Bimodal fluxes of near-relativistic electrons during the onset of solar particle events

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1 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 8, 45 4, doi:./jgra.5446, 3 Bimodal fluxes of near-relativistic electrons during the onset of solar particle events Y. Y. Kartavykh,, W. Dröge, and B. Klecker 3 Received December ; revised 8 April 3; accepted 6 May 3; published 5 July 3. [] We report for several solar energetic particle events (SEPs) intensity and anisotropy measurements of energetic electrons in the energy range 7 to 5 kev as observed with the Wind and ACE spacecraft in June. The observations onboard Wind show bimodal pitch angle distributions (PADs), whereas ACE shows PADs with one peak, as usually observed for impulsive injection of electrons at the Sun. During the time of observation Wind was located upstream of the Earth s bow shock, in the dawn-noon sector, at distances of 4 to 7 R E from the Earth, and magnetically well connected to the quasi-parallel bow shock, whereas ACE, located at the libration point L, was not connected to the bow shock. The electron intensity-time profiles and energy spectra show that the backstreaming electrons observed at Wind are not of magnetospheric origin. The observations rather suggest that the bimodal electron PADs are due to reflection or scattering at an obstacle located at a distance of less than 5 R E in the antisunward direction, compatible with the bow shock or magnetosheath of the magnetosphere of the Earth. For a modeling of the observations, we have performed transport simulations which include the effects of pitch angle diffusion, adiabatic focusing, and reflection at a boundary close to the point of observation. The results of the simulations demonstrate that the bimodal PADs are compatible with the reflection of electrons at a nearby boundary, at distances of 7 R E. This finding is supported by the orbital configuration and the magnetic field direction: Whereas ACE is not connected, Wind is well connected to the magnetosphere of the Earth. Citation: Kartavykh, Y. Y., W. Dröge, and B. Klecker (3), Bimodal fluxes of near-relativistic electrons during the onset of solar particle events, J. Geophys. Res. Space Physics, 8, 45 4, doi:./jgra Introduction [] Electrons of solar origin, discovered in the 96s [e.g., Van Allen and Krimigis, 965]. have been observed since then in near-earth space over a wide range of energies from a few kev to tens of MeV [Lin, 974, 985; Lin et al., 996; Lin, 998]. During solar maximum, impulsive solar electron events are observed times per month [Lin, 987], with 6% of the events extending to energies above 5 kev [Lin, 985]. Electron intensity-time profiles, event onsets, and anisotropy measurements have been used extensively to infer acceleration and propagation characteristics at the Sun and in interplanetary space [Krucker et al., 999; Dröge, 3; Dröge et al., ]. Many of these events Some of the work presented in this manuscript also appears as Astrophysical Journal article volume 765, p. 99, doi:.88/4-637x/ 765//99. These papers represent work that was originally collaborative but then proceeded separately. Ioffe Physical-Technical Institute, St. Petersburg, Russia. Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Würzburg, Germany. 3 Max-Planck-Institut für Extraterrestrische Physik, Garching, Germany. Corresponding author: W. Dröge, Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Emil-Fischer-Str. 3, DE-9774 Würzburg, Germany. (droege@astro.uni-wuerzburg.de) 3. American Geophysical Union. All Rights Reserved /3/./jgra (3% [Haggerty and Roelof, ]) with moderate electron intensities (mostly between 3 and 5 particles per cm sr sec MeV in the energy range 38 6 kev) show beamlike field-aligned pitch angle distributions, suggesting weak pitch angle scattering during interplanetary propagation [Haggerty and Roelof, ]. [3] Bidirectional electron pitch angle distributions are often observed in the solar wind, for example, in the energy range of the solar wind electron strahl ( ev [Pilipp et al., 987]). The strahl flows away from the Sun along the heliospheric magnetic field lines. Counterstreaming beams or bidirectional solar wind electron distributions (BDEs) are formed when field lines are connected to the Sun on both ends. It is usually assumed that these closed loops arise from coronal mass ejections (CMEs) and their interplanetary counterparts, interplanetary coronal mass ejections (ICMEs). Thus, BDEs are widely used as a signature to identify ICMEs in solar wind data [e.g., Gosling et al., 987; Wimmer-Schweingruber et al., 6, and references therein]. [4] However, counterstreaming electrons in the solar wind energy range can also be generated on open field lines. An example in the near-earth environment is reflection of electrons by the bow shock of the magnetosphere of the Earth. Reflected solar wind electrons can be observed out to distances of the libration point L, provided the spacecraft is magnetically well connected to the magnetosphere

2 KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES [Stansberry et al., 988]. The analysis of three-dimensional electron distribution functions in the energy range ev measured with the 3DP/EESA-L electrostatic analyzer onboard Wind closer to the bow shock showed that these backstreaming solar wind electrons can be understood in terms of magnetic mirroring at the increasing magnetic field of the bow shock [Larson et al., 996]. [5] At higher electron energies between 3 and 3 kev, bidirectional PADs have been reported during the onset phase of several SEPs and were explained by a reflecting boundary at distances of..4 AU beyond the Earth orbit [Malandraki et al., ; Tan et al., 9]. A recent detailed study of the 4 September solar energetic particle event with Wind and SOHO showed that the observed time delays between outward and inward streaming electrons and protons can be consistently explained with a reflective boundary