ON THE SOLAR ORIGINS OF OPEN MAGNETIC FIELDS IN THE HELIOSPHERE

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1 The Astrophysical Journal, 687: , 2008 November 1 # The American Astronomical Society. All rights reserved. Printed in U.S.A. ON THE SOLAR ORIGINS OF OPEN MAGNETIC FIELDS IN THE HELIOSPHERE David M. Rust, 1 Dennis K. Haggerty, 1 Manolis K. Georgoulis, 1 Neil R. Sheeley, 2 Yi-Ming Wang, 2 Marc L. DeRosa, 3 and Carolus J. Schrijver 3 Received 2008 March 14; accepted 2008 July 17 ABSTRACT A combination of heliospheric and solar data was used to identify open magnetic fields stretching from the lower corona to Earth orbit. 35 near-relativistic electron beams detected at the ACE spacecraft labeled the heliospheric segments of the open fields. An X-ray flare occurred <20 minutes before injection of the electrons in 25 events. These flares labeled the solar segment of the open fields. The flares occurred in western-hemisphere active regions (ARs) with coronal holes whose polarity agreed with the polarity of the beam-carrying interplanetary fields in 23 of the 25 events. We conclude that electron beams reach 1 AU from open AR fields adjacent to flare sites. The Wang & Sheeley implementation of the potential-field source-surface model successfully identified the open fields in 36% of cases. Success meant that the open fields reached the source surface within 3 heliographic deg of the interplanetary magnetic field connected to ACE at 1 AU. Inclusion of five near misses improves the success rate to 56%. The success rate for the Schrijver & DeRosa PFSS implementation was 50%. Our results suggest that, even if the input magnetic data are updated frequently, the PFSS models succeed in only 50% of cases to identify the coronal segment of open fields. Development of other techniques is in its infancy. Subject headinggs: solar-terrestrial relations solar wind Sun: corona Sun: magnetic fields Sun: particle emission 1. INTRODUCTION Most of the Sun s open magnetic fields are anchored in holes that resemble very dark oceans or lakes in the X-ray corona. The largest coronal holes cover the north and south poles. At the minimum phase of the 11 yr solar cycle, the polar coronal holes account for nearly all of the field lines that stretch out from the Sun and fill the heliosphere. But when the Sun is active, some open fields are anchored in sunspots or in dark bays in equatorial zones (Nolte et al. 1976), most of which are close to X-rayemitting and flaring magnetic loops. At sunspot maximum, the open flux in the active-region holes is comparable to that in the polar holes near sunspot minimum. Svestka et al. (1977) published the first convincing case studies of these active-region (AR) coronal holes. Subsequent work, e.g., by Wang & Sheeley (1990, 2003), showed that the open fields from the poles and other oceansized coronal holes carry the fast solar wind, whereas the slow solar wind seems to come from (1) the boundaries of large holes; (2) the AR holes; and (3) helmet streamers. Sources (1) and (2) have open fields that stretch into the heliosphere, whereas the fields of helmet streamers are mostly closed, perhaps feeding mass to the slow wind (Hick et al. 1995) by sporadic instabilities (Einaudi et al. 1999). Current models (Schrijver & DeRosa 2003; Wang & Sheeley 1992) of the coronal magnetic fields show quite reliably where the polar fields stretch into the heliosphere, and so they can effectively predict fast solar wind streams. It is less clear that they can do the same for the open fields associated with AR coronal holes. So we conducted a sensitive test to determine just how accurately the models describe the open AR fields. We used a combination of in situ electron beam measurements and remote 1 The Johns Hopkins University Applied Physics Laboratory, Johns Hopkins Road, Laurel, MD Code 7672, Space Science Division, Naval Research Laboratory, Washington, DC Lockheed Martin Advanced Technology Center, 3251 Hanover Street B/252, Palo Alto, CA solar observations to identify a set of open fields for which both the solar and heliospheric positions are known to within a few heliographic degrees. Then we examined the open fields predicted by the models. The models did very well at identifying the open AR fields. They were much less successful in predicting just where the open AR fields connected to the interplanetary magnetic field. 2. ELECTRON BEAMS AS TRACERS OF OPEN FIELDS The hard X-ray and radio bursts associated with most solar flares are conclusive evidence that electrons are being accelerated to near-relativistic energies (Liu et al. 2004). The bulk of the electrons remain in the corona, trapped in closed magnetic fields, where they lose their energy through collisions in the solar atmosphere. The collisions cause local heating, which produces soft X-ray and H flares, which we assume occur near the acceleration site. In some flares, a small fraction of the energetic electrons ends up on open fields and propagates out to the heliosphere, where the spectra, intensity, and angular distribution of the electrons can be measured in situ. Linking these electrons to the flares provides a way to trace the open fields from the base of the corona to 1 AU. Classen et al. (2003) studied the hard X-ray and type II and IV metric radio events associated with a beam of near-relativistic electrons (e-beam) detected by the WIND spacecraft on 2002 June 2. Electrons produced by coronal shock waves generate type II events, and near-relativistic electrons trapped in coronal magnetic fields generate type IV events. In the event studied, Classen et al. concluded that the WIND-detected e-beam had an onset coinciding in time with bursts of type IV emission. The type II associated shock would have accelerated the electrons within seconds, so shock acceleration can be ruled out in this case. Instead, Classen et al. suggested that the e-beam was produced by some reconnection process in the low corona, as evidenced by the bursts of type IV emission.

