Study of Post Flare Loops

# On the Brightening Propagation of Post-Flare Loops Observed by TRACE

Leping Li and Jun Zhang National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China; lepingli;zjun@ourstar.bao.ac.cn
###### Abstract

Examining flare data observed by TRACE satellite from May 1998 to December 2006, we choose 190 (151 M-class and 39 X-class) flare events which display post-flare loops (PFLs), observed by 171 Å and 195 Å wavelengths. 124 of the 190 events exhibit flare ribbons (FRs), observed by 1600 Å images. We investigate the propagation of the brightening of these PFLs along the neutral lines and the separation of the FRs perpendicular to the neutral lines. Observations indicate that the footpoints of the initial brightening PFLs are always associated with the change of the photospheric magnetic fields. In most of the cases, the length of the FRs ranges from 20 Mm to 170 Mm. The propagating duration of the brightening is from 10 minutes to 60 minutes, and from 10 minutes to 70 minutes for the separating duration of the FRs. The velocities of the propagation and the separation range from 3 km s to 39 km s and 3 km s to 15 km s, respectively. Both of the propagating velocities and the separating velocities are associated with the flare strength and the length of the FRs. It appears that the propagation and the separation are dynamically coupled, that is the greater the propagating velocity is, the faster the separation is. Furthermore, a greater propagating velocity corresponds to a greater deceleration (or acceleration). These PFLs display three types of propagating patterns. Type I propagation, which possesses about half of all the events, is that the brightening begins at the middle part of a set of PFLs, and propagates bi-directionally towards its both ends. Type II, possessing 30, is that the brightening firstly appears at one end of a set of PFLs, then propagates to the other end. The remnant belongs to Type III propagation which displays that the initial brightening takes place at two (or more than two) positions on two (or more than two) sets of PFLs, and each brightening propagates bi-directionally along the neutral line. These three types of propagating patterns can be explained by a three-dimensional magnetic reconnection model.

Sun: flares —Sun: corona—Sun: UV radiation—Sun: magnetic fields

## 1 Introduction

Flares are one of the most spectacular phenomena in solar physics. They are sudden brightening in the solar atmosphere, and consist of a number of components including loops, ribbons, arches, remote patches, surges, erupting filaments, and other expanding coronal features (Martin, 1989). They have been studied morphologically from direct images (e.g. Krucker et al., 2000; Fletcher et al., 2001; Kundu et al., 2001) and spectroscopically from spectrograms (e.g. Moore, 1976; Cowan et al., 1973; Acton et al., 1985; Cully et al., 1997; Grigis et al., 2005b) at different wavelength regions. Like most dynamic phenomena on the solar surface, the occurrence of solar flares is closely related to the presence and evolution of solar magnetic fields, especially the complicated, non-potential magnetic configuration (Rust, 1972; Patterson & Zirin, 1981; Moore et al., 1984). Flares can be caused by rotating sunspot (Brown et al., 2003; Tian et al., 2006; Zhang et al., 2007), magnetic flux emergence (Ishii et al., 1998; Wang et al., 2004; Li et al., 2007), magnetic flux cancellation (Livi et al., 1989; Wang et al., 1992, 1993; Zhang et al., 2001a, b, 2002), magnetic shear (Kusano et al., 2004; Wang et al., 2006; Ji et al., 2006; Su et al., 2007), and so on.

The chromospheric flare (e.g. Fang et al., 2000; Falchi et al., 2002; Cheng et al., 2006; Hudson, 2007) is easier to be observed, especially with the help of an H filter. Larger flares often occur right after the sudden disappearance of a filament (Kuperus et al., 1981; Ding et al., 2003; Sterling et al., 2005; Jiang et al., 2006a, b; Chifor et al., 2007). In this case, the flare generally has the form of two flare ribbons (FRs) which lie on both sides of the location of the former filament. During flare decay phase, the FRs move apart. The separation of these FRs has been used to estimate the electric field in the reconnecting current sheet (e.g. Qiu et al., 2002; Asai et al., 2004b) and also the coronal magnetic field strength and the reconnection rate (e.g. Isobe et al., 2002b, 2005). Many authors have observed the parallel and antiparallel movements of the FRs along the arcade (Hoyng et al., 1981; Takakura et al., 1983; Fletcher & Hudson, 2002; Liu et al., 2004; Qiu et al., 2004; Siarkowski & Falewicz, 2004).

