Interplanetary magnetic field polarities inferred from the north south cosmic ray anisotropy

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A2, 1069, doi: /2002ja009509, 2003 Interplanetary magnetic field polarities inferred from the north south cosmic ray anisotropy M. Laurenza and M. Storini IFSI-CNR, Rome, Italy G. Moreno Department of Physics, La Sapienza University, Rome, Italy Z. Fujii Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Japan Received 30 May 2002; revised 5 December 2002; accepted 12 December 2002; published 7 February [1] The interplanetary magnetic field sector polarity at the Earth s location can be inferred from ground measurements of the cosmic ray north-south anisotropy. We present here the results of a systematic comparison between inferred and directly measured polarities in the period from January 1971 through December The overall success rate of the prediction method is 72%, in rather good agreement with previous findings. On the other hand, our analysis shows for the first time the limits of the method and calls for warning in its use. In fact, it turns out that the inferred polarities are affected by a bias, which becomes more relevant around the sunspot minimum. Even though the bias cannot be removed, it is possible to select conditions, occurring for 30% of the time, under which the inferred polarities are very reliable (the success rate being 95%). INDEX TERMS: 2134 Interplanetary Physics: Interplanetary magnetic fields; 2104 Interplanetary Physics: Cosmic rays; 2162 Interplanetary Physics: Solar cycle variations (7536); 2114 Interplanetary Physics: Energetic particles, heliospheric (7514); KEYWORDS: interplanetary magnetic sector polarity, cosmic ray anisotropy, muon telescope data Citation: Laurenza, M., M. Storini, G. Moreno, and Z. Fujii, Interplanetary magnetic field polarities inferred from the north south cosmic ray anisotropy, J. Geophys. Res., 108(A2), 1069, doi: /2002ja009509, Introduction [2] It has been known for many years that the interplanetary magnetic field (IMF) sector polarity can be inferred from ground measurements of either the geomagnetic field at high latitudes or the north-south anisotropy of the cosmic ray (CR) flux. The first technique, which has been so far the most widely used, is based on the so-called Svalgaard- Mansurov effect [Svalgaard, 1968; Mansurov, 1969; Mansurov and Mansurova, 1970; Friis-Christensen et al., 1972], which states that the IMF sectors, when passing the Earth, produce systematic daily variations of the polar geomagnetic field. More precisely, the induced perturbations have different signatures, according to the IMF polarity: during a positive (away from the Sun) sector, the disturbance field is directed away from the Earth at both poles; during a negative (toward the Sun) sector, the disturbance field is directed toward the Earth at both poles. [3] Extensive studies of the long-term evolution of the solar sector structure have been accomplished in the past, using the geomagnetic technique [e.g., Svalgaard, 1972; Campbell and Matsushita, 1973; Svalgaard and Wilcox, Copyright 2003 by the American Geophysical Union /03/2002JA ; Wilcox and Scherrer, 1972, 1981; Moussas and Tritakis, 1982]. However, this method has been strongly criticized by several authors [Fougère, 1974, 1989; Russell and Rosemberg, 1974; Fougère and Russell, 1975; Russell et al., 1975]. A more reliable way of estimating the IMF sector polarities from geomagnetic activity has been recently discussed by Vennerstroem et al. [2001]. [4] On the other hand, besides the geomagnetic method, even the technique of inferring the IMF polarities from the north-south CR anisotropy deserves more attention. In fact, as we will show in Figure 1, satellites and space probes are far from monitoring continuously the interplanetary space. Therefore indirect estimates of the IMF polarity are expected to play a major role in future investigations of the interplanetary phenomena. [5] The CR method is based on the finding that the toward and away sectors of the IMF are associated with different characteristic variations of the directional measurements of the CR flux [Swinson, 1969]. In fact, on days when the IMF points away from the Sun, the CR flow is directed northward, whereas on days when the IMF points toward the Sun, the CR flow is directed southward at the Earth s location. This north-south (N-S) anisotropy of the CR flux may be derived from the difference (1) between the responses of northern and southern neutron monitors (see SSH 4-1

