On radial heliospheric magnetic fields: Voyager 2 observation and model

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A5, 1205, doi: /2002ja009809, 2003 On radial heliospheric magnetic fields: Voyager 2 observation and model C. Wang, 1,2 J. D. Richardson, 3 L. F. Burlaga, 4 and N. F. Ness 5 Received 4 December 2002; revised 4 February 2003; accepted 25 February 2003; published 22 May [1] The heliospheric magnetic field (HMF) direction, on average, conforms well to the Parker spiral. However, numerous examples of events where the HMF is oriented in nearradial directions for many hours have been reported on the basis of observations inside 5 AU from spacecraft such as ISEE-3 and Ulysses. The magnetic field data observed by Voyager 2 from launch in 1977 through the end of 1982 (i.e., between 1 and 10 AU) were searched for all instances of radial fields with durations of 6 hours or more. Radial fields of significant durations at large distances are unusual as the Parker spiral is very tightly wound. The radial HMF events in the inner heliosphere typically occur at times when the solar wind speed is declining gradually, while they tend to be associated with steady wind speeds at distances beyond 6 AU. The durations of these events appear to be independent of distance and solar cycle, with an average duration of 11 hours. They generally are not associated with interplanetary coronal mass ejections (ICMEs). Possible generation mechanisms of the radial field events related to speed variations near the Sun are investigated by use of a MHD model. We find that a noticeable low-speed plateau of limited duration in solar wind speed near the Sun can produce radial field events having durations of the order of 10 hours in the heliosphere as observed by Voyager 2. INDEX TERMS: 2134 Interplanetary Physics: Interplanetary magnetic fields; 2164 Interplanetary Physics: Solar wind plasma; 7524 Solar Physics, Astrophysics, and Astronomy: Magnetic fields; 7546 Solar Physics, Astrophysics, and Astronomy: Transition region; KEYWORDS: interplanetary magnetic fields, solar wind plasma Citation: Wang, C., J. D. Richardson, L. F. Burlaga, and N. F. Ness, On radial heliospheric magnetic fields: Voyager 2 observation and model, J. Geophys. Res., 108(A5), 1205, doi: /2002ja009809, Introduction [2] The solar photospheric magnetic field is complex and highly variable, with an average magnetic field strength of about 1 G (Gauss) although inside sunspots the field can reach a few thousand Gauss. The solar wind consists of fully ionized plasma (electrons and ions). Its conductivity is high, so the magnetic field is frozen into the plasma. Within a few solar radii, the field is forced to be radial because of the effect of the accelerating solar wind on the field configuration. The outward-convected field is named the heliospheric magnetic field (HMF). The Sun s rotation, when coupled with the radial solar wind flow, winds up the field lines to form Archimedean spirals. In the solar equatorial plane, the equation for the Archimedean spiral is 1 Laboratory for Space Weather, Chinese Academy of Science, Beijing, China. 2 Also at Center for Space Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. 3 Center for Space Research, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. 4 Laboratory for Extraterrestrial Physics, NASA-GoddardSpace Flight Center, Greenbelt, Maryland, USA. 5 Bartol Research Institute, University of Delaware, Newark, Deleware, USA. Copyright 2003 by the American Geophysical Union /03/2002JA009809$09.00 SSH 9-1 given by r = V(f f 0 )/ + r 0, where V is the solar wind speed, is the solar rotation rate ( radians s 1 ), f 0 and r 0 are the source longitude and source radius, respectively [Parker, 1958, 1963]. This model of the spiral magnetic field is now commonly referred to as Parker s model. The magnetic field in the equatorial plane can be expressed in polar coordinates as B =(B r, B f ) and the angle f s between the magnetic field directions and the radius vector from the Sun is f s =tan 1 (B f /B r ). For large distances, this expression can be approximated by f s =tan 1 (r/v). At Earth orbit (1 AU), f s 45 under typical solar wind conditions. While the magnetic field lines are nearly radial close to the Sun, they are normally nearly perpendicular to the radial direction beyond 5 10 AU. [3] Parker s model of the heliospheric