The expected imprint of flux rope geometry on suprathermal electrons ...

Ann. Geophys., 27, 4057–4067, 2009 www.ann-geophys.net/27/4057/2009/ © Author(s) 2009. This work is distributed under the Creative Commons Attribution 3.0 License.

Annales Geophysicae

The expected imprint of flux rope geometry on suprathermal electrons in magnetic clouds M. J. Owens1 , N. U. Crooker2 , and T. S. Horbury1 1 Space

and Atmospheric Physics, The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, UK 2 Center for Space Physics, Boston University, Boston MA 02215, USA Received: 1 June 2009 – Revised: 20 August 2009 – Accepted: 14 October 2009 – Published: 26 October 2009

Abstract. Magnetic clouds are a subset of interplanetary coronal mass ejections characterized by a smooth rotation in the magnetic field direction, which is interpreted as a signature of a magnetic flux rope. Suprathermal electron observations indicate that one or both ends of a magnetic cloud typically remain connected to the Sun as it moves out through the heliosphere. With distance from the axis of the flux rope, out toward its edge, the magnetic field winds more tightly about the axis and electrons must traverse longer magnetic field lines to reach the same heliocentric distance. This increased time of flight allows greater pitch-angle scattering to occur, meaning suprathermal electron pitch-angle distributions should be systematically broader at the edges of the flux rope than at the axis. We model this effect with an analytical magnetic flux rope model and a numerical scheme for suprathermal electron pitch-angle scattering and find that the signature of a magnetic flux rope should be observable with the typical pitch-angle resolution of suprathermal electron data provided ACE’s SWEPAM instrument. Evidence of this signature in the observations, however, is weak, possibly because reconnection of magnetic fields within the flux rope acts to intermix flux tubes. Keywords. Interplanetary physics (Interplanetary magnetic fields; Energetic particles) – Solar physics, astrophysics, and astronomy (Flares and mass ejections)

1

Introduction

Coronal mass ejections (CMEs) are huge expulsions of solar plasma and magnetic field through the corona and out into the heliosphere, known to be the major cause of severe geomagnetic disturbances (e.g., Cane and Richardson, 2003). Correspondence to: M. J. Owens ([email protected])

The interplanetary manifestations of CMEs (ICMEs) provide critical information about their magnetic configuration and orientation, which may prove key in constraining theories of CME initiation as well as aiding our understanding of the evolution of ejecta during their transit from the Sun to 1 AU. A variety of signatures are used to identify ICMEs from in situ data, including, but not limited to, low proton temperatures, counterstreaming suprathermal electrons, reduced magnetic field variance and enhanced ion charge states. See Wimmer-Schweingruber et al. (2006) for a more complete review. Magnetic clouds (MCs), a subset of ICMEs comprising somewhere between a quarter to a third of all ejecta (e.g., Cane and Richardson, 2003), are further characterized by a smooth rotation in the magnetic field direction and an enhanced magnetic field magnitude (Burlaga et al., 1981). The field rotation has been attributed to a magnetic fluxrope (MFR, Lundquist, 1950) and commonly modeled as a constant-α force-free MFR (Burlaga, 1988; Lepping et al., 1990), where currents are assumed to be field aligned and α is the constant relating the current density J to the magnetic field vector B. This enables single-point, in situ, time series to be interpreted in terms of the large-scale structure of the ejection. The present study addresses the behavior of suprathermal electrons in magnetic clouds. In general, suprathermal electrons (i.e., >70 eV) are of key interest to studies of the solar wind because the field-aligned “strahl” acts as an effective tracer of heliospheric magnetic field topology. A single strahl indicates open magnetic flux (Feldman et al., 1975; Rosenbauer et al., 1977), while counterstreaming electrons (CSEs) often signal the presence of closed magnetic loops with both foot points rooted at the Sun (Gosling et al., 1987). A strong field-aligned strahl is expected and observed in the ambient solar wind near 1 AU, as even an initially isotropic distribution near the Sun will undergo pitch-angle focusing due to conservation of magnetic moment in a decreasing magnetic field intensity. Strahl widths at 1 AU, however, are much

Published by Copernicus Publications on behalf of the European Geosciences Union.

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broader than would be expected from focusing alone, suggesting significant pitch-angle scattering must occur (e.g., Pilipp et al., 1987). Indeed, with increasing distance from the Sun, pitch-angle scattering becomes increasingly important because the rate of focusing decreases owing to the increasing angle between the spiraling magnetic field direction and intensity gradient (Owens et al., 2008). This results in the strahl width increasing with heliocentric distances (Hammond et al., 1996). For closed magnetic loops in an ICME, the antisunward motion of the loop apex will mean that intransit scattering on the increasingly longer field-line will result in eventual loss of the sunward beam and, hence, loss of the CSE signature, which has important implications for the interpretation of the solar cycle evolution of the heliospheric magnetic field (Owens and Crooker, 2006, 2007). The flux rope structure of magnetic clouds means the field-line length is shortest at the axis of the MFR, increasing toward the edge as the field winds about the axis. Indirect evidence for the varying length of field lines in magnetic clouds was found in the arrival-time dispersion of solar flare electrons intermittently injected into the October 1995 magnetic cloud (Larson et al., 1997). (Chollet et al., 2007) recently used bursts within energetic particle dispersions within an ICME to infer a jumbled mix of field-line lengths from ∼1 to 3.5 AU. While energetic particle events can only be used to calculate field-line length in a very limited number of ICMEs, field-line length should also have an effect on suprathermal electrons, which continually stream away from the Sun along field lines. Since the suprathermal electron time of flight and, hence, pitch-angle scattering time, increases with field-line length, the strahl width should exhibit a characteristic signature as a flux rope convects past an observer at 1 AU. To characterize the expected imprint of flux rope geometry on suprathermal electron observations, we combine two forms of modeling. In Sect. 2, an analytical MFR model is used to calculate the length of magnetic field lines which connect an observer inside an MC to the Sun. In Sect. 3 a numerical model of suprathermal electron evolution is used to estimate the suprathermal electron strahl widths corresponding to the MFR magnetic field line lengths. Finally, in Sect. 5 we look for the predicted variation in strahl width in ACE observations of magnetic clouds.