2 SSH 4-2 LAURENZA ET AL.: INTERPLANETARY MAGNETIC FIELD POLARITIES isotropic fluctuations. In addition, the observations are, in that case, performed by a single observatory, thus eliminating the uncertainties inherent to the comparison of data taken with different instruments. So far the technique of inferring the IMF polarity from the N-S CR anisotropy has been used in only few studies [e.g., Kondo et al., 1975; Mori et al., 1975, 1980; Mori and Nagashima, 1979]. On the other hand, the actual reliability of the method was not investigated in detail. [6] Our purpose here is to test the CR muon method using a large set of data. The comparison of the inferred IMF polarities with those derived from measures of spacecraft borne magnetometers points to a bias affecting the former. Even though this bias cannot be eliminated, we will single out conditions under which the method gives the most reliable results. This will allow us to use with greater confidence the inferred polarities in periods when direct measurements of the IMF are not available. Figure 1. (a) Yearly coverage of the direct IMF measurements supplied by NASA. (b) Percentages of days during which at least 18 hourly averages of the IMF measurements were available. Bercovitch [1970] and Iucci and Storini [1972] for early works) or (2) between northern and southern viewing muon telescopes at a single site [Nagashima et al., 1972]. The former method is less satisfactory because (1) the intensity of the CR nucleonic component undergoes larger isotropic fluctuations (of the order of 1%) which greatly perturb the small N-S anisotropy (0.1%) and (2) the comparison of measurements performed in two observatories in different places and using different instruments is subject to unavoidable uncertainties. The latter method, instead, is based on muon monitor records, which are related to higher primary CR rigidities, so that the observed fluxes undergo smaller 2. Data Set Used [7] Our analysis is based on two sets of data, taken in the period from January 1971 through December 1997: 1. Daily values of the IMF polarities derived from measurements carried out by a variety of spacecraft and made available as OMNI data by the NSSDC web site These polarities (which in the following will be referred to as measured polarities ) were obtained as follows. Each daily average of the IMF vector (B) was projected into the ecliptic and its angle (f) with the X axis of the GSE reference system was computed. The polarity was then defined to be positive (away from the Sun) if 90 < f < 180, negative (toward the Sun) if 270 < f < 360, and mixed in the other cases (i.e., if B pointed in sectors which were forbidden by the Parker spiral model). Measured polarities were available in 7649 out of the 9862 days considered in our analysis. Figure 1a gives the yearly coverage of the measurements. Note, however, that many daily polarities were derived from a limited number of hourly averages: this is apparent in Figure 1b which gives yearly percentages of days when at least 18 hours of measurements were available. 2. Daily values of the GG index, defined by Mori and Nagashima [1979] as GG ¼ ½ðI N I S ÞþðI N I E ÞŠ=2; where each term denotes a directional component of the CR muon flux having the central direction of its viewing cone pointing toward the zenith angle of 49 in the north (I N ), the south (I S ), and the east (I E ) directions, respectively. Data used to compute the GG indices were supplied by the multidirectional muon telescope at Nagoya (geographical latitude: N; geographical longitude: E; altitude: 77 m above sea level) [Sekido et al., 1975]. An average value (GG B ) of GG was computed over each Bartels rotation and it was then subtracted from the daily values. The differences (GG = GG GG B ) allow us to infer the IMF polarity. In fact, GG > 0 corresponds to a CR intensity in the Northern Hemisphere higher than in the Southern Hemisphere and hence to an IMF directed toward

