of Semi- empirical Atmospheric ModelsBy the use of both Ha and Call 8542 A line profles, semi-empirical atmospheric models of the MFs cannow be computed with less ambiguity. The method of the nOn-LTE computation is similar to that givenby Fang et al. (1993), that is, we used two atomic models, one a four-level plus continuum for hydrogen,one a five-level plus continuum for calcium. The statistical equilibrium equation and the transfer equation,coupled with the hydrostatic equilibrium and the particle conservation equations, were solved iteratively.To ensure sufficient convergence, more than 12000 iterations were taken, until the relative difference in themean intensity between the last two iterations is within 10-5 for hydrogen and 10-8 for calcium.The thermal semi-empirical models for the two typical MFs (Nos. 1 and 3) are computed, which canwell reproduce both the observed Ha and Call 8542 A line profiles. Figures 5- 6 give the thermal semi-empirical atmospheric models and both the observed and computed line profiles of the two MFs. For com-parison, the temperature distributions of the semi-empirical models for a plage (P) given by Fang et al.(2001), for a typical faint fare (F1) given by Machado et al. (1980), and for the quiet- Sun model (VALC)given by Vemazza et al. (1981), are also shown in these figures. It can be seen from Figures 5- 6 that acommon characteristic of the thermal models is the obvious heating in the chromosphere. The tempera-ture enhancement is about 1000- -2200 K. The higher value corresponds to the temperature bump up in thelow-chromosphere. The temperature increase is higher for the bright MF than that for the faint one.However, since magnetic reconnection is probably the mechanism for flares of all sizes (Parker 2001),including MFs, energetic particles should be produced durin中國煤化工ing that electronbeam bombardment is more effective than proton beam bombjet al. (1993) andHEnoux et al. (1995), we also compute the non-thermal semiYHc N M H Gcitation and ion-ization by electron beam bombardment included, assuming that the reconnection site is in the chromosphere.The reason is that the heating resulted from magnetic reconnection is significant in the low-chromosphere.602C.Fang,Y.H.Tang&Z.XuIFLOG MlaCall 8B5425EsE(A)Fig. 6 Same as Fig. 5, but for the faint MF (No. 3). The same Gaussian macro-turbulence velocity is adopted to convolve the computed line profiles.According to the magnetic reconnection scenario, during the magnetic reconnection oppositely-orientedelectron beams are ejected from the reconnection site, so in our computation both upward and downwardbombardments are considered.Following the theory given by Fang et al. (1993) and Henoux et al. (1995), for an electron beam bom-bardment, the non-thermal collisional excitation and ionization rates of hydrogen from its ground level 1 tothe higher levels 2- 4 and the continuum C, can be taken, to a good approximation, asCi2≈2.94x 10101dE"and C13 ≈5.35 x 1091 dEHndtn1 dt1 dEHmC14≈1.91x 109-一，and C1c≈1.73x 10(1)n幾1 dtThe non-thermal collisional excitation and ionization rates of Call can be expressed asC14≈2.38 x 1010n1dt’Cis≈4.25x 101n1 diC1c≈4.69 x 1010where n1 is the ground level population. The excitation and ionization from the higher levels are negligible.Here dEH /dt is the rate of energy deposition due to the excitation and ionization of hydrogen by an electronbeam. Neglecting the return current effects in a dense atmos中國煤化工is givenby Emsie(1978) and Chambe & Henoux (1979) asYHCNMH GdEHu2-1 du=a -xmuA' r(總)(8-2)(3)(1- u)+4，Spectral Analysis and Atmospheric Models of