North-south asymmetry of the location of the heliospheric current

sheet revisited

G. Erd}os1 and A. Balogh2

Received 3 July 2009; revised 9 September 2009; accepted 5 October 2009; published 27 January 2010.

[1] The possible latitudinal offset of the location of the heliospheric current sheet (HCS)is an important question, since it has impact on the understanding of various phenomenaincluding the solar dynamo and the modulation of cosmic rays. In the declining phaseof the previous, 22nd solar cycle, in 1993, a southward displacement of the HCS by 10�was proposed to explain the north-south asymmetry of energetic charged-particlefluxes measured by Ulysses. Other observations supported the north-south asymmetryas well, and it is now widely accepted by the scientific community that in 1993, the HCSwas displaced 10� southward. However, in reality, the Ulysses magnetic fieldmeasurements did not give direct evidence for such a large displacement of the HCS. Herewe revisit the question and extend our previous study for the declining phase of solar cycle23 as well. Careful analysis of the HCS crossings observed by Ulysses during the fastlatitude scans shows that a southward displacement of the HCS by 2�–3� is possible andconsistent with the data for cycles 22 and 23. The impact of the HCS location on thelatitudinal gradients of energetic particle fluxes is discussed.

Citation: Erd}os, G., and A. Balogh (2010), North-south asymmetry of the location of the heliospheric current sheet revisited,

J. Geophys. Res., 115, A01105, doi:10.1029/2009JA014620.

1. Introduction

[2] The primary scientific objective of the Ulysses spaceprobe, orbiting the Sun at high inclination angle with respectto the ecliptic, has been to make in situ observation of thevarious plasma, field, and particle parameters at differentheliographic latitudes [Wenzel et al., 1992]. Launched in1990, it has, to date, completed almost three orbits around theSun. The orbital period is 6.2 years, close to half a solaractivity cycle, well suited to observe the various states of theSun between activity levels at comparable epochs. Thecharacteristic properties of the heliosphere (solar wind andmagnetic field parameters) evolve in time, primarily on thescale of the solar cycle. The changes through the solar cycleare themselves a function of, primarily, the heliolatitude ofthe observations. The so-called fast latitude scan sectionsof the Ulysses trajectory that occurred around the perihelionof the orbit are of particular importance, to study heliosphericstructure as a function of heliolatitude, including any possiblenorth-south asymmetry of the heliosphere. During the fastlatitude scan the spacecraft travels from the South Pole to theNorth Pole in about a year; therefore, time variations asso-ciated with the solar cycle are expected to be minimal butmay still not be completely negligible in certain respects.[3] During the first fast latitude scan that occurred in the

declining phase of solar cycle 22, in 1994–1995, Ulysses

discovered a north-south asymmetry in the latitudinal gra-dient of the energetic particle fluxes [Simpson et al., 1996,Heber et al., 1996a, 1996b]. It was observed that the particleflux is roughly symmetric around a heliospheric latitudeabout 10� south rather than around the heliographic equator.The discovery has been interpreted as being due to alatitudinal offset of the heliospheric current sheet (HCS),by 10� to the south [Simpson et al., 1996]. Although adetailed examination of the Ulysses magnetic field measure-ments failed to prove such an offset of the HCS [Erd}os andBalogh, 1998], the idea that the heliosphere was asymmetric,based primarily on the observation of an offset in the sym-metry of the energetic particle gradients, has been widelyaccepted by the scientific community.[4] The possibility that the heliosphere has a north-south

asymmetry has attracted a considerable interest. Taking thesubject in a more general context, such an asymmetry shouldoriginate from an asymmetry of the boundaries, i.e., eitherfrom the inner boundary (solar origin) or from the outer one(effect of the interstellar interface). Both possibilities areinteresting. For the latter, the interstellar interface is clearlynot symmetric (motion of the local interstellar cloud, direc-tion of the interstellar magnetic field [see Pogorelov et al.,2009a]). That outer interface certainly influences the propa-gation of cosmic rays into the heliosphere, an effect that canbe seen even close to the Sun although much reduced bymodulation through the heliosphere. If the outer boundaryintroduced the asymmetry in the energetic particle intensitiesobserved as an asymmetric latitudinal gradient (or rather onethat is symmetric around a heliolatitude different from zero),then the asymmetry would not be seen in the solar wind andmagnetic field properties, as these are related to their regions

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, A01105, doi:10.1029/2009JA014620, 2010ClickHere

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1Department of Space Physics, KFKI Research Institute for Particle andNuclear Physics, Budapest, Hungary.

