The interplanetary magnetic field: Radial and latitudinal dependences

ISSN 1063-7729, Astronomy Reports, 2013, Vol. 57, No. 11, pp. 844–859. c© Pleiades Publishing, Ltd., 2013.Original Russian Text c© O.V. Khabarova, 2013, published in Astronomicheskii Zhurnal, 2013, Vol. 90, No. 11, pp. 919–935.

The Interplanetary Magnetic Field:Radial and Latitudinal Dependences

O. V. Khabarova*

Pushkov Institute of Terrestrial Magnetism and Radiawave Propagation (IZMIRAN)Russian Academy of Sciences

Received March 1, 2013; in final form, April 4, 2013

Abstract—Results of the analysis of spacecraft measurements at 1–5.4 AU are presented within the scopeof the large-scale interplanetary magnetic field (IMF) structure investigation. The work is focused onrevealing of the radial IMF component (Br) variations with heliocentric distance and latitude as seenby Ulysses. It was found out that |Br| decreases as ∼r−5/3 in the ecliptic plane vicinity (±10◦ oflatitude), which is consistent with the previous results obtained on the basis of the analysis of in-eclipticmeasurements from five spacecraft. The difference between the experimentally found (r−5/3) and commonlyused (r−2) radial dependence of Br may lead to mistakes in the IMF recalculations from point to point inthe heliosphere. This can be one of the main sources of the “magnetic flux excess” effect, which is exceedingof the distantly measured magnetic flux over the values obtained through the measurements at the Earthorbit. It is shown that the radial IMF component can be considered as independent of heliolatitude in arough approximation only. More detailed analysis demonstrates an expressed |Br| (as well as the IMFstrength) increase in the latitudinal vicinity of ±30◦ relative to the ecliptic plane. Also, a slight increase ofthe both parameters is observed in the polar solar wind. The comparison of the Br distributions confirmsthat, at the same radial distance, Br values are higher at low than at high latitudes. The analysis of thelatitudinal and radial dependences of the Br distribution’s bimodality is performed. The Br bimodality ismore expressed at high than in the low-latitude solar wind, and it is observed at greater radial distances athigh latitudes. The investigation has not revealed any dependence between Br and the solar wind speedV . The two-peak distribution of the solar wind speed as measured by Ulysses is a consequence of a stronglatitudinal and solar cycle dependence of V . It is shown that the solar wind speed in high latitudes (above±40◦) anti-correlates with a solar activity: V is maximum during solar-cycle minima and minimum at themaximum of solar activity.

DOI: 10.1134/S1063772913110024

1. INTRODUCTION

Investigations of the large-scale structure of theinner heliosphere continue to be relevant up to now.In spite of the accepted view that the interplanetarymagnetic field (IMF) is “frozen-in” to the solar windplasma, propagating along the Parker spiral, reportsof disagreements between the theory and observa-tions continue [1–3]. Numerous databases of solarwind parameters obtained from the space era begin-ning allow implementation of more and more detailedmulti-spacecraft analysis of the heliospheric plasmaproperties at different solar cycle phases, heliocentricdistances, longitudes and latitudes. As a result, aquantity of the accumulated material transforms intoa new quality of understanding of the solar wind pro-cesses, but the number of contradictions increasestoo.

*E-mail: [email protected]

It should be taken into account that Parker’smodel is stationary (as well as other models usingthe Parker solution), and some part of deviations fromthe model may be explained by this fact (a history ofattempts to improve the original model is presentedin the review [4]). However, the use of a model orhypothesis which consistently produces significantmistakes may impact negatively the space weatherprognoses quality and retard the advance of solar-terrestrial physics.

Most serious concerns about the quasi-Parkermodels are mainly lodged by empiricists who performcomparative analysis of predictions of the IMF pa-rameters at the Earth’s orbit with distant spacecraftmeasurements and recalculate the IMF strength fromone point to another. The main problem is thatthe solar wind speed (as well as the IMF sign) at1 AU can be calculated by most models with prettygood accuracy, but the IMF strength and the IMFdirection can not be predicted in the same way and

844

THE INTERPLANETARY MAGNETIC FIELD 845

with the same accuracy [2, 5, 6]. For instance,the radial IMF component Br (the RTN coordinatesystem) is theoretically the most easily predictableIMF parameter, decreasing with distance as r−2

in accordance with the Parker’s model, but no oneof commonly accepted models does provide withadequate Br prediction at 1 AU [6]. The discrepanciesare significant even at solar activity minima, and,during maxima, the correlation between the predictedand calculated Br values goes below any reasonablestatistical level. At the same time, semi-empiricalmodels exceed purely theoretical ones by the IMFbehavior predictions’ quality [7].

Besides, an effect of the “magnetic flux excess”was reported in [8]. The total magnetic flux in theheliosphere FS can be calculated as:

FS = 4π|Br|r2. (1)

According to the Parker’s theory, FS should beconstant everywhere in the heliosphere under at least∼27 days (one Carrington rotation period) averaging,but in fact there is a difference between FS fromdistant spacecraft and near-Earth measurements at1 AU [8]. The difference was found to be increasingwith distance. It becomes so large at r > 2.5 AU thatit can not be ignored.

