North-South Asymmetry of the Location of the Heliospheric Current Sheet Revisited G

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, A01105, doi:10.1029/2009JA014620, 2010 Click Here for Full Article

North-south asymmetry of the location of the heliospheric current sheet revisited G. Erdo}s1 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 phenomena including the solar dynamo and the modulation of cosmic rays. In the declining phase of 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-particle fluxes measured by Ulysses. Other observations supported the north-south asymmetry as well, and it is now widely accepted by the scientific community that in 1993, the HCS was displaced 10° southward. However, in reality, the Ulysses magnetic field measurements did not give direct evidence for such a large displacement of the HCS. Here we revisit the question and extend our previous study for the declining phase of solar cycle 23 as well. Careful analysis of the HCS crossings observed by Ulysses during the fast latitude scans shows that a southward displacement of the HCS by 2°–3° is possible and consistent with the data for cycles 22 and 23. The impact of the HCS location on the latitudinal gradients of energetic particle fluxes is discussed. Citation: Erdo}s, 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 discovered a north-south asymmetry in the latitudinal gradient of the energetic particle fluxes [Simpson et al., 1996, [2] The primary scientific objective of the Ulysses space Heber et al., 1996a, 1996b]. It was observed that the particle probe, orbiting the Sun at high inclination angle with respect flux is roughly symmetric around a heliospheric latitude to the ecliptic, has been to make in situ observation of the about 10° south rather than around the heliographic equator. various plasma, field, and particle parameters at different The discovery has been interpreted as being due to a heliographic latitudes [Wenzel et al., 1992]. Launched in latitudinal offset of the heliospheric current sheet (HCS), 1990, it has, to date, completed almost three orbits around the by 10° to the south [Simpson et al., 1996]. Although a Sun. The orbital period is 6.2 years, close to half a solar detailed examination of the Ulysses magnetic field measure- activity cycle, well suited to observe the various states of the ments failed to prove such an offset of the HCS [Erdo}s and Sun between activity levels at comparable epochs. The Balogh, 1998], the idea that the heliosphere was asymmetric, characteristic properties of the heliosphere (solar wind and based primarily on the observation of an offset in the sym- magnetic field parameters) evolve in time, primarily on the metry of the energetic particle gradients, has been widely scale of the solar cycle. The changes through the solar cycle accepted by the scientific community. are themselves a function of, primarily, the heliolatitude of [4] The possibility that the heliosphere has a north-south the observations. The so-called fast latitude scan sections asymmetry has attracted a considerable interest. Taking the of the Ulysses trajectory that occurred around the perihelion subject in a more general context, such an asymmetry should of the orbit are of particular importance, to study heliospheric originate from an asymmetry of the boundaries, i.e., either structure as a function of heliolatitude, including any possible from the inner boundary (solar origin) or from the outer one north-south asymmetry of the heliosphere. During the fast (effect of the interstellar interface). Both possibilities are latitude scan the spacecraft travels from the South Pole to the interesting. For the latter, the interstellar interface is clearly North Pole in about a year; therefore, time variations asso- not symmetric (motion of the local interstellar cloud, direc- ciated with the solar cycle are expected to be minimal but tion of the interstellar magnetic field [see Pogorelov et al., may still not be completely negligible in certain respects. 2009a]). That outer interface certainly influences the propa- [3] During the first fast latitude scan that occurred in the gation of cosmic rays into the heliosphere, an effect that can declining phase of solar cycle 22, in 1994–1995, Ulysses be seen even close to the Sun although much reduced by modulation through the heliosphere. If the outer boundary 1Department of Space Physics, KFKI Research Institute for Particle and introduced the asymmetry in the energetic particle intensities Nuclear Physics, Budapest, Hungary. observed as an asymmetric latitudinal gradient (or rather one 2International Space Science Institute, Bern, Switzerland. that is symmetric around a heliolatitude different from zero), then the asymmetry would not be seen in the solar wind and Copyright 2010 by the American Geophysical Union. magnetic field properties, as these are related to their regions 0148-0227/10/2009JA014620$09.00