2 636 RUST ET AL. Vol. 687 Haggerty & Roelof (2002) did a statistical analysis of 79 e-beam events. They inferred that the electrons were typically injected onto the open fields with a delay of 10 minutes after the start of the electromagnetic emissions (including metric and decametric type III radio bursts). They suggested that the escaping electrons were not directly related to those that generated the electromagnetic emissions. They concluded, contrary to Classen et al., that escaping near-relativistic electrons are accelerated and/or injected by an outgoing coronal shock (V 1000 km s 1 ). The launch of the shock would correspond to the onset of the electromagnetic emissions. We studied a subset of Haggerty & Roelof s events, namely, only the 35 events with highly focused electron beams. We wanted to trace the fields from the low corona to 1 AU using only the events least likely to be influenced by shocks or mass ejections. As described in x 3, we found that 2/3 of such beams can be associated with flares adjacent to AR coronal holes. In using these events, we suppose that the electrons come promptly and directly from the corona along the quiescent spiral interplanetary magnetic field to in situ detectors near Earth. However, for another view, see Cane (2003). Maia & Pick (2004) used radio spectrograms and radioheliograms to study another subset of the events from Haggerty & Roelof (2002). They concluded that e-beam event injection and weak type III bursts begin simultaneously. For events that include a panoply of radio emissions, they found that the electron release time always coincided with the onset of or with major changes in the radio emissions. They concluded that the good association of coronal radio emission events with the inferred electron beam release times suggests a common acceleration mechanism. From a comparison of images of coronal mass ejections (CMEs) and radioheliograms showing type IV continuum emission sources relatively low in the corona, Maia & Pick concluded that the acceleration process is below the leading edge of any associated CME. 3. DESIGN OF THE STUDY Our study began with a set of impulsive near-relativistic (0:4 < v/c < 0:8) e-beam events detected by the Electron, Proton, and Alpha Monitor (EPAM; Gold et al. 1998) aboard the Advanced Composition Explorer (ACE) spacecraft (Stone et al. 1998) at the L1 point near Earth. The electron observing component of the EPAM instrument consists of three separate telescopes (four energy channels in the range kev) mounted at angles of 30,60, and 150 with respect to the spacecraft spin axis. Because of the spin of the spacecraft, the EPAM instrument has nearly 4 sr coverage. Two of the telescopes use a thin foil technique (at 60 and 150 ) that blocks low-energy ions but allows the near-relativistic electrons to reach the (solid state) detectors. The other telescope (mounted at 30 ) uses rare-earth magnets to drive the electrons away from the direction of normal incidence and into a detector that has no direct view of the instrument aperture. This deflected-electron detector makes unambiguous measurements of the electron spectra and is the primary source of the data used in this study. For inclusion in our study, an e-beam event must have had a distinct rise phase. In addition, the angular distribution must show that the electrons were aligned with the interplanetary magnetic field (IMF), and there must have been a dispersion in velocities to prove that the onset of the event is not a spatial effect, i.e., an ongoing event that is convected over the spacecraft. Such events, which are frequent, occur when electrons are injected onto field lines that are not initially connected to the spacecraft. EPAM has recorded well over 700 electron events in 10 yr of operation, and more than 2/3 of them were delisted because of questionable timing. We also threw out events that had a relatively gradual rise to peak intensity and a very gradual decline. These events were probably caused by electron acceleration in shocks associated with CMEs (Simnett et al. 2002), which greatly distort the heliospheric fields. We kept only beam events that had a nearly symmetrical Gaussian time profile with a FWHM (full width at half-maximum) of <20 minutes. These rapid-rise-and-fall events were chosen to minimize the chance that transport effects, such as interaction with a CME, could influence the inferred injection time at the corona. By limiting ourselves to impulsive and beamlike (scatter-free) events, we could safely assume that the electrons path back to the corona followed highly ordered open fields. When an electron event arrives during a choppy field period with highly variable plasma flows, the angular distribution is isotropic. We do not include those types of events in our analysis. From hundreds of energetic electron events recorded by EPAM, we found only 35 qualifying events between the beginning of measurements with EPAM in 1997 and 2001 December 14, the date when the Yohkoh spacecraft ceased operating. We tried to find the flares associated with the 35 e-beam events. Our primary sources of flare data were the archive of Yohkoh fulldisk soft X-ray images (Acton et al. 1992) and the NOAA GOES X-ray flare reports. When there was no timely X-ray image, we used the H flare positions reported by the NOAA Space Weather Prediction Center to put the flares in the correct coronal magnetic field context. We estimated the beams injection times at the Sun. Three methods were used to estimate the path length to the corona along the IMF, and thus to obtain an estimate of the energetic electron transit time: (1) assume, as in Haggerty & Roelof (2002), that the electrons traveled scatter-free at 0 pitch angle from the Sun to 1 AU along a spiral magnetic field of length 1.2 AU, which is the length given by Parker s (1958) solar wind model when the wind speed is a steady 400 km s 1 ; (2) assume that the electrons follow an ambient windspeed path whose length depends on the speed of the local plasma near the onset of the event (Nolte & Roelof 1973); and (3) adopt a path length consistent with the beam s velocity dispersion (typically called the 1/ method; Krucker et al. 1999). For each of the near-relativistic electron beam events on our final list, we calculated the injection times implied by the first two methods. Linghua Wang and Sam Krucker (2007, private communication) provided injection times from WIND 3DP observations by using the 1/ method. Next, we searched the NOAA flare lists and the Yohkoh full-disk movies for flares occurring not more than 20 minutes before the calculated electron injection time. To compare the flare onset and peak emission times to the e-beam injection times, we subtracted the 500 s light travel time from the event times recorded at Earth. Out of the 35 candidate events in the period of interest, we found 25 with a cotemporal flare whose position could be determined from either the X-ray images or the H reports. 