Microflares603F1VALC--2L0GM.5FtaCall 8542.5 E0.5-202a\ (&)(A) .Fig.7 Same as Fig.6, but for the non-thermal semi-empirical model of the bright MF (No. 1). The electronbeam fuxFi=1x 1010 ergcm 2s- , the low cut-off energy E1 = 20 keV, and the power indexδ= 5.where x is the degree of ionization. The particle fux is supposed to be proportional to E-心，with a lowcut-off energy E1. Fi is the total energy input fux above E1. The meaning of other physical quantities canbe found in the original references.We solve iteratively the rate equation that includes the non-thermal collisional excitation and ionizationrates, coupled with the transfer equation, the hydrostatic equilibrium and the particle conservation equa-tions. For an assumed electron beam fux and power index, we compute the non-thermal semi-empiricalmodels. The computed model for the bright MF (No. 1) and the corresponding computed line profiles aregiven in Figure 7. In this case we took an electron beam fux of F= 1 x1040 erg cm-2 s-',a powerindex ofδ = 5, and the low cut-off energy E1 = 20keV. From Figures 5- -7 it can be seen that both thethermal and non-thermal theoretical line profiles can well reproduce the observed profles. The two modelshave the common feature of a temperature bump in the low-chromosphere. The temperature enhancementis about 2200 K above the quite-Sun VALC model. This gives additional evidence for our assumption thatthe reconnection site is in the low-chromosphere. However, for the case with non-thermal effects included,the required temperature enhancement is reduced by 100- -150 K, while the required temperature bump upis almost the same. It is particularly necessary for reproducing the intensity enhancement at the center ofthe CaIl 8542 A line.The computed thermal and non- thermal semi -empirical atmospheric models for the bright MF (No. 1)are given in Tables 2 and 3, respectively, where H is the height, M the column mass density, T the temper-ature, Vi the micro-velocity, nH the hydrogen density and ne the electron density.4.2 Energetics of the MicroflaresBy using the semi-empirical atmospheric models of the MFs, the radiative energy can be estimated asfollows: considering that the main heating regions are in the low-chromosphere, we use radiative losses toevaluate the radiative energy Er:D。中國煤化工(4)E,= 5 SMFCNMHGwhere D is the lifetime of the MF. The heating duration is assumeu to比UIL. AS we do not know theexact duration of the faint MF (No.3), we just take it to be 15 min. SMF is the area of the MF whichcan be evaluated by the MF size listed in Table 1. In the formula h1 and h2 are the lower and the upper604C.Fang,Y.H.Tang&Z.XuTable 2 Thermnal Semi -Empirical Model of the Bright Microfare No.1)NoMTVt .nH。，neg(km); (g cm~2)(K) (kms-1)__ (cm-3)(cm-0.14993E+09 0.33730E-03 99500 0.98E+01 0.320E+12 0.386E+120.14988E+09 0.33735E-03 66600 0.90E+01 0.479E+12 0.576E+120.14950E+09 0.33800E-03 35300 0.80E+01 0.906E+12 0.109E+130.14601E+09 0.349610E-03 19082 0.66E+01 0.173E+13 0.190E+130.14468E+09 0.357780E-03 9802 0.65E+01 0.351E+13 0.318E+130.14335E+09 0.370450E-03 8661 0.58E+01 0.489E+13 0.111E+130.14145E+09 0.398287E-03 81090.53E+01 0.691E+130.580E+120.13474E+09 0.536779E-03 7703 0.47E+01 0.109E+14 0.378E+120.12564E+09 0.854175E-03 7286 0.38E+01 0.197E+14 0.281E+1210.11496E+09 0.159967E-02 6719 0.31E+01 0.419E+14 0.188E+1211 0.10533E+09 0.298241E-02 63520.25E+01 0.839E+14 0.169E+12120.98035E+080.491555E-02 6035 0.20E+01 0.146E+15 0.157E+12130.90259E+08 0.855122E-02 58110.14E+01 0.265E+150.176E+12140.84615E+08 0.130232E-01 5570 0.92E+00 0.421E+15 0.170E+12is0.78772E+08 0.203976E-01 5456 0.78E+00 