2

Magnetic flux rope model

The classic model for a magnetic cloud-associated flux rope, the constant-α force-free flux rope (Burlaga, 1988; Lepping et al., 1990), assumes the magnetic cloud can locally be approximated as a 2-dimensional cylindrical structure with a circular cross-section. The field is entirely axial at the center of the rope, becoming increasingly poloidal toward the outer edge. It is useful to define a parameter Y , the ratio of the distance from the flux rope axis, r, to radius of the flux rope, Ann. Geophys., 27, 4057–4067, 2009

r0 . The magnetic field of a force-free flux rope is then given by: BAX (Y ) = B0 J0 (αY ) BPOL (Y ) = ± B0 J1 (αY )

(1)

where BAX and BPOL are the magnetic field strengths along the axial and poloidal directions, respectively. The poloidal component takes positive or negative values depending on the sense of rotation of the magnetic field about the axis (i.e., the chirality of the flux rope). J0 and J1 are zero and first order Bessel functions of the first kind, respectively. α is a constant which determines the outer edge of the flux rope. It is normally assumed to be 2.408, which effectively sets the outer edge of the flux rope at the point where the field first becomes entirely poloidal (Burlaga, 1988; Lepping et al., 1990). The angle of the magnetic field to the axial direction, θ, is a function of Y : tan θ =

BAX J0 (αY ) = BPOL J1 (αY )

(2)

We initially adopt this simple force-free geometry, later modifying the model to incorporate effects which will substantially alter the estimate of field-line length L connecting a 1AU observer to the Sun. The left-hand panel of Fig. 1 defines the basic parameters: The rope is of radius r0 . At a distance r from the axis, the field takes the form of a helix about the axis, shown as the solid/dashed blue line, and makes an angle θ to the axis. The field makes one complete revolution about the axis in a height, H , along the axis. For an axis of length LAX , the field makes N revolutions (in the example shown, N∼1.8). The right-hand panel shows the curved face of the cylinder unrolled to form a flat plane. The relations between θ, H, LAX , N, r, r0 and the length of the field line, L, are easier to visualize in this way. It can immediately be seen that the length of the field line is: q L = L2AX + (2N π r)2 (3) and substituting N H =LAX and H =2π r/ tan θ gives: L=

LAX cos θ

(4)

Thus for a force-free flux rope, the length of the magnetic field line depends only on θ (which, in turn, is solely a function of Y ) and the length of the axial field line. L is independent of the radius of the flux rope, as the number of revolutions per unit axial length is linearly related to r, the distance from the axis. To estimate LAX , it is necessary to extend the 2dimensional force-free model to a more global configuration. Assuming the flux rope plasma moves radially but the foot points of the flux rope remain connected to the Sun, as suggested by observations (Gosling et al., 1987), the axial field www.ann-geophys.net/27/4057/2009/

Owens et al.: Suprathermal electron signatures of flux ropes M. J. Owens et al.: Suprathermal electron signatures of flux ropes

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3

Fig. 1. The left-hand panel shows the cylindrical geometry implied by a force-free flux rope. The rope is of radius r0 . At a distance r from the1.axis, field takes theshows form of helix about geometry the axis, shown as by theasolid/dashed bluerope. line,The and rope makes angle θrto The field Fig. Thethe left-hand panel thea cylindrical implied force-free flux is an of radius At aaxis. distance r from 0 . the complete the axis in the a height, H , along For an axis length , thean field makes revolutions themakes axis, one the field takesrevolution the form about of a helix about axis, shown as the the axis. solid/dashed blueofline, andLAX makes angle θ toNthe axis. The(in field the case N ∼1.8). The right-hand panelinshows the H, curved face the cylinder unrolled to form a flat The relations between(in makes oneshown complete revolution about the axis a height, along theofaxis. For an axis of length LAX , theplane. field makes N revolutions H, Lshown r, r∼0 and length of the field line, L arethe easier to visualize in this way. unrolled to form a flat plane. The relations between theθ,case 1.8).theThe right-hand panel shows curved face of the cylinder AX , N,N θ, H, LAX , N, r, r0 and the length of the field line, L are easier to visualize in this way.

will lie predominantly along the Parker Spiral. Thus at a heliocentric R, the axislatitude, makes anΩangle γ to the radial: where λ is distance the heliographic = 2π/T SID , and rotation period of the Sun. L TSID is the sidereal is thereAX R γ = arctan (5) cos λ fore given by: V CR Z 1AU dR where λ is the heliographic latitude, =2π/TSID , and TSID LAX = (6) is the sidereal rotation period of the Sun. LAX is therefore cos γ 0 given by: We now the effect of expansion to allow for axZ include AU dR ial curvature1 effects, and later in this Section, we incorporate LAX = (6) a more realistic cross-sectional topology. Expansion is ascos γ 0 sumed to be self-similar about the axis, consistent with the We now include the effect of expansion to allow for axial linearly declining profiles observed magnetic curvature effects,speed and later in this section,within we incorporate clouds (Owens et al., 2005). Thus while the axis of theisflux a more realistic cross-sectional topology. Expansion asrope moves antisunward at a cruise speed V , the edges of CR sumed to be self-similar about the axis, consistent with the thelinearly flux rope move away from the axis at a speed V . The EX declining speed profiles observed within magnetic radius of(Owens the fluxetrope varies with disclouds al., therefore 2005). Thus while theheliocentric axis of the flux tance ropeas: moves antisunward at a cruise speed VCR , the edges of the flux VEXrope R move away from the axis at a speed VEX . The r0radius = of the flux rope therefore varies with heliocentric dis(7) VCR tance as: The left of Figure 2 shows a snapshot of the model VEXpanel R r0 = flux rope using paramters VCR = 400km/s and VEX (7) = V 100km/s, CR typical magnetic cloud values (Owens et al., 2005). left paneldistance of Fig. 2ofshows theblack model flux AThe heliocentric 1 AU aissnapshot shown asofthe dotted rope using paramters V =400 km/s and V =100 km/s, CR curve, while the Sun is represented by a solidEXblack circle. typical cloud values et al., 2005). helioOnly themagnetic half of the flux rope(Owens which provides the A shortest centric distance of 1 AU is shown as the black dotted curve, magnetic connection between the Sun and 1 AU is shown. while the Sun represented a solid circle.by Only the Field lines at Yis = 0, 0.3, 0.6byand 0.9 black are shown black, half of the flux rope which provides the shortest magnetic blue, green and red lines, respectively. Numerically inteconnection betweenalong the Sun andhelical 1 AU ispath shown. lines grating the distance each givesField field-line at Y =0, 0.3, 0.6 and 0.9 are shown by black, blue, green lengths of 1.17, 1.23, 1.68 and 5.19 AU, respectively. and red lines, respectively. Numerically integrating the distance The open circles in the right panel of Figure 2 show the field-line length between 1 AU and the Sun as a function of www.ann-geophys.net/27/4057/2009/