3 LAURENZA ET AL.: INTERPLANETARY MAGNETIC FIELD POLARITIES SSH 4-3 the Sun (negative polarity); GG < 0 corresponds to a CR intensity in the Southern Hemisphere higher than in the Northern Hemisphere and hence to an IMF directed away from the Sun (positive polarity). Days with jggj < are taken as days with no definite polarity. The inferred polarities obtained in this way covered almost continuously the entire period of interest (9567 out of the 9862 days considered). Table 1. Percentage of Success (S) in Inferring the IMF Polarities From GG Values In Situ Data Gaps Not Exceeding Number of Days 15 hours % 12 hours % 9 hours % 6 hours % S 3. Preliminary Data Analysis [8] As a first step in our analysis, we selected in our data set only the days (7408 out of 9862) for which measured and inferred polarities were both available. The comparison between simultaneous data may lead to one of the following three situations, which we refer to as agreements, disagreements, and uncertainties, respectively. Agreements are cases when the measured and inferred polarities are consistent with each other (i.e., both are positive or both negative). Disagreements are cases when the measured and inferred polarities are inconsistent with each other (i.e., one is positive and the other is negative). Uncertainties are cases when a significant comparison cannot be accomplished because the measured and/or the inferred polarities are mixed. It turns out that out of the 7408 days considered, agreements were 4490, disagreements were 1735, and uncertainties were [9] We then define a success rate of the method (S) as the ratio between the number of agreements (A) and the total number of cases when the comparison was significant (i.e., the sum of the agreements and disagreements A + D). We got S = A/(A + D) = 72%. This value is in rough agreement with previous results of Mori et al. [1980] who, using a much shorter database ( ), obtained annual success rates ranging from 73% to 79%. We will discuss in section 6 the differences between the success rates of the two analyses. [10] On the other hand, the success rate of 72% resulting from our analysis is not large enough to ensure that the inferred IMF polarities be always correct. Our main purpose here is, in fact, to single out conditions under which the inference method can be applied with the greatest confidence. To pursue this objective, it is convenient to consider first the measured and the inferred polarities separately, in order to recognize the uncertainties affecting each set of data. The next two sections will deal with that issue. 4. Analysis of the Reliability of the Measured Polarities [11] The significance of the measured IMF polarities may be uncertain due to two different causes: 1. Gaps in the data. The satellites are not monitoring continuously the interplanetary space mainly because they spend, during each orbit, part of the time inside the Earth s bow shock or the magnetosphere. In fact, as shown in Figure 1b, many daily polarities were not computed from 24 hours of data and hence have a limited statistical significance. 2. Mixed polarities. As said in section 2, the polarities were assigned considering only the daily average of the IMF direction. Therefore fields, whose directions fluctuated randomly during a day, could have been averaged out, leading to a vector with an apparently well-defined polarity. [12] The occurrence of the above effects may be tested considering the hourly averages of the IMF from which daily polarities were computed. We used these data to select subsets of measured polarities, which should be more reliable. To do so, we discarded days with mixed polarities (i.e., with some hourly averages showing a polarity opposite to that of the daily average) and days having gaps exceeding given levels (15, 12, 9, and 6 hours, respectively). We repeated the analysis described in section 3 on each subset of data, obtaining the results summarized in Table 1. [13] We first note that data meeting the above criteria (given in the second column of Table 1) are few compared with the total (7408). However, this also proves the uncertainties affecting the measured polarities. In fact, only in as few as 5% of days a stable polarity was observed and measurements covered at least 6 hours. [14] It is also seen that the success rate of the inferring method steadily increases when only the most reliable measured polarities are considered. In particular, when the analysis is restricted to days with at least 18 hours of coherent polarity (last line in Table 1), S attains a value of 83%, which is substantially larger than that (72%) obtained considering the whole set of data. [15] We can then conclude that the inferring method is certainly more accurate than it appeared from past analysis. Nevertheless, its success rate (83%) is still well below 100%. Thus we now turn to consider the possible sources of errors affecting the inferred polarities. 