0.674E+15 0.199E+1216 0.75859E+08 0.255100E-01 5621 0.75E+00 0.818E+15 0.294E+12170.72698E+08 0.321819E-01 5888 0.73E+00 0.985E+15 0.514E+12180.69321E+08 0.408100E-01 6148 0.70E+00 0.120E+16 0.919E+12190.65838E+08 0.516600E-01 63290.64E+00 0.147E+16 0.150E+13200.62235E+08 0.654600E-01 6478 0.62E+00 0.182E+16 0.240E+1321 0.58606E+08 0.830200E-01 6355 0.60E+00 0.235E+16 0.230E+1322 0.56845E+08 0.934497E-01 6193 0.59E+00 0.272E+16 0.187E+1323 0.55151E+08 0.105130E+00 6000 0.58E+00 0.316E+16 0.147E+13240.51916E+08 0.132730E+00 5701 0.56E+00 0.420E+16 0.111E+13250.48885E+08 0.167330E+000.54E+00 0.559E+16 0.950E+1226 0.46729E+08 0.199110E+00 5100 0.52E+00 0.705E+16 0.939E+1227 0.45375E+08 0.223085E+00 4996 0.52E+00 0.806E+16 0.101E+1328 0.40875E+08 0.330423E+00 4815 0.66E+00 0.124E+17 0.137E+13290.30811E+080.792164E+00 4983 0.76E+00 0.287E+17 0.314E+13300.25838E+08 0.120233E+01 5127 0.90E+00 0.423E+17 。0.482E+1330.20883E+08 0.179833E+0153280.11E+01 0.609E+170.754E+13320.17191E+08 0.240056E+01 55210.12E+01 0.785E+17 0.110E+1433 0.14722E+08 0.288863E+01 5761 0.14E+01 0.905E+17 0.160E+1434 0.12747E+08 0333218E+01 5940 0.14E+01 0.101E+18 0.227E+143:0.90502E+07 0.428258E+01 6392 0.16E+01 0.121E+18 0.572E+14360.71305E+07 0.484757E+01 6740 0.17E+01 0.130E+18 0.112E+I5370.52083E+070.543782E+01 73260.17E+01 0.134E+18 0.303E+1538 0.33066E+07 0.604445E+01 7886 0. 18E+010.138E+18 0.693E+1539 0.14140E+07 0.666258E+01 8481 0.18E+01 0. 140E+180. 148E+164000000+000 0.713133E+01 90300.18E+01 0.140E+18 0.272E+16heights of the MF heating atmospheric region, respectively, and R is the non-LTE radiative losses in unitsoferg cm -3 s~ 1 , which was computed with the semi- empirical formula, given by Gan & Fang (1990):R = nHnea(H)f(T)，(5)wherea(H)= a1(H) + a2(H),loga1(H)=2.75x 10-3H - 5.445,a2(H) = 2.3738 x 10中國煤化工f(T)= 1.547 x 10-23(2TYHCNMHG.The net radiative energy of the MF can be evaluated byOE= Er- Eq ,(6)Spectral Analysis and Atmospheric Models of Microflares605Table 3 Non-thermal Semi-empirical Model of the Bright Microflare (No.1)NoVtnH。ne。.(km)(g cm-2)(K)__ (kms-1)__ (cm-3)(cm- 30.15043E+09 0.307300E -03 99500 0.98E+01 0.292E+12 0.351E+120.15037E+09 0.307349E -03 66600 0.90E+01 0.436E+12 0.525E+120.14996E+09 0.308001E-03 35300 0.80E+01 0.825E+12 0.992E+120.14735E+09 0.315212E-03 21350 0.69E+01 0.140E+13 0.153E+130.14510E+09 0.327780E-03 9802 0.65E+01 0.328E+13 0.242E+130.14367E+09 0.340450E-03 88610.58E+01 0.447E+13 0.102E+130.14151E+09 0.368287E-03 81090.53E+010.637E+13 0.525E+120.13448E+09 0.506779E-03 75530.47E+01 0.107E+140.330E+120.12531E+09 0.824175E-03 7116 0.38E+01 0.197E+14 0.257E+120 0.11460E+09 0.156967E 02 6619 0.31E+01 0.419E+14 0.198E+121 0.10508E+09 0.295241E- 02 6202 0.25E+01 0.852E+14 0.173E+1212 0.97853E+08 0.488555E-02 5975 0.20E+01 0.147E+15 0.188E+1213 0.92791E+08 0.702300E -025800 0.16E+01 0.218E+15 0.202E+124 0.84582E+08 0.129932E-01 55000.92E+00 0.426E+15 0.255E+125 0.78836E+08 0.203676E-01 5356 0.78E+00 0.686E+15 0.401E+126 0.75974E+08 0.254800E-01 5501 0.75E+00 0.835E+15 0.619E+127 0.72896E+08 0.321519E-01 5728 0.73E+00 0.101E+16 0.131E+1318 0.69601E+08 0.407800E-01 5984 0.70E+00 0.123E+16 0.765E+1219 0.66193E+08 0.516300E 016209 0.64E+00 ”0.150E+16 0.184E+13)0.62643E+08 0.654300E- 0164590.62E+00 0.182E+160.254E+1321 0.60818E+08 0.736919E-01 6489 0.61E+00 0.204E+16 0.290E+13? 0.58068E+08 0.881900E- 01 6419 0.59E+00 0.247E+16 0.288E+1323 0.56616E+08 0.970995E-01 6309 0.58E+00 0.277E+16 0.251E+1324 0.53748E+08 0.118130E+00 6078 0.57E+00 0.350E+16 0.191E+1325 0.50531E+08 0.149036E+00 5669 .55E+00 0.474E+16 0.120E+1326 0.47542E+08 0.187775E+0053500.53E+00 0.633E+16 0.103E+1327 0.45422E+08 0.223055E+00 50960.52E+00 0.790E+16 0.105E+1328 0.40884E+08 0.330393E+00 4825 0.66E+00 0.124E+17 0.138E+1329 0.30811E+08 0.792134E+00 4983 0.76E+00. 