magnetic field direction is strongly supported by spacecraft observations within 10 AU [e.g., Behannon, 1978; Thomas and Smith, 1980; Burlaga et al., 1984; Behannon et al., 1989; Forsyth et al., 1996]. Even out to the distant heliosphere (beyond 30 AU), the magnetic field direction can be described to good approximation by Parker s model based on magnetic field experiments on Voyagers 1 and 2 [Burlaga et al., 2002]. The distributions of the azimuthal magnetic field directions (l) [Burlaga, 1995] have roughly Gaussian distributions with peaks at the Parker angles. However, non- Parker fields have been known to exist for many years. One of the earliest observations was discussed by McCracken

2 SSH 9-2 WANG ET AL.: RADIAL HELIOSPHERIC MAGNETIC FIELDS and Ness [1966]. Schatten [1972] reviewed the subject of non-archimedean magnetic fields and he showed how such fields can be produced by azimuthal velocity gradients. Burlaga and Barouch [1976] discussed how draping of the interplanetary field around the Coronal Mass Ejection (CME) plasma clouds, shocks/discontinuities, convected structures, stream interactions, waves and turbulence, and nonzero azimuthal component of the magnetic field near the Sun, all could produce non-parker fields in the heliosphere. For example, magnetic clouds and other ejecta can have magnetic field structure and orientation significantly different from that predicted by the Parker s simple model on a relatively large scale [Burlaga et al., 1981; Gosling, 1990]. Observations of the magnetic filed orientation in corotating rarefaction regions (CRRs) reveal that the filed can be significantly more radial than predicted by the Parker model [Murphy et al., 2002]. [4] In rare cases, we observe nearly radial heliospheric magnetic fields for extended time periods when far from the Sun. Such unusual field configurations are remarkable, as the Parker spiral is much tighter at large distances. Using ISEE-3 data at Earth, Neugebauer et al. [1997] defined radial field periods as times when jb r j/b > 0.9 (i.e., f s < 25.8 from radial), where B r is the radial component of the field and B is the field strength, for 6 hours or longer. They found that (1) the average duration of the radial field events is a little less than 10 hours; (2) 20 out of 21 events occurred during periods of decreasing solar wind flow speed, with the last event accompanied by a steady flow speed; (3) about 1/2 of all such events were clearly not associated with CMEs. Jones et al. [1998] searched Ulysses observations from 1990 though 1997 for radial field periods fitting the same angular criteria, thus extending such studies out to 5.5 AU and to heliographic latitudes of 80. They found (1) all these events are associated with periods of declining and steady solar wind speeds; (2) 2/3 of their events were unrelated to CMEs in the solar wind; (3) All but 3 of the events occurred at latitudes less than 40. However, Jones et al. did not report durations except for the 7 events with the most radial fields (f s < 15 ), whose durations range from 6 to 12 hours. Gosling and Skoug [2002] also showed examples of radial fields observed by Ulysses and inferred additional characteristics of the radial field events including (1) their association with both CME and non-cme flows, (2) that they are relatively common at high latitudes during active solar times; (3) that at distances beyond 3 AU they often have durations of a day or longer, equal to or greater than the longest durations observed at 1 AU by ISEE-3; (4) and that they typically occur during only a portion of a declining solar wind speed interval. The existence of radial field events of significant duration thus is well established from observations; however, their origins remain an enigma. Several causes mentioned above have been suggested, but none of them seem to account for the observations. Most recently, Gosling and Skoug [2002] proposed that these nearly radial field events result from temporally abrupt and semi-permanent decreases in solar wind speed. The abrupt flow speed change may result from an interchange reconnection of field lines that extend into the heliosphere with closed coronal loops [Fisk et al., 1998; Schwadron, 2002]. Gosling and Skoug [2002] used a Figure 1. Radial distance and heliolatitude of Voyager 2 from 1977 to kinetic approach to illustrate how this mechanism