4. MODELS OF THE MAGNETIC FIELDS IN THE CORONA The previous section described how we extrapolated the field lines from 1 AU back to the Sun, actually to a spherical surface at 2.5 R from Sun center. The next step was to map the field lines from this spherical source surface down to the base of the corona. Perhaps the most accurate way to do this would be to use global magnetohydrodynamics ( MHD) model of the coronal fields (e.g., Linker et al. 1999), however, these simulations are too slow for practical use on a large number of events. Instead,

3 No. 1, 2008 SOLAR ORIGINS OF OPEN MAGNETIC FIELDS 637 we relied on recent versions of the classic potential field source surface ( PFSS) model (Altschuler et al. 1977; Levine et al. 1977b; Sakurai 1982). Although many simplifying assumptions are necessary to produce the PFSS closed-form solutions, the model has quite successfully detailed the origins of the solar wind (e.g., Levine et al. 1977a; Neugebauer et al. 1998; Wang & Sheeley 1994). The fields in the corona are assumed to be current-free and to become radial at the source surface at 2.5 R. The real coronal fields, especially in growing ARs, will have currents, so the PFSS model cannot be 100% correct. Gilbert et al. (2007) discuss the limitations of the PFSS model but still emphasize its utility for identifying coronal hole boundaries. We used two popular PFSS models, one implemented by Wang & Sheeley (WS) and one by Schrijver & DeRosa (2003; SDR). They incorporate many improvements over earlier implementations, for example, in the descriptions of the surface magnetic fields (Wang & Sheeley 1992). The WS model improves on the earlier extrapolations of Altschuler et al. and Levine et al. by assuming a radially oriented photospheric field. The field lines are matched to this radial component B r rather than the measured line-of-sight fields B n. This procedure gives much stronger polar fields near sunspot minimum, and produces much better agreement with a wide range of observations. The input magnetograms for the WS model came from the Mount Wilson Observatory (Ulrich et al. 2002). We applied a line-profile saturation correction (Wang & Sheeley 1995) to the data, multiplying the measured values by sin 2 (latitude). The SDR model (Schrijver & DeRosa 2003) is based on a surface-flux transport model (Schrijver & Title 2001), which tracks the evolution of the magnetic flux on the solar photosphere. This evolution is based on the same dynamical processes that occur on the Sun, such as the shearing and advection on large scales caused by differential rotation and poleward meridional circulation. Also simulated are the merging, fragmentation, and random walk dispersal of the individual flux elements occurring on smaller scales. MDI full-disk magnetograms (Scherrer et al. 1995) are directly inserted into the model ( assimilated ) as they become available (typically every 96 minutes) to capture the effects of ARs as soon as they emerge. The assimilation window includes all points within about 60 of disk center. Unlike the WS version, which is based on static, once-per-carrington-rotation synoptic maps, magnetic flux in the SDR model continues to evolve even when it is not on the observable side of the Sun. At high latitudes beyond the assimilation window, convection and meridional flows continue to transport magnetic flux poleward to simulate the development and evolution of the polar cap fields. A full-sun magnetic map snapshot of this evolving model is taken every 6 hr. These snapshots are the input data for the PFSS extrapolations. Is there any advantage to simulating all these effects or to updating the input data several times per day? Or does the WS model, which is updated only once per month, identify open fields in ARs just as well as the more complex SDR model? 5. STATISTICAL OVERVIEW Table 1 lists the 25 e-beam events for which an X-ray or H flare started within a 20 minute window before e-beam injection. In 10 cases out of the original sample of 35, neither the H observers nor the X-ray imager recorded a flare in the 20 minute window. It is not surprising to have some events without corresponding flares because there are many gaps, including some extending for several hours, in H and Yohkoh flare coverage. Of the 25 flares associated with the remaining e-beams, Yohkoh SXR images revealed 15. H observers in the NOAA network reported nine. Kahler (2001) reported one other. Most of the flares were small: there were four B-, 17 C- and four M-class flares, according to the NOAA GOES soft X-ray monitor. How many of the associations can be attributed to chance? There was an average of 9.6 GOES-reported flares per day on the days with e-beam events, so there was a flare approximately every 150 minutes. Assuming that the probability of any one event being a chance hit is 20 minutes/150 minutes 0:13, and assuming that flares occur independently of each other, then we may use the binomial probability function to calculate the probability of 25 chance hits out of 35 trials. It is less than The probability of 8 chance hits is >96%, so we may conclude that most of the associations were causal. The average start time of e-beam injection for the events listed in Table 1 was 9.6 minutes after soft X-ray flare onset and only 2 minutes after the peak of X-ray emission. These results are consistent with other studies, i.e., ( Haggerty & Roelof 2002; Krucker et al. 1999). It is difficult to estimate the potential errors in these onset differences, but the greatest uncertainty is in the e-beam transit time. We computed the transit times for all events three ways, using the 1.2 AU Parker spiral, ambient windspeed path, and 1/ methods. As shown in Figure 1, the differences among these methods were generally less than 3 minutes. No method consistently gave longer transit times than the others. Table 1 also shows that all but one of the e-beam events were AR associated. In all but two cases, the Yohkoh images revealed a dark vein, spot, or bay near the flare sites, indicating that there were open fields near the flaring