in the antisolar direction, at a distance of.4 AU, far beyond the orbit of Earth [Tan et al., 9]. [6] In the present study we analyze the PADs of nearrelativistic electrons in the energy range of 7 to 5 kev during the early phase of three impulsive solar energetic electron events observed in June. We compare the PADs as observed onboard Wind close to the bow shock at distances of 4 to 8 R E from Earth with the PADs observed onboard ACE at 35 R E. The observations onboard Wind show bidirectional PADs, whereas ACE shows PADs with one peak, aligned with the interplanetary magnetic field, as usually observed for impulsive injection of electrons at the Sun. The bidirectional PADs observed onboard Wind suggest backscattering or reflection downstream of the point of observation. The short time delay between outflowing and backstreaming electrons of s (the resolution of our measurement) suggests reflection or backscattering downstream at distances 5 R E, suggestive of the bow shock or the magnetosheath of the Earth. [7] In section 4 of the paper we use a phenomenological approach for modeling the electron observations. We will first use the intensity and anisotropy measurements obtained with ACE/EPAM to derive the injection profile at the Sun and the scattering parameters in interplanetary space. Then we combine the interplanetary propagation with three simple models for the reflection of electrons at the bow shock and their propagation through the magnetosheath. Y GSE (R E ) 5 5 SOHO ACE 5 B B ACE ACE B ACE B Wind B Wind Wind 5 5 X GSE (R E ) June 4 Earth nominal bow shock Figure. Positions of ACE and Wind on 4 June, projected into the XY GSE plane. The lines across Wind and ACE are linearly extrapolated magnetic field lines of in situ observations at the time of maximum intensity of 4 kev electrons (7:36 UT). The arrows indicate the direction of the magnetic field. by re-binning the two-dimensional angular phase space into a one-dimensional phase space with 6 bins (maximum), based on the magnetic field direction provided by the Wind Magnetic Field Investigation (MFI) [Lepping et al., 995]. The EPAM/LEFS6 instrument onboard ACE provides electron intensities from 45 kev to 35 kev organized into four energy channels. The LEFS6 telescope samples an annulus centered at 6 ı ( 5 ı ) to the approximately sunward pointing spin axis of ACE and has eight 45 ı sectors. The corresponding eight pitch angles are computed from the direction of the sector center and the magnetic field direction, measured with the ACE magnetometer (MAG) [Smith et al., 998]. [9] At the time of the observations, Wind was in the dawnnoon sector, at distances of 4 to 8R E from the Earth, upstream of the quasi-parallel bow shock, in the foreshock region of the magnetosphere of the Earth. ACE was located at the libration point L, at distances of 35R E, upstream of the Earth. Figure shows the positions of ACE and Wind, together with the nominal locations of the bow shock [Cairns et al., 995] and magnetopause [Shue et al., 997] of the Earth. 5. Instrumentation [8] The electron data used in this paper have been obtained with the Wind 3DP Plasma and Energetic Particle experiment [Lin et al., 995] and the EPAM instrument [Gold et al., 998] onboard the Advanced Composition Explorer (ACE), respectively. The Wind 3DP solid state telescopes (SSTs) detect electrons from 5 kev to kev. Each of the five double-ended telescopes covers a 36 ı ı full width at half maximum field of view. Thus, five telescopes cover a 8 ı ı slice and provide, in combination with the spacecraft spin, full 4 steradian coverage [Lin et al., 995]. The onboard processing provides various telemetry products; in this paper we are using electron intensities in seven energy channels and the 4 solid angle samples with roughly equal geometric factor (out of a total of 48). Electron pitch angle distributions are generated Observations [] We investigate the intensity-time profiles and pitch angle distributions of electrons in the energy range 7 to 5 kev during several solar energetic particle (SEP) events. Figure shows for the SEP event on 4 June (from top to bottom) the X-ray emission at.5 4 and 8 Å (GOES), radio emission in the frequency range of. to MHz (Wind/Waves, [Bougeret et al., 995]), sector averages of the electron intensity in four energy channels from 53 to 3 kev (ACE/EPAM/LEFS6), and omnidirectional intensity in seven energy channels between 7 and 57 kev (Wind 3DP/SST), the electron PAD at 4 kev (Wind 3DP/SST), and plasma and magnetic field measurements as obtained with the Wind MFI and SWE [Ogilvie et al., 995] experiments, and the ACE MAG and SWEPAM [McComas et al., 998] experiments, respectively. This event has been

3 KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES Intensity (cm sr s kev) ACE EPAM 45 6 kev electrons * June 4 7:3 7:34 UT Wind 3DP 3 48 kev electrons June 4 7: UT.5.5 Figure 3. Electron pitch angle distributions near the intensity maximum. The energy ranges for Wind and ACE are 3 48 kev and 45 6 kev, respectively. The ACE electron flux is multiplied by a factor to account for the somewhat higher energy. Figure. Time history on 4 June of (from top to bottom) X-ray flux (GOES), Wind/Waves radio wave emission, ACE/EPAM/LEFS6 sector average electron fluxes, Wind/3DP/SST omnidirectional electron fluxes, pitch angle distribution of Wind/3DP/SST 4 kev electrons, observations of interplanetary magnetic field in polar coordinates, and solar wind speed, observed onboard Wind (red lines) and ACE (blue lines), respectively. studied previously by several authors [Simnett et al., ; Ho et al., 3; Wang et al., 5; Sun et al., ]. [] A type III burst observed by Wind/Waves at 7:3 UT indicates the injection of electrons at the Sun at 6:55 UT. The intensity-time profiles at ACE and Wind show a fast rise to maximum at event onset (at 7:7 UT for electron energies of 75 3 kev at ACE), velocity dispersion, and intensity maxima within less than 3 min, indicative of impulsive injection