Accompanying the FRs is a system of post-flare loops (PFLs) which initially appears at low altitude and then moves upward into the corona in consort with the motion of the ribbons (Moore et al., 1980). A classical description of the PFLs, as seen in H images, was first given by Bruzek (1964) who noted that the ribbons essentially lie at the footpoints of the loop system, which forms a series of arcades (Lin et al., 2003). These arcades are also frequently seen in the X-ray images recorded by Soft X-ray Telescope (SXT) (Tsuneta et al., 1991) aboard Yohkoh (Ogawara et al., 1991), in the extreme ultraviolet (EUV) images from EIT (Extrmeme-ultraviolet Imaging Telescope, Delaboudinière et al., 1995) aboard the Solar and Heliospheric Observatory (SOHO) (Dimingo et al., 1995), and also in the EUV images from Transition Region and Coronal Explorer (TRACE) (Handy et al., 1999). The formation of transient large-scale PFLs or post-eruptive arcades (PEAs) has been widely studied (e.g. Carmichael, 1964; Sturrock, 1966; Hirayama, 1974; Kopp & Pneuman, 1976; Cargill et al., 1983; Webb & Hundhausen, 1987; Svestka et al., 1997; Tripathi et al., 2004; Tripathi, 2005, 2006b). Hudson et al. (1998), Sterling et al. (2000) and Tripathi (2006b) studied a set of individual events about the relationship between PFLs and Coronal Mass Ejections (CMEs). The propagation of the loop formations along the neutral line, together with the separation of the FRs perpendicular to the neutral line was reported by Isobe et al. (2002a). Grigis & Benz (2005a) found a RHESSI observation showing that the hard X-ray (HXR) sources do not show the separation from the neutral line, but instead they move along the neutral line (see also Goff et al., 2007). Tripathi et al. (2006a) investigated the relationship between the brightening propagation of the PEAs and the erupting filament/prominence. They reported two types of propagation of the brightening, and the propagating direction was consistent with the erupting direction of the filaments.

Due to the extremely low density and high temperature of the corona, measurements of the magnetic field are restricted to lower layers of the solar atmosphere. For this reason, extrapolation techniques, which attempt to reconstruct the coronal field from measured boundary values in the photosphere (or low chromosphere), are the prime tool for quantitative investigations of the coronal magnetic field (Valori et al., 2005). Some authors used the methods of extrapolation to study the evolution of flare loops in active region (e.g. Yan et al., 1995; Wang et al., 2001; Wiegelmann et al., 2005; Amari et al., 2006; Zhao et al., 2008).

Magnetic reconnection of solar coronal loops is considered to be the main process that causes solar flares and possibly coronal heating. It is widely believed to be a mechanism of magnetic energy release (see reviews by Shibata, 1999; Martens, 2003), and plays an important role in various explosive phenomena in astrophysical, space, and laboratory plasmas (Biskamp, 1993; Tajima & Shibata, 1997; Priest & Forbes, 2000). The evidence of magnetic reconnection found by space observations includes the cusp-shaped PFLs (Tsuneta et al., 1992), the loop-top hard X-ray source (Masuda et al., 1994), the reconnection inflow (Yokoyama & Shibata, 2001; Lin, 2005), downflows above PFLs (McKenzie & Hudson, 1999; Innes et al., 2003; Asai et al., 2004a), plasmoid ejections (Shibata et al., 1995; Ohyama & Shibata, 1997; Ohyama & Shitaba, 1998), etc. Two-dimensional (e.g. De Young et al., 1971; Winglee et al., 1991; Hu et al., 1995; Forbes et al., 1995; Yokoyama & Shibata, 1998; Zhang et al., 2006) and three-dimensional simulations (e.g. Wu et al., 1992; Magara et al., 1999; Miyagoshi et al., 2004; Aulanier et al., 2006; Birn et al., 2006) are widely used to study the magnetic reconnection in process of flares and CMEs.