2International Space Science Institute, Bern, Switzerland.

Copyright 2010 by the American Geophysical Union.0148-0227/10/2009JA014620$09.00

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of origin in the solar atmosphere. However, any north-southasymmetry in the solar wind or magnetic field would there-fore suggest a solar origin, since a disturbance in the outerheliosphere cannot propagate to the inner heliosphere againstthe supersonic wind. There is, however, an effect that isrelated to the outer boundary that can influence the helio-sphere: this is the effect of interstellar pickup ions on the solarwind [Gloeckler and Geiss, 2001]. A deflection of theinterstellar hydrogen flow in the inner heliosphere by about4�–5� with respect to the essentially nondeflected neutralhelium flow was shown to exist by Lallement et al. [2005],although the effect of the pickup ions according to numericalsimulations may be quite small [Pogorelov et al., 2009b].[5] A solar origin of the north-south asymmetry of the

HCS may have a large impact on theoretical models of solarmagnetism, including dynamo and coronal models. A closelyrelated near-Sun observation, that of nonradial streamers,was discussed by Wang [1996] before the Ulysses observa-tions prompted a study of the possible causes of the asym-metry in the HCS. Coronal streamers are the near-Sunsignatures of the coronal magnetic neutral line, and therefore,the systematic observation of nonradial streamers implies thepossibility of a similar inclination of the HCS with respect tothe coronal equator. Wang [1996] explained the nonradialgeometry of the coronal streamers by the confinement ofcurrents into thin sheets and relatively strong quadrupoleand/or higher-order multipole terms in the photosphericmagnetic field. The two related phenomena observed in theheliospheric medium, the possible asymmetry in the magneticfields in the Northern and Southern hemispheres and the offsetof the HCS, may be due to different but also related phenom-ena in the Sun’s magnetic state around solar minimum.FollowingWang’s [1996] explanation for nonradial streamers,the asymmetry in the heliospheric magnetic field may beattributed to the evolution of the coronal magnetic quadrupoleterm. The offset, however, may be caused by an inclined‘‘fossil’’ dipole term [Bravo and Gonzales-Esparza, 2000].The possible presence of the latter field had been proposed byBravo and Stewart [1995] to explain the wavy behavior of theheliomagnetic neutral line in the potential field version of thesource surface models of the corona around solar minimum.Similar considerations concerning the solar and heliosphericasymmetry have been presented more recently by Mordvinov[2007]. A detailed assessment of the respective polarity areason the coronal source surface model based on magnetogramsobtained by the Wilcox Solar Observatory was carried out byZhao et al. [2005], who concluded that the asymmetry at thesource surface was consistent with the heliospheric results bySmith et al. [2000b].[6] Evidence for the asymmetry in the heliosphere and the

southward offset of the HCS have been interpreted jointly asevidence for a quadrupole moment and nonaxisymmetry inthe solar dynamo by Mursula and Hiltula [2004]. The tilt ofthe solar magnetic dipole near the 1996 solar minimum (alsocovered by the first Ulysses fast scan in heliolatitude) hasbeen examined byNorton et al. [2008], using observations bythe Solar and Heliospheric Observatory (SOHO) and KittPeak magnetograms. Their results are consistent with arelatively small (5�–10�) tilt of the HCS for that epoch. Itcan be envisaged that the asymmetry, as indeed the tilt of thesolar dipole, may change with the solar cycle as well or evenwith the 22-year magnetic cycle (the Hale cycle).

[7] The Ulysses discovery of the asymmetry in the particleflux stimulated research for asymmetries in the magneticfield and plasma parameters. Those efforts included theUlysses observation of the north-south asymmetry in thesolar wind flow velocity, density, and temperature [McComaset al., 2000]. This study has found that there was only a smalldifference in solar wind speeds between south and north butlarger differences in the mass flux; hence, the pressure of thesolar wind was found to be greater in the south than in thenorth around the solar minimum in 1996. However, despitethe apparently systematic differences in all the parameters, nostatistically satisfactory quantitative conclusion could bereached, given the variability of the parameters, concerningasymmetries in the solar wind parameters between south andnorth. It appears that larger differences were more likely dueto the evolving solar wind properties from the late decliningphase to solar minimum. Solar wind composition measure-ments on Ulysses and the assessment of the implied temper-atures of the northern and southern coronal holes have ledZhang et al. [2002] to conclude that there was a lastingasymmetry in the temperature and areas of the two coronalholes.[8] Using the Operating Missions as a Node on the