along each helical path gives field-line lengths of 1.17, 1.23, 1.68 and 5.19 distance fromAU, therespectively. MFR axis. We find the following funcThe open in as thethe rightsolid panelblack of Fig. 2 show the field-detional form,circles shown line, adequately line length 1 AU and the Sun as a function of disscribes the between model points: tance from the MFR axis. We find the following functional form, shown as the solid black line, adequately describes the L[AU ] = 0.631 − 0.1176 tan(−0.288Y − 1.285) (8) model points: L[AU ] = 0.631 − 0.1176 1.285) (8) Finally, we include the tan(−0.288Y effect of MFR−cross-sectional elongation in the non-radial direction. Magnetic clouds at 1 Finally, we include the effect of MFR cross-sectional elon-AU are known be highly distortedMagnetic from theclouds circular gation in theto non-radial direction. at 1 crossAU section assumed by the force-free approximation. Even if are known to be highly distorted from the circular crossa flux rope has abycircular cross-section near the Sun, will section assumed the force-free approximation. Evenit if become elongated in the non-radial direction by maintaining a flux rope has a circular cross-section near the Sun, it will a constant angularinwidth as it travels to 1 AU Newkirk become elongated the non-radial direction by (e.g., maintaining et al., 1981; McComas et al., 1988; Riley and Crooker, 2004; a constant angular width as it travels to 1 AU (e.g., Newkirk Owens, 2006). While it is difficult to analytically incorpoet al., 1981; McComas et al., 1988; Riley and Crooker, 2004; rate this2006). effect While into theit flux rope model presentedincorpohere, the Owens, is difficult to analytically increase in field-line can be approximated by considrate this effect into thelength flux rope model presented here, the ering theinincrease path length the flux cross increase field-lineinlength can be around approximated byrope considering the The increase pathinlength aroundpanel the flux rope cross section. solidinlines the middle of Figure 2 repsection. The solid lines in the middle of Fig. rep-0.6 resent model field non-elongated field panel lines for Y =20.3, resent model field non-elongated field lines for Y =0.3, 0.6 and 0.9 for a force-free flux rope with its axis at 1 AU, which and 0.9 for a force-free flux rope with its axis at 1 AU, which has traveled from the Sun at VCR = 400km/s and undergone has traveledatfrom at VCR =400 km/s and the undergone expansion VEXthe=Sun 100km/s. Thus at 1 AU, flux rope expansion at V =100 km/s. Thus at 1 AU, the flux rope EX of 2VEX AU/VCR . The dashed has a radial width lines rephas a radial width of 2V AU/V . The dashed lines rep-the EX CR for a flux rope with resent the equivalent cross-section resent the equivalentspeeds cross-section for a radial flux rope with same characteristic and, hence, width at 1theAU same characteristic speeds and, hence, radial width at AU as the force-free example but for a MFR which has1underas the force-free example but for a MFR which has undergone the kinematic distortion expected from radial propagagone the kinematic expected frominradial propagation (Owens et al.,distortion 2006). The increase field-line length et al., 2006). The increase in field-line length tion (Owens per turn of the magnetic field about the axis is found to be per turn of the magnetic field about the axis is found to be ∼ 1.7Y . This correction is applied to circular cross section estimates of field line length to approximate the effect Ann. Geophys., 27, 4057–4067, 2009

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Owens et al.: Suprathermal electron signatures of flux ropes

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10

Field line length [AU]

8

6

4

2

0

0

0.2

0.4

0.6

0.8

1

Distance from flux rope axis [r/r ] 0

Fig. 2. The left panel shows a snapshot of the model magnetic flux rope. A heliocentric distance of 1 AU is shown as the black dotted curve, while the Sun is represented by a solid black circle. Only the half of the flux rope which provides the shortest magnetic connection between the Sun and 1 AU is shown. Field lines at Y =0, 0.3, 0.6 and 0.9 are shown by black, blue, green and red lines, respectively. Solid lines in the center panel show a cross-section of the flux rope at 1 AU, while the dashed lines show how the cross-section is modified by kinematic Fig. 2.distortion. The left panel shows a snapshot the model rope. A1-AU heliocentric distance of 1 AU shownfrom as the dotted curve, The right panel shows theoflength of themagnetic field linesflux connecting to the Sun as a function of is distance theblack flux rope axis, while with the Sun represented a solid ablack circle. Only the half of the flux rope which provides the shortest magnetic connection between solidis(dashed) lines by indicating flux rope with a circular (kinematically-distorted) cross section.

the Sun and 1 AU is shown. Field lines at Y = 0, 0.3, 0.6 and 0.9 are shown by black, blue, green and red lines, respectively. Solid lines in the center panel show a cross-section of thetoflux rope at 1 AU, while the lar dashed show how the cross-section by kinematic ∼1.7Y . This correction is applied circular cross section windlines speed experienced by electronsisismodified held constant at distortion. The right panel shows the to length of the fieldthe lines connecting 1-AU to theWe Sun as a function of distance fluxgeomrope axis, estimates of field line length approximate effect of 400 km/s). choose not to use the exactfrom MFRthefield with solid (dashed) lines indicatingshown a flux rope a circular (kinematically-distorted) cross cross-sectional elongation, as thewith dashed line in the etry outlined in the section. previous section, as it would require exright-hand panel of Fig. 2. The best fit is given by: tremely high spatial and temporal resolution due to the large gradients in the magnetic field direction, making it compuL[AU ] = 1.07elongation, − 0.20 tan(−0.288Y (9) commonly-used suprathermal energy band forincharof cross-sectional shown as − the1.285) dashed line in the tationally prohibitive. Note thatelectron the electron model used acterizing the strahl (e.g., et al.,effects: 2008). Changright-hand panel of Figure 2. The best fit is given by: this study only accounts forAnderson the two major ing magnetic field strength, which adiabatically focuses elec3 Suprathermal electron evolution The model field-line length is adjusted by over- or underL[AU ] = 1.07 − 0.20 tan(−0.288Y − 1.285) (9) trons, and time of flight, which allows greater pitch-angle winding a Parker Spiral magnetic field (though the bulk solar The model of Owens et al. (2008) is used to determine the exscattering to occur. The orientation of the field does not have wind speed experienced by electrons is held constant pected strahl width for a given pitch-angle scattering rate and a direct effect, other than directing electrons into regions at of 400 3 Suprathermal electron evolution km/s). We choose not to use the exact MFR field geomefield-line length. This numerical scheme iteratively solves different field strength. Thus while the over/under-wound try outlined the will previous Section, it wouldadiabatic require exelectron heliocentric distance and pitch-angle, allowing for Parker spiralinfield not capture theasrepeated The model of Owens et al. (2008) is used to determine the exmovement along the magnetic field direction and convectremely and of temporal resolution the large focusinghigh and spatial defocusing electrons traversingdue thetohelical pected strahl width for a given pitch-angle scattering rate and tion with the bulk solar wind motion. Electrons undergo the gradients in theofmagnetic field direction, compumagnetic field a flux rope, it will capturemaking the net itpitchfield-line length.effects Thisofnumerical solves competing adiabatic scheme focusing iteratively from conservation angle focusing and the net amount tationally prohibitive. Note that of thescattering electronexperienced model used in electron heliocentric distance and pitch-angle, allowing of magnetic moment and pitch-angle scattering towardfor an by the electrons. this study only accounts for the two major effects: Changmovement along the magnetic field direction and convecisotropic distribution. The radial evolution of the supratherscattering is performed in an ad-hocfocuses manner,elecingPitch-angle magnetic field strength, which adiabatically tion with the bulkstrahl solar width wind in motion. the mal electron the fastElectrons solar windundergo can be well by Gaussian broadening the PA distribution at each time trons, and time of flight, which allows greater pitch-angle competing effects adiabatic focusing from conservation matched by thisofscheme (Owens et al., 2008). step, pushing the distribution toward isotropy. A broadenscattering to occur. The orientation of the field does not have of magnetic toward an In thismoment study weand use apitch-angle grid of 500scattering cells in electron pitchfactor of σ =0.0014 applied each second was found to aing direct effect, other than directing electrons into regions of angledistribution. (P A) space, The equally spaced in cos PofA.theGrid cells are isotropic radial evolution supratherbest match the observed strahl width in the fast solar wind different field strength. Thus while the over/under-wound spaced bystrahl 0.01 AU in heliocentric Although are (Hammond et al., 1996; Owens et al., 2008). In this study, mal electron width in the fast distance. solar wind can bewe well Parker spiral field willare notused: capture the solar repeated adiabatic interested strahl widths at et 1 AU, the simulation domain three levels of scattering The fast wind level, matched by thisinscheme (Owens al., 2008). focusing and defocusing of electrons traversing the helical extends out to 2 AU to capture the contribution of electrons taken as “medium” scattering, and “low” and “high” levels In this study we use a grid of 500 cells in electron pitch◦ and thus magnetic field of a flux rope, it will capture the net pitchwhich are scattered to pitch angles greater than 90 of scattering at half and double this value, respectively. The angle (P A) space, equally spaced in cos P A. Grid cells are angle focusing and the net amount of scattering experienced propagate sunward. A time step of 100 s and a solar wind model width at 1 AU is then computed from the model PA spaced by 0.01 AU in heliocentric distance. Although we are speed (VSW ) of 400 km/s are used. Electron energy is set at by the electrons. distribution using the same fitting procedure as Hammond interested in strahl widths at 1 AU, the simulation domain 272 eV, as this is the center value of the most commonlyet al. (1996) and Owens et al. (2008). Suprathermal electron Pitch-angle scattering is performed in an ad-hoc manner, extends to 2 AU to electron capture energy the contribution of electrons usedout suprathermal band for characterizing pitch-angle distributions are fit with the following functional ◦ by Gaussian broadening the PA distribution at each time step, whichthe arestrahl scattered to pitch angles greater than 90 and thus (e.g., Anderson et al., 2008). form: pushing the distribution toward isotropy. A broadening facpropagate A time step isofadjusted 100 seconds a soThesunward. model field-line length by over-and or underlar wind speed (VSW Spiral ) of 400 km/s are Electron tor of σ = 0.0014 applied each second was found to best winding a Parker magnetic fieldused. (though the bulkenso-