loops. By vein we mean a narrow dark feature typically cutting through the middle of the AR. Spot refers to a round dark feature surrounded by bright AR loops, and a bay is a dark feature on the periphery of an AR. The polarity of the photospheric magnetic fields under these dark features agreed with the polarity of the interplanetary fields prevailing during the e-beam events in 23 of the 25 cases. This is consistent with correct identification of the coronal sites of electron injection. If the associations of flares and e-beams were purely by chance, the polarities should disagree about half the time. The event on 1997 November 28 is one case where the photospheric field and the IMF direction did not agree, but because the flare occurred at E54, it probably had nothing to do with the e-beam, and this temporal association was a chance event. The 2000 December 28 electron event was associated with a flare in a region of mostly positive photospheric fields, yet the IMF was negative (directed sunward). Neither PFSS implementation succeeded in connecting the open fields near the flare site with the IMF. For all 25 events, we compared the positions of the dark (AR coronal hole) features with synoptic maps of open field regions computed with the WS and SDR implementations of the PFSS model. Cases where a model did or did not produce a patch of open fields coinciding with a dark vein, spot, or bay are labeled Y and N in the fourteenth and fifteenth columns of Table 1, respectively. These columns refer to the WS and SDR implementations, respectively. Where there was no predicted open field patch within 3 heliographic degrees (36 Mm), we entered an N in the table. We were surprised at how often the models were successful in showing open fields coinciding with the AR coronal holes. The WS implementation of the model updates the photospheric fields only once per month, yet it correctly identified the open fields in 80% of the events. The SDR implementation, which updates the photospheric fields every 6 hr, did even better: it identified the open field patches 100% of the time. We note, however, that for 13 events in , there was no

4 TABLE 1 Electron Beam Events and Associated Solar Features Date E-beam Injection at Sun ( hr) X-ray Onset at Sun ( hr) X-ray e-beam Onset Diff (minutes) X-ray Rise Time (minutes) Flare Position Latitude (deg) Longitude (deg) NOAA AR Yohkoh Image ( hh:mm:ss UT) GOES Flare Class Open Field Present Connects to IMF Coronal Hole Type ( WS) (SDR) ( WS) (SDR) 1997 Nov N19 W :12:40 B4 Bay Y Y Y Y 1997 Nov N19 E H C2 Vein Y Y N N 1998 Jul N16 W :34:29 13:17:43 C4 Bay Y No data 1 No data 1998 Jul N15 W :24:43 B9 None Y No data 2 No data 1998 Aug S23 W :50:42 M1 Spot N No data N No data 1998 Aug S23 W H C2 Spot N No data N No data 1998 Aug S23 W :30:44 C3 Spot N No data N No data 1998 Sep S16 W :22:55 C1 Bay N No data N No data 1998 Sep N22 W H C1 Vein Y No data Y No data 1998 Sep N17 W Pos. at 22:11:53 B8 Vein Y No data Y No data 1998 Dec N24 W H C5 Vein Y No data 1 No data 1998 Dec N25 W H C5 Vein Y No data 1 No data 1999 Jan N21 W H C3 Spot Y No data 1 No data 1999 Jan N19 W H C2 Spot Y No data Y No data 1999Jan N20 W From prior event C2 Vein Y No data Y No data 1999 May N23 W :13:21 M5? (at limb) N Y N N 1999 Sep N19 W :07:14 B4 Non-AR Y Y Y Y 1999 Sep N14 W :27:25 C1 Vein Y Y Y Y 2000 Feb S16 W H C1 Bay Y Y Y N 2000 Mar S15 W :40:26 C3 Vein Y Y N Y 2000 Mar S12 W :30:18 C4 Vein Y Y N Y 2000 May N20 W Ref. Kahler (2001) M1 Vein Y Y 1 N 2000 Aug N28 W :38:35 C3 Bay Y Y Y N 2000 Dec N15 W :14:21 C4 Spot Y Y N Apr N17 W H M3 Spot Y Y N Y

5 SOLAR ORIGINS OF OPEN MAGNETIC FIELDS 639 Fig. 1. Comparison of the predicted electron injection times according to the three methods discussed in the text. In most cases the difference in predicted injection time was less than 3 minutes. Fig. 2. EPAM records of the near-relativistic electron beam fluxes in the events of 1997 November 23, 1998 July 11, and 2000 December 28. MDI data, so the number of tests was half the number used for the WS implementation. Now let us consider the models success rates in identifying coronal field lines that connect to the source surface and to the IMF leading to ACE. Of course, we cannot model the connection with the tools at hand. We declare success when the coronal fields intersect the source surface within 3 heliographic degrees of the imputed IMF leading to ACE at 1 AU. We declare a near miss when the fields nearly intersect, i.e., they may be as much as 13 (1 day s solar rotation) apart. The WS version successfully showed connections from the open field patches to the extrapolated IMF in 36% of cases. Inclusion of five near misses improves the success rate to 56%. Table 1 shows that the success rate for the SDR version was 50%. There were no near misses. The sixteenth and seventeenth columns document these results. Y indicates a connection and N indicates no connection. Where there is a number, it indicates that the modeled field lines came within that number of days rotation of making a connection. In only 12 cases were we able to compute field lines with both models. In those cases the WS model was successful 42% of the time and the SDR model 50% of the time. Including the near miss on 2000 May 1 gives WS a score of 50%. However, the models should be tested with a larger data set. The number of tests of the SDR technique was only 12, and tests of the WS technique were only 24. The SOHO outage in prevented more tests of the SDR technique. Based on what we have, however, we can conclude that the two implementations of the PFSS model are about equally successful in indicating the correct coronal connection to the IMF. How these connections were determined can be illustrated by discussing several typical cases. 6. THREE EXAMPLE ELECTRON BEAM EVENTS AND THEIR FLARES November 23 As Figure 2a shows, EPAM detected an increase in electrons with energies of kev (velocity 0:55c) starting at 10:19 UT on 1997 November 23. The angular distribution of the velocity vectors was peaked in the direction of the IMF. The spectrum of the electron beam was very soft with only an E 6 spectral exponent. The electron intensities began rising sharply at 10:19 UT, with the higher energy channel reaching peak intensity at about 10:20 UT. The lower energy channel reached a peak at about 10:25 UT. Metric type III and decametric type III bursts were associated with this event. The WIND WAVES instrument observed the decametric type III from 2 R all the way to 1 AU. The November 23 event was clearly due to a beam of nearrelativistic electrons injected into open fields somewhere in the solar corona. To estimate the time of electron injection at the Sun, we divided the assumed Parker spiral path length of 1.2 AU by the speed of the electrons in channel 2, and we subtracted this transit time, 20.5 minutes, from the event onset time at 1 AU. We got an injection time of 09:58:29 UT. At about that instant, a small flare rated only B4 on the NOAA scale occurred in AR 8108 at N19 W45. It started at 10:02 UT, as recorded by a NOAA GOES satellite and the Yohkoh SXT. Figure 3 shows a Yohkoh image of