Internet (OMNI) magnetic field data set from 1964, whichcovers almost two 22-year Hale cycles,Mursula and Hiltula[2003] have shown a southward displacement of the averagelocation of the HCS by a few degrees at solar minima,independent of magnetic polarity (i.e., in the same directionin both even or odd cycles). Northward displacement of thestreamer belt at solar minimum of cycle 22 was observed byMursula et al. [2002]; this is also supported by the Ulyssesfirst fast latitude scan [Crooker et al., 1997].[9] As mentioned earlier, a southward displacement of the

HCS by Ulysses was discussed during the first fast latitudescan by Smith et al. [2000b]. In fact, the result, an apparentoffset of �10�, is largely backed only by in-ecliptic mag-netic field measurements by the Wind spacecraft near theEarth, following the interpretation of the cosmic ray latitu-dinal gradient observations in terms of an asymmetry of theheliosphere, as indicated by the HCS. The arguments infavor of the large latitudinal offset of the HCS assumed timevariations of the polar magnetic flux during Ulysses’s fastscan, which are not supported by direct observations in theUlysses data. While it appears that both solar and indirectheliospheric data (cosmic ray latitudinal gradients and themagnetic sector ratios) indicate an offset of the HCS, thesubject remains controversial because the extent to whichthese indicators have a unique explanation in the offset ofthe HCS is uncertain. We find it appropriate to revisit thequestion of the latitudinal offset of the HCS as measured byUlysses, partly because other studies have extended theindirect observations of an asymmetrical HCS into previoussolar cycles [Mursula and Hiltula, 2004; Mursula, 2007]and partly because now we have another two fast latitudescans by Ulysses, in 2001 and 2006, that provide extraopportunities to determine the latitudinal offsets and, inaddition, to make comparisons between cycles 22 and 23.

2. Method of Data Analysis

[10] During fast scans from about 45� south to 45� north,Ulysses travels with a very nearly constant latitudinal

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velocity of about 0.75�/d. This velocity is fast, consideringthat Ulysses therefore moves about 20� in heliolatitudeduring each solar rotation. On the other hand, the time takenby Ulysses from pole to pole is close to a year, during whichtime the solar conditions can evolve significantly. Never-theless, the Ulysses orbit provides a good compromise thatcovers well the celestial sphere, corotating with the Sun, witha reasonably fine latitudinal resolution.[11] From the solar wind velocity measured onboard, and

knowing the position of Ulysses, we can calculate thetheoretical Parker spiral of the magnetic field line intersect-ing the spacecraft. Projecting the measured magnetic fieldvector on the spiral gives a component that is pointing eitheraway from or toward the Sun along the Parker spiral. This istaken to be the measure of the polarity of the magnetic fieldat the location of Ulysses. On average, the magnetic fieldhas a well-defined positive, ‘‘away’’ polarity or a negative,‘‘toward’’ polarity for intervals of several days or even aweek or more, generating the characteristic two or fourmagnetic sector pattern that evolves from one solar rotationto the next [see Ness and Wilcox, 1964; Thomas and Smith,1980; Bruno and Bavassano, 1997]. When measured atheliolatitudes poleward of the excursion of the HCS, theobservations provide a uniform polarity that is the dominantpolarity corresponding to the polar coronal hole, north orsouth, respectively, around solar minimum.[12] Since we are interested in the solar origin of the

heliospheric magnetic field, it is customary to map theobserved quantities back to the Sun. This approach elimi-nates some relatively obvious variations connected to theorbital motion of Ulysses and offers a more direct compar-ison with solar/coronal models such as the source surfacepotential field model [see Wang and Sheeley, 1992, 1995;Hoeksema, 1995].[13] When mapping back the observed characteristic of

the magnetic field such as the magnetic polarity to thesurface of the Sun, the solar wind travel time from its sourceto the point of observation needs to be taken into account.