The magnetic reconnection model proposed by Carmichael (1964), Sturrock (1966), Hirayama (1974) and Kopp & Pneuman (1976) (the CSHKP model) suggests that magnetic field lines successively reconnect in the corona. This model explains several well-known features of solar flares, such as the growth of flares loops with a cusp-shaped structure and the formation of the H two-ribbon structures at their footpoints. In recent decades, this model has been further extended (e.g. Pneuman, 1981; Priest & Forbes, 1990, 2000, 2002; Moore & Roumeliotis, 1992; Moore et al., 2001; Shibata, 1999; Yokoyama & Shibata, 2001; Lin et al., 2000; Lin, 2004).

In this paper, we mainly study the dynamic evolution of a larger sample of flare events, including the propagation of the PFLs along the neutral lines and the separation of the FRs away from the neutral lines. This investigation will provide some information of 3-dimensional magnetic reconnection in the process of flare. The criteria for the data selection and the methods of the data analysis are described in section 2. In section 3, we summarize our statistical results. Conclusions and brief discussion are shown in section 4.

## 2 Data and Observations

We checked all the 75 X-class and 509 M-class flare events observed by TRACE from May 1998 to December 2006. 39 X-class and 151 M-class flare events which display PFLs are chosen as our sample (see Table 1). The TRACE mission explores the dynamics and evolution of the solar atmosphere from the photosphere to the corona with high spatial and temporal resolution (Handy et al., 1999). It observes the photosphere (white-light, WL), the transition region (1216, 1550, and 1600 Å) and the 1-2 MK corona (171, 195, and 284 Å). In this work, we mainly use the 171 and 195 Å images to study the propagation of the brightening of the PFLs, and the 1600 Å observations to the separation of the FRs. We also use TRACE WL observations and magnetic field observations of SOHO/MDI (Scherrer et al., 1995) to investigate the variation of the source region of these flare events.

### 2.1 Methods

In order to study the dynamic evolution of the larger sample of flare events quantificationally, we determine a set of parameters to describe the evolution of the PFLs and the FRs for each event in our sample. These parameters include the propagating duration (PD), propagating velocity (V) and acceleration (a) of the PFLs, the separating duration (SD) and separating velocity (V) of the FRs, the length (Len) of the FRs at the maximum of the flare, the flare class (FC) and the flare duration (FD). Because some events in the sample are not completely observed, we can not get all the parameters simultaneously for all the cases. Among the 190 flare events, 183 display clear evolution of the PFLs observed by TRACE 171 and 195 Å images, so we can measure the three parameters V, a and PD. TRACE 1600 Å observations can clearly detect the FRs. In our sample, 124 events are also observed by TRACE 1600 Å wavelength, so we measure the parameter Len for these events. 101 of the 124 events show clear kinetics of the FRs, we measure V and SD for these cases. Table 2 lists the measured events of these parameters.

In order to illustrate how to measure these parameters, we show a flare event observed on the disk at the heliographic position S05 W54 on 2001 March 20 in Fig. 1. Figure 1a shows the initial brightening of PFLs at 02:41 UT. L and L in Fig. 1b represent the distance of the propagation of the PFLs towards southeast along different FRs from 02:41 UT to 03:16 UT, as well as L and L, towards northwest. The total value of these four distance represents the distance of the propagation (L) of the PFLs from 02:41 UT to 03:16 UT:

 Lp=L11+L12+L21+L22 . (1)

L and L in Fig. 1c show the distance of the propagation of the PFLs toward southeast from 02:41 UT to 03:52 UT, as well as L and L, towards northwest. The distance of the propagation of PFLs from 02:41 UT to 03:52 UT is:

 Lp=L31+L32+L41+L42 . (2)

By using the method shown above, we obtain a series of propagating distance of the PFLs with time, and a series of propagating velocities is derived. Both the initial propagating time (t) and the end propagating time (t) of the brightening of the PFLs are determined from the series of velocities. We define t to be the time when the propagation velocity drops to 1/e of the peak value. The parameter PD of the PFLs is the duration of t and t. The distance versus time plot for the propagation of the PFLs between t and t for the event showed in Fig. 1 is indicated in Fig. 2. We use a linear polynomial fit to the data points to get the parameters V, and second order polynomial fit for a. Similar to the determination of t and t, the initial separating time (t) and the end separating time (t) of the FRs are obtained from 1600 Å observations. The parameter SD is the duration from t to t. Figures 1d-1f are series of 1600 Å images observed by TRACE. L and L in Fig. 1f represent the distance of the separation of the FRs from 02:25 to 03:27 UT towards northeast and southwest, respectively. The distance of the separation (L) of the FRs is

 Ls=L51+L52 . (3)

We got the parameter V using the similar method as to get V. The length of the FRs is measured from 1600 Å image (see Fig. 1e) while the FRs are well developed. L and L represent the length of two FRs, respectively. We get Len by using

 Len=L61+L622. (4)

The projection effects are corrected using trigonometric function when we got the parameters V, a, V and Len.

The parameter FC, the peak X-ray flux of the associated flare, is recorded by GOES-10 soft X-ray 1-8 Å flux intensity, and FD, the duration between the beginning time and the ending time of the flares, by Solar-Geophysical Data. While studying the evolution of the PFLs of these events, we find that the PFLs display three types of propagating patterns. Type I is that the brightening begins at the middle part of a set of PFLs, and then propagates bi-directionally towards its both ends. Type II shows that the brightening firstly appears in one end of a set of PFLs, then propagates to the other end. There are two (or more than two) initial brightening involved in Type III propagation, each brightening takes place in the middle of a set of PFLs, then propagates bi-directionally. The following are three examples of flare events which are displayed to describe the three types of propagation.

### 2.2 M 9.8 Flare on 2005 September 17

Type I propagation is characterized by an M 9.8 flare event occurred at the heliographic position S11 W51 on 2005 September 17. We show the time sequence of 171 Å images in the top panels of Fig. 3. The brightening of the PFLs is firstly seen at 06:04 UT, and the outer edges of the PFLs are outlined as dotted curves in Fig. 3a. The propagation of the PFLs ended at 06:24 UT (see Figure 3c). From these panels, we notice that the initial brightening of this event occurs at the middle part of a set of PFLs, then propagates bi-directionally towards its both ends (see white arrows in Fig. 3c).

We examine the evolution of photospheric magnetic field and the change of continuum intensity by using the observations of SOHO/MDI and TRACE WL, respectively. Figure 3d is the magnetogram before the flare, as well as Fig. 3e, after the flare. Figure 3f displays the difference image of these two magnetograms. The regions in white brackets show the change of photospheric magnetic field, and the variation of unsigned magnetic flux is about 310 Mx. The TRACE WL images before and after the flare are presented in Figs. 3g and 3h, respectively. We show their difference image in Fig. 3i, and find the change of the continuum intensity (denoted by white brackets). Comparing Figs. 3f and 3i with Figs. 3a and 3c, we note that the regions showing obvious changes of photospheric magnetic field and continuum intensity are associated with the initial brightening of the PFLs (see the brackets in Figs. 3a and 3c). In other words, the initial brightening is related to the magnetic variation on the photosphere.

### 2.3 M 2.0 Flare on 1999 January 18

The M 2.0 flare event on 1999 January 18, which occurred at the heliographic position N19 E03, is used to describe Type II propagation. Figures 4a and 4c are the TRACE 171 Å images showing the beginning and the ending propagation of the brightening of the PFLs. Figure 4b is an image during the propagation. It appears that the initial brightening occurs at the southern end of a set of PFLs, and then propagates towards northeastern end (see the white arrow in Fig. 4c).