6 640 RUST ET AL. Vol. 687 Fig. 3. Yohkoh SXT image of the northwest quadrant of the solar disk showing the flare of 1997 November 23 at 1012:40 UT. The proximity of the dark bay, signifying open fields, to the bright flare loop suggests that reconnections between open and closed fields could act there to accelerate electrons. the flare. When the flare start time is corrected for the 500 s light travel time from the Sun, we find an X-ray emission start time of 09 hr minutes UT, which is only 4.84 minutes before the estimated electron injection time. When the 1/ method is used, the estimated injection time is only 0.2 minutes different. As Figure 3 shows, the flare was a bright loop adjacent to a dark bay, which is the signature of open field lines. Perhaps the closed fields in the bright loop were reconnecting with the open fields in the dark bay. Figure 4, from Shimojo & Shibata (2000), illustrates their reconnection jet model of small solar flares, which may explain our observations. According to the model, new flux emerges in a region adjacent to open field lines and undergoes reconnections that inject energetic electrons into some of the closed loops and into the open fields. The WS and SDR models of the corona both indicate that the flaring loop was adjacent to an open field region in the northern hemisphere on the west side of AR Figure 5 shows two images of the solar disk as it appeared about the time of the November 23 flare. On the left image, which is an MDI magnetogram, black (white) contours outline the open positive (negative) field regions. On the right is a Yohkoh X-ray image. The dark bay just west of the AR pointed out in Figure 3 is included in the toe of the open field region (outlined with a white contour for visibility) that extends from the north pole. All contours refer to the SDR model, but the WS results were similar, so we conclude that both models successfully identified the open fields in this case. But did the open fields connect to the IMF leading to ACE? To answer this question, we extrapolated the fields from the base of the corona upward to the source surface. Then we extrapolated the IMF sunward from ACE, using the ambient windspeed method (Nolte & Roelof 1973). Figure 6 shows that the ACE-connected fields did meet the open fields (white and red lines) from the flare region on November 23. Figure 6 is a synoptic map of the photospheric magnetic fields for 1997 November. The small red disk shows where the IMF and coronal fields meet. In this case, both the WS (white lines) and the SDR (red lines) models successfully connected the flare Fig. 4. Shimojo & Shibata model offlaring loops adjacent to open fields. Electrons accelerated at the reconnection point heat the plasma at the base of the field lines, causing the flare, and some of them escape along the fields that open to the upper right in this figure (figure reprinted with permission from Shimojo & Shibata 2000, ApJ, 542, 1100).

7 No. 1, 2008 SOLAR ORIGINS OF OPEN MAGNETIC FIELDS 641 Fig. 5. Sun as it appeared on 1997 November 23. Left: MDI magnetogram at 1248 UT. Right: Yohkoh SXT filtergram at 1214 UT. NOAA AR 8108 dominates the northern hemisphere. The PFSS model implemented by Schrijver & DeRosa (2003) shows an area of open fields (white and black contours) extending from the polar coronal hole into the AR where the flare occurred. site ( yellow star in the northern hemisphere) to the IMF. The SDR implementation showed connections, indicated by black lines, to open fields in the southern hemisphere in the days before and after the flare. The WS model showed connections to the northern hemisphere open fields on the days before and after the flare. Except for the day of the flare, it is not clear which connections the real fields followed July 11 As Figure 2b shows, EPAM recorded an increase in nearrelativistic electron flux starting at 13:00 UT on 1998 July 11. The increase was observed up to 315 kev (0.7c). The peak intensities showed velocity dispersion characteristic of a broad spectrum of electrons injected at once onto the IMF. Higher energy electrons arrive and peak before the lower energy ones. In addition, their angular distribution showed that they were streaming along the IMF in a tight pattern. The peak intensity spectrum of the event followed an E 3 power law. Of the three example events discussed here, this one had the hardest energy spectrum and the tightest angular distribution. Metric type III and decametric type III radio bursts were associated with this event, but there was no microwave burst. The event was associated with a C4 flare in AR 8264 at N16 W68. Using a path length of 1.2 AU, we calculated that e-beam injection at the Sun started at 12 hr 46.8 minutes UT. The corresponding X-ray flare started at 12 hr 34.6 minutes UT, so the Fig. 6. Synoptic chart of the magnetic fields at the base of the corona during Carrington rotation 1929, i.e., 1997 November The vertical axis is sine latitude and the horizontal axis is Carrington longitude. The light and dark gray patches denote predominantly positive and negative fields, respectively, in the photosphere. Areas filled with colored dots denote open coronal fields, according to the WS model. The predicted solar wind speed from the colored patches is highest for red and lowest for blue. The string of purple crosses parallel to the equator shows the calculated track of ACE s connection via the IMF to the source surface at 2.5 R. The straight white lines show where open fields in the WS model connect to the ACE track. The straight black lines show the open field connections predicted by the SDR model. Ayellow star at longitude 120 marks the site of the 1997 November 23 flare. The red lines highlight the connection from the flare to the IMF to ACE,aspredicted by the SDR model. The large red disk on the track of ACE connections marks the predicted connection point on November 23.