Normally, this is a simple procedure; radial expansion andinertial motion of the plasma are reasonably good andgenerally applicable approximations. The velocity of thesolar wind is available from Ulysses measurements (cour-tesy of D. McComas; see Bame et al. [1992]). This results ina heliospheric longitude of the plasma source at the Sun,which is generally a decreasing function of the time ofobservation at Ulysses. An example for the solar longitudeversus time of measurement function is shown in Figure 1,calculated from the position of Ulysses and from the solarwind velocity measured onboard for about a 2 month periodin 2002, from 28 July to 13 August. If the position ofUlysses were fixed and if the solar wind velocity werestationary, then the heliolongitude of the plasma sourcewould be a linear function of the time of observations atUlysses; the relationship is therefore represented by a straightline parallel to the dashed lines shown in Figure 1. The slopeof these lines is simply the equatorial angular velocity of theSun, as Ulysses, being in an inertial orbit around the Sun,moves at about the solar rotation angular velocity withrespect to the solar surface but in the opposite direction.However, as can be seen in Figure 1, there are significantdeviations from the straight line because of the orbital motionof Ulysses and because of variations in the solar windvelocity. The effect of the orbital motion is small, as statedabove. However, the radial velocity of the observer introdu-ces a Doppler-type shift of the rotation rate of the Sun, whichshould be carefully corrected when north-south asymmetriesare to be studied, because the radial velocity of Ulysses hasopposite signs at the two hemispheres.[14] Figure 1 shows that there are large deviations from

the equatorial rotation rate due to fast wind–slow windinteractions. When a fast wind stream follows a slow-windstream, a rarefaction region forms, and the correspondinglongitude of the plasma source decreases rapidly in time. Incontrast, when slow wind follows fast wind, the plasmasource remains close to the same longitude for a time interval,called a dwell [Nolte et al., 1977]. It is customary to analyzethe magnetic sectors by dividing the time series of themagnetic polarity in Carrington (or Bartels) rotation periods[see, e.g., Smith et al., 1986]. However, if we are interested toreconstruct the geometry of the current sheet, in particular toestablish its north-south displacement or tilt angle, then weneed to compare the longitudes that the opposite polaritysectors cover rather than comparing the times when they wereobserved. Figure 1 illustrates the danger of analyzing the databy the time of observations rather than by the longitude of theplasma source. The horizontal heavy lines (see the time scaleon the top of Figure 1) mark the time intervals when positivemagnetic polarity was observed, which covered 52% of thetotal time; that is, the dominant polarity seems positive.However, in reality, the dominant polarity was negative inthis particular case because the longitude of the footpoint ofthe magnetic field lines with positive polarity covered 46% ofthe total section only (see the vertical heavy lines at the right-hand scale). The uneven mapping of the time to longitude, asshown in Figure 1, is connected to variations in the solar windspeed. Because recurrent fast solar wind streams may becoupled with recurrent magnetic sectors in corotating inter-action regions over several solar rotations a persistent andsignificant bias may be introduced in the positive-negativepolarity ratios if the intervals are evaluated in terms of the

Figure 1. Heliographic longitude of the plasma sourceintersecting Ulysses between 28 July and 13 August 2002 asa function of the time of observations. The thick horizontallines at the top correspond to the time intervals of positivepolarities; the thick vertical lines on the right correspond tothe same intervals of positive polarities in solar longitude.The inset is a magnified image (not to scale) to illustrate themethod of interpolating algorithm of the dwells.

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times of observations rather than in the corresponding solarlongitude intervals.[15] There are extreme cases of dwells when the longi-

tude versus time function becomes nonmonotonic. This is anunphysical situation, since the fast plasma will not overtakethe slow one; therefore, the assumption of ballistic plasmatrajectories is no longer valid. This case needs a much moresophisticated treatment, which involves MHD modeling.Single spacecraft measurements do not provide the neces-sary details of the boundary conditions for such a calculation;therefore, we have used a simple interpolation algorithm inorder to avoid a multivalued function when mapping of thetime of measurement to solar longitude. The inset in Figure 1explains the algorithm, where first, the section of the multi-valued part of the function should be identified (see thearrows). Then the section is replaced by linear interpolation.This simple procedure, although not very precise, mimics thestream-stream interaction and resolves the unphysical aspectof the calculated dwells. At the interface, the fast wind willslow down, and the slowwind will be accelerated; this resultsin a qualitatively similar distortion of the function as thelinear interpolation used in these cases.