5. Analysis of the Reliability of the Inferred Polarities [16] The procedure used to infer the IMF polarities from the GG indices has an obvious bias. During each Bartels rotation, the numbers of positive and negative values of GG tend to be equal. This is because GG values were computed subtracting from the single values of GG their 27 day average. As positive (negative) values of GG correspond to negative (positive) IMF polarities, the total amplitudes of the positive and negative sectors will also be approximately equal in each solar rotation. On the other hand, this should not always occur. In fact, during some parts of a solar cycle, the heliospheric neutral sheet may cut the ecliptic in such a way that the positive or the negative sectors have an amplitude larger than the sectors of the opposite polarity [Tritakis, 1984]. In that case, the inferred polarities are subject to errors. [17] The occurrence of the above effect may be tested comparing the histograms of the amplitudes of positive and negative IMF sectors during each Bartels rotation obtained

4 SSH 4-4 LAURENZA ET AL.: INTERPLANETARY MAGNETIC FIELD POLARITIES Figure 3. Time history of the measured (top) and inferred (bottom) IMF polarities during two Bartels rotations: 2219 (upper: from 25 January 1996 to 21 February 1996) and 1913 (lower: from 12 June 1973 to 8 July 1973). Figure 2. (top) Histograms of the total amplitude of the positive IMF sectors passing the Earth during each Bartels rotation, in the period from January 1971 to December Measured and inferred polarities are as indicated in the figure. Units are fraction of rotation. (bottom) Histograms, as in the upper panel, of the total amplitude of the negative IMF sectors. from the two data sets (see Figure 2). As one could have expected, the histograms of the inferred polarities are narrower than the others and peaked at 0.5 Bartels rotation (while those of the measured polarities show a plateau from 0.4 to 0.6 rotation). [18] The top panel of Figure 3 compares the measured and inferred polarities taken during a very peculiar Bartels rotation (from 25 January 1996 to 21 February 1996 during a minimum phase of the solar cycle). Spacecraft observations indicate that the negative sectors were covering almost the whole rotation, but this trend is absent in the inferred data. In this case, the failure of the inferring method is evident. However, one should keep in mind that the situation described in the figure is very unusual (no other similar rotations occurred during the period studied). In fact, in only 3% of the examined rotations one polarity is observed for over 70% of the time. The bias described above is intrinsic to the method used to derive the polarities. Nevertheless, its effects may drastically be reduced if one discards the GG values closer to zero, which most probably may lead to a wrong estimate of the IMF polarity. [19] We have thus built two new subsets of inferred polarities, removing each GG whose absolute value was smaller than a given threshold. The chosen thresholds were the standard error on the mean (s m ) and the standard deviation (s), both calculated for each 27-day data set. We found that 81% of the absolute values of GG were greater than s m, while 30% of them exceeded s. Performing the analysis described in section 3 on each subset of inferred polarities (and using all the measured polarities) leads to the results shown in Table 2. Table 2. Percentage of Success (S) in Inferring the IMF Polarities From GG Values With jggj > s m or s (See Text) jggj> Number Days S s m % s %

5 LAURENZA ET AL.: INTERPLANETARY MAGNETIC FIELD POLARITIES SSH 4-5 Table 3. Percentage of Success (S) in Inferring the IMF Polarities From GG Values During Different Solar Activity Phases a Solar Cycle Phase Number of Days Periods S S Minimum 1310 July 1975 June % 84% January 1985 December 1986 July 1995 June 1997 Increasing 959 July 1997 June % 89% January 1987 December 1988 July 1997 December 1997 Maximum 2093 January 1971 December % 89% July 1979 June 1982 January 1989 June 1992 Decreasing 1863 January 1973 June % 95% July 1982 December 1984 July 1992 June 1995 a The first value, in each phase of the cycle, refers to the analysis performed with all data; the second one refers to that performed using only days when jggj > s and the measured polarity was coherent for at least 15 hours. [20] As expected, the success rate of the method increases when the inferred polarities based on the smallest values of jggj are discarded. We note, in particular, that for jggj > s we get S = 86%, a value which is substantially larger than that (72%) obtained when all the inferred polarities were included in the analysis. 