A01105 1of8 A01105 ERDO} S AND BALOGH: NORTH-SOUTH ASYMMETRY OF HCS REVISITED A01105 of origin in the solar atmosphere. However, any north-south [7] The Ulysses discovery of the asymmetry in the particle asymmetry in the solar wind or magnetic field would there- flux stimulated research for asymmetries in the magnetic fore suggest a solar origin, since a disturbance in the outer field and plasma parameters. Those efforts included the heliosphere cannot propagate to the inner heliosphere against Ulysses observation of the north-south asymmetry in the the supersonic wind. There is, however, an effect that is solar wind flow velocity, density, and temperature [McComas related to the outer boundary that can influence the helio- et al., 2000]. This study has found that there was only a small sphere: this is the effect of interstellar pickup ions on the solar difference in solar wind speeds between south and north but wind [Gloeckler and Geiss, 2001]. A deflection of the larger differences in the mass flux; hence, the pressure of the interstellar hydrogen flow in the inner heliosphere by about solar wind was found to be greater in the south than in the 4°–5° with respect to the essentially nondeflected neutral north around the solar minimum in 1996. However, despite helium flow was shown to exist by Lallement et al. [2005], the apparently systematic differences in all the parameters, no although the effect of the pickup ions according to numerical statistically satisfactory quantitative conclusion could be simulations may be quite small [Pogorelov et al., 2009b]. reached, given the variability of the parameters, concerning [5] A solar origin of the north-south asymmetry of the asymmetries in the solar wind parameters between south and HCS may have a large impact on theoretical models of solar north. It appears that larger differences were more likely due magnetism, including dynamo and coronal models. A closely to the evolving solar wind properties from the late declining related near-Sun observation, that of nonradial streamers, phase to solar minimum. Solar wind composition measure- was discussed by Wang [1996] before the Ulysses observa- ments on Ulysses and the assessment of the implied temper- tions prompted a study of the possible causes of the asym- atures of the northern and southern coronal holes have led metry in the HCS. Coronal streamers are the near-Sun Zhang et al. [2002] to conclude that there was a lasting signatures of the coronal magnetic neutral line, and therefore, asymmetry in the temperature and areas of the two coronal the systematic observation of nonradial streamers implies the holes. possibility of a similar inclination of the HCS with respect to [8] Using the Operating Missions as a Node on the the coronal equator. Wang [1996] explained the nonradial Internet (OMNI) magnetic field data set from 1964, which geometry of the coronal streamers by the confinement of covers almost two 22-year Hale cycles, Mursula and Hiltula currents into thin sheets and relatively strong quadrupole [2003] have shown a southward displacement of the average and/or higher-order multipole terms in the photospheric location of the HCS by a few degrees at solar minima, magnetic field. The two related phenomena observed in the independent of magnetic polarity (i.e., in the same direction heliospheric medium, the possible asymmetry in the magnetic in both even or odd cycles). Northward displacement of the fields in the Northern and Southern hemispheres and the offset streamer belt at solar minimum of cycle 22 was observed by of the HCS, may be due to different but also related phenom- Mursula et al. [2002]; this is also supported by the Ulysses ena in the Sun’s magnetic state around solar minimum. first fast latitude scan [Crooker et al., 1997]. Following Wang’s [1996] explanation for nonradial streamers, [9] As mentioned earlier, a southward displacement of the the asymmetry in the heliospheric magnetic field may be HCS by Ulysses was discussed during the first fast latitude attributed to the evolution of the coronal magnetic quadrupole scan by Smith et al. [2000b]. In fact, the result, an apparent term. The offset, however, may be caused by an inclined offset of 10°, is largely backed only by in-ecliptic mag- ‘‘fossil’’ dipole term [Bravo and Gonzales-Esparza, 2000]. netic field measurements by the Wind spacecraft near the The possible presence of the latter field had been proposed by Earth, following the interpretation of the cosmic ray latitu- Bravo and Stewart [1995] to explain the wavy behavior of the dinal gradient observations in terms of an asymmetry of the heliomagnetic neutral line in the potential field version of the heliosphere, as indicated by the HCS. The arguments in source