can explain some of the basic features of radial field events observed by ISEE-3 and Ulysses. This model predicts, for example, that the durations of these events increase with heliocentric distance. It is the first physical model, to our knowledge, to track the origin of the radial magnetic field events. However, since it is a kinetic model, dynamical processes are not included and thus this model cannot give a complete picture of the development and evolution of a radial HMF event in the heliosphere. [5] In this study, we search Voyager 2 data for radial field events between 1 and 10 AU, which extends the data base on these events beyond 5 AU. Furthermore, we use a MHD model to test the Gosling and Skoug hypothesis and explore other possible mechanisms. Voyager 2 observations of the radial field events are presented in Section 2. The numerical model and simulation results are described in Section 3. Section 4 concludes this paper with summary and discussions. 2. Voyager 2 Observation 2.1. Data [6] Voyager 2 has made solar wind observations since launch in We searched Voyager 2 magnetometer hourly average data for radial field events, following the same definition given by Neugebauer et al. [1997], jb r j/b > 0.9 for 6 or more consecutive hours. In the outer heliosphere the interplanetary magnetic field strength decreases with distance as approximately 1/R, where R is the heliocentric distance. Owing to contamination by the spacecraft generated magnetic field, the interplanetary magnetic field becomes increasingly difficult to measure accurately at larger distances. The uncertainty in the measurement of each of the components of the magnetic field observed by the Voyager 2 is approximately 0.05 nt. In this paper, we limit our study in the Voyager 2 data from launch to the end of 1982, when the magnetic field measurements are of high quality. Figure 1 shows the trajectory of Voyager 2, with heliolatitude plotted versus distance during this time

3 Figure 2. Parameters recorded by Voyager 2 during the February 1978 radial field period. From top to bottom, the quantities plotted are the solar wind speed (V), proton temperature (T), proton number density (N), magnetic field strength (B), and the ratio of the radial component of the magnetic field to the total field magnitude (B r /B), respectively. Vertical lines bracket the time intervals of the period. Voyager 2 was near the equatorial plane and travelled from 1 AU to 10 AU Radial Field Events [7] Figure 2 shows a 10-day plot of hourly average solar wind data from 1978 at a heliocentric distance of 2.4 AU as an example to illustrate some typical characteristics of the radial field events. The solar wind speed, proton temperature, proton number density, magnetic field strength and the ratio of the radial component of the magnetic field to the total field are shown. Vertical lines bracket the time interval of the radial magnetic field event. Assuming the event persists across the data gap, this event lasts at least 13 hours. The event is associated with a decline of the solar wind speed and with moderately low plasma density and temperature. The magnetic field strength is also relatively low during this event. In an attempt to determine whether this event is associated with a CME, we use helium abundance enhancements (HAEs) as indicators of ICMEs. Large He ++ /H + density ratios (greater than 10% for at least 12 hours) can be used to track CMEs through the outer heliosphere, at least for the subset of CMEs which have this property [Wang and Richardson, 2001], although HAE events are rare in Voyager 2 observations. If helium abundance enhancements are observed within three days of the radial field periods, we then regard them as roughly associated. Using this criterion, the event in Figure 2 is probably unrelated to CMEs, which is typical for the radial field events. [8] At larger distances (beyond 6 AU), radial events are more likely to occur when the solar wind speed is little changed (steady speed). As shown in Table 1, more than WANG ET AL.: RADIAL HELIOSPHERIC MAGNETIC FIELDS SSH % of the events show little speed change across the event. Figure 3 shows an example of a radial field event at the end of 1980 at 7.9 AU. This event is again accompanied by little change in speed and a relatively low proton temperature. As in the event at 2.4 AU, the plasma density is