at the Sun, and propagation in interplanetary space with only weak scattering [Haggerty and Roelof, ]. Under these conditions, PADs with only peak along the magnetic field direction would be expected. Note that the magnetic field at both ACE and Wind points into the sunward direction for this event (Figure ), i.e. outward streaming electrons have 8 ı pitch angle. However, the observations on Wind show, in addition to the outward streaming electrons, over an extended time period of h backward streaming electrons with somewhat lower intensity (Figure, fifth panel). Later in the event, at 8:4 UT, probably related to a change of the azimuth angle and elevation angle of the interplanetary magnetic field (IMF), the backstreaming electrons disappear. During the onset of the particle event, Wind was positioned at X = 57., Y = 53.4, and Z = 7.3 ( 43 ı from the Earth-Sun line), while ACE was positioned at X = 3.3, Y = 37., and Z = 4.4, (GSE coordinates, units of Earth radii, see Figure ). Figure also indicates the direction of the magnetic field, measured locally at Wind and ACE, projected into the X-Y (GSE) plane, and extrapolated to the nominal Earth s bow shock. Considering also that the magnetic field elevation angle at Wind was small for 45 min after event onset ( was in the range of ı to 3 ı ), Figure suggests that Wind was magnetically well connected to the bow shock during the event onset whereas ACE was not. [] Next, we analyze the pitch angle distributions observed on Wind and ACE. Figure 3 shows the PADs observedonwindandaceat3to48kevand45to6 kev, respectively, for a 4 min time period near the intensity 47

4 Intensity (cm sr s kev) Ap Wind/3DP 3 48 kev electrons ACE/EPAM LEFS kev electrons * KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES June Time (hours) Figure 4. Anisotropy analysis of 4 kev electrons. (top) The ACE EPAM (blue) and Wind 3DP (red) omnidirectional electron flux at 45 6 kev and 3 48 kev, respectively. (bottom) The first-order anisotropy. maxima at the corresponding energies. Here the ACE PADs are taken at a slightly later (3 min) time and multiplied by a factor of to account for the lower energy of the Wind measurement. Figure 3 demonstrates the striking difference of the PADs as observed onboard Wind and ACE. Whereas the PADs of the outflowing electrons are similar, with a somewhat steeper decrease toward 9 ı pitch angle on Wind, backstreaming electrons are only observed onboard Wind. The backstreaming electrons are peaked at a cosine of the pitch angle of.7.8 ( 35 ı 45 ı )where =cos# is the particle s pitch angle cosine. The first-order anisotropy is computed from the polynomial fit, using equidistant grid points in the range. Weuseathird- order polynomial fit of these pitch angle distributions to infer omnidirectional intensities and first-order anisotropies. The omnidirectional intensities are computed by integrating over the polynomial fit in the range. The first-order anisotropy parallel to the mean magnetic field can be defined as A p (t) = 3 R + df(, t) R + d f(, t) () [3] Figure 4 (top panel) shows the omnidirectional electron intensity-time profiles. In order to account for the lower energy of the measurement with the Wind 3DP/SST instrument, the ACE/EPAM fluxes are normalized to the fluxes observed onboard Wind, using a multiplication factor of.. This factor is consistent with the different energy ranges of Wind and ACE, and a spectral slope of.5 as observed at Wind in this energy range (as will be shown in Figure 6). The bottom panel shows the first-order anisotropy. Whereas the measurement onboard ACE shows a large first-order anisotropy ( A p ), as expected for the propagation of near-relativistic electrons with weak interplanetary scattering [e.g., Haggerty and Roelof, ], the electron fluxes observed on Wind show only a small first-order anisotropy ( A p ). Figure 5 shows a comparison of the electron PADs observed on Wind for several energy channels in the range 7 to 8 kev. The PADs are averaged over a 4 48 min period at the time of maximum intensity of the selected energies. The outflowing electrons show a large decrease of the intensity with increasing pitch angle that is less pronounced at higher energies, as expected for impulsive electron events with energy-dependent pitch angle scattering [Dröge, 3]. Figure 5 also shows that backstreaming electrons are observed at all energy channels from 7 to 8 kev. [4] In Figure 6 we compare the energy spectra of the outflowing electrons with the spectra of backstreaming electrons, taking 4 min averages at the maximum intensity of the 4 June SEP event, using the pitch angle cosine with maximum intensity for electrons from the solar and antisolar direction, respectively. As already evident from Figure 5, the intensities of backstreaming electrons are only slightly smaller (less than a factor of ) than the intensity of outflowing electrons. The energy spectra are very similar, with spectral slopes steepening from.9 to 5. between 7 and 8 kev. [5] We investigated several other impulsive electron events in June when Wind was in the morning - noon sector, upstream and magnetically well connected to the Earth s bow shock and found two more cases with bidirectional PADs of near-relativistic electrons at Wind, where large field-aligned (beamlike) PADs have been reported at ACE [Simnett et al., ; Haggerty and Roelof, ]. Figure 7 shows an overview of the event of 5 June in the same format as Figure. During the onset of the particle event, Wind was positioned at X = 33., Y = 67.8, and Z = 7. ( 64 ı from the Earth-Sun line), while ACE was positioned at X = 36., Y = 39.4, and Z = 6.6 Intensity (cm sr s kev) 3 June 4 Wind 3DP pitch angle distributions at time of maximum 4 kev 65 kev 7 kev 8 kev 7 kev.5.5 Figure 5. Electron pitch angle distributions taken at the times of maximum intensity at the indicated energies during the solar particle event on 4 June. Note that opposite to Figure 3, here a logarithmic scale is used for the intensity.