3. Magnetic Polarity in the Helioshpere:Ulysses Observations

[16] Equipped with all the necessary tools, we can con-struct the polarity of the heliospheric magnetic field at theSun as measured by Ulysses during fast latitude scans. InFigure 2, the color code gives the magnetic polarity, withred and blue referring to outward and inward sectors,respectively. Note that intermediate colors on this ‘‘rain-bow’’ scale, i.e., light blue, green, and yellow, are rare,backing the previous evidence that the measured magneticfield vectors follow the Parker field lines quite closely. Thethick and color-coded lines show the trajectory of Ulysses ina frame corotating with the Sun’s equatorial rate. Theposition of Ulysses is mapped back to the Sun; the slightdeviations from a ‘‘regular’’ spiraling line are due to themapping procedure as discussed above. Earlier, Forsyth et

al. [1996a] showed the three-dimensional map of themagnetic polarity observed during the first fast latitude scanin early 1995; this figure extends those observations to thesecond and third fast latitude scans. We can see that in 1995,corresponding to the declining phase of cycle 22, the north-ern polarity was positive; the southern polarity was neg-ative; and the two hemispheres were separated by amoderately inclined current sheet. In 2001, at solar maxi-mum, the inclination of the current sheet was large [Jones etal., 2003], and eventually, it flipped over at the time of themagnetic field reversal in 2000. In 2007, corresponding tothe declining phase of cycle 23, the current sheet was againless inclined, in a way similar to the observations during thefirst fast latitude scan, but the polarity was reversed.[17] The calculation of the magnetic polarity at fast

latitude scans, as shown in Figure 2, allows us to determinesolid angles that the positive and negative polarities coveron the source surface. If the average location of the HCS issymmetric with respect to the equator of the Sun, then thearea of the Northern and Southern hemispheres should besame. A more detailed test is the determination of thecumulative solid angle as follows [Erd}os and Balogh,1998]: Starting from the southern polar pass of Ulysses,we can integrate the step function, representing the magneticpolarity in equation (1a) by longitude and latitude along thetrajectory of Ulysses in the frame corotatingwith the Sunwithequatorial rotation rate (equation (1b)):

S l;Qð Þ ¼ �1 negative sector;þ1 positive sector;

�ð1aÞ

A Qð Þ ¼ZQ

S�pole

Z2p

0

S l0;Q0ð Þcos Q0ð Þdl0dQ0: ð1bÞ

This will provide a function of the time of observation andtherefore of q, which can be interpreted as the cumulative

Figure 2. Polarity of the magnetic field in the heliosphere, as observed by Ulysses during three fastlatitude scans in 1995, 2001, and 2007. Using solar wind velocity data measured aboard, the magneticpolarities were mapped back to the source surface of the Sun.

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solid angle at the source surface, taking into account thesign of the underlined magnetic polarity from the SouthPole to the latitude of Ulysses. The cumulative solid angleshould return to zero level by the end of the fast scan at thenorthern polar pass. If not, the reason is that the areas of thetwo magnetic polarities are not the same in the Northern andSouthern hemispheres. Since the total magnetic flux of theSun should be zero, the difference in the areas should becompensated by different average magnitude of Br on thesource surface. The measure of the difference in the areas isvery sensitive to a possible latitudinal offset of the currentsheet.[18] The heavy lines in Figure 3 show the cumulative area

function as defined above for the first and third fast latitudescans (Figures 3 (top) and 3 (bottom), respectively). If thecurrent sheet was flat and was coinciding with the equator,then the function would be ±2p at zero latitude, where thesign equals the magnetic polarity of the Southern Hemi-sphere. (More precisely, the value is somewhat less than 2pbecause Ulysses is not starting the fast latitude scan exactlyat the southern pole.) However, the current sheet was tiltedand warped; therefore, Ulysses crossed it several times,resulting in waves in the area function. The importantquestion is whether or not the lines return to zero level atthe northern pass.