ergy is set at 272eV, as this is the center value of the most Ann. Geophys., 27, 4057–4067, 2009

match the observed strahl width in the fast solar wind (Hamwww.ann-geophys.net/27/4057/2009/



length, the maximum time of flight of an anti-sunward propagating electron to a 1−AU observer will be 1 AU/VSW .

110 100

Strahl width [degrees]

90

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σ = 0.0028: FWHM = 103 − 54.2 exp (−0.44 L + 0.28)

80

4

Model time series

We now combine the MFR and electron scattering models to produce the expected suprathermal electron time series at σ = 0.0014: 60 1 AU. The first step is to generate field-line lengths connectFWHM = 74.6 − 40.3 exp (−0.30 L + 0.14) ing an observer at 1 AU to the Sun as a magnetic cloud prop50 agates out through the heliosphere. As the expansion speed 40 σ = 0.0007: of magnetic clouds is often a significant fraction of the cruise FWHM = 50.8 − 22.0 exp (−0.32 L + 0.34) speed (Owens et al., 2005), we build up a true time series of 30 the model parameters by time evolving past a fixed point at 20 1 AU rather than take a radial slice through a snapshot of the 0 5 10 15 Field line length [AU] MFR model. For this initial time series, the observer is assumed to pass directly through the axis of the flux rope (i.e., through Y =0), Fig. 3. The of varying scattering rate and field-line length of varying scattering rate effect and field-line length on the strahl FWHM at 1 AU. Ason expected, increased of flight butthethis is latertime relaxed when comparing to observations. A strahl FWHM at L 1 AU. Ashowever, expected,thethe increased time of flight lines results inthe a broader strahl. As → ∞, strahl width asymptotes well before isotropy is achieved. This cruise (expansion) speed of 400 (100) km/s is used. The top e of flight of the electrons, Sunresults to the observer, has astrahl. maximum value ofhow1AU/VSW due to the convection of the along longerfrom fieldthe lines in a broader As L→∞, panel of Fig. 4 shows the resulting time series of the magwith the bulk ever, solar the wind. strahl width asymptotes well before isotropy is achieved. netic field line length in the flux rope connecting the 1-AU This is because the time of flight of the electrons, from the Sun to observer to the Sun, with solid (dashed) lines representing the observer, has a maximum value of 1 AU/VSW due to the conthiswind. magnetic cloud compared ambient condi-(kinematically distorted) flux rope. ns a circularto cross-section vection of the magnetic field line withpressed the bulkinsolar tions. See, however, Event B. Note the logarithmic scale on the y-axis. The second panel # The magnetic field data for Events " es shows theCresult combining the field-line length with the B and are notofshown, −P A2 but Table 1 lists the ratios of the eigenvalues scattering code produce a time series of 272 eV electron in thetovariance j (P A) = K0 + K1 exp (10) K3 directions to quantify the quality pitch-angle of the flux rope signature. density at 1 AU. This type of plot is commonly we look for the expected suprathermal Also listed are model values of Y ,used the closest approach of the re of a magnetic flux rope in the ACE to display suprathermal electron observations. It shows (P A) Three is the magnetic differential electron flux at pitch angle are both spacecraft to the axis, which small. flux at a given energy level, normalized to the Comas et al.,where 1998) jdata. the electron K0 describes the selected electron density of top the halo and 3 de- 7 show A, B, and C PinA, Table 1, have been maximum The panels ofKFigure the 272and eV minimum suprather- densities at each time step, as a termines the width of the strahl (the full width at half maxind Richardson (2003) ICME list (available at mal electron pitch-angle distributions, normalized at each function of pitch angle and time. The strahl width exhibits √ mum is given by FWHM=2 (ln 2)K K1 for is the r.unh.edu/mag/ace/ACElists/ICMEtable.html) time3 ).step, themaximum three magneticacloud For each trend. The third panel shows the clear intervals. broad-narrow-broad ◦ electron density of the strahl aboveevent, K0 . we compute the flux in thecomputed orm and range of strahl widths. 0◦ and 180 strahls (i.e.,for high (red), medium (green) and strahl widths 3 shows the effect of varying scattering rate and Figure K1 in Equation 10) throughout low the (blue) magnetic cloud interws data from Event A. There is a clear rolevels of pitch-angle scattering, for circular crossfield-line indicative length onofthea magstrahl width gnetic field direction, val, at and1 AU. defineAstheexpected, dominant strahl as that with and the highest section (solid) kinematically-distorted (dashed) flux rope ◦ This is reflected in the ratios eigenflux. For Event the dominant strahl is The at 180 pitchpanel an- shows the strahl width normalized the increased timeofoftheflight along longer field linesAresults in models. bottom agnetic field variance listed in Tagle, with an are order magnitude electron thanin the event. This normalized width a broaderdirections strahl. The three levels of scattering fit of with an tohigher the mean strahlflux width os, typically exponential >4, indicatefunction, strong flux ropethe following any 0◦ strahl. We note, however, that the dominant strahl to give relations: is independent of the scattering rate and only a function of Bothmer and Schwenn, 1998)). Fitting the is not always as easy to define, particularly in events with −1 field-line length. = 0.0007[s : observed (11)signature. a strong counterstreaming For event A, there is 006) magneticσ cloud model to ]the The maximum change in strahl width expected through a ests the spacecraft passed close◦ )to=the clear − broadening FWHM( 51 axis − 22 expa [0.34 0.32LAUof ] the strahl near the center of the cloud 1FWHM, is cloud. a useful parameter for assessing whether spite the apparently near-perfect conditions, and evidence of counterstreamingMFR, near the rear of the σ = 0.0014[s −1 ] : or not the flux rope should be observable with nature of a dip in suprathermal electron strahl This intermingling of apparently open and closed fieldssignature is ◦ FWHM( ) = 75 − 40 exp − 0.30L [0.14 ] a given instrument: If 1FWHM is below the pitch-angle AU not uncommon within magnetic clouds (e.g., Crooker et al., ent. This conclusion would not change if al◦effect cannot be measured. Figure 5 shows −1 resolution, the 2008). The dominant strahl for Event B is at 0 pitch anoundaries were chosen as the strahl σ = 0.0028[s ] : observed as a A. function gle. It is much broader than the 1FWHM strahl in Event Finally,of the closest approach of the obore and after the period of magnetic field ro◦ FWHM( ) = 103 − 54 exp [0.28 − 0.44LAU ] ◦ er, not wider, than inside the event. Note, Event C has a very narrow strahl at 180 , close to,a but server to the axis of MFR (i.e., the minimum value of Y , theAs pitch-angle resolution often of thereferred standardtoSWEPAM the ambient where solar wind, strahl width islengthabove LAU the is the field-line in AU. L→∞, howas the “impact parameter”). The color code er than in theever, magnetic As the asymptotes fieldsuprathermal electron data,iswith intermittent the cloud. strahl width well before isotropy is the same counterstreamas in Fig. 4. Very few magnetic clouds are actuected to be shorter in theThis ambient solar wind throughout cloud. three events highlight the and thus the minimum value of Y achieved. is because the totaling radial velocitythe of an elec-Theseally encountered “on axis”, , pitch-angletron scattering mustby be V greatly suplarge event-to-event variability in the suprathermal electron sampled by the observer is normally >0. Although 1FWHM is given +V cos γ , where V is the electron SW k k speed along the magnetic field direction and γ is the angle drops with impact parameter, there is still significant variaof the field to the radial direction. The first term represents tion in the strahl width even when the observer passes far the propagation of magnetic field lines out from the Sun at (e.g., Y ∼0.5) from the axis of the flux rope, particularly for the bulk solar wind speed. Thus regardless of the field-line higher scattering rates. For extreme glancing encounters of 70