5 KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES Intensity (cm sr s kev) 3 June 4 Wind 3DP time of maximum spectra solar reflected energy ranges are 3 to 48 kev (Wind/3DP) and 45 to 6 kev (ACE/EPAM), respectively. Whereas ACE shows, as in the other events, beamlike electron distributions with a maximum intensity at 3 ı pitch angle (the lowest pitch angle covered by ACE/EPAM/LEFS6 during this time period), the electron PADs observed onboard Wind are bimodal, with two peaks, one at 8 ı pitch angle, and a second peak with backstreaming electrons, at pitch angles of 3 ı 45 ı. 3 Energy (kev) Figure 6. Energy spectra of electrons from the solar direction and reflected electrons taken at the times of maximum intensity during the solar particle event on 4 June. The maximum background determined from the pre-event flux was % at the highest energy and has been subtracted. (GSE coordinates, units of Earth radii). The X-ray emission (GOES) and Wind/Waves radio emission (. MHz) show several events indicating the acceleration (GOES) and injection (Wind) of electrons at the Sun during the time period 5 June, 8: 4: UT. A large increase of interplanetary electron intensities with event onset at 9:5 UT (at ACE [ Haggerty and Roelof, ]) is following type III bursts at 9:4 UT and 9:48 UT. The electron PAD at 4 kev as observed with Wind/3DP shows a bidirectional distribution with intensity maxima at ı 3 ı pitch angle and somewhat lower intensities with a broader maximum at 35 ı for backstreaming electrons. The backstreaming electrons disappear at :36 UT, possibly related to large directional changes of the IMF. At :, for example, increases to 4 ı and decreases to ı at :4. [6] Another interplanetary event with bidirectional electron PADs was observed on 8 June. Figure 8 shows an overview of this event, in the same format as Figure. During the onset of the particle event Wind was positioned at X =.8, Y = 45., andz = 4. ( 9 ı from the Earth-Sun line), while ACE was positioned at X = 43., Y = 34., and Z = 3.5(GSE coordinates, units of Earth radii). GOES X-ray and Wind/Waves data indicate several events with electron acceleration (GOES) and injections of electrons (Wind) at the Sun, between 8:3 and 4: UT. The impulsive intensity increase of near-relativistic electrons in interplanetary space with electron event onset at 9:8 UT (at ACE [Haggerty and Roelof, ]) is following the type III burst observed at Wind at 8:5 UT. This event shows a pronounced bidirectional electron pitch angle distribution at 4 kev (fifth panel) between event onset and :3 UT. After 9:45 UT, the backstreaming electrons are seen only intermittently, probably due to large variations of the angle of the IMF. The intensity increase observed after :3 UT, more pronounced on Wind than on ACE, is probably due to another electron event not discussed in this paper. [7] In Figure 9 we present detailed electron PADs for the 8 June event, in the same format as Figure 3. The Figure 7. Time history of solar X-ray and radio emission, energetic electrons, and solar wind plasma data during the 5 June event (same format as Figure ). 49

6 KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES observed on Wind is small, consistent with the bimodal PAD shown in Figure 9. [9] Figure shows the projection of the Wind orbit, spacecraft locations, together with the nominal locations of the bow shock [Cairns et al., 995] and magnetopause of the Earth [Shue et al., 997]. The in situ magnetic field directions during the time of maximum intensity of 4 kev electrons, extrapolated to the bow shock, suggest that Wind was well connected to the quasi-parallel bow shock in all three events, whereas ACE was not connected. ACE and Wind observations show fundamentally different pitch angle distributions: Whereas the observations onboard Wind show bidirectional PADs, ACE shows PADs with one peak, aligned with the IMF, as usually observed for impulsive injection of electrons at the Sun. The flattening of the electron pitch angle distributions at energies above 4 kev as apparent in Figure 6 is qualitatively consistent with a scattering mean free path of electrons increasing with decreasing energy, as it is expected in this energy range from extended quasi-linear theories of particle transport [Dröge, 3]. [] The PADs onboard Wind with a maximum of backstreaming electrons at 3 ı 45 ı suggest backscattering from a region with increased turbulence, or reflection at a boundary located in the downstream direction of the spacecraft. Upper limits on the distance of this region can be obtained from the time delay between the electrons from the solar and antisolar direction. In recent work [Tan et al., 9], an energy-dependent time delay between outflowing and backstreaming electrons was observed during the 4 September SEP event, with a delay of 3 min for 4 kev electrons, suggesting a magnetic mirror point at.4 AU. This was consistent with the location of the compression region in front of a preceding CME. In all three events with bidirectional PADs of near-relativistic electrons found in June, the time delay between electrons from the sunward and antisunward direction was much smaller, implying backscattering or reflection from a nearby region. This is illustrated for the 4 June SEP event with Figure 8. Time history of solar X-ray and radio emission, energetic electrons, and solar wind plasma data during the 8 June event (same format as Figure ). [8] In Figure we present the anisotropy analysis for the 8 June event, in the same format as Figure 4. The top panel of the figure shows the electron intensities in the energy ranges of 3 to 48 kev (Wind 3DP/SST) and 45 to 6 kev (ACE/EPAM), respectively. The bottom panel presents the result of the anisotropy analysis (equation ()). The large first-order anisotropies as observed on ACE show again the beamlike PAD. The first-order anisotropy as Intensity (cm sr s kev) ACE EPAM 45 6 kev electrons * June 8 9: 9:4 UT Wind 3DP 3 48 electrons June 8 9:3 9:7 UT.5.5 Figure 9. Electron pitch angle distributions near the intensity maximum for the 8 June event. The energy ranges for Wind and ACE are 3 48 kev and 45 6 kev, respectively. The ACE electron flux is multiplied by a factor of for normalization. 4