[19] Inspecting Figure 3, we can establish that in both fastlatitude scans, the area function returned almost to zero atthe northern polar passes, but some deviations existed. Inorder to quantify the deviations, we have modeled the effectof the north-south offset of the current sheet. We assumeda neutral line at the source surface corresponding to a flatcurrent sheet, with its normal tilted by 30� away from thesolar rotation axis. Then, the north-south offset of the neu-tral line was introduced by distorting the flat current sheetinto a cone in 5� steps. This tilted and offset current sheet isrotated around the solar rotation axis, and the area functionis calculated along the orbit of Ulysses. The results areshown by the thin lines in Figure 3, where the labels markthe latitudinal offsets (cone angle) of the model currentsheet. We can see that for both fast scans in 1995 and 2007,a southern latitudinal offset of the current sheet by 2�–3� ispossible. However, a southern latitudinal offset by as largeas 10� seems inconsistent with our analysis, in agreementwith our earlier study for the 1995 epoch [Erd}os and Balogh,1998].[20] The number of magnetic field lines with positive

polarity should be strictly the same as that with negativepolarity. Therefore, any latitudinal offset of the current sheetshould be balanced with different averaged magnetic fieldstrength in the Northern and Southern hemispheres. Themagnetic field strength can be characterized by Br r

2, whichis the radial component of the field vector, normalized to1 AU. Table 1 show the normalized radial field averagesmeasured by Ulysses during the first and third fast latitudescans (cycles 22 and 23, respectively). BS is the southernmagnetic field averages, measured from 80�S to 40�S. BN isthe magnetic field averages for the Northern Hemisphere.We can see that for the declining phases of both sunspotcycles, the magnetic field was slightly stronger in theSouthern Hemisphere than in the Northern Hemisphere.The values of offsets in the HCS location are given thatare necessary to compensate the stronger southern field inorder to keep the positive and negative magnetic flux inbalance. This calculation assumes that we can extrapolatethe magnetic field strength measured at high latitude(greater than 40�, north or south) down to the currentsheet. It is remarkable that the latitudinal offset values ofthe current sheet, determined from the balance of themagnetic flux (offset values in Table 1), are consistentwith the offset values determined from the sector cross-ings of Ulysses (see Figure 3). One exemption is perhapsthat a larger offset was obtained from the flux balanceargument than from the cumulative area calculation forcycle 23, but the sign of the offset (i.e., to the south) wasconsistent in both cases.[21] Only the latitudinal offset during the first and third

fast latitude scans have been discussed so far. The secondfast latitude scan occurred during solar maximum condi-tions, in 2001. The observations coincided with the polarityreversal of the Sun [Jones et al., 2003]. As a consequence,the tilt of the current sheet was large, almost 90�, as we cansee in Figure 2 (middle). In such a case, we cannot speakabout the north-south displacement of the current sheet.However, the cumulative area function still can be deter-mined. Analysis has shown that during the second fastlatitude scan the area of the hemisphere with positivemagnetic polarity was slightly larger than the one with

Figure 3. Cumulative area function, as defined byequation (1). The thick line denotes the Ulysses observa-tions during the first and third fast latitude scan of Ulysses(blue and red mark negative and positive magnetic polarities,respectively). The thin lines denote model current sheet withlatitudinal offsets from 10�S to 10�N, in 5� steps.

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negative polarity. We could model the deviation with a fewdegree offset of the current sheet. However, time variationsassociated with the polarity reversal of the Sun, whichhappened during the time interval considered, make theinterpretation of the offset difficult.

4. Discussion

[22] The Ulysses magnetic field observations duringthe first and third fast latitude scans, corresponding to thedeclining phase of cycles 22 and 23, have shown that thesolid angles occupied by the positive and negative magneticpolarities on the solar wind source surface are almost thesame. The small difference can be reproduced with theassumption of a southward displacement of the heliosphericcurrent sheet by a few degrees. This latitudinal offset of thecurrent sheet is also supported by the magnetic field obser-vation of Ulysses at high latitude. According to that, strongermagnetic field was observed on the Southern Hemispherethan on the Northern Hemisphere. The argument is that themagnetic flux of the opposite polarities should be in balance;therefore, the north-south asymmetry of the magnetic fieldstrength requires a displacement of the current sheet. Notethat in both solar cycles analyzed, the displacement of thecurrent sheet was in the same direction (i.e., southward), inspite of the opposite magnetic field configurations betweenthe two adjacent solar cycles. The observations of Ulyssessupport the work of Mursula and Hiltula [2003], whichshowed the southward displacement of the heliosphericcurrent sheet by a few degrees through several solar cycles.[23] Ironically, the research of the north-south asymmetry