slightly lower than normal; however the magnetic field strength has a different behavior from the previous example. This event also has no association with a CME. [9] Radial field events in the heliosphere are rare. We have found a total of 35 radial field events in Voyager 2 observations from 1977 to 1982, so they are detected on 1.8% of the days with Voyager 2 data. Table 1 summarizes the detailed properties of these events. The first three columns of Table 1 give the start time, location and duration of each of the 35 radial field events. Some events are much longer than 6 hours, with the longest duration a little more than 1 day, but we do not see any very long-lived events such as the six-day event recorded by Ulysses in early January 1997 [Jones et al., 1998]. The yearly averages of duration are plotted in Figure 4, with the error bar indicating the standard deviation. The average duration of all events is 11 hours. During the time period considered, the average duration appears to be little changed with time (thus also with distance and solar cycle). This result provides an extra constraint on models. Another remarkable feature is that all these events occur when the solar wind speed is gradually decreasing or little changed, which is consistent with results nearly radial magnetic field. Table 1. Summary of Radial Field Events Observed by Voyager 2 From 1977 to 1982 Start Time, decimal year Distance, AU Duration, hours V Decrease? CME? yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes steady yes steady steady steady steady steady steady steady steady yes steady yes steady steady yes yes yes steady steady steady steady

4 SSH 9-4 WANG ET AL.: RADIAL HELIOSPHERIC MAGNETIC @r ¼ S 2 3 r 2 r r 2 rv r r 2 rv f U ¼ r 2 B r rb f 6 r 2 1 g 1 p þ 1 2 rv2 þ B 2 5 2m 0 ð2þ Figure 3. A radial field event at the end of 1980 at a radial distance of 7.9 AU (same format as Figure 2). from ISEE-3 [Neugebauer et al., 1997] and Ulysses [Jones et al., 1998]. Beyond 6AU, most events are associated with nearly steady solar wind flow speeds. Of all these events, only about 10% are related to CMEs. Note that since we determine CMEs only by the signatures of helium abundance enhancements, which is a subset of CMEs, this percentage should be regarded as a lower limit. 3. Numerical Model [10] Since CMEs change the magnetic field structure dramatically, naturally they are first thought to be the primary cause of the radial HMF events. Certainly, we observe many examples which belong to this category. However, the majority of these events appear to be unrelated to CMEs. Several mechanisms have been envisioned, but no quantitative or qualitative model has yet been developed on the basis of these ideas. Most recently, Gosling and Skoug [2002] proposed that these nearly radial field events result from temporally abrupt and semi-permanent decreases in solar wind flow speed, and discussed some consequences of this idea using a kinematic model. In this section, we will use a MHD model to test their hypothesis and explore other possible solar origins of the HMF events in the heliosphere Governing Equations and Numerical Methods [11] Since the Voyager 2 trajectory is not far from solar equatorial plane, without losing generality we confine our computations to this plane for simplicity. In addition, we assume axisymmetric solar wind flow and that the velocity and magnetic field have components only in this plane: u ¼ u r^r þ v j^j; B ¼ B r^r þ B j^j Under these assumptions, we have basically one-dimensional (two-component) MHD equations in the corotating coordinate system: ð1þ and 2 F ¼ 6 4 r 2 rv r r 2 p þ rv 2 r þ 1 ðb 2 f 2m B2 r 0 r 2 rv r v p hi 1 B r B f m 0 r 2 g v r g 1 þ 1 2 v2 0 rv r B f v f B r 1 B f v f B r v r B f m r 2p þ rv 2 f þ 1 B 2 r GM s þ r 2 r 2 r þ 2rv f m 0 r 1 r B r B f rv r v f r 2 ð2rv r Þ S ¼ m rv r ð 2 r GM s Þ Where v f = u f r, u f is the azimuthal flow speed in the laboratory coordinate system. The angular rate of the Sun s rotation is = rad s 1 and the polytropic index g is taken as 5/3. The other notation is conventional [e.g., Wu et al., 1978] and is used without description. The fluid satisfies the equation of state p = rrt where T is the temperature and R is the gas constant. The equations are solved using the piecewise parabolic method (PPM) [Collela and Woodward, 1984; Dai and Woodward, 1995]. [12] The computational domain is 0.1 AU r 10 AU with a uniform mesh of r = AU. We limit the computational domain to the region where the solar wind speed exceeds the sound speed and Alfven speed in order to avoid the complication involved in transonic flows. We normalized all the quantities according to the typical values at 0.3 AU; that is, the number density, temperature, mag-