7 Intensity (cm sr s kev) Ap Wind/3DP 3 48 kev electrons ACE/EPAM LEFS kev electrons * KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES June Time (hours) Figure. Electron pitch angle distributions near the intensity maximum for the 8 June event. The energy ranges for Wind and ACE are 3 48 kev and 45 6 kev, respectively. The ACE electron flux is multiplied by a factor of for normalization. Figure, showing with high time resolution the intensity of 4 kev electrons measured onboard Wind for the pitch angles of ı to 9 ı (backstreaming electrons) and 9 ı to 8 ı (outflowing electrons), respectively. Figure demonstrates that within the time resolution of the measurement of s, the intensities of outflowing and backstreaming electrons increase simultaneously during event onset. This places a reflecting boundary or scattering region for 4 kev electrons with an intensity maximum at a pitch angle cosine of.7 (Figures 3 and 9) at 5R E. With the distances of Wind from the Earth during the June events ranging from 4 to 8 R E, this would suggest backscattering or reflection from a region as close as the bow shock or the magnetosheath of the Earth. 4. Transport Modeling [] It has been demonstrated that bidirectional PADs of suprathermal electrons in the energy range ev observed upstream of the bow shock can be well described by the combined effects of the cross-shock potential and adiabatic mirroring at the bow shock [Larson et al., 996]. However, there are at least two complications: The observations of our study have been obtained in a location magnetically connected to the quasi-parallel bow shock with its intrinsically complex structure including short, large amplitude magnetic structures (SLAMS) [e.g., Burgess et al., 5, and references therein]. The other complication is the large gyroradius of near-relativistic electrons. The gyroradii of 7 to 8 kev electrons ( to 8 km in a 5 nt magnetic field) are of the same order as typical gradient scales of the magnetic field in SLAMS ( to 5 km [Lucek et al., 4]). Therefore adiabatic reflection may not be an appropriate assumption in this energy range. On the other hand, for nearly perpendicular shocks, it was shown that the magnetic moment of an energetic particle (in the frame where the electric field vanishes and the plasma flow is parallel to the magnetic field) 4 is approximately conserved [Sarris and van Allen, 974; Toptygin, 98]. Numerical trajectory tracing of ions indicates that the adiabatic treatment is a reasonable approximation even for general oblique shocks [Terasawa, 979]. One of the main differences between the two approaches is that the loss cone is partly filled in the nonadiabatic case, in particular for a quasi-parallel shock, and depends on particle speed and shock geometry [Terasawa, 979]. [] If we assume adiabatic reflection of the electrons at the bow shock and ignore the above mentioned complications, the conservation of the first adiabatic invariant implies sin #/sin # = B /B, with magnetic fields of B and B upstream and downstream of the bow shock, respectively. With typical values of B /B in the range of.5 to.5 [e.g., Lucek et al., 4], we expect a loss cone # loss in the range of 3 ı to 45 ı. This is qualitatively consistent with the intensity maximum of the backstreaming electrons at pitch angles of 3 ı 45 ı as observed for the 4 and 8 June events (Figures 3 and 9). The partly filled loss cone at pitch angles 3 ı might be due to the intrinsically complex structure of the quasi-parallel bow shock or due to nonadiabatic motion of the particles as discussed above. Another possible mechanism is scattering of SEP electrons in the magnetosheath. If the scattering mean free path in the magnetosheath is of the order of R E as suggested by measurements of magnetospheric ( kev) electrons [e.g., Bieber and Stone, 98], this would result in an isotropic distribution in the magnetosheath. Electrons propagating back into the upstream region would be collimated by the drop in magnetic field strength and the superposition of electrons from the solar and antisolar direction could result in the observed bidirectional PADs. [3] In the following we will employ a phenomenological approach for modeling the observed electron intensitytime profiles and anisotropies. First, we use the intensity and anisotropy measurements obtained with ACE/EPAM to derive the injection profile of the solar electrons close to the Sun and the scattering parameters in interplanetary space. Then we combine the interplanetary propagation with three Y GSE (R E ) Wind positions and connecting field lines June 4 June 5 June 8 Wind orbit 5 X GSE (R E ) Earth magnetopause bow shock Figure. Projection of Wind orbit (dashed), spacecraft positions (circles), and extrapolated magnetic field directions (colored lines) into the XY GSE plane for the three SEP events observed on 4, 5, and 8 June, respectively. The magnetic field direction is taken during the time of maximum intensity of 4 kev electrons. 5

8 Figure. (top) High time resolution anisotropy and (bottom) intensity-time profile of 4 kev electrons for the SEP event observed on 4 June (blue: outflowing, black: backstreaming). models for particle reflection and transmission, assuming () a pitch angle-dependent reflecting boundary at a distance of 7 R E in the antisolar direction (approximately at the distance of the bow shock for the events observed), with only weak scattering in the magnetosheath, () adiabatic transmission through the boundary with weak scattering in the magnetosheath, including diffusion back upstream, and (3) strong scattering in the magnetosheath with adiabatic motion of the particles when crossing the boundary in both directions. [4] The appearance of solar particle events observed in the near-earth environment reflects the combination of a number of physical processes. For particles originating from solar flares, these processes include acceleration in the flaring region, some kind of transport in the solar corona to a magnetic field line connected with the observer, and transport in the solar wind. In the undisturbed solar wind, i.e., in the absence of CMEs and shocks, the latter can usually be described as adiabatic motion along the average interplanetary magnetic field (assumed to be an Archimedian spiral [see Parker, 963]) and pitch angle scattering of the fluctuations superimposed on the field. Diffusion perpendicular to the magnetic field is caused by interactions with fluctuations which scatter the particles gyrocenter from one field line to another and by the combined effects of parallel transport and field line mixing [e.g., Jokipii and Parker, 969; Matthaeus et al., 3]. Transport perpendicular to the average field also arises due to the action of an induced electric field, E = V sw B, wherev sw is the solar wind velocity and B denotes the magnetic field (corotation [Ng and Gleeson, 97]). Depending on particle species and energy, also convection and energy losses in the interplanetary medium can be of importance for the transport process. [5] Transport equations for the evolution of the particle s gyro-averaged phase space density f(r, p,, t) (where r is the location in the heliosphere relative to the center of KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES 4 the Sun, t is the time, and p and = cos# denote the particles momentum and pitch angle cosine, respectively) which include all the above effects have been presented by Zhang et al. [9] and Dröge et al. []. Note that f(r, p,, t) is proportional to the flux or intensity of the particles, I(r, E,, t), here formulated as function of the kinetic energy E, which is usually the