6. Analysis of the Solar Cycle Effects [21] It is known that the shape of the heliospheric neutral sheet changes during a solar cycle [Hoeksema, 1992]. In general, this surface cut the ecliptic plane in such a way that positive and negative sectors passing the Earth cover equal fractions of a solar rotation. This could not be true, however, around the sunspot minimum, when the neutral sheet is very close to the solar equator. In fact, in that case, depending on the position of the Earth (above or below the solar equator), sectors of a given polarity may become dominant because of the low inclination of the neutral sheet. This situation contributes also to the well known Rosemberg and Coleman effect [Rosemberg and Coleman, 1969]. [22] We can then expect the bias affecting the inferred polarities to be more relevant in the minimum than in other parts of the cycle. To test this guess, we separated all the available data in four sets, corresponding respectively to minimum, increasing, maximum and decreasing solar activity, respectively. Table 3 gives the time intervals we attributed to each phase of the cycle along with the corresponding values of the success rate of the method. It is seen that S attains its lowest value (66%) in the minimum phase of the cycle and its highest value (76%) in the decreasing phase when the IMF sectors are usually stable and the neutral sheet is more inclined with respect to the solar equator (conditions which should indeed ensure that positive and negative IMF sectors have near equal amplitudes). [23] The above finding also allows us to interpret the slight discrepancy, noted in section 3, among our results and those previously obtained by Mori et al. [1980]. In fact, the last analysis covered a period (from January 1971 through August 1975) of declining solar activity, during which the inferred polarities are expected to be more reliable. Thus the average success rate (75%) found by these authors is fully consistent with the value of 76% we obtained for the decreasing phase of the solar cycle. [24] If we then restrict the analysis to days when jggj > s and the measured polarities were coherent for at least 15 hours (conditions occurring in 1005 days in the period considered) the values of S given in the last column of Table 3 are obtained. It is seen that during the declining phase of the cycle the success rate of the method reaches the value of 95%. 7. Attempts to Improve the Reliability of the IMF Inferred Polarities [25] The procedure used to derive the IMF polarities from the GG values (see section 2) is not entirely satisfactory in two respects: 1. The choice of Bartels rotations to perform the GG averages is little justified at the beginning (or at the end) of each rotation, when one subtracts from a daily value of GG an average corresponding to the 27 days following (or preceding) the considered date. 2. As we have pointed out in section 5, the amplitudes of the positive and negative sectors during a Bartels rotation are sometimes different, leading to a bias in the estimate of the inferred polarities. [26] We investigated the possibility of improving our analysis, taking into account the questions arose above. The first problem may be indeed overcome by subtracting from each GG value an average over a time interval centered about the given day (rather than the average on a Bartels rotation). The second problem may be softened by averaging GG over periods longer than 27 days (e.g., 55 days); in fact, the total amplitudes of positive and negative sectors become almost identical over a sufficiently long timescale. [27] Table 4 compares the results of the previous analysis, performed by averaging GG over Bartels rotations, with those obtained using GG moving averages over 27 or 55 Table 4. Percentage of Success (S) in Inferring the IMF Polarities by Averaging the GG Values in Three Different Ways as Described in the Text Bartels Rotation Averages Moving Averages Over 27 Days Moving Averages Over 55 Days 72% 73% 72%