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Ann. Geophys., 27, 4057–4067, 2009

ns et al.: Suprathermal electron signatures of flux ropes M. J. Owens et al.: Suprathermal electron signatures of flux ropes 15 10 5 3 2 1

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Fig. 4. The model flux rope field-line lengths and expected suprathermal electron signatures. Solid (dashed) lines represent a circular cross-section (kinematically-distorted) flux rope. The top panel shows a time series of field line length connecting an observer to the Sun. Note flux the logarithmic scale on the y-axis. and The second panel suprathermal shows the normalized 272eVsignatures. electron pitch-angle whichlines exhibits a clear 4. The model rope field-line lengths expected electron Soliddensity, (dashed) represent a circul broad-narrow-broad trend through the flux rope. The third panel shows strahl FWHM for high (red), medium (green) and low (blue) levels section (kinematically-distorted) flux rope. The top panel shows a time series of field line length connecting an observer to the Su of pitch-angle scattering. The bottom panel shows the strahl width normalized to the mean width, in the same format.

the logarithmic scale on the y-axis. The second panel shows the normalized 272eV electron pitch-angle density, which exhibits a cle -narrow-broad trend through the flux rope. The third panel shows strahl FWHM for high (red), medium (green) and low (blue) leve flux ropes, The where the minimum intersected by an width observing 5 Observations ch-angle scattering. bottom panel Yshows the strahl normalized to the mean width, in the same format.

spacecraft is >0.5, the field rotation signature will be significantly weaker, and the event is unlikely to be classified as a 5.1 Case studies magnetic cloud. TheEvent SWEPAM instrument In thisλsection weMlook the suprathermal Start (McComas et al., 1998) Endon Y electron INT /λ IN for λ Mexpected AX /λINT the ACE spacecraft collects electron data in approximately signature of a magnetic flux rope in the ACE SWEPAM (Mc20/8/1998 UTSWEPAM 21/8/1998 2000 UT 23.4 0.12listed as A, 6◦ ×20◦ A angular bins. For the0600 standard suprather1998) data. Three3.75 magnetic clouds, Comas et al., mal electron set, the data is then into 9◦ resoluB data 4/3/1998 1300 UTbinned 6/3/1998 0900 UTB, and C in15.5 Table 1, have been4.13 selected from0.10 the Cane and tion in pitch-angle space. Figure 5 shows that under most cirRichardson (2003) ICME list (available at http://www.ssg.sr. C 28/10/2000 2100 UT 29/10/2000 2200 UT 3.15 7.03 0.27 cumstances the difference in strahl width across a flux rope unh.edu/mag/ace/ACElists/ICMEtable.html) for their classic should be more than twice this SWEPAM resolution angle form and range of strahl widths. 1. Start and endclearly timesobservable. of three examples of classic magnetic clouds selected from the Cane and Richardson (2003) ICME li and thus Figure 6 shows data from Event A. There is a clear rotation /λM IN and λM AX /λINT are the ratios of magnetic field variances the variance directions. Y isofthe closest flux approach of t in theinmagnetic field direction, indicative a magnetic ving spacecraft to the flux rope axis inferred from a flux rope model rope. fit. This is reflected in the ratios of the eigenvectors in the magnetic field variance directions listed in Table 1 (High ratios, typically >4, indicate strong flux rope signatures (e.g., Bothmer and Schwenn, 1998)). Fitting the Owens et al.

erties of magnetic clouds (see also Anderson et al., ). Ann. Geophys., 27, 4057–4067, 2009 e black lines in the middle panels of Figure 7 show the l width, computed from the observed pitch-angle distrins using Equation 10. Solid (dashed) colored lines show

in the same format. In all three magnetic clouds, the expecte imprint of flux rope geometry on the suprathermal electro www.ann-geophys.net/27/4057/2009/ is absent. 5.2 Statistical survey