observable. If the assumption is made that the scattering of the particles at magnetic fluctuations is strong and the resulting distribution is always nearly isotropic, the above effects can be incorporated into a diffusion-convection equation for an omnidirectional particle density which only depends on r, t and p (or energy [see Parker, 965]). The electrons analyzed in this work have so high speeds that effects of convection and adiabatic energy losses in the expanding solar wind are not significant during their transport to AU. Possible energy losses due to the generation of Langmuir waves and related type III bursts had been investigated by Ergun et al. [998] who found that they seem to be restricted to electron energies below kev. A recent study on the evolution of the spectra of solar flare electrons in the inner heliosphere [Reid and Kontar, ] suggests that at close distances to the Sun (up to solar radii), the emission of Langmuir waves can have a strong effect on electrons with energies below 4 kev. As the electrons considered here have energies which are mostly above 4 kev, and the modeling of their propagation starts at an inner boundary of solar radii (details will be given below), we believe that an inclusion of energy losses would not significantly change the results obtained in this work and that they can be safely neglected. Observations of cross field gradients in impulsive solar particle events, which are observed as dropouts and cutoffs in the intensity profiles of low-energy ions and electrons and caused by the convection of magnetic flux tubes past the observer that are alternately filled and devoid of flare particles, indicate a rather small value of the ratio of the perpendicular to parallel diffusion coefficients [cf. Mazur et al., ; Dröge et al., ; Chollet and Giacalone, ]. In accordance with the above, energy losses and transport perpendicular to the interplanetary magnetic field are usually neglected in the modeling of impulsive solar electron events, and the assumption is made that the propagation condition in the flux tubes convected past the spacecraft remain constant during the time of an electron event (typically several hours). However, as the scattering of electrons in the energy range of tens to hundreds of kev is often rather weak and the resulting anisotropies are high, a pitch angle-dependent transport model has to be used. The propagation of electrons can then basically be considered as one-dimensional spatial transport along the magnetic field line (or flux tube), and the quantitative treatment of the evolution of the particle s reduced phase space density f(s,, t) is described by [e.g., + D = Q(s, p,, t) () [6] Here we assume that the interplanetary particle transport takes place in a plane that is perpendicular to the rotational axis of the Sun and that the magnetic field lines along which the particles propagate resemble classical Parker spirals. The distance along the magnetic field line s(r) can be calculated from the solar wind speed V sw and the equatorial rotation frequency of the Sun as a function of the radial

9 KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES distance from the Sun r (both taken with respect to the center of the Sun) as s(r) = r p +(ar) + ar a ln + p +(ar) (3) where a = V sw /. The systematic forces are characterized by L(s) the focusing length in the diverging magnetic field B, while the stochastic forces are described by the pitch angle diffusion coefficient D (). The injection of particles onto the connecting field line, assumed to take place at a distance of.5 AU ( solar radii) from the Sun, is given by the source function Q(s,, t). Note that this injection function also absorbs processes which the particles undergo during their propagation in complex magnetic fields close to the Sun and that it therefore might not be directly related to the energy spectrum of the particles in the acceleration region and associated electromagnetic emission. [7] As analytical solutions of equation () are not known, numerical methods have to be used. Techniques based on finite-differences schemes were applied by Ng and Wong [979],Schlüter [985], Ruffolo [99], and others. Another possibility is to transform equation () into the corresponding Ito stochastic differential equations [Gardiner, 983]: ds(t) =vdt (4) d(t) = p v D dw (t)+ L ( dt the goal of deriving the injection function and the interplanetary transport parameters. To achieve this, it is important to not only model the isotropic part of the distribution function but also make use of the information contained in its angular dependence, or the first- (equation ()) and higherorder anisotropies parallel to the magnetic field. Different fitting/modeling techniques have been used to extract information from the particle data about the transport process, including the traditional method of fitting by eye [e.g., Dröge, 3; Dröge and Kartavykh, 9], with an emphasis on the early phase of the event, an automated piecewise linear fitting method which minimizes a value [Ruffolo et al., 998], or by procedures that use an estimator of the goodness of the fit [e.g., Maia et al., 7; Agueda et al., 8]. Comparison between the various methods has shown that they give similar results in most cases. Here we adopt the by eye method and will refer to it, because it is not based on a rigorous mathematical treatment, as modeling rather than fitting. If the scattering is sufficiently strong, f(s,, t) adjusts rapidly to a nearly isotropic distribution, and the solutions of equations (),(4), and (5) become similar to those of a spatial diffusion model. The mean free path k which relates the pitch angle scattering rate to the spatial diffusion parallel to the ambient magnetic field is given by [Hasselmann and Wibberenz, 968] k = 3v 8 Z + d ( ) D () (7) which can be solved by means of Monte Carlo simulations (W (t) denotes a Wiener process). Both of the above methods have also been extended to include effects of convection and energy losses due to adiabatic deceleration in the expanding solar wind [e.g., Ruffolo, 995; Kocharov et al., 998; Dröge et al., 6; Qin et al., 6; Agueda et al., 8]. For the pitch angle diffusion coefficient, we make a product ansatz of the form: D (s, E, ) = (s, E) q + H ( ) (6) which partially resembles the result of standard quasi-linear theory (QLT) [cf. Jokipii, 966] and additionally introduces a parameter H which can phenomenologically describe an enhancement of scattering through = by nonresonant and nonlinear effects. The parameter q denotes the spectral index of the magnetic fluctuations along the field, which is here assumed to be a single power law in wave number. Typical values are q =.67 for a Kolmogorov spectrum, and a variation of H between.5 and.5, corresponding to weaker to stronger scattering through =dueto theabove mentioned effects. Information about the spatial variation of the scattering and of its dependence