As this event was not observed by SOHO/MDI, we use TRACE WL images to study the change of the continuum intensity (the bottom panels of Fig. 4) which are relevant to this event. Figures 4d and 4e are the observations before and after the flare, and Fig. 4f is their difference image. The regions inside the square brackets in Fig. 4a show the footpoints of the initial brightening of the PFLs. We overlay these square brackets on Fig. 4f, and find that the initial brightening of the PFLs is associated with the change of the continuum intensity.

### 2.4 M 1.5 Flare on 2002 October 25

The M 1.5 flare event on 2002 October 25 occurred at the heliographic position N28 W11. This event is employed to display Type III propagation. Figure 5a shows the initial brightening of the PFLs in the southwest of the FRs, with dotted curves outlining the outer edge of the PFLs. Then this brightening propagates towards northeast and southwest (see the black arrows showed in Fig. 5c). Figure 5b presents the brightening of another set of PFLs (marked by the dashed line). This brightening also propagates towards northeast and southwest (see the white arrows in Fig. 5c). From these panels, we notice that the PFLs are consist of two sets of independent brightening loops in different places in the active region, then each brightening propagates bi-directionally towards its both sides.

Figures 5d and 5e are longitudinal magnetograms before and after the flare observed by SOHO/MDI, respectively. Figure 5f shows their difference signal. We mark the regions of the PFL footpoints as brackets in Figs. 5a-5b and overlay these regions on the difference magnetogram (see Fig. 5f). It indicates that the regions of the initial brightening are associated with the change of the photospheric magnetic field, as presented in section 2.2.

## 3 Statistical Results

In this work, eight parameters (PD, V and a of PFLs, SD, V and Len of FRs, FC and FD) are considered to characterize the kinematics of the PFLs and the FRs, and listed in Table 2.

By examining the TRACE observations of all the flare events, we have determined PD of 183 events and SD of 101 events. Figure 6a shows the distribution of PD (solid lines) and SD (dotted lines). PD ranges from 10 to 60 minutes in nearly 90 of the cases, with the peak of the distribution lying close to 25 minutes. The average value of all the PDs is 33 minutes. Similarly, almost 90 of the SDs range from 10 to 70 minutes, with average duration of 38 minutes. Besides PD and SD, we have also exhibited the distribution of V (solid lines) and V (dotted lines) in Fig. 6b. Most of the Vs range from 3 to 33 km s, and the average velocity is 17.9 km s. It indicates that 76 of the Vs range from 3 to 15 km s, with the average value of 7.2 km s.

In order to explore the physical connection of these parameters, we study the one-to-one correspondence among them. It appears that FD is associated with PD and SD, and the longer the FD is, the longer the PD and the SD are, as displayed in Fig. 7. The Len of the FRs, which ranges mainly from 20 to 170 Mm and may represent the length of the current sheet along the neutral line, is associated with FC and weakly associated with FD (see Fig. 8). It looks like that more powerful flares correspond to longer FRs. V and V are two important parameters, as they represents the kinetics of the propagation of the PFLs and the separation of the FRs. Figure 9 shows the correspondence of V and V with some relevant parameters. Generally, both of V and V increase as the flare becomes more powerful (see Figs. 9a and 9c). Figures 9b and 9d show the relationship between the velocity and Len of the FRs, separately for V (Fig. 9b), and V (Fig. 9d). It displays that both V and V increase from several km s to tens of km s, as Len increases from tens of Mm to hundreds of Mm.

The separation of the FRs, considered to be the representation of continuing magnetic reconnection and upwards moving reconnection sites, has been well studied. The propagation of the PFLs, which may reflect the signature of successive magnetic reconnection along the neutral line, is rarely taken into account. In our statistical results, we notice that V is associated with V (see Fig. 10a), that is V increases as V increases. Besides the velocity, a is also an important parameter to study the evolution of the PFLs. Figure 10b shows the relationship between a and V. The diamonds represent the positive accelerations of the brightening propagation, as well as the asterisks, decelerations. Among these 183 events, 135 are decelerated, possessing 74, and 48 accelerated, occupying 26. There is also a trend that the greater the V is, the larger the deceleration (or acceleration) is.