surface models of the corona around solar minimum. favor of the large latitudinal offset of the HCS assumed time Similar considerations concerning the solar and heliospheric variations of the polar magnetic flux during Ulysses’s fast asymmetry have been presented more recently by Mordvinov scan, which are not supported by direct observations in the [2007]. A detailed assessment of the respective polarity areas Ulysses data. While it appears that both solar and indirect on the coronal source surface model based on magnetograms heliospheric data (cosmic ray latitudinal gradients and the obtained by the Wilcox Solar Observatory was carried out by magnetic sector ratios) indicate an offset of the HCS, the Zhao et al. [2005], who concluded that the asymmetry at the subject remains controversial because the extent to which source surface was consistent with the heliospheric results by these indicators have a unique explanation in the offset of Smith et al. [2000b]. the HCS is uncertain. We find it appropriate to revisit the [6] Evidence for the asymmetry in the heliosphere and the question of the latitudinal offset of the HCS as measured by southward offset of the HCS have been interpreted jointly as Ulysses, partly because other studies have extended the evidence for a quadrupole moment and nonaxisymmetry in indirect observations of an asymmetrical HCS into previous the solar dynamo by Mursula and Hiltula [2004]. The tilt of solar cycles [Mursula and Hiltula, 2004; Mursula, 2007] the solar magnetic dipole near the 1996 solar minimum (also and partly because now we have another two fast latitude covered by the first Ulysses fast scan in heliolatitude) has scans by Ulysses, in 2001 and 2006, that provide extra been examined by Norton et al. [2008], using observations by opportunities to determine the latitudinal offsets and, in the Solar and Heliospheric Observatory (SOHO) and Kitt addition, to make comparisons between cycles 22 and 23. Peak magnetograms. Their results are consistent with a relatively small (5°–10°) tilt of the HCS for that epoch. It can be envisaged that the asymmetry, as indeed the tilt of the 2. Method of Data Analysis solar dipole, may change with the solar cycle as well or even [10] During fast scans from about 45° south to 45° north, with the 22-year magnetic cycle (the Hale cycle). Ulysses travels with a very nearly constant latitudinal

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Normally, this is a simple procedure; radial expansion and inertial motion of the plasma are reasonably good and generally applicable approximations. The velocity of the solar wind is available from Ulysses measurements (cour- tesy of D. McComas; see Bame et al. [1992]). This results in a heliospheric longitude of the plasma source at the Sun, which is generally a decreasing function of the time of observation at Ulysses. An example for the solar longitude versus time of measurement function is shown in Figure 1, calculated from the position of Ulysses and from the solar wind velocity measured onboard for about a 2 month period in 2002, from 28 July to 13 August. If the position of Ulysses were fixed and if the solar wind velocity were stationary, then the heliolongitude of the plasma source would be a linear function of the time of observations at Figure 1. Heliographic longitude of the plasma source Ulysses; the relationship is therefore represented by a straight intersecting Ulysses between 28 July and 13 August 2002 as line parallel to the dashed lines shown in Figure 1. The slope a function of the time of observations. The thick horizontal of these lines is simply the equatorial angular velocity of the lines at the top correspond to the time intervals of positive Sun, as Ulysses, being in an inertial orbit around the Sun, polarities; the thick vertical lines on the right correspond to moves at about the solar rotation angular velocity with the same intervals of positive polarities in solar longitude. respect to the solar surface but in the opposite direction. The inset is a magnified image (not to scale) to illustrate the However, as can be seen in Figure 1, there are significant method of interpolating algorithm of the dwells. deviations from the straight line because of the orbital motion of Ulysses and because of variations in the solar wind velocity of about 0.75°/d. This velocity is fast, considering velocity. The effect of the orbital motion is small, as stated that Ulysses therefore moves about 20° in heliolatitude above. However, the radial velocity of the observer introdu- during each solar rotation. On the other hand, the time taken ces a Doppler-type shift of the rotation rate of the Sun, which by Ulysses from pole to pole is close to a year, during which should be carefully corrected when north-south asymmetries time the solar conditions can evolve