on the particle energy E (which we use from now on instead of the momentum for a more direct relation to the energy ranges of the electron observations) is absorbed in the coefficient (E, s). Inprinciple, the parameters q and H, and the resulting pitch angle dependence of the scattering can also vary with radial distance, but we consider them here as being constant, in order not to introduce too many free parameters. [8] Solutions of the above transport equation have been widely used to model in situ observations of SEP events with 43 [9] A radial mean free path can be defined in a similar manner as r = k cos,where (r) is the angle between the radial direction and the magnetic field. The mean free path is often used as a convenient parameter to characterize the varying degrees of scattering from one solar particle event to another, even when it adopts values close to or larger than the observers distance from the Sun and the transport process cannot be considered as spatial diffusion. For modelings of observed particle data, often a power law dependence of the pitch angle diffusion coefficient, or the corresponding mean free path, as a function of radial distance is assumed, e.g., r / r b. For undisturbed solar wind conditions in many events a constant, r (b = ) is found to be sufficient for a good fit [e.g., Kallenrode et al., 99]; sometimes values of b slightly above or below zero or a spatially constant k give better results. By means of equation (3), a specified radial dependence of the pitch angle diffusion coefficient or of the related mean free path can easily be transformed into a dependence on the distance along the magnetic field line s(r) and vice versa. In a number of solar events, signatures such as a slow decrease in the intensity profile and a simultaneous fast drop in the first-order anisotropy, or counterstreaming electron beams have indicated the presence of a reflecting boundary, which could represent effects of a kink or magnetic bottle configuration in the magnetic flux tube in which the particles propagate at distances of a few tens of an AU downstream of the Earth [e.g., Bieber et al., ; Tan et al., 9]. [3] For an attempt to model the bimodal electron fluxes observed in the foreshock region by Wind, we chose the 4 June 4 solar event because the radio data suggest a single injection of electrons, and the near-earth magnetic field is

10 Injection Intensity (cm sr s kev) Ap Time (hours) Figure 3. Modeling of the time profiles of (top) injection, (middle) intensity, and (bottom) anisotropy (absolute value) of 45 6 kev electrons observed on ACE on 4 June. Red lines show prediction from a finite differences (FD) solution of the focused transport equation for monoenergetic electrons of 53 kev and a spatially constant mean free path of k =.6AU. The injection profile is normalized to its maximum value. relatively undisturbed, providing an almost continuous connection of Wind to the bow shock during the first hour of the electron event. We will first determine the propagation conditions on interplanetary field lines not connected to the bow shock by performing a modeling of the ACE/EPAM observations. With the derived transport coefficients, we will then try to reproduce the Wind electron data in a similar energy range by phenomenologically taking into account the effects of the bow shock and/or the magnetosheath through a reflecting boundary and/or a region of enhanced scattering. As ACE does not measure electrons below 45 kev, the lowest possible energy channel to use from Wind is the one detecting electrons in the range 3 48 kev. We note that the effect of electron reflection at the bow shock is visible up to energies of 8 kev, although it seems to decrease in strength with energy (see Figure 5). We will therefore analyze here the two lowest suitable energy ranges on Wind and ACE, respectively, and postpone the investigation of a possible energy dependence of the reflection mechanism to a later study. 4.. Electron Fluxes at L [3] A modeling of the ACE/EPAM 45 6 kev electron fluxes during the 4 June 4 event, performed with our finite-differences scheme, is shown in Figure 3. The following assumptions were made: a constant value of the solar wind speed of 435 km/s throughout the time interval under consideration (see Figure ), a distance along the field line connecting to the Sun of s =.6 AU, an inner reflecting boundary at r =.5AU, an outer absorbing boundary at r =3AU, and monoenergetic electrons at 53 kev which approximately corresponds to the center of the above energy KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES 44 interval. Energy losses of the electrons are neglected. The modeling of the intensity and anisotropy together is crucial for deriving the particle injection profile. Otherwise, effects of prolonged injection could not be separated from diffusive delays in the interplanetary medium. The anisotropy and the pitch angle distributions from which it is derived contain key information on the strength of scattering in the interplanetary medium. The time dependence of the injection on the modeling of the observed intensity and anisotropy-time profiles was performed utilizing a convolution of the impulsive solution with a time-dependent source function Q(s, E,, ): I(s, E,, t) = Z t d I (s, E,, t ) Q(s, E,, ) (8) [3] Considering the intensity and anisotropy-time profiles, we came to the conclusion that the fast rise to the maximum, but relatively slow decline of the intensity following the maximum, suggests that the scattering increases as a function of radius, at least beyond AU. For the modeling of this event, we therefore assumed a spatially constant parallel mean free path (corresponding to r cos ) which approximately resembles the above features. A good agreement between predictions from the finite-differences model and observed intensity and anisotropy-time profiles (Figure 3), as well as the pitch angle distribution around the time of maximum intensity (Figure 4), was obtained for the following parameters: k =.6AU, q =.67, H =.5, and a piecewise linear injection function as shown in the top panel of Figure 3. The injection function, defined as the rate at which particles are injected onto the footpoint (at r =.5AU) of the Sun-Earth magnetic field line as a function of time, was specified for five discrete time values: one each for the start and for the maximum of the injection, and three for the decay phase. The integral in equation (7) was then approximated by a sum. We note that the injection profile was solely derived from the modeling and no input from solar X-ray or radio measurements during the particle onset Intensity (cm sr s kev) Figure 4. Pitch angle distribution of 45 6 kev electrons during the 4 June particle events at the time of maximum intensity. Dots show ACE/EPAM observation, and solid line shows prediction from a finite differences (FD) solution with parameters specified in Figure 3.