5 WANG ET AL.: RADIAL HELIOSPHERIC MAGNETIC FIELDS SSH 9-5 Figure 4. events. Yearly average durations of the radial field netic field strength are taken as 120 cm 3, K, and 45 nt, respectively. We can specify all quantities at the inner boundary, since the flow is supersonic there. Outflow conditions are applied at the outer boundary at 10 AU. A numerical calculation is then carried out until a steady state solution is reached. This initial steady state corresponds to the solution of Weber and Davis [1967]. We then initiate speed variations at the inner boundary to investigate their effects on the heliospheric magnetic field Model Results [13] First, we introduce the following speed discontinuity at the inner boundary to illustrate how the heliospheric magnetic field is modified if the solar wind speed suddenly and semipermanently drops from 700 to 400 km s 1 as proposed by Gosling and Skoug [2002]: 8 < 700 km s 1 if t < 0 V ¼ : 400 km s 1 if t 0 [14] These values are chosen since the effect is more profound when the speed decrease is large. This is consistent with the observation of a boundary layer surrounding a corotating stream near 0.3 AU emanating from a coronal hole [Burlaga et al., 1978]. They found that the speed dropped from 625 to 345 km s 1 over an angle of 12 degrees, corresponding to a velocity shear of >130 km s 1 degree 1. We follow the development and evolution of the radial HMF in a qualitative way. Figure 5 shows the model results at two different times, t = 5 days (solid lines) and t = 20 days (dotted lines) after the speed decrease is initiated at the inner boundary at t = 0. We show from the top to bottom the solar wind speed, temperature, number density, magnetic field strength and the ratio of the radial component of the magnetic field to the field strength, respectively. A rarefaction region is formed by the abrupt flow speed drop, producing the radial field periods bracketed by the vertical lines. We change only the speed at the inner boundary and leave the other parameters unchanged. Since the trailing slow solar wind falls behind the leading solar wind flow, the region between these two flows keeps expanding, resulting in a low density, low temperature, and low magnetic field solar wind structure within the radial field period, as would be expected. Note that we plot solar wind parameters as functions of distance at two different times in the Figure 5. A stationary spacecraft would see a gradual decline in flow speed and a decrease in temperature, density and magnetic field strength as the solar wind structure passes by. The magnetic forces and gas pressure forces round off the sharp edges of the field line kink, as illustrated by the kinematic model of Gosling and Skoug [2002], and change the abrupt flow speed decrease into a gradual spatial flow speed decline. As time goes by, the radial field kink keeps growing while propagating out and the speed gradient becomes smaller. We plot the durations of the radial field period which would be observed at 1 to 9 AU in Figure 6, with a linear fit to the data shown by the solid line. The duration of the radial field event increases linearly with heliocentric distance, as also predicted by the kinetic model. However, this feature is not supported by the Voyager 2 observations given in the Section above. [15] Consequently, in an attempt to reproduce this feature too, we construct a modified speed function at the inner boundary as follows: km s 1 if t < 0 >< V ¼ km s 1 if 0 t t 0 >: 700 a km s 1 if t t 0 where t 0 = 12 hours. We hypothesize that the speed decrease is temporary and let the speed decrease abruptly Figure 5. Model results at time t = 5 days (solid lines) and t = 20 days (dotted lines) after a sudden speed decrease from 700 to 400 km s 1. Shown are the solar wind speed (V), temperature (T), number density (N), magnetic field strength (B), and the ratio of the radial component of the magnetic field to the magnetic field strength from top to bottom panels, respectively.