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Table 1. Start and end times of three examples of classic magnetic clouds selected from the Cane and Richardson (2003) ICME list. λINT /λMIN and λMAX /λINT are the ratios of magnetic field variances in the variance directions. Y is the closest approach of the observing spacecraft to the flux rope axis inferred from a flux rope model fit. Event

Start

End

λINT /λMIN

λMAX /λINT

Y

A B C

20 Aug 1998 06:00 UT 4 Mar 1998 13:00 UT 28 Oct 2000 21:00 UT

21 Aug 1998 20:00 UT 6 Mar 1998 09:00 UT 29 Oct 2000 22:00 UT

23.4 15.5 3.15

3.75 4.13 7.03

0.12 0.10 0.27


Also listed are model values of Y , the closest approach of the spacecraft to the axis, which are both small. 40 The top panels of Fig. 7 show the 272 eV suprathermal 35 electron pitch-angle distributions, normalized at each time step, for the three magnetic cloud intervals. For each event, 30 we compute the flux in the 0◦ and 180◦ strahls (i.e., K1 in Eq. 10) throughout the magnetic cloud interval, and define 25 the dominant strahl as that with the highest flux. For Event 20 A the dominant strahl is at 180◦ pitch angle, with an order of magnitude higher electron flux than any 0◦ strahl. We note, 15 however, that the dominant strahl is not always as easy to 10 define, particularly in events with a strong counterstreaming Low scattering Medium scattering signature. For Event A, there is a clear broadening of the 5 High scattering strahl near the center of the cloud and evidence of counter0 streaming near the rear of the cloud. This intermingling of 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 apparently open and closed fields is not uncommon within Closest approach to axis [Y] magnetic clouds (e.g., Crooker et al., 2008). The dominant strahl for Event B is at 0◦ pitch angle. It is much broader ximum expectedFig. change in strahl width, a measure of how readily the flux rope signature should be observable, as a function 5. The maximum expected change in strahl width, a measure of than the strahl in Event A. Finally, Event C has a very narrow pproach of the observer to the axis of the event (i.e., the minimum value of Y , often referred to as the “impact parameter”). ◦ close to, but above the pitch-angle resolution how readily the flux rope signature should be observable, as a funcstrahlin at is the same as Figure 4. Although ∆FWHM drops off with impact parameter, there is significant variation the180 strahl ,width tion of the closest approach of the observer to the axis of the event observer passes far (e.g., Y ∼ 0.5) from the axis of the flux rope. of the standard SWEPAM suprathermal electron data, with (i.e., the minimum value of Y , often referred to as the “impact paintermittent counterstreaming throughout the cloud. These rameter”). The color code is the same as Fig. 4. Although 1FWHM three events highlight the large event-to-event variability in each event, the dominant strahl is determined narrows toward the axis andinthen drops off with impact parameter, there is significant variation the broadens again toward the the suprathermal electron properties of magnetic clouds (see ven magnetic cloud thethe strahl strahl boundaries, width even and when observeropposite passes edge. far (e.g., Y ∼0.5) from also Anderson et al., 2008). ing Equation 10. The left-hand panel of Figure We have combined an analytical magnetic flux rope model the axis of the flux rope. erposed epoch plot of the strahl width as a funcwith a numerical suprathermal electron The scattering to in the middle panels of Fig. 7 show the blackcode lines expressed as a fraction of the event’s duration. estimate this expected imprint of flux rope width, geometry on strahl computed from the observed pitch-angle distrilines show the model predictions in the same suprathermal electrons in magnetic clouds. The field-line butions using Eq. (10). Solid (dashed) colored lines show (2006) magnetic cloud model to the observed time series ure 4, assuming on-axis encounters of magnetic length is found to increase by more than an order of magthe model strahl widths for circular (kinematically-distorted) suggests the spacecraft passed close to the axis (Y =0.12). his view, which covers a wide range of strahl nitude from the axis to the edge of the flux rope. The ascross-section flux ropes using the inferred values of Y listed ommodate the Despite full range the of scattering constants, apparently near-perfect conditions, the expected sociated variation in strahl width at 1AU , however, is not d epoch plot shows little variation, preas extreme because convection field1.lines with Low, medium and high levels of pitch-angle scatin Table signature of a dipand inthe suprathermal electron strahl width isof magnetic pe signature does appearThis to beconclusion present. In would the ambient solar wind imposes a maximum time ofby the blue, green and red lines, respecteringelectron are shown not not present. not change if alternative right-hand panel shows the same strahl width flight of 1AU/V of field-line SW , independent tively. length. The bottom panels show the normalized strahl widths cloud boundaries were chosen as the strahl observed immeed to the mean strahl width within an event. In expected variation in strahl width is found to be dein the same format. In all three magnetic clouds, the expected diately of before and after theinperiod The of magnetic field rotation here is some evidence the predicted trend pendent on the level of scattering in the sense that magnetic of flux rope geometry on the suprathermal electrons is narrower, not wider, than inside the event. Note, however, ons, with an asymmetric dip in strahl width toclouds with broader strahls throughout imprint should exhibit a more er of magneticthat clouds. Theambient trend, however, is is absent. in the solar wind, the strahl width is generally pronounced flux rope imprint. If, however, the strahl width is than predictedbroader by the models. than in the magnetic cloud. As the normalised to field-line the averagelength strahl width observed in the event, flux rope signature independent of the Statistical scattering rate. is expected to be shorter in the the ambient solar windisthan in 5.2 survey the be fluxgreatly rope signature to be observable, the maximum the cloud, pitch-angle scatteringFor must suppressed change in strahl width through a flux rope, ∆F W HM , must ons in this magnetic cloud compared to ambient conditions. See, In this section we statistically survey magnetic cloud be above the pitch-angle resolution of the instrument used to however, Event B. suprathermal profiles. All the events classified as measure the suprathermal electron distribution. For the electron stannetic flux rope, the varying pitch of the helical magnetic clouds in the Cane and Richardson (2003) ICME The magnetic field data for Events B and C are not shown, dard ACE SWEPAM data set (McComas et al., 1998), this ans that their lengths vary substantially between ◦ cut-off point is 9 . Even for magnetic cloud encounters far 1 lists the ratios of the eigenvalues in the variance list observed between 1998 and 2007 (74 events) are conbut Table n observer. This, in turn, affects the supratherthe axis the flux rope, this signature should, prin- event, the dominant strahl is determined time of flight and, hence, the pitch-anglethe scatdirections to quantify qualityfrom of the fluxofrope signature. sidered. Forineach ∆ Strahl width [degrees]

45

ciple, be observable for a range of scattering rates. he strahl width observed as a flux rope convects observer is therefore expected to exhibit a charSuprathermal electron observations for three classic examation from a broad strahl at the outer edge that ples of magnetic clouds were examined. There was large www.ann-geophys.net/27/4057/2009/