11 was used. In principle, discrepancies between the onset of X- ray and radio emissions and the start of the injection profile can be used to obtain information about the lateral transport of the particles to the connecting field line, but we will not consider this further here. 4.. Electron Fluxes in the Foreshock Region [33] The pitch angle distributions observed on Wind during the events considered here show some similarity to observations of solar wind electrons reflected at the bow shock during quiet times [Larson et al., 996], and solar particles reflected at interplanetary shocks located at.3 AU downstream of the Earth [Tan et al., 9; Wang et al., ]. Because the bimodal patterns are not observed at ACE which is located relatively close to L and because there is almost no delay between electrons arriving from the sunward and antisunward direction (within the s time resolution of the instrument, see Figure ), we conclude that they are caused by a nearby obstacle of limited extent. [34] For the modeling of the Wind electrons, we incorporated a composite medium into our (still one-dimensional) transport model, consisting of the solar wind, the bow shock, and the magnetosheath. A similar approach was used by Palmer [98] in an analysis of electrons in the magnetosheath, although based on a spatial diffusion model. For solving the pitch angle dependent transport equation we used here the method of stochastic differential equations (equations (3) and (4)). The electron transport now proceeds in the following way: Electrons are injected at s =.5AU with a power law energy spectrum (extending from 3 to 48 kev, power spectral index =.5, cf. Figure 6) and with the time profile derived for the electrons observed by ACE. Subsequently, the electrons propagate along the interplanetary magnetic field, where they pass the location of Wind at s =.64 AU (cf. Figure ). Because the separation between the two spacecraft during the events of our study is of the order of 5 R E (cf. Figure ), we treat the mean free path relevant for the electrons observed on Wind as a free parameter. Studies of the correlation scale of plasma and magnetic field parameters obtained from measurements on the two spacecraft during the year indicate correlation scales of 9 R E for the total magnetic field [Wicks et al., 9]. We therefore decided not to use for Wind the same transport parameters as derived for ACE because we cannot exclude the possibility that the scattering conditions in flux tubes separated by the above distance are somewhat different. In order to not introduce too many modeling parameters, we take the same values for q, H, and the radial dependence of k as for the ACE modeling and assume that the mean free path is energy independent over the above energy interval. [35] When the electrons reach the bow shock at s =.67 AU, they are either reflected and propagate sunward again, or they are transmitted and enter the magnetosheath. Transmitted particles follow the field line in the magnetosheath, but according to a parallel mean free path which might be different from the one in the solar wind. We assume that after R E, the field line exits the magnetosheath and continues in the solar wind. Electrons are allowed to pass the latter boundary without adiabatic changes in their pitch angle. In principle, they can be scattered through 9 ı in the solar wind beyond the magnetosphere and go back through the magnetosheath and into the foreshock region. The electrons are KARTAVYKH ET AL.: BIMODAL ELECTRON FLUXES 45 Intensity (cm sr s kev) Ap Ap Time (hours) Figure 5. Modeling of the time-intensity and anisotropy profiles of 4 kev electrons observed on Wind on 4 June with a Monte Carlo solution of the focused transport equation. A constant k =.65AU was assumed. followed for h in the simulation and counted at s =.64 AU whenever they cross this distance. The question arises whether or not particles which are reflected at an obstacle located around AU might turn around again between the Earth and the Sun due to pitch angle scattering or mirroring in the converging magnetic field and contribute significantly to the flux observed by spacecraft in the near-earth environment. Such an effect has indeed been reported by Wang et al. [] for the reflection of electrons at a CME/shock structure.3 AU downstream of the Earth, and for very weak scattering conditions. However, the observed peak fluxes of the reflected particles reached only a few percent of the peak fluxes of the direct particles. The situation in our case is different in so far as in comparison with an interplanetary CME, the Earth s bow shock is a very small obstacle as viewed from the vicinity of the Sun. By the time an electron which is reflected at the bow shock returns from the vicinity of the Sun, the field line it is attached to will likely not be connected to the near-earth environment anymore due to corotation. Similarly, the probability is expected to be small that a particle that exits the magnetosheath and scatters through = in the interplanetary medium beyond AU will go through the magnetosheath again and reach the foreshock region. The flux in the antisunward direction observed on Wind at later times ( h after the onset) will consist mainly of electrons which have been scattered in the solar wind and transported, together with the magnetic field lines they are attached to, into the foreshock region by corotation. We therefore assume that the results of our log (Intensity (cm sr s kev) ).5.5.5