In this study, we classify the propagation of the PFLs into three types. The information of these three types of propagation is showed in Table 3. It appears that the events displaying Type I propagation are almost half of all the events.

## 4 Conclusions and Discussion

We have studied the evolution of the PFLs and the FRs of the 190 flare events, and obtained the following results.

1. Both of PD and SD are associated with FD. The longer the FD is, the longer the PD and the SD are. The length of the FRs mainly ranges from 20 to 170 Mm. It is associated with FC, but weakly associated with FD. It increases as FC (FD) increases.

2. V ranges mainly from 3 km s to 33 km s, and V, from 3 km s to 15 km s in 76 of the cases. V and V are dynamically coupled, V increases as V increases. Both of V and V are positively correlated with FC and Len of the FRs. The brightening of the PFLs do not evenly propagate, 74 of the PFL events are decelerated, and 26, accelerated.

3. There are three types of propagation of the PFLs. Type I, possessing 49.5 of all the events, is that the brightening begins at the middle part of a set of PFLs, and then propagates bi-directionally towards its both ends. Type II, in possession of 30, displays that the brightening firstly appears in one end of a set of PFLs, then propagates to the other end. Type III, occupying 20.5, shows that the initial brightening takes place at two (or more than two) positions on two (or more than two) sets of PFLs, and each brightening propagates bi-directionally.

The main error source of our measurement of the velocities (V and V) is due to the uncertainty of the outer edges. In our study, two pixels error has been used. As the average PD (SD) is 33 (38) minutes, the error of V (V) is 0.4 (0.3) km s, which is much less than the velocities showed in Table 1. So the values of these velocities are reliable.

Several authors have paid attention to the propagation of the PFLs. Isobe et al. (2002a) reported that V is about 3-30 km s by using the data from Yohkoh/SXT (Tsuneta et al., 1991), and 50-150 km s in Grigis & Benz (2005a) from RHESSI observations. Based on the SOHO/EIT observations, Tripathi et al. (2006a) studied several flare events relevant to long filament eruptions. They presented that V of the PEAs ranges from 20 to 111 km s. In this paper, we show that V is mainly from 3 to 33 km s, which is consistent with Isobe et al. (2002a), but somewhat smaller than that of Tripathi et al. (2006a). The velocity difference between ours and Tripathi et al. may result from two aspects. The first aspect is the sample. Our sample contains hundreds of cases. The second is the datum source. We employ the TRACE data which have higher spatial (1) and temporal (1 minute) resolution. V of the FRs have been intensively studied, but the value are varied distinctly, e.g. 20-100 km s in Qiu et al. (2002), 0-85 km s in Asai et al. (2004b, 2006) and 20-70 km s in Temmer et al. (2007). By employing the TRACE 1600 Å observations, Isobe et al. (2005) obtained V of 6.7-12 km s near the impulsive phase of the flares. Our results about V (3-15 km s) are well in agreement with that of Isobe et al. (2005).