8 642 RUST ET AL. Vol. 687 Fig. 7. One of many small flares in AR The arrow points to the flare at 0203 UT on 1998 July 10, which occurred on the western edge of the active region and adjacent to a dark bay. Note the radial dark channels signifying open fields. The flare at 1247 UT the next day almost certainly occurred in the same place, although there was no Yohkoh X-ray image at that time. injection took place 12.2 minutes after the onset of the flare and 7 minutes after the peak of the X-ray emission. The 1/ method gave an injection time of only 4 minutes after the X-ray peak. The Yohkoh images from the period showed repeated flaring adjacent to a dark bay on the western side of the AR. Since there was no Yohkoh coverage exactly during the flare, the flare position was obtained from H observations. There was a pointlike X-ray brightening in the same part of AR 8264 on the previous day (Fig. 7), and the July 11 flare was probably homologous with that one. The Yohkoh movies for the period show a number of dark radial channels that appear to outline open fields. The roots of the channels appear around the boundary of the dark bay. They are faintly visible in Figure 7. Because MDI was not operating during the second half of 1998, we have no PFSS field model from Schrijver & DeRosa. The Wang & Sheeley implementation is shown in Figure 8. WS used magnetograms from the Mount Wilson Observatory to specify the fields at the base of the corona. Their model indicates that, on the day of the flare, the field lines stretching from ACE were connectedtoopenfieldsoriginating in a hole in the southern hemisphere. So the model correctly identified a small coronal hole near the flaring region, but it did not predict that the fields from the hole were connected with ACE during the July 11 event December 28 On 2000 December 28 at 02:20 UT, EPAM intercepted a nearrelativistic electron beam with energies up to 175 kev, and Fig. 8. Section of the synoptic map for Carrington rotations 1937 and The red dot in the middle shows the connection point for fields stretching to ACE on 1998 July 11. The yellow star just above it shows the location of the C4 flare in the northern hemisphere, near a coronal hole (blue patch). The white lines show that the WS model predicted that the field lines from the northern hole were connected to the ACE trace several days earlier, but not on July 11.

9 No. 1, 2008 SOLAR ORIGINS OF OPEN MAGNETIC FIELDS 643 Fig. 9. The 2000 December 28 flare peaked at 02 hr 18.3 minutes UT as seen from 1 AU, or 02 hr 10 minutes UT at the Sun. The calculated e-beam injection time was 02 hr 10.7 minutes UT. Notice the distinct dark spot west of the flare as shown by the white arrow in this Yohkoh X-ray image. some indication of electrons with even higher energies ( Fig. 2c). The electrons were mostly aligned with the IMF. The spectrum followed an E 3:3 power law. Solar phenomena associated with the injection of this beam included metric and decametric type III bursts, a type V burst, a SXR flare (Fig. 9) of NOAA GOES class C4, and an H subflare at N15 W38 in AR There was also a small CME, but no type II or IV bursts to indicate electron acceleration associated with the CME. The e-beam injection time was 02 hr 13.3 minutes according to the 1.2 AU method and 02 hr 7.2 minutes according to the 1/ method. The SXR flare onset time was 02 hr 6.7 minutes and the peak was 4 minutes later. So the e-beam injection and SXR flare were virtually simultaneous. The Yohkoh image (Fig. 9) of the flare and its surroundings reveals a dark bay on the western side of the AR, which is very much like the dark (coronal hole) patches seen in the other examples presented here. In agreement with the X-ray images, the WS and the SDR PFSS models both identify a small patch of open fields near the flaring AR (Fig. 10). But both models failed to show that the open fields were connected to ACE on December 28. Instead, they predicted that ACE at 1 AU was connected to open fields from the hole in the southern hemisphere. 7. DISCUSSION AND CONCLUSIONS Because they travel at almost the speed of light, flare-initiated beams of near-relativistic electrons are effectively instantaneous probes of open coronal magnetic fields. We intercepted the electron beams near Earth with the EPAM instrument on the ACE spacecraft and determined their likely injection times at the Sun. To most effectively use the beams as probes, we had to identify their injection sites, too. For 25 e-beam events at 1 AU, we were able to locate flares that started <20 minutes before the estimated injection time. 80% of the flares occurred between 30 and 80 heliographic degrees west of the central meridian, which is where the IMF at Earth usually connects to the Sun. We could not identify flares with the remaining 10 similar e-beams in the study interval, which extended from 1997 August to 2001 December. This is not surprising, considering that there were many gaps in flare monitoring with solar imagers. We assumed that the beams were produced near the flares, and the assumption is supported by statistical arguments. Given an average interval of 150 minutes between flares, the probability that fewer than 8 of the 25 flare/beam associations could be due to chance is >96%. The assumption of flare/beam association is also consistent with the fact that all the flaring ARs had an adjacent coronal hole, which is the signature of open magnetic fields. The polarity of the photospheric field in the AR coronal holes agreed with the IMF polarity in 23 of the 25 events. This further supports the validity of the flare/ beam associations. Our finding that the e-beams follow open fields rooted in or near ARs agrees with the Pick et al. (2006) and Wang et al. (2006) result that 3 He-rich impulsive particle events come from small, flaring ARs located next to coronal holes. These authors also found a correlation with EUV jet events occurring near the particle injection times. The reconnection jet flare model (Shimojo & Shibata 2000) may explain the association of e-beams, open fields, Fig. 10. Synoptic map of Carrington rotation 1971 showing the magnetic fields at the base of the corona on 2000 December 28. Black patches denote negative fields and white patches denote positive fields. The arrow points to the region with open fields (black contoured line) in the positive fields of AR The flare ( yellow star at longitude 320 ) associated with the e-beam injection occurred on the boundary of the patch of open fields. The straight white lines depict open fields that the SDR model indicated were connected with the ACE track. But there was no connection linking the flare to ACE on the 28th. Instead, the model shows a connection (red disk) from ACE to a region in the southern hemisphere.