significantly. Never- are to be studied, because the radial velocity of Ulysses has theless, the Ulysses orbit provides a good compromise that opposite signs at the two hemispheres. covers well the celestial sphere, corotating with the Sun, with [14] Figure 1 shows that there are large deviations from a reasonably fine latitudinal resolution. the equatorial rotation rate due to fast wind–slow wind [11] From the solar wind velocity measured onboard, and interactions. When a fast wind stream follows a slow-wind knowing the position of Ulysses, we can calculate the stream, a rarefaction region forms, and the corresponding theoretical Parker spiral of the magnetic field line intersect- longitude of the plasma source decreases rapidly in time. In ing the spacecraft. Projecting the measured magnetic field contrast, when slow wind follows fast wind, the plasma vector on the spiral gives a component that is pointing either source remains close to the same longitude for a time interval, away from or toward the Sun along the Parker spiral. This is called a dwell [Nolte et al., 1977]. It is customary to analyze taken to be the measure of the polarity of the magnetic field the magnetic sectors by dividing the time series of the at the location of Ulysses. On average, the magnetic field magnetic polarity in Carrington (or Bartels) rotation periods has a well-defined positive, ‘‘away’’ polarity or a negative, [see, e.g., Smith et al., 1986]. However, if we are interested to ‘‘toward’’ polarity for intervals of several days or even a reconstruct the geometry of the current sheet, in particular to week or more, generating the characteristic two or four establish its north-south displacement or tilt angle, then we magnetic sector pattern that evolves from one solar rotation need to compare the longitudes that the opposite polarity to the next [see Ness and Wilcox, 1964; Thomas and Smith, sectors cover rather than comparing the times when they were 1980; Bruno and Bavassano, 1997]. When measured at observed. Figure 1 illustrates the danger of analyzing the data heliolatitudes poleward of the excursion of the HCS, the by the time of observations rather than by the longitude of the observations provide a uniform polarity that is the dominant plasma source. The horizontal heavy lines (see the time scale polarity corresponding to the polar coronal hole, north or on the top of Figure 1) mark the time intervals when positive south, respectively, around solar minimum. magnetic polarity was observed, which covered 52% of the [12] Since we are interested in the solar origin of the total time; that is, the dominant polarity seems positive. heliospheric magnetic field, it is customary to map the However, in reality, the dominant polarity was negative in observed quantities back to the Sun. This approach elimi- this particular case because the longitude of the footpoint of nates some relatively obvious variations connected to the the magnetic field lines with positive polarity covered 46% of orbital motion of Ulysses and offers a more direct compar- the total section only (see the vertical heavy lines at the right- ison with solar/coronal models such as the source surface hand scale). The uneven mapping of the time to longitude, as potential field model [see Wang and Sheeley, 1992, 1995; shown in Figure 1, is connected to variations in the solar wind Hoeksema, 1995]. speed. Because recurrent fast solar wind streams may be [13] When mapping back the observed characteristic of coupled with recurrent magnetic sectors in corotating inter- the magnetic field such as the magnetic polarity to the action regions over several solar rotations a persistent and surface of the Sun, the solar wind travel time from its source significant bias may be introduced in the positive-negative to the point of observation needs to be taken into account. polarity ratios if the intervals are evaluated in terms of the

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Figure 2. Polarity of the magnetic field in the heliosphere, as observed by Ulysses during three fast latitude scans in 1995, 2001, and 2007. Using solar wind velocity data measured aboard, the magnetic polarities were mapped back to the source surface of the Sun. times of observations rather than in the corresponding solar al. [1996a] showed the three-dimensional map of the longitude intervals. magnetic polarity observed during the first fast latitude scan [15] There are extreme cases of dwells when the longi- in early 1995; this figure extends those observations to the tude versus time function becomes nonmonotonic. This is an second and third fast latitude scans. We can see that in 1995, unphysical situation, since the fast plasma will not overtake corresponding to the declining phase of cycle 22, the north- the slow one; therefore, the assumption of ballistic plasma ern