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6. Event A magnetic cloud observedininAugust August1998. 1998.The Thepanels, panels,from from top top to to bottom eV electron Fig.Fig. 6. Event A:A: A magnetic cloud observed bottom are: are: The The272 272eV electronpitch-angle pitch-angledistribution, distribution, the magnetic field magnitude, the inand out-of-ecliptic magnetic field angles, the solar wind flow speed, the inand the magnetic field magnitude, the in- and out-of-ecliptic magnetic field angles, the solar wind flow speed, the in- andout-of-ecliptic out-of-eclipticsolar solar wind flow angles, proton densityand andproton protontemperature. temperature.The Theboundaries boundaries of of the the magnetic magnetic cloud wind flow angles, thethe proton density cloud are are shown shown by bythe thesolid solidvertical verticallines. lines.AA kinematically-distorted flux rope modelfitfittotothe theobserved observedmagnetic magneticfield field time time series series (not (not shown), shown), suggests kinematically-distorted flux rope model suggests the theaxis axisofofthe theflux fluxrope ropepassed passed within r/r0 =0.12 of ACE at the point of closest approach. The dominant strahl, at 180◦◦ pitch angle, remains ∼75◦◦width throughout the within r/r0 = 0.12 of ACE at the point of closest approach. The dominant strahl, at 180 pitch angle, remains ∼ 75 width throughout the magnetic cloud. Thus the expected suprathermal electron signature of a magnetic flux rope is not present. magnetic cloud. Thus the expected suprathermal electron signature of a magnetic flux rope is not present.

within the given magnetic cloud widths, boundaries, event-to-event variation in strahl but and nonetheofstrahl the widthexhibited is fit using (10). flux The rope left-hand panel of events the Eq. expected signature. WeFig. also8 shows a superposed epoch plotofof74 themagnetic strahl width as a funcperformed an statistical survey clouds. Altion ofthetime, expressedepoch as a fraction the event’s here duration. though superposed analysisof performed reThe colored the model predictions in the varisame moves much oflines the show information about event-to-event format as Fig. 4, assumingsome on-axis encounters of expected magnetic ability, there is nevertheless evidence of the clouds. In this view, which covers a wide range of strahl strahl width variation, though it is a much weaker signature widths to accommodate the full range of scattering constants, than the models predict. This aspect of the study clearly mersuperposed epoch plot shows little variation, and the preits the further, more detailed, investigation. dicted flux rope signature does not appear to be present. In Possible reasons why the observed strahl width variation is contrast, the right-hand panel shows the same strahl width weaker than predicted can be broadly categorized into unmet data normalized to the mean strahl width within an event. In assumptions about the magnetic field structure of magnetic this format, there is some evidence of the predicted trend in clouds and the suprathermal electron scattering. the observations, with an asymmetric dip in strahl width toAssuming first that the field-line has been accu-is ward the center of magnetic clouds.length The trend, however, rately determined, it is necessary to consider the assumpmuch weaker than predicted by the models. tions made in determining the associated strahl width at 1 AU. The model of Owens et al. (2008) assumes that all scattering undergone by suprathermal electrons occurs in pitch-

Ann. Geophys., 27, 4057–4067, 2009

6 Conclusions angle space, and electrons do not lose or gain energy. There is support for this assumption in the observed conservation of electrons scattered to pitch the halo at helical a given Inside a magnetic flux from rope, the the strahl varying of the energy (Maksimovic et al., 2005), but the postulated energy field lines means that their lengths vary substantially between loss by cross-field drift in the motional electric field has yet the Sun and an observer. This, in turn, affects the supratherto be evaluated [J. R. Jokipii and N. A. Schwadron, personal mal electron time of flight and, hence, the pitch-angle scatcommunication, 2008,width 2009]. We are assuming that tering time. The strahl observed as aalso flux rope convects there no systematic the scattering properties past ais1-AU observer isvariation therefore in expected to exhibit a characteristic variation from a broad strahlscattering at the outer that within a MFR by applying the same rateedge throughnarrows toward the axis and then broadensatagain toward out the structure. If scattering is enhanced the axis of a the flux opposite edge. toward the outer edge, it will act against the rope and reduces field-line length variation and reduce the flux rope signature We have combined an analytical magnetic flux rope model on suprathermal Thereelectron is no reason to expect with a numericalelectrons. suprathermal scattering code this to behavior, but we cannot imprint discountoftheflux possibility. estimate this expected rope geometry on suprathermal electrons in assumption magnetic clouds. Themade field-line The most fundamental we have about length is found to increase by more than an order mag-it the structure of a magnetic cloud is that, locally atofleast, nitude afrom axis to the edgefields of thethat fluxincrease rope. The asforms flux the rope with helical in pitch sociated variation in strahl width at 1 AU, however, is not from the straight central axis to the tightly wound edge. This as extreme because convection of magnetic field lines with www.ann-geophys.net/27/4057/2009/

Owens et al.: Suprathermal electron signatures of flux ropes M. J. Owens et al.: Suprathermal electron signatures of flux ropes 4065 Event B

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Fig. 7. The suprathermal electron properties inside the three magnetic cloud case studies. The top panels show the normalized pitch-angle Fig. 7. The suprathermal electron properties inside the three magnetic cloud case studies. The top panels show the normalized pitch-angle distribution within the clouds. The black lines in the middle panels show the widths of the dominant strahls, computed from a Gaussian fit in distribution within the clouds. The black lines in the middle panels show the widths of the dominant strahls, computed from a Gaussian fit in pitch-angle space, with the colored lines showing the expected strahl width variations for different flux rope encounters (in the same format pitch-angle space, with the colored lines showing the expected strahl width variations for different flux rope encounters (in the same format as Fig. 4). The bottom panels show the normalized strahl widths in the same format. as Figure 4). The bottom panels show the normalized strahl widths in the same format. 100 1.4 A second possibility is a systematic increase in adiabatic focusing 1.3 with distance from the magnetic cloud axis, counteracting the extra scattering time from increased field line 1.2 length. The peak magnetic field intensity is often located close 1.1 to the centre of a magnetic cloud, so if the foot point field strength back at the Sun is uniform, this suggests that 1 there 0.9 is a greater variation in field strength between the Sun and 1 AU close to the edges of the flux rope, and hence a 0.8 stronger focusing effect. Further observational analysis and 0.7 efforts are required to establish the significance of modelling 0 0.2 0.4 0.6 0.8 1 this effect. Fraction of cloud duration

Normalised strahl width


is the widely accepted explanation for the observed magnetic 90 field rotation and is thus unlikely to be an unmet assumption 80 weak flux rope imprint, however, there responsible for the has been recent speculation that a field rotation may not al70 ways indicate a flux rope structure (Jacobs et al., 2009). 60

Setting α equal to 2.408, which implicitly assumes the 50 flux rope edge to be occur where the field becomes entirely poloidal, also has40implications for the findings in this study. 30 is not so tightly wound, or the outer, If the flux rope field tightest-wound fields 0are removed by 0.2 0.4 magnetic 0.6 reconnection 0.8 1 Fraction of cloud with the ambient solar wind (Schmidt and duration Cargill, 2003), then the expected variation in field-line length, and hence Acknowledgements. Research at Imperial College London is strahl width, will be reduced. The fact that the field in the Fig. 8. A superposed epoch plot of the strahl widths in all 74 magnetic clouds catalogued CaneNC andisRichardson between 1998 and funded by STFCby (UK), funded by(2003) NSF grant ATM-0553397. maximum variance direction is often seen to rotate through 2007. Coloured lines show the model predictions in the same format asWe Fig. 4. In the right panel there is some evidence of the predicted ◦ have benefited from the availability of ACE magnetic field (PI: a full 180 , however, in Event A, argues in favor of our trend in the normalizedasstrahl width observations. C. Smith) and SWEPAM (PI: D. McComas) data. MO thanks assumption about α. Benoit Lavraud of CESR (Toulouse), for useful discussions.