0.287E+17 0.315E+1330 0.25838E+08 0.120230E+01 5127 0.90E+00 0.423E+17 0.482E+1331 0.20883E+08 0.179830E+01 5328 0.11E+01 0.609E+17 0.755E+132 0.17192E+08 0.240053E+01 55210.12E+01 0.785E+17 0.1 10E+1433 0.14722E+08 0.288860E+01 57610.14E+01 0.905E+17 0.160E+144 0.12747E+08 0.333215E+01 5940 0.14E+01 0.101E+18 0.227E+1435 0.90503E+07 0.428255E+01 6392 0.16E+01 0.121E+18 0.572E+1436 0.71305E+07 0.484754E+01 6740 0.17E+01 0.130E+18 0.112E+1537 0.52084E+07 0.543779E+01 7326 0.17E+01 0.134E+18 0.303E+1538 0.33066E+07 0.604442E+01 78860.18E+01 0.138E+18 0.693E+15390.14140E+07 0666255E+01 84810.18E+01 0.140E+18 0.148E+164000000E+00 0.713130E+01 9030 0.18E+01 0.140E+18 0.272E+16where Eq =呈SMr f Rqdh is the total radiative losses of the quiet Sun atmospheric model VALC. Wetake S Rqdh= 4.6x 106 erg cm-2 s-1 from Vernazza et al. (1981). In fact, our results indicate that Eqis about one or two orders of magnitude smaller than Er.By use of the line-of-sight velocity measurement near the MFs, the lower limit of the kinetic energycan be estimated asE, = 1.4mHofSMFrnxdh，(7)where nH is the hydrogen density in the heating region of中國煤化工the mass that isinvolved in motion and we assume f = 0.1. The reasons anYHconnection flowsrefer mainly to a pair of oppositely-oriented plasmoids (see e.. CNM H Gou osevatosmass motions are seen near, but not exactly at, the locations of the MFs, as indicated in Section 3.3. Thus,it seems that the heated plasma could not be fully ejected during the magnetic reconnection. The coefficient606C.Fang,Y.H.Tang&Z.Xu.Table 4 Parameters used to Estimate the Energy of the Two MFsMFh_(km) (km) (km) (km) (km s- 1(erg)No.1 434 1440 434 8622.(0.53.8x1028 1.5 x1027No.3 399 14663997953.1 x10273.8 x10251.4 comes from the consideration of helium and other elements on the Sun, and corresponds to the meandensity of the Sun (see Cox 1999). In Equation (7) h3 and hs are, respectively the lower and upper heightsof the MF heating bump up area, determined by using the semi-empirical model of the MF. Due to the rapiddecrease of the hydrogen density with height, the contribution of the higher layers is small. The measuredline-of-sight velocity U is about 2 km s 1 for the bright MF (No.1), and and 0.5 km s - 1 for the faint MF(No.3).By use of the Equations (6) and (7), the energies of the two typical MFs can be estimated, as listed inTable 4. It can be seen that the total energy of the MFs is about 1027 to 4x 1028 erg, and the energy of thebrighter MF is larger than the fainter one.5 DISCUSSION AND CONCLUSIONSUsing the THEMIS spectropolarimetric data, we have obtained the spectra of Ha, Call 8542A, andFeI 6302 A lines for five well-observed MFs. These spectral data were obtained simultaneously and with ahigh spatial resolution: this allows us make a good deduction of the the characteristics of the MPs.The most obvious feature of the MF spectra is the emission at the centers of both the Ha andCalI 8542 A lines. This implies that the heating of the Ho MF atmosphere occurs mainly in the chro-mosphere.Three of the five MFs are located near the longitudinal magnetic polarity inversion lines (within 6 ")and all five are accompanied by mass motions (from 0.5 to several km s- ). These facts imply that Ha MFsare probably caused by magnetic reconnection in the lower solar atmosphere. Two of the MFs are locatedin unipolar regions. However, this can not rule out the possibility of magnetic