6 SSH 4-6 LAURENZA ET AL.: INTERPLANETARY MAGNETIC FIELD POLARITIES Table 5. Percentage of Success (S) in Inferring the IMF Polarities From GG Values for Days of Coherent In Situ Polarities (See Section 4) jggj> Number of Days S s m % s % days. The differences are not significant. In particular, the success rate of the method does not increase, as one may have expected, by increasing the length of the averaging period to 55 days. This trend is most probably due to long term variations of the GG values. We then conclude that the standard procedure used to derive the IMF polarities cannot be significantly improved by averaging the GG values over different time intervals. 8. Discussion and Conclusions [28] The analysis carried out in the previous sections has shown that both the measured and the inferred IMF polarities are subject to noticeable uncertainties. If one considers only the most reliable measured polarities (see section 4), the success rate of the inferring method turns out to be 83%. This value is large enough to ensure the validity of the method. The bottom panel of Figure 3 shows a remarkable example of how accurate, in most cases, the inferred polarities are. On the other hand, the inferred polarities suffer a bias, which becomes more relevant near the sunspot minimum. This bias, as we have shown in section 7, cannot be eliminated because it is inherent in the method itself used to derive the IMF polarities. [29] As wrong polarities most often derive from small jggj, the inferring method becomes more reliable for increasing values of jggj. To investigate the last issue more quantitatively, we considered only the days with a well defined measured polarity (i.e., the ones with at least 18 hours of a coherent polarity, see last line in Table 1) along with the two subsets of inferred polarities defined in Table 2 (i.e., the ones having absolute values of jggj greater than fixed thresholds, s m and s, respectively). Performing on these data the analysis described in section 3, we obtained the results shown in Table 5. [30] Table 5 allows us to evaluate the confidence level of polarities inferred in different cases. We note, in particular, that when jggj > s (a condition occurring for 30% of the whole examined period) the success rate is close to 100% (whatever be the phase of the solar cycle). The data set considered in the second line of Table 5 consists of only 131 days. However, relaxing somewhat the conditions to be satisfied by the measured polarities by including in the analysis all days with at least 15 hours of a coherent measured polarity, we obtained a much wider set of data (1005 data) and a still quite high success rate (90%). We recall also that the success rate of the method further increases up to 95% in the declining phase of the solar cycle, as shown in the last column of Table 3. [31] On the other hand, we stress that the IMF polarities inferred from the CR anisotropy are a sort of average performed over a distance of one Larmor radius of the cosmic ray particles (0.2 AU). Therefore it is not expected that they match in 100% of cases with the polarities measured by spacecraft at a given location in space. [32] We then conclude that the method of inferring polarities from the CR north-south anisotropies can significantly implement direct observations of the IMF. In fact, the inferred polarities are almost certainly correct for 30% of time (jggj > s) while they are quite reliable for another 51% of time (jggj > s m ). For the remaining time, the predictions of the method should be taken with caution, especially near the sunspot minima. Therefore the method helps in obtaining a more continuous coverage of the interplanetary field polarity, particularly in periods of declining solar activity (which are normally longer than the increasing ones) and is useful in many studies of the solar, interplanetary and magnetospheric phenomena. On the other hand, this work shows for the first time the limits of the method and calls for warning in its use. [33] Acknowledgments. Work partly supported by the Antarctic Research Program of Italy in the frame of Science for Solar-Terrestrial Relations. M.L. thanks a CNR fellowship. [34] Shadia Riffai Habbal thanks both referees for their assistance in evaluating this paper. References Bercovitch, M., Determination of the heliocentric cosmic ray density gradient using neutron monitor data, Acta Phys. Hung., 29, Suppl. 