Magnetic reconnection may be at least a partial explanasolar wind imposes a maximum electron time of For the flux rope signature to be observable, the maximum tionthe forambient the weak flux rope signature in suprathermal elecflight of 1 AU/VSW , independent of field-line length. change in strahl width through a flux rope, 1FWHM, must trons. Near the Sun reconnection is known to open up the be above the pitch-angle resolution of the instrument used to The expected variation in strahl width is found to be deReferences closed loops within magnetic clouds (Crooker and Webb, measure the suprathermal electron distribution. For the stanpendent on the level of scattering in the sense that magnetic 2006). This process will move the flux rope foot points about dard ACE B. SWEPAM data et T., al.,and 1998), this Anderson, R., Skoug, R. set M.,(McComas Steinberg, J. McComas, clouds with broader strahls throughout should exhibit a more at the photosphere but is unlikely to significantly affect the D. J.: point Comparison the Width and Intensity the Suprathermal cut-off is 9◦ . of Even for magnetic cloudofencounters far pronounced flux rope imprint. If, however, the strahl width is field-line length. Magnetic reconnection between different Electron Strahl in General Solar and ICME Wind., from the axis of the flux rope, thisWind signature should,Solar in prinnormalised to the average strahl width observed in the event, fluxthe tubes the magnetic cloud (Gosling et al., 2007), AGU Meeting for Abstracts, ciple, beFall observable a rangepp. of A1580+, scattering2008. rates. fluxwithin rope signature is independent of the scattering rate. would serveplot to of mix lines of different Fig. 8. however, A superposed epoch thefield strahl widths in all 74 length magnetic clouds catalogued by CaneR.:and 1998 and Bothmer, V. and Schwenn, TheRichardson structure and(2003) origin between of magnetic and possibly reduce electron signature. clouds4.inIn thethe solar wind, Ann.there Geophys., 16,evidence 1–24, 1998. 2007. Coloured lines show the thesuprathermal model predictions in the same format as Figure right panel is some of the predicted Ann. Geophys., 27, 4057–4067, 2009 trend in thewww.ann-geophys.net/27/4057/2009/ normalized strahl width observations.

4066


Suprathermal electron observations for three classic examples of magnetic clouds were examined. There was large event-to-event variation in strahl widths, but none of the events exhibited the expected flux rope signature. We also performed an statistical survey of 74 magnetic clouds. Although the superposed epoch analysis performed here removes much of the information about event-to-event variability, there is nevertheless some evidence of the expected strahl width variation, though it is a much weaker signature than the models predict. This aspect of the study clearly merits further, more detailed, investigation. Possible reasons why the observed strahl width variation is weaker than predicted can be broadly categorized into unmet assumptions about the magnetic field structure of magnetic clouds and the suprathermal electron scattering. Assuming first that the field-line length has been accurately determined, it is necessary to consider the assumptions made in determining the associated strahl width at 1 AU. The model of Owens et al. (2008) assumes that all scattering undergone by suprathermal electrons occurs in pitch-angle space, and electrons do not lose or gain energy. There is support for this assumption in the observed conservation of electrons scattered from the strahl to the halo at a given energy (Maksimovic et al., 2005), but the postulated energy loss by cross-field drift in the motional electric field has yet to be evaluated (J. R. Jokipii and N. A. Schwadron, personal communication, 2008, 2009). We are also assuming that there is no systematic variation in the scattering properties within a MFR by applying the same scattering rate throughout the structure. If scattering is enhanced at the axis of a flux rope and reduces toward the outer edge, it will act against the field-line length variation and reduce the flux rope signature on suprathermal electrons. There is no reason to expect this behavior, but we cannot discount the possibility. The most fundamental assumption we have made about the structure of a magnetic cloud is that, locally at least, it forms a flux rope with helical fields that increase in pitch from the straight central axis to the tightly wound edge. This is the widely accepted explanation for the observed magnetic field rotation and is thus unlikely to be an unmet assumption responsible for the weak flux rope imprint, however, there has been recent speculation that a field rotation may not always indicate a flux rope structure (Jacobs et al., 2009). Setting α equal to 2.408, which implicitly assumes the flux rope edge to be occur where the field becomes entirely poloidal, also has implications for the findings in this study. If the flux rope field is not so tightly wound, or the outer, tightest-wound fields are removed by magnetic reconnection with the ambient solar wind (Schmidt and Cargill, 2003), then the expected variation in field-line length, and hence strahl width, will be reduced. The fact that the field in the maximum variance direction is often seen to rotate through a full 180◦ , however, as in Event A, argues in favor of our assumption about α.

Ann. Geophys., 27, 4057–4067, 2009

Magnetic reconnection may be at least a partial explanation for the weak flux rope signature in suprathermal electrons. Near the Sun reconnection is known to open up the closed loops within magnetic clouds (Crooker and Webb, 2006). This process will move the flux rope foot points about at the photosphere but is unlikely to significantly affect the field-line length. Magnetic reconnection between different flux tubes within the magnetic cloud (Gosling et al., 2007), however, would serve to mix field lines of different length and possibly reduce the suprathermal electron signature. A second possibility is a systematic increase in adiabatic focusing with distance from the magnetic cloud axis, counteracting the extra scattering time from increased field line length. The peak magnetic field intensity is often located close to the centre of a magnetic cloud, so if the foot point field strength back at the Sun is uniform, this suggests that there is a greater variation in field strength between the Sun and 1 AU close to the edges of the flux rope, and hence a stronger focusing effect. Further observational analysis and modelling efforts are required to establish the significance of this effect. Acknowledgements. Research at Imperial College London is funded by STFC (UK), NC is funded by NSF grant ATM-0553397. We have benefited from the availability of ACE magnetic field (PI: C. Smith) and SWEPAM (PI: D. McComas) data. MO thanks Benoit Lavraud of CESR (Toulouse), for useful discussions. Editor in Chief W. Kofman thanks S. Kahler and another anonymous referee for their help in evaluating this paper.

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