of the location of HCS was largely motivated by theasymmetry observed in the latitudinal gradient of energeticparticle fluxes. However, the observed displacement of theHCS is just a few degrees south, which does not give aconvincing explanation for the particle data. The problem isthat the apparent latitudinal asymmetry of the particle fluxdata is much more, about 10�, than that of the HCS. Aquestion, however, is as follows: What is the connectionbetween the latitudinal gradient of the particle flux and thelocation of the current sheet?[24] Answering the question needs the modeling of the

transport of energetic particles through the heliosphere.This is an extensively studied subject [see, e.g., Heber andPotgieter, 2008, and references therein]; here, we givesome arguments only explaining the main processes qualita-tively. Considering drift motion effects, positively chargedparticles, detected by Ulysses during cycle 22, entered theheliosphere at the poles. As they moved toward Ulysses, theyremained in the high-latitude regions, at least in the outerheliosphere. In the outer heliosphere, where most of themodulation is taking place, the observed particles did notcross the current sheet, which is limited to low latitudes at

solar minimum. Therefore, the position of the current sheetwas not likely to influence directly the flux of energeticprotons or ions, observed by Ulysses close to the minimum ofcycle 22. However, the offset of the HCS has an indirecteffect on the modulation of particles through the magnitudeof the magnetic field. As was discussed in the previousparagraph, the latitudinal offset of the HCS should becompensated by different radial component of the magneticfield in the Northern and Southern hemispheres. This wouldresult in a different scattering mean free path of the particlesin the two hemispheres, because of the difference in thegyroradius of ions. Note that according to most of the models,the scatteringmean free path of energetic particles scales withtheir gyroradius.[25] Simple considerations given above suggest that the

latitude of the average position of the HCS is not necessarilyidentical with the symmetry point of the latitudinal gradientof particle fluxes, as had been suggested earlier to explainparticle observations [see McKibben, 2001, and referencestherein]. This could explain why the latitudinal offset ofHCS (2�–3�S) and the symmetry point of particle flux(10�S) differ significantly. However, the offset of the HCSis quite small and makes it hard to develop models, resultingin a large latitudinal asymmetry in the particle flux. Earliercalculations used a latitudinal offset of the HCS as large as10�S, mostly inferring from models extrapolating the photo-spheric magnetic field observations to the source surface ofthe solar wind [Hoeksema, 1995]. We would like to pointout here that such a large offset of the current sheet isinconsistent with the Ulysses magnetic field observations.[26] In order to explain any north-south asymmetry of the

energetic particle fluxes, the relevant magnetic field obser-vation is the radial component of the field close to the polesrather than the location of the current sheet. Ulysses was theonly spacecraft to make measurements at the right placebut possibly at the wrong time. Ulysses passed through thesouthern and northern polar regions about a half year earlierand later, respectively, than when the particle flux observa-tion was carried out close to the equator. Ulysses did notmeasure a significant difference in radial component of themagnetic field at the poles [Forsyth et al., 1996a]. Smith etal. [2000a] have pointed out that time variation may beinvolved during the 1 year that elapsed between the twopolar passes, and therefore, the magnetic field could havebeen different at the southern pole than at the northern polewhile Ulysses was near the solar equator. This was sup-ported by magnetic field observations by the Wind space-craft, which obtained measurements at the right time but inthe wrong place, i.e., in the ecliptic rather than at highlatitude. Smith et al. [2000b] noticed the difference betweenthe radial magnetic field measured by Wind in positive andnegative magnetic sectors, and those values were extrapo-lated to high latitude (according to the magnetic cycle, thenegative and positive sectors were extrapolated to the south-ern and northern poles, respectively).[27] The question is, Which extrapolation is correct: the

extrapolation in time (for Ulysses observations) or the extrap-olation in heliographic latitude (for Wind observations)?Ulyssesmeasured a time variation of themagnetic flux [Smithand Balogh, 2008] but on a large time scale corresponding tothe 11 year solar cycle. Although variation on a shorter timescale cannot be totally excluded, the extrapolation in time

Table 1. Radial Component of the Magnetic Fielda

BS BN BS/BN Offset

Cycle 22 3.41 nT 3.05 nT 1.12 3.24�SCycle 23 2.61 nT 2.16 nT 1.21 5.45�S

aNormalized to 1 AU. Measured by Ulysses Between 40� and 80�latitude during the first and third fast latitude scans. Comparison of theSouthern and Northern hemispheres and the corresponding latitudinal offsetof the HCS, determined from the flux balance criteria.