2, , Campbell, W. H., and S. Matsushita, Correspondence of solar field sector direction and polar cap geomagnetic field changes for 1965, J. Geophys. Res., 78, , Fougère, P. F., Dependence of inferred magnetic sector structure upon geomagnetic and solar activity, Planet. Space Sci., 22, , Fougère, P. F., Comment on inferred and measured interplanetary sector structure, J. Geophys. Res., 94, , Fougère, P. F., and C. T. Russell, Comment on Interplanetary magnetic structure, , by L. Svalgaard and Correspondence of solar field sector direction and polar cap geomagnetic field changes for 1965, by W. H. Campbell and S. Matsushita, J. Geophys. Res., 80, , Friis-Christensen, E., K. Lassen, J. Wilhelm, J. M. Wilcox, W. Gonzalez, and D. S. Colburn, Critical component of the interplanetary magnetic field responsible for large geomagnetic effects in the polar cap, J. Geophys. Res., 77, , Hoeksema, J. T., Large-scale structure of the heliospheric magnetic field: , in Solar Wind Seven, edited by E. Marsch and R. Schwenn, pp , Pergamon, New York, Iucci, N., and M. Storini, The north-south anisotropy and the cosmic-ray radial gradient in the vicinity of the Earth, Nuovo Cimento Soc. Ital. Fis. B, 10, , Kondo, I., Z. Fujii, and K. Nagashima, North-south asymmetry of cosmic ray flux and polarity of interplanetary magnetic field, Proc. Int. Conf. Cosmic Rays 14th, 4, , Mansurov, S. M., A new evidence of a relationship between magnetic fields in space and on Earth, Geomagn. Aeron., 9, , Mansurov, S. M., and L. G. Mansurova, The relationship between the magnetic fields in space and at the Earth s surface, Ann. Geophys., 26, , Mori, S., and K. Nagashima, Inference of sector polarity of the interplanetary magnetic field from the cosmic ray north-south asymmetry, Planet. Space Sci., 27, 39 46, Mori, S., S. Yasue, and M. Ichinose, Three-dimensional anisotropy of high energy cosmic rays and its relation to the interplanetary magnetic field, Tech. Rep. DPSU 76 01, Shinshu University, Matsumoto, Japan, Mori, S., S. Yasue, Y. Munukata, and K. Nagashima, Inference of sector polarity of the interplanetary magnetic field from the cosmic ray northsouth asymmetry, Sol. Terr. Predict. Proc., 3, B-1 B-12, Moussas, X., and B. Tritakis, Latitudinal and solar cycle dependence of the interplanetary magnetic field predominant polarity, Solar Phys., 75, , Nagashima, K., K. Fujimoto, Z. Fujii, H. Ueno, and I. Kondo, Threedimensional cosmic ray anisotropy in interplanetary space Origin of solar semidiurnal variation, Rep. Ionos. Space Res. Jpn., 26, 31 68, 1972.

7 LAURENZA ET AL.: INTERPLANETARY MAGNETIC FIELD POLARITIES SSH 4-7 Rosemberg, R. L., and P. J. Coleman Jr., Heliographic-latitude dependence of the dominant polarity of the interplanetary magnetic field, J. Geophys. Res., 74, , Russell, C. T., and R. L. Rosemberg, On the limitation of geomagnetic measures of interplanetary magnetic polarity, Solar Phys., 37, , Russell, C. T., R. K. Burton, and R. L. McPherron, Some properties of the Svalgaard A/C index, J. Geophys. Res., 80, , Sekido, Y., K. Nagashima, I. Kondo, H. Ueno, K. Fujimoto, and Z. Fujii, Report of Cosmic Rays Research Lab., N.1, , Nagoya University, Nagoya, Japan, Svalgaard, L., Sector structure of the interplanetary magnetic field and daily variations of the geomagnetic field at high latitudes, Geophys. Pap. R-6, Danish Meteorol. Inst., Copenhagen, Svalgaard, L., Interplanetary magnetic sector structure, , J. Geophys. Res., 77, , Svalgaard, L., and J. M. Wilcox, Long term evolution of solar sector structure, Solar Phys., 41, , Swinson, D. B., Sideral cosmic-ray diurnal variations, J. Geophys. Res., 74, , Tritakis, V. P., Heliospheric current sheet displacements during the solar cycle evolution, J. Geophys. Res., 89, , Vennerstroem, S., B. Zieger, and E. Friis-Christensen, An improved method of inferring interplanetary sector structure, J. Geophys. Res., 106, 16,011 16,020, Wilcox, J. M., and P. H. Scherrer, Annual and solar magnetic-cycle variations in the interplanetary magnetic field, , J. Geophys. Res., 77, , Wilcox, J. M., and P. H. Scherrer, What causes the warp in the heliospheric current sheet?, J. Geophys. Res., 86, , Z. Fujii, Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Japan. M. Laurenza and M. Storini, Istituto di Fisica dello Spazio Interplanetario CNR, Via del Fosso del Cavaliere, 100, Rome, Italy. ifsi.rm.cnr.it; G. Moreno, Dipartimento di Fisica, Università La Sapienza, Piazzale Aldo Moro, 2, Rome, Italy.