It is basically accepted that the separation of the FRs and the propagation of the PFLs can be considered the signature of the successive magnetic reconnection along different directions. SD represents the duration of the magnetic reconnection where the reconnection points move upward, and PD, along the neutral lines. Both SD and FD determine the duration of flares. That is the reason why both SD and PD are associated with FD (see Figs. 7a-b). Lots of researchers have employed V to estimate the reconnection rate, they derived that the reconnection rate is very sensitive to V (e.g. Isobe et al., 2002b, 2005). Investigation of the propagation of the PFLs and the separation of the FRs simultaneously will provide us with 3-dimensional picture of magnetic reconnection in the process of flares. In our study, we find that V of the PFLs is associated with V of the FRs (see Fig. 10a). This indicates that the separation of the FRs and the propagation of the PFLs are dynamical coupled. Our results show that both V of the FRs and V of the PFLs are associated with FC (see Figs. 9a and 9c). As FC represents the maximum energy release rate of the flares, this implys that V and V may also reflect the magnetic reconnection rate. Len of the FRs may be the length of the current sheet along the neutral line. Both V of the FRs and V of the PFLs are associated with Len of the FRs (see Figs. 9b and 9d). This may result from the magnetic configuration of the source region of the flare. Tripathi et al. (2006a) have suggested that the longer the FRs is, the less magnetically complex the flare region is. We speculate that the brightening of the PFLs propagates easily in a simple magnetic configuration, and so do the FRs separate. All the parameters and the relationships between these parameters we discussed here will help us to better understand 3-dimensional magnetic reconnection, and provide an observational character for theoretical study and simulation of 3-dimensional magnetic reconnection.

By investigating 17 events, Tripathi et al. (2006a) found two types of propagation of the brightening of the PEAs associated with asymmetric eruptions and symmetric eruptions of filaments, respectively. We have studied a much larger sample with higher spatial and temporal resolution observations, and found three types of propagation of the PFLs. Type I and Type II propagation are similar to those two types of propagations reported by Tripathi et al. (2006a). Type III propagation indicates that sometimes two or more than two sets of PFLs are involved in a flare event. All the three types of the propagation of the PFLs may be explained by schematic diagrams shown in Fig. 11 (see also Shiota et al., 2005; Tripathi et al., 2006a). Figure 11a shows the explanation of Type I propagation. The X-point of the magnetic reconnection site occurs over the middle part of a set of loops (marked by Reconnection), then continuing magnetic reconnection occurs bi-directionally, thus results in the brightening of the PFLs appearing in the middle of the set of loops and propagating towards two opposite directions (see the grey thick arrows) as expected from the standard model. The white hollow arrows represent the separating direction of the FRs. Figure 11b illustrates that the magnetic reconnection site occurs over one end of a set of loops (mark by Reconnection), then the magnetic reconnection develops continuously towards the other end (see the black thick arrow). This mechanism can be employed to explain the observations of Type II propagation that the brightening of the PFLs occurs at one end of a set of PFLs and propagates from one end to the other one. Type III propagation displays a complex evolution pattern of the PFLs. We suggest that there are two (or more than two) magnetic reconnection sites (see Fig. 11c) which locate in two (or more than two) magnetic flux system. After the magnetic reconnection occurs, each of the brightening of the PFLs propagates bi-directionally along the neutral lines (see the black thick arrows). We check the MDI magnetograms and the TRACE WL observations of these events (e.g. see the examples displayed in Figs. 3-5), and find that the magnetic activity are clearly seen at the footpoints of the initial brightening of the PFLs. According to the observations of these three types of propagation, we propose that all the propagation of the PFLs are caused by magnetic reconnection. There is only one set of magnetic flux system involved in Type I and Type II propagation. The only difference of these two types of propagation is the position of the magnetic reconnection site. There are two or more than two sets of PFLs heated in the process of flare in Type III propagation. So the different appearance of these three types of the propagating PFLs may be determined by two effects. One is the different position of the magnetic reconnection site, the other is the different magnetic configuration of the source region of the flare.

Further studies using the data observed by Solar Terrestrial Relations Observatory (STEREO) will give us a more clear three-dimensional stereoscopic pictures about the evolution of the PFLs. Vector magnetograms (e.g. from Hinode) with higher spatial and temporal resolution are likely to uncover the magnetic configuration in detail. Moreover, complex three-dimensional simulation will be required to understand the dynamic behavior of the PFLs and the FRs.

The authors are indebted to the TRACE and SOHO/MDI teams for providing the data. The work is supported by the National Natural Science Foundations of China (G10703007, 10573025, 10603008, 40674081, and 10733020), the CAS Project KJCX2-YW-T04, and the National Basic Research Program of China under grant G2006CB806303.

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