10 644 RUST ET AL. Vol. 687 jets, and bright flare loops. Energetic electrons are injected onto both closed and open fields in this model, and that would be consistent with the close association of e-beams and flares. Nitta et al. (2006) published similar findings. The reliable associations of e-beams with flares near AR coronal holes allowed us to test two implementations of the potentialfield-source-surface (PFSS) model of coronal fields. The model correctly identified the open AR fields, which are revealed by dark holes, veins, and bays in X-ray images, in 80% (WS model) and 100% of cases (SDR model) with adequate photospheric magnetograph coverage. These good results are encouraging, but not surprising. The models ought to be best at finding the open fields near sunspot maximum, which is when our test events occurred. Errors due to the poorly observed polar photospheric fields are expected to lead to errors in the models near sunspot minimum but not near sunspot maximum, when the well-observed lowlatitude fields mostly determine the locations of the open fields in the ecliptic plane. A repeat of our test at sunspot minimum, using STEREO data, for example, would probably yield worse results. Neither model was very successful in finding the field lines as identified by the electron beams that extended from the AR coronal holes to the ACE spacecraft. The WS implementation placed open magnetic fields on the source surface near the extrapolated IMF in only 36% of cases. Inclusion of five near misses improves the success rate to 56%. The success rate for the more sophisticated SDR implementation of the PFSS model was 50%. We conclude that there is no apparent advantage to frequently updating the photospheric fields, as Schrijver & DeRosa do. Nitta & DeRosa (2008) similarly found that the PFSS model could not reliably identify AR open fields associated with flares with type III radio bursts. Type III bursts are excited by 6 kev electrons that follow open fields from flare sites (Haggerty & Roelof 2006). There are plans for a heliospheric space mission that could provide timely observations of fields on the Sun s hemisphere that cannot be seen from Earth. Our results suggest that the PFSS model is the limiting factor in field line mapping, not the quality of the input data. Before we can exploit better data, from the Sun s back side, for example, we need better models. Our results show that current-free models cannot reliably trace the coronal fields that connect ARs to the heliosphere, as represented by any of three plausible extrapolations of the IMF from 1 AU (215 R ) down to the source surface at 2.5 R. Dunn et al. (2005) have gone beyond the classic PFSS and heliospheric field models that we used. They combined the Stanford current-sheet source-surface (CSSS) model (Hoeksema et al. 1983) with data on the solar wind trajectory, which can sometimes be derived in real time from interplanetary scintillation measurements. Because the CSSS model introduces an intermediate, current-carrying spherical surface between the photosphere and the spherical source surface where the fields become radial, it probably gives a better description of the fields from the low corona to 15 R from the Sun. Dunn et al. tried to reproduce the daily variations in solar wind velocity and magnetic field orientation, but the results were disappointing and insensitive to higher time resolution in the input magnetic data. Thus, their result is consistent with ours; it shows that the real improvements they made in the PFSS/ heliospheric field models did not materially improve IMF forecasts. Faced with the practical imperative to map open fields somehow, we and Gilbert et al. (2007), for example, have developed magnetic field extrapolation schemes that run fast on desktop computers but lack the detailed physics usually incorporated in MHD models, which currently run to slowly for routine predictions. We tried the AR field line extrapolation technique devised by Georgoulis & Rust (2007), which is based on simulated annealing (see, e.g., Press et al. 1992). It identifies footpoint pairs in an AR and the magnetic flux committed to the connections between them. It computes a conductivity matrix by simultaneously minimizing the flux imbalance and the overall length of the connections. Minimum flux imbalance and overall separation length naturally suggest a minimum-energy solution. It has not been proved that the technique converges on the minimum-energy solution, but the result satisfies the divb ¼ 0 condition, and comparisons with other extrapolations suggest that the technique achieves a realistic simulation of open and closed AR fields. For 11 of the 25 events shown in our Table 1, we used the simulated annealing technique and high-resolution MDI magnetograms of the ARs to calculate the magnetic connections in the corona. We found unconnected fields with typical fluxes of ð1 5Þ ; Mx where the WS and SDR models predict open magnetic fields. These unconnected fields could close either in the Sun or stretch into the heliosphere; the connectivity analysis alone could not provide definitive answers, of course, because the calculations were local, not global. However, the good agreement between the open fields predicted by the PFSS model and the unconnected fluxes strongly implies that the unconnected fields do not close back on the Sun, but rather that they extend to remote locations in the heliosphere. Of course, to be useful the technique must be validated with many more comparisons and transformed into a global model. Gilbert et al. (2007) also introduced a novel mathematical scheme for extrapolating open field lines that avoids the complexity of an MHD model. The basic assumption is that open fields rooted in the photosphere can move around ( relax ) on a succession of larger and larger spherical surfaces in the corona and heliosphere until they are uniformly distributed. Gilbert