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during the fast latitude scan appears to be correct. Thissuggests that the assumption of the significantly differentmagnetic field at the southern and northern poles whileUlysses crossed the equatorial region is not totally convinc-ing. As for the extrapolation in latitude, in the fast solar wind,Ulysses did not observe significant variations in the magneticflux by heliographic latitude [Forsyth et al., 1996a]; there-fore, the extrapolation by latitude also looks correct. Smith[2007] explained the latitudinal independence of the mag-netic flux by the superradial expansion of the solar wind closeto the Sun. The idea is that the pressure of the magnetic fieldfalls much more rapidly by radial distance from the Sun thanthat of the plasma. Therefore, in the region of a few solarradii, the magnetic pressure may dominate, resulting in non-radial plasma flow. An excess magnetic pressure at the highfield regions can divert the plasma flow, which finally equal-izes the magnetic flux at larger distances. This makes theextrapolation of the equatorial measurements by Wind up tothe poles plausible. However, there is an inconsistency inthis argument. If the nonradial solar wind expansion issufficiently effective to equalize the magnetic pressure at allheliographic latitudes, then the magnetic pressure equilib-rium should be applied to the two sides of the current sheet aswell. However, this is not supported by even the Windobservations, which showed different magnetic fluxes inthe opposite magnetic polarity sectors. Note that Ulyssesmeasured the latitudinal independence of the magnetic flux athigher heliographic latitudes close to solar minimum (in bothcycles 22 and 23), which corresponded to observations in thefast solar wind. In the slow solar wind, the magnetic flux hasmuch larger fluctuations in time, making it difficult to studyits latitudinal dependence.[28] The hemispherical particle flux asymmetry could

also be due to the asymmetric locations and areas of thepolar coronal holes (or, somewhat equivalently, to thestructure of the streamer belt) as proposed by Heber et al.[1998]. In addition, the overwinding of the heliosphericmagnetic field in one hemisphere [Forsyth et al., 1996b]was considered by Heber and Burger [1999] as a potentialalternative explanation. The consequences for the diffusiontensor due to the asymmetry of the heliospheric magneticfield with respect to the neutral line that would underlie theexplanation of asymmetric particle fluxes were examined byHattingh et al. [1997].[29] As a conclusion, magnetic field observations by

Ulysses did not give clear evidence and clear explanationfor the asymmetry of the latitudinal gradient of energeticparticles observed by Ulysses during the first fast latitudescan in 1995 in terms of a southward displacement of theheliospheric current sheet. One remark is that the reality ofthe observation in the latitudinal asymmetry of the particleflux might also be questioned as perhaps due to a temporalevolution suggested by Heber et al. [1998]. For the samereason as was argued by Smith et al. [2000b] that timevariation during the fast latitude scan could be involved in themagnetic field measurement, we may also consider that timevariation of similar extent in the particle flux, coupled withthe latitudinal motion of Ulysses, would result in spuriouslatitudinal asymmetry in the particle flux observations.[30] An interesting finding of the magnetic field obser-

vation of Ulysses is that the areas of positive and negative

polarity sectors on the solar wind source surface tend to beclosely equal. This can be explained as follows: at smallradial distances from the Sun, the solar wind flow may bediverted from the radial one by magnetic pressure, whichresults in a quasi-equal magnetic field line density at largerdistances. However, for both cycles 22 and 23, a slight butpersistent southward displacement of the current sheet by afew degrees and a corresponding slightly stronger magneticfield at the South Pole than at the North Pole is consistentwith the magnetic field observation of Ulysses. If furtherinvestigations confirm this small north-south asymmetry,the explanation would be a challenge for solar physicists.

[31] Acknowledgments. Part of this work was carried out while G.E.was a guest of the International Space Science Institute, Bern, Switzerland.The research was partly supported by Hungarian Science Fund OTKAK-62617.[32] Amitava Bhattacharjee thanks Bernd Heber and Nikolai Pogorelov

for their assistance in evaluating this paper.

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�����������������������A. Balogh, International Space Science Institute, Hallerstrasse 6, CH-3012

Bern, Switzerland.G. Erd}os, Department of Space Physics, KFKI Research Institute for

Particle and Nuclear Physics, PO Box 49, Budapest, H-1225 Hungary.(erdos@rmki.kfki.hu)

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