polarity was positive; the southern polarity was neg- trajectories is no longer valid. This case needs a much more ative; and the two hemispheres were separated by a sophisticated treatment, which involves MHD modeling. moderately inclined current sheet. In 2001, at solar maxi- Single spacecraft measurements do not provide the neces- mum, the inclination of the current sheet was large [Jones et sary details of the boundary conditions for such a calculation; al., 2003], and eventually, it flipped over at the time of the therefore, we have used a simple interpolation algorithm in magnetic field reversal in 2000. In 2007, corresponding to order to avoid a multivalued function when mapping of the the declining phase of cycle 23, the current sheet was again time of measurement to solar longitude. The inset in Figure 1 less inclined, in a way similar to the observations during the explains the algorithm, where first, the section of the multi- first fast latitude scan, but the polarity was reversed. valued part of the function should be identified (see the [17] The calculation of the magnetic polarity at fast arrows). Then the section is replaced by linear interpolation. latitude scans, as shown in Figure 2, allows us to determine This simple procedure, although not very precise, mimics the solid angles that the positive and negative polarities cover stream-stream interaction and resolves the unphysical aspect on the source surface. If the average location of the HCS is of the calculated dwells. At the interface, the fast wind will symmetric with respect to the equator of the Sun, then the slow down, and the slow wind will be accelerated; this results area of the Northern and Southern hemispheres should be in a qualitatively similar distortion of the function as the same. A more detailed test is the determination of the linear interpolation used in these cases. cumulative solid angle as follows [Erdo}s and Balogh, 1998]: Starting from the southern polar pass of Ulysses, 3. Magnetic Polarity in the Helioshpere: we can integrate the step function, representing the magnetic polarity in equation (1a) by longitude and latitude along the Ulysses Observations trajectory of Ulysses in the frame corotating with the Sun with [16] Equipped with all the necessary tools, we can con- equatorial rotation rate (equation (1b)): struct the polarity of the heliospheric magnetic field at the Sun as measured by Ulysses during fast latitude scans. In 1 negative sector; Figure 2, the color code gives the magnetic polarity, with SðÞ¼l; Q ð1aÞ red and blue referring to outward and inward sectors, þ1 positive sector; respectively. Note that intermediate colors on this ‘‘rain- bow’’ scale, i.e., light blue, green, and yellow, are rare, ZQ Z2p backing the previous evidence that the measured magnetic field vectors follow the Parker field lines quite closely. The AðÞ¼Q SðÞl0; Q0 cosðÞ Q0 dl0dQ0: ð1bÞ thick and color-coded lines show the trajectory of Ulysses in Spole 0 a frame corotating with the Sun’s equatorial rate. The position of Ulysses is mapped back to the Sun; the slight deviations from a ‘‘regular’’ spiraling line are due to the This will provide a function of the time of observation and mapping procedure as discussed above. Earlier, Forsyth et therefore of q, which can be interpreted as the cumulative

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[19] Inspecting Figure 3, we can establish that in both fast latitude scans, the area function returned almost to zero at the northern polar passes, but some deviations existed. In order to quantify the deviations, we have modeled the effect of the north-south offset of the current sheet. We assumed a neutral line at the source surface corresponding to a flat current sheet, with its normal tilted by 30° away from the solar rotation axis. Then, the north-south offset of the neutral line was introduced by distorting the flat current sheet into a cone in 5° steps. This tilted and offset current sheet is rotated around the solar rotation axis, and the area function is calculated along the orbit of Ulysses. The results are shown by the thin lines in Figure 3, where the labels mark the latitudinal offsets (cone angle) of the model current sheet. We can see that for both fast scans in 1995 and 2007, a southern latitudinal offset of the current sheet by 2°–3° is possible. However, a southern latitudinal offset by as large as 10° seems inconsistent with our analysis, in agreement with our earlier study for the 1995 epoch [Erdo}s and Balogh, 1998]. [20] The number of magnetic field lines with positive polarity should be strictly the same as that with negative polarity. Therefore, any latitudinal offset of the current sheet should be balanced with different averaged magnetic field strength in the Northern and Southern hemispheres. The 2 magnetic field strength can