reconnection, because inthe quasi-separatrix layers, where the the magnetic reconnection can occur (see Priest & Forbes 1999, andreferences therein), the line-of-sight component of the magnetic feld can be unipolar.Using non-LTE theory, we computed thermal semi-empirical models for one typical bright MF (No.1)and one faint MF (No.3). By including the non-thermal effects, we also obtained the non-thermal semi-empirical models. Our results indicate that the required extra heating in the chromosphere is about 1000 -2200K, and the higher value corresponds to the temperature bump up in the low-chromosphere, as clearlyshown in Figures 5 and 6. It can account for the main spectral features of MFs, particularly the centralemission of the Call 8542 A line. Moreover, if the non-thermal effects are included, the required extraheating can be reduced further. The reason is: If the non-thermal effect is included, then the particle beamwill deposit their energy in the surrounding area, and contribute to the line emissions (e.g. Fang et al.1993). This will reduce the contribution from the thermal component in the chromosphere, so the thermaltemperature is reduced.The semi empirical models and the measured line-of-sight velocities near the MFs can be used toestimate both the radiative and kinetic energies. Our results indicate that the total energy is about 1027 to4x 1028 erg, and that the energy of the brighter MFs is larger than that of the fainter MFs.It is worthwhile to compare MFs with Ellerman Bombs (EBs), which are small short-lived bright fea-tures observed best in the wings of chromospheric lines. Recently, we have analyzed some high-resolutionspectra of EBs, and found that the temperature enhancement is about 600-1300 K, and is located mainly inthe low-chromosphere and upper photosphere (Fang et al. 2006). By comparing the thermal semi-empiricalmodels for EBs and MFs, it can be seen that the temperature- rnd lower than theMFs. Both of them could probably be caused by magnetic re中國煤化工atmosphere, butthe location of the magnetic reconnection is probably deeperHCNMHGanbeverifiedbysome future numerical simulation.Spectral Analysis and Atmospheric Models of Microflares607As a summary, we give conclusions as follows:1. The most obvious characteristic of the Ha MF spectra is an excess emission at the centers of both Haand Call 8542 A lines.2. Among the five well-observed MFs three are located near longitudinal polarity magnetic inversion lines,while two are located in unipolar regions. All the MFs are accompanied by mass motions. These implythat Ha MFs are probably produced by magnetic reconnection in the solar low-chromosphere.3. For the first time both thermal and non-thermal semi-empirical atmospheric models for bright andfaint MFs are given. Their common characteristic is the heating in the lower solar atmosphere withtemperature enhancement of about 1000- -2200 K. In particular, there is a temperature bump up in thelow-chromosphere. If the non-thermal effects are included, the required temperature increase in thechromosphere will be reduced.4. The radiative and kinetic energies for one bright and one faint MF have been estimated. The resultsindicate that the total energy of the MFs is 1027 - 4x 1028 erg, and the energy of the brighter MFs islarger than that of the fainter one.Acknowledgements We would like to give our sincere thanks to Dr. G. Ceppatelli, Dr. C. Briand and otherstaff at the Spanish Observatorio del Teide of the Institute de Astrofisica de Canarias for their enthusiastichelp during C.F and Y.H.T's stay there. 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