6 SSH 9-6 WANG ET AL.: RADIAL HELIOSPHERIC MAGNETIC FIELDS Figure 6. Durations of the radial field events that would be observed at different distances. A linear fit is shown by the solid line. from 700 km s 1 to 350 km s 1 for 12 hours, then reset the speed to a percentage a of its original value. This is consistent with the observation of a heliospheric plasma sheet with low speeds between the rear interface of one corotating stream and the front interface of a following stream [Burlaga et al., 1990]. However, the results of our calculation are not restricted to corotating streams. We did the same calculations as above, and show the results in Figure 7 for a recovery factor a = 0.9; that is, the flow speed is back to 90% of its original value. We therefore introduce a more complex speed function at the inner boundary and, as a result, see more complicated solar wind structures at larger distances. The radial field region still forms in the heliosphere with similar solar wind characteristics to those for the simple speed discontinuity, but the duration of the radial field event differs significantly from the above scenario. The magnetic field radial kink is little changed from 2 to 8 AU, but the speed gradient is much less. The durations at different radial distances are plotted with asterisks in Figure 8. After a small increase in duration from 1 AU to 2 AU, the radial field period seems unchanged with distance, which is consistent with Voyager observations. Of course, we took a = 0.9 arbitrarily. If a = 1.0, the duration of the radial field events decreases with distance, since the trailing solar wind has enough momentum to overtake the radial field structure and will eventually destroy it at larger distances. Since our purpose is to demonstrate the likely origin of the radial field events in the heliosphere, we do not try to match the exact durations of each observed radial field event, and we do not attempt to model specific types of flows such as corotating streams. Such matches are likely attainable by varying the duration t 0 and recovery factor a in the speed function introduced at the inner boundary. Figure 7. Model results from speed variations at inner boundary; see text for details. [17] 1. Radial heliospheric magnetic field events are rare in the outer heliosphere. They are detected on 1.8% of the days of Voyager 2 data. [18] 2. These events are associated with gradually declining or steady solar wind flow speed; at distances between 6 and 10 AU, they tend to be associated with steady solar wind speeds. [19] 3. Only a small portion of these events seem to be related to CMEs. [20] 4. Plasma temperatures are generally lower than in the ambient solar wind during the radial magnetic field periods. 4. Discussion and Summary [16] In this study we present 5 years of observations of radial field periods (jb r j/b > 0.9 for 6 or more hours) as Voyager 2 travelled from 1 to 10 AU from 1977 to These observations, which significantly deviate from the Parker model, are summarized here. Figure 8. distances. Durations of radial field events at different

7 WANG ET AL.: RADIAL HELIOSPHERIC MAGNETIC FIELDS SSH 9-7 [21] 5. The durations of the radial magnetic field events appear to be independent of distance, with an average duration of 11 hours. [22] Most of these results are similar to those obtained by ISEE-3 [Neugebauer et al., 1997] and Ulysses [Jones et al., 1998] within 5 AU. The existence of radial fields far out in the heliosphere is remarkable, as the Parker spiral at greater distances is much tighter. [23] The origin of the radial magnetic field events remains mysterious. Using a 1-D two components MHD model in the solar equatorial plane, we explore the dynamical consequences of the mechanism suggested by Gosling and Skoug [2002], that the radial HMF events result from temporally abrupt and semipermanent decreases in solar wind flow speed. The numerical results show the radial fields are associated with gradual flow speed declines and predict increased durations at larger heliocentric distances. However, Voyager 2 observations do not show longer durations at large distances. Therefore, in an attempt to model the nearly constant average duration of the radial HMF events with distance, we propose here that the sudden speed decreases only last for a certain amount of time (e.g., 12 hours), and that then the solar wind speed at least partially recovers. The model results using this speed profile at the inner boundary reproduce the basic features of the nearly radial field events observed by Voyager 2, including their nearly radial fields, their association with gradual flow speed declines, and their