be characterized by Br r , which is the radial component of the field vector, normalized to 1 AU. Table 1 show the normalized radial field averages Figure 3. Cumulative area function, as defined by measured by Ulysses during the first and third fast latitude equation (1). The thick line denotes the Ulysses observa- scans (cycles 22 and 23, respectively). BS is the southern tions during the first and third fast latitude scan of Ulysses magnetic field averages, measured from 80°Sto40°S. BN is (blue and red mark negative and positive magnetic polarities, the magnetic field averages for the Northern Hemisphere. respectively). The thin lines denote model current sheet with We can see that for the declining phases of both sunspot latitudinal offsets from 10°Sto10°N, in 5° steps. cycles, the magnetic field was slightly stronger in the Southern Hemisphere than in the Northern Hemisphere. The values of offsets in the HCS location are given that are necessary to compensate the stronger southern field in solid angle at the source surface, taking into account the order to keep the positive and negative magnetic flux in sign of the underlined magnetic polarity from the South balance. This calculation assumes that we can extrapolate Pole to the latitude of Ulysses. The cumulative solid angle the magnetic field strength measured at high latitude should return to zero level by the end of the fast scan at the (greater than 40°, north or south) down to the current northern polar pass. If not, the reason is that the areas of the sheet. It is remarkable that the latitudinal offset values of two magnetic polarities are not the same in the Northern and the current sheet, determined from the balance of the Southern hemispheres. Since the total magnetic flux of the magnetic flux (offset values in Table 1), are consistent Sun should be zero, the difference in the areas should be with the offset values determined from the sector cross- compensated by different average magnitude of B on the r ings of Ulysses (see Figure 3). One exemption is perhaps source surface. The measure of the difference in the areas is that a larger offset was obtained from the flux balance very sensitive to a possible latitudinal offset of the current argument than from the cumulative area calculation for sheet. cycle 23, but the sign of the offset (i.e., to the south) was [18] The heavy lines in Figure 3 show the cumulative area consistent in both cases. function as defined above for the first and third fast latitude [21] Only the latitudinal offset during the first and third scans (Figures 3 (top) and 3 (bottom), respectively). If the fast latitude scans have been discussed so far. The second current sheet was flat and was coinciding with the equator, fast latitude scan occurred during solar maximum condi- then the function would be ±2p at zero latitude, where the tions, in 2001. The observations coincided with the polarity sign equals the magnetic polarity of the Southern Hemi- reversal of the Sun [Jones et al., 2003]. As a consequence, sphere. (More precisely, the value is somewhat less than 2p the tilt of the current sheet was large, almost 90°, as we can because Ulysses is not starting the fast latitude scan exactly see in Figure 2 (middle). In such a case, we cannot speak at the southern pole.) However, the current sheet was tilted about the north-south displacement of the current sheet. and warped; therefore, Ulysses crossed it several times, However, the cumulative area function still can be deter- resulting in waves in the area function. The important mined. Analysis has shown that during the second fast question is whether or not the lines return to zero level at latitude scan the area of the hemisphere with positive the northern pass. magnetic polarity was slightly larger than the one with

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a Table 1. Radial Component of the Magnetic Field solar minimum. Therefore, the position of the current sheet

BS BN BS/BN Offset was not likely to influence directly the flux of energetic Cycle 22 3.41 nT 3.05 nT 1.12 3.24°S protons or ions, observed by Ulysses close to the minimum of Cycle 23 2.61 nT 2.16 nT 1.21 5.45°S cycle 22. However, the offset of the HCS has an indirect aNormalized to 1 AU. Measured by Ulysses Between 40° and 80° effect on the modulation of particles through the magnitude latitude during the first and third fast latitude scans. Comparison of the of the magnetic field. As was discussed in the previous Southern and Northern hemispheres and the corresponding latitudinal offset paragraph, the latitudinal offset of the HCS should be of the HCS, determined from the flux balance criteria. compensated by different radial component of the magnetic field in the Northern and Southern hemispheres. This would negative polarity. We could model the deviation with a