et al. conclude with their relaxation model that open fields, distributed on the photosphere according to the PFSS model, say, will achieve the nearly uniform distribution of the open fields mapped by the Ulysses spacecraft. These authors suggest that areas of the corona with mostly closed fields, which might include ARs, for example, could make a substantial contribution to the slow solar wind because of imbedded open fields. These thinly distributed open fields will change the distribution of radial fields at 2.5 R and thus change where the open fields of coronal holes end up in the heliosphere. Although we did not explicitly test the model of diffuse open fields advocated by Fisk (2005) and discussed by Gilbert et al. (2007), our results tend not to support it. If open field lines are everywhere in the corona, reconnections between open and closed fields, as in the reconnection jet model, would occur just about everywhere and not just near AR coronal holes. Instead, our energetic electron beam data suggest that most reconnection events take place near AR open fields and are recorded as flares. There were 10 e-beam events in our sample that had no clearly associated flare, but in most of those cases there were gaps in Yohkoh coverage. We suggest that there are few detectable reconnection events involving open fields other than those adjacent to ARs. In summary, the PFSS models correctly identify open fields at the base of the corona, but the fields extrapolated outward to 2.5 R connect to the correct heliospheric fields only about half the time. Improving the time resolution of the input magnetograms or using the Stanford CSSS model plus IPS observations to better determine the solar wind speed does not seem to help. The open-field relaxation model of Gilbert et al. (2007) does not require current-free fields, and it does reproduce the nearly uniform IMF sampled by Ulysses. It fails, however, to explain the

11 No. 1, 2008 SOLAR ORIGINS OF OPEN MAGNETIC FIELDS 645 inverse relation of solar wind speed to coronal hole expansion ( Wang & Sheeley 2006). Furthermore, to explain the slow solar wind, it requires that at least 50% of the open flux originate in areas without obvious coronal holes, contrary to the implications of our study and to Gosling et al. (1981). In short, no model reliably identifies open fields and their extension to 1 AU. A dramatic improvement in MHD model computing speed may be the only answer to the challenge that NASA posed in their Targeted Research and Technology Program. NASA supported this work with grant NNG 05GM69G from the NASA Living With a Star Targeted Research and Technology program. We benefited greatly by participating in the TR&T Focus Team on Connecting the Sun to the Heliosphere. The injection times using the velocity dispersion technique were obtained with WIND 3DP observations and the analysis was provided by Linghua Wang and Sam Krucker. The work could not have been done without the Yohkoh Soft X-ray Telescope images. We are grateful to John Biersteker for preparing the Carrington synoptic maps. Acton, L., et al. 1992, Science, 258, 618 Altschuler, M. D., Levine, R. H., Stix, M., & Harvey, J. 1977, Sol. Phys., 51, 345 Cane, H. V. 2003, ApJ, 598, 1403 Classen, H. T., Mann, G., Klassen, A., & Aurass, H. 2003, A&A, 409, 309 Dunn, T., Jackson, B. V., Hick, P. P., Buffington, A., & Zhao, X. P. 2005, Sol. Phys., 227, 339 Einaudi, G., Boncinelli, P., Dahlburg, R. B., & Karpen, J. T. 1999, J. Geophys. Res., 104, 521 Fisk, L. A. 2005, ApJ, 626, 563 Georgoulis, M. K., & Rust, D. M. 2007, ApJ, 661, L109 Gilbert, J. A., Zurbuchen, T. H., & Fisk, L. A. 2007, ApJ, 663, 583 Gold, R. E., et al. 1998, Space Sci. Rev., 86, 541 Gosling, J. T., Asbridge, J. R., Bame, S. J., Feldman, W. C., Borrini, G., & Hansen, R. T. 1981, J. Geophys. Res., 86, 5438 Haggerty, D. K., & Roelof, E. C. 2002, ApJ, 579, , Adv. Space Res., 38, 1001 Hick, P., Jackson, B. V., Rappoport, S., Woan, G., Slater, G., Strong, K., & Uchida, Y. 1995, Geophys. Res. Lett., 22, 643 Hoeksema, J. T., Wilcox, J. M., & Scherrer, P. H. 1983, J. Geophys. Res., 88, 9910 Kahler, S. W. 2001, J. Geophys. Res., 106, Krucker, S. M., Larson, D. E., Lin, R. P., & Thompson, B. J. 1999, ApJ, 519, 864 Levine, R. H., Altschuler, M. D., & Harvey, J. W. 1977a, J. Geophys. Res., 82, 1061 Levine, R. H., Altschuler, M. D., Harvey, J. W., & Jackson, B. V. 1977b, ApJ, 215, 636 Linker, J. A., et al. 1999, J. Geophys. Res., 104, 9809 Liu, C., Qiu, J., Gary, D. E., Krucker, S. M., & Wang, H. 2004, ApJ, 604, 442 REFERENCES Maia, D. J. F., & Pick, M. 2004, ApJ, 609, 1082 Neugebauer, M., et al. 1998, J. Geophys. Res., 103, Nitta, N. V., & DeRosa, M. L. 2008, ApJ, 673, L207 Nitta, N. V., Reames, D. V., DeRosa, M. L., Liu, Y., Yashiro, S., & Gopalswamy, N. 2006, ApJ, 650, 438 Nolte, J. T., & Roelof, E. C. 1973, Sol. Phys., 33, 483 Nolte, J. T., et al. 1976, Sol. Phys., 46, 303 Parker, E. N. 1958, ApJ, 128, 664 Pick, M., Mason, G. M., Wang, Y. M., Tan, C., & Wang, L. 2006, ApJ, 648, 1247 Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. 1992, Numerical Recipes in FORTRAN (Cambridge: Cambridge Univ. Press) Sakurai, T. 1982, Sol. Phys., 76, 301 Scherrer, P. H., et al. 1995, Sol. Phys., 162, 129 Schrijver, C. J., & DeRosa, M. L. 2003, Sol. Phys., 212, 165 Schrijver, C. J., & Title, A. M. 2001, ApJ, 551, 1099 Shimojo, M., & Shibata, K. 2000, ApJ, 542, 1100 Simnett, G. M., Roelof, E. C., & Haggerty, D. K. 2002, ApJ, 579, 854 Stone, E. C., Frandsen, A. M., Mewaldt, R. A., Christian, E. R., Margolies, D., Ormes, J. F., & Snow, F. 1998, Space Sci. Rev., 86, 1 Svestka, Z., Solodyna, C. V., Howard, R., & Levine, R. H. 1977, Sol. Phys., 55, 359 Ulrich, R. K., Evans, S., Boyden, J. E., & Webster, L. 2002, ApJS, 139, 259 Wang, Y. M., Pick, M., & Mason, G. M. 2006, ApJ, 639, 495 Wang, Y. M., & Sheeley, N. R., Jr. 1990, ApJ, 355, , ApJ, 392, , J. Geophys. Res., 99, , ApJ, 447, L , ApJ, 587, , ApJ, 653, 708