nearly constant average durations. Thus we believe that speed variations near the Sun, similar to the form we suggested here, can cause the radial field events in the heliosphere. We plan to pursue other possibilities using 2-D or 3-D MHD simulations in the future. [24] In the Parker spiral model (as well as in our MHD calculations), the field is assumed to be radial near the Sun. However, Burlaga and Barouch [1976] used a kinematic approach and found that the field direction is very sensitive to the orientation of the magnetic field as well as velocity shears near the Sun; and small departures from the spiral angle cause a large spread about the spiral angle at large distances, the spread increasing with distance. Thus the observed variation in the direction of the magnetic field in the heliosphere might be partly the result of relatively small fluctuations in the direction of the magnetic field near the Sun. This effect could be also studied by a MHD model. [25] Over the years, Voyager 2 observations show that the directions of hourly averages of the magnetic field tend to have Gaussian distributions with peaks at the Parker angles. The l-distribution (the angle l is zero for a field directed away from the Sun) is usually 2 Gaussian distributions. Our study concerns only those fields near 0 and 180 these fields are rarely if ever 0, there are always radial fields in the magnetometer data. They appear to be just the tails of two Gaussian distributions, rather than separate peaks. One might think they are produced by waves or turbulence. However, all the radial field events (of extended intervals as we defined them) observed by Voyager 2 up to 1982 occur when the flow speeds are gradually declining or remain steady; none occur when the solar wind speed is increasing. This result is not consistent with the hypothesis that the radial fields are simply the result of waves and turbulence. Rather, the radial fields of significant duration on the tail of the distribution are more likely to be the heliospheric remnants of solar wind structure such as CMEs or the speed variations we discussed in this paper. Extending this study using Voyager observations from beyond 10 AU would provide more insight into the physical process (propagation and evolution) of the radial heliospheric field events, but more careful examination of the field measurements in the weak-field region of the outer heliosphere is needed before this study can be performed. [26] Acknowledgments. The work at MIT was supported under NASA contract from JPL to MIT and NASA grant NAG C. Wang was supported in part by NNSFC of China and the onehundred talent program of the Chinese Academy of Sciences. [27] Shadia Rifai Habbal thanks Robert J. Forsyth and another referee for their assistance in evaluating this paper. References Behannon, K. W., Heliocentric distance dependence of the interplanetary magnetic field, Rev. Geophys., 16, 125, Behannon, K. W., L. F. Burlaga, J. T. Hoeksema, and L. W. Klein, Spatial variation and evolution of heliosphere sector structure, J. Geophys. Res., 94, 1245, Burlaga, L. 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8 SSH 9-8 WANG ET AL.: RADIAL HELIOSPHERIC MAGNETIC FIELDS Schatten, K. H., Large-scale properties of the interplanetary magnetic field, in Solar Wind, edited by C. P. Sonett, P. J. Coleman Jr., and J. M. Wilcox, NASA Spec. Publ., SP-308, 65 pp., Schwadron, N. A., An explanation for strongly underwound magnetic field in co-rotating rarefaction regions and its relatioship to footpoint motion on the sun, Geophys. Res. Lett., 29(14), 1663, doi: /2002gl015028, Thomas, B. T., and E. J. Smith, The Parker spiral configuration of the interplanetary magnetic field between 1 and 8.5 AU, J. Geophys. Res., 85, 6861, Wang, C., and J. D. Richardson, Voyager 2 observations of helium abundance enhancements from 1 60 AU, J. Geophys. Res., 106, 5683, Weber, E. J., and L. Davis Jr., The angular momentum of the solar wind, Astrophys. J., 148, 216, Wu, S. T., M. Dryer, Y. Nakagawa, and S. M. Han, Magnetohydrodynamics of atmospheric transients, 2. Two-dimensional numerical results for a model solar corona, Astrophys. J., 219, 324, C. Wang, Laboratory for Space Weather, Chinese Academy of Sciences, P.O. Box 8701, Beijing , China. (cw@spaceweather.ac.cn) J. D. Richardson, Center for Space Research, Massachusetts Institute of Technology, , Cambridge, MA 02139, USA. ( jdr@space.mit.edu) L. F. Burlaga, Laboratory for Extraterrestrial Physics, NASA-Goddard Space Flight Center, Greenbelt, MD 20771, USA. (Leonard.F.Burlaga@ nasa.gov) N. F. Ness, Bartol Research Institute, University of Delaware, Newark, DE 19716, USA. (nfness@udel.edu)