few result in a different scattering mean free path of the particles degree offset of the current sheet. However, time variations in the two hemispheres, because of the difference in the associated with the polarity reversal of the Sun, which gyroradius of ions. Note that according to most of the models, happened during the time interval considered, make the the scattering mean free path of energetic particles scales with interpretation of the offset difficult. their gyroradius. [25] Simple considerations given above suggest that the latitude of the average position of the HCS is not necessarily 4. Discussion identical with the symmetry point of the latitudinal gradient [22] The Ulysses magnetic field observations during of particle fluxes, as had been suggested earlier to explain the first and third fast latitude scans, corresponding to the particle observations [see McKibben, 2001, and references declining phase of cycles 22 and 23, have shown that the therein]. This could explain why the latitudinal offset of solid angles occupied by the positive and negative magnetic HCS (2°–3°S) and the symmetry point of particle flux polarities on the solar wind source surface are almost the (10°S) differ significantly. However, the offset of the HCS same. The small difference can be reproduced with the is quite small and makes it hard to develop models, resulting assumption of a southward displacement of the heliospheric in a large latitudinal asymmetry in the particle flux. Earlier current sheet by a few degrees. This latitudinal offset of the calculations used a latitudinal offset of the HCS as large as current sheet is also supported by the magnetic field obser- 10°S, mostly inferring from models extrapolating the photo- vation of Ulysses at high latitude. According to that, stronger spheric magnetic field observations to the source surface of magnetic field was observed on the Southern Hemisphere the solar wind [Hoeksema, 1995]. We would like to point than on the Northern Hemisphere. The argument is that the out here that such a large offset of the current sheet is magnetic flux of the opposite polarities should be in balance; inconsistent with the Ulysses magnetic field observations. therefore, the north-south asymmetry of the magnetic field [26] In order to explain any north-south asymmetry of the strength requires a displacement of the current sheet. Note energetic particle fluxes, the relevant magnetic field obser- that in both solar cycles analyzed, the displacement of the vation is the radial component of the field close to the poles current sheet was in the same direction (i.e., southward), in rather than the location of the current sheet. Ulysses was the spite of the opposite magnetic field configurations between only spacecraft to make measurements at the right place the two adjacent solar cycles. The observations of Ulysses but possibly at the wrong time. Ulysses passed through the support the work of Mursula and Hiltula [2003], which southern and northern polar regions about a half year earlier showed the southward displacement of the heliospheric and later, respectively, than when the particle flux observa- current sheet by a few degrees through several solar cycles. tion was carried out close to the equator. Ulysses did not [23] Ironically, the research of the north-south asymmetry measure a significant difference in radial component of the of the location of HCS was largely motivated by the magnetic field at the poles [Forsyth et al., 1996a]. Smith et asymmetry observed in the latitudinal gradient of energetic al. [2000a] have pointed out that time variation may be particle fluxes. However, the observed displacement of the involved during the 1 year that elapsed between the two HCS is just a few degrees south, which does not give a polar passes, and therefore, the magnetic field could have convincing explanation for the particle data. The problem is been different at the southern pole than at the northern pole that the apparent latitudinal asymmetry of the particle flux while Ulysses was near the solar equator. This was sup- data is much more, about 10°, than that of the HCS. A ported by magnetic field observations by the Wind space- question, however, is as follows: What is the connection craft, which obtained measurements at the right time but in between the latitudinal gradient of the particle flux and the the wrong place, i.e., in the ecliptic rather than at high location of the current sheet? latitude. Smith et al. [2000b] noticed the difference between [24] Answering the question needs the modeling of the the radial magnetic field measured by Wind in positive and transport of energetic particles through the heliosphere. negative magnetic sectors, and those values were extrapo- This is an extensively studied subject [see, e.g., Heber and lated to high latitude (according to the magnetic cycle, the Potgieter, 2008, and references therein]; here, we give negative and positive sectors were extrapolated to the south- some arguments only explaining the main processes qualita- ern and northern poles, respectively). tively. Considering drift motion effects, positively charged [27] The question is, Which extrapolation is correct: the particles, detected by Ulysses during cycle 22, entered the extrapolation in time (for Ulysses observations) or the extrap- heliosphere at the poles. As they moved toward Ulysses, they olation in heliographic latitude (for Wind observations)? remained in the high-latitude regions, at least in the outer Ulysses measured a time variation of the magnetic flux [Smith heliosphere. In the outer heliosphere, where most of the and Balogh, 2008] but on a large time scale corresponding to modulation is taking place, the observed particles did not the 11 year solar cycle. Although variation on a shorter time cross the current sheet, which is limited to low latitudes at scale cannot be totally excluded, the extrapolation in time

6of8 A01105 ERDO} S AND BALOGH: NORTH-SOUTH ASYMMETRY OF HCS REVISITED A01105 during the fast latitude scan appears to be correct. This polarity sectors on the solar wind source surface tend to be suggests that the assumption of the significantly different closely equal. This can be explained as follows: at small magnetic field at the southern and northern poles while radial distances from the Sun, the solar wind flow may be Ulysses crossed the equatorial region is not totally convinc- diverted from the radial one by magnetic pressure, which ing. As for the extrapolation in latitude, in the fast solar wind, results in a quasi-equal magnetic field line density at larger Ulysses did not observe significant variations in the magnetic distances. However, for both cycles 22 and 23, a slight but flux by heliographic latitude [Forsyth et al., 1996a]; there- persistent southward displacement of the current sheet by a fore, the extrapolation by latitude also looks correct. Smith few degrees and a corresponding slightly stronger magnetic [2007] explained the latitudinal independence of the mag- field at the South Pole than at the North Pole is consistent netic flux by the superradial expansion of the solar wind close with the magnetic field observation of Ulysses. If further to the Sun. The idea is that the pressure of the magnetic field investigations confirm this small north-south asymmetry, falls much more rapidly by radial distance from the Sun than the explanation would be a challenge for solar physicists. that of the plasma. Therefore, in the region of a few solar radii, the magnetic pressure may dominate, resulting in non- [31] Acknowledgments. Part of this work was carried out while G.E. radial plasma flow. An excess magnetic pressure at the high was a guest of the International Space Science Institute, Bern, Switzerland. The research was partly supported by Hungarian Science Fund OTKA field regions can divert the plasma flow, which finally equal- K-62617. izes the magnetic flux at larger distances. This makes the [32] Amitava Bhattacharjee thanks Bernd Heber and Nikolai Pogorelov extrapolation of the equatorial measurements by Wind up to for their assistance in evaluating this paper. the poles plausible. However, there is an inconsistency in this argument. If the nonradial solar wind expansion is References sufficiently effective to equalize the magnetic pressure at all Bame, S. J., D. J. McComas, B. L. Barraclough, J. L. Phillips, K. J. Sofaly, heliographic latitudes, then the magnetic pressure equilib- J. C. Chavez, B. E. Goldstein, and R. K. Sakurai (1992), The Ulysses rium should be applied to the two sides of the current sheet as solar wind plasma experiment, Astron. Astrophys. Suppl. Ser., 92, well. However, this is not supported by even the Wind 237–265. Bravo, S., and J.-A. 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Lazarus, J. L. Phillips, J. T. Steinberg, A. Szabo, R. P. its latitudinal dependence. Lepping, and E. J. Smith (1997), Coronal streamer belt asymmetries and [28] The hemispherical particle flux asymmetry could seasonal solar wind variations deduced from Wind and Ulysses data, also be due to the asymmetric locations and areas of the J. Geophys. Res., 102, 4673–4679, doi:10.1029/96JA03681. Erdo}s, G., and A. Balogh (1998), The symmetry of the heliospheric current polar coronal holes (or, somewhat equivalently, to the sheet as observed by Ulysses during the fast latitude scan, Geophys. Res. structure of the streamer belt) as proposed by Heber et al. Lett., 25, 245–248, doi:10.1029/97GL53699. [1998]. In addition, the overwinding of the heliospheric Forsyth, R. J., A. Balogh, T. S. Horbury, G. Erdo¨s, E. J. Smith, and M. E. 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