Many works have been dedicated to investigationsof the “flux excess” effect, and several explanationshave been suggested (from the kinematic effect toincorrect averaging methods) [9–11]. In the originalpaper [8], the mean of the module of the radial IMFcomponent 〈|Br|〉 was used, but authors of someother papers prefer to use a module of the mean|〈Br〉| [9–11]. It should be noted that 〈|Br|〉 and|〈Br〉| are not identical as Br ranges from negativeto positive values. Sometimes it is supposed thatthere is no difference between 〈|Br|〉 and |〈Br〉| for arather large temporal averaging interval, sometimesthe opposite opinion prevails [8–12].

Absence of clear understanding of physical causesof the effect leads to the application of specific cor-rection factors, special methods of data processingand other artificial techniques. At the same time, thecorrectness of the formula (1) has not been subjectto question in the literature. Let’s consider herea hypothesis that the problem is not due to someunclear physical effects, but to the fact that Br doesnot depend on the heliocentric distance as r−2. Thisquestion was raised in [13], and it will be discussed indetails among other questions in the current paper.

Point-to-point IMF recalculations in the helio-sphere and FS conservation are based on the Parker’stheory invariant Br · r2. However, according to therecent multi-spacecraft data analysis, Br · r2 is not

conserved in the inner heliosphere [13]. Measure-ments of the Helios 2, IMP8, Pioneer Venus Or-biter, and Voyager 1 spacecraft measured IMF from0.29 AU to 5.0 AU in the increasing phase of the solarcycle (from 1976 to 1979) allowed make such a con-clusion [13]. Results of calculation for the Parker’smodel (recalculations of the source surface magneticfield along the Parker spiral as r−2) and the pure radialexpansion model (when the magnetic field decreasesas r−2, but not along the spiral) are given in Fig. 1a,which represents the merged figures 1–2 from [13].

Observations show that the radial IMF compo-nent decreases with distance as r−5/3, rather thanas r−2. At the same time, the tangential componentbehavior was found to be corresponding to the ex-pected law (r−1), and the IMF strength B ∝ r−1.4.The difference between the observed and calculatedBr values is greatest at small heliocentric distances,where the observed field may several times exceedthe values calculated through the models using theParker solution. At r > 5 AU, the difference is not sosignificant.

The model’s quality can be improved through theapplication of some corrections, for example, by mul-tiplying the obtained values by some constant orsummarizing them with some additional field. In theresult, the both model curves seen in Fig. 1a belowthe experimental one will be shifted up and coincidewith observations better. These methods are usu-ally used for best correspondence of calculations with1 AU observations. The fitting methods are typicallyperformed just for two points: “the source surface”—“the Earth’s orbit.” Unfortunately, as was mentionedabove, the acceptable agreement is not reached evenat 1 AU, and discrepancies inevitably become greaterat other distances.

In addition, another consequence of insufficientunderstanding of the large-scale IMF behavior wasdemonstrated in [13]: there is an effect of unexpectedvanishing of the Br distribution’s bimodality withdistance. At the Earth’s orbit, the Br distributionhas a well-known two-humped (bimodal) view be-cause of the expressed sector structure of the IMFin the Earth’s vicinity. As a result, a Br histogramcontains two quasi-normal overlapping distributionscorresponding to the IMF measurements in positiveand negative sectors. Earlier, it was commonly sup-posed that such a pattern should be observed at leastup to the first turn of the Parker spiral, when the spiralgets perpendicular to the sunward direction (whichoccurs at distances >5 AU at any solar wind speeds).Meanwhile, the experimental data by Helios 2, IMP8,Pioneer Venus Orbiter, Voyager 1, and Ulysses donot confirm that. In fact, bimodality vanishes withdistance very rapidly: it is clear at 0.7–1.0 AU, it is

ASTRONOMY REPORTS Vol. 57 No. 11 2013

846 KHABAROVA

2

01

|

B

r

|

, nT

r

, AU

4

0 1

(a)

r

, AU

4

6

8

10

12

2 3 4 5 6

|

B

r

|

= 2.3953

r

–1.6139

2 3 4 5

8

12

16

20

24

28

32

36

(b)

|

B

r

|

, nT

Helios 2 Pioneer Venus IMP8 Voyager 1

Parker spiral

Radial propagation (

r

–2

)

Observations (3.8

r

–5/3

)

Fig. 1. Br(r)—the radial IMF component’s variation with heliocentric distance. (a) Comparison of the measured Br (squares)with Parker’s model (triangles) and the calculations according to a model of the radial expansion (points), which does not takeinto account propagation time along the spiral. See details in [13]. (b) Br(r) near the ecliptic plane (±10◦ by latitude) asmeasured by Ulysses. The hourly data of the module Br are used for the entire period of the measurements (number of points:33251). The approximation curve is shown by white color.

seen worse at 2–3 AU, and it disappears completelyat 3–4 AU.

This is most likely a consequence of a radial in-crease of the solar wind turbulence, which resultsin disappearance of the clear sector structure muchcloser to the Sun than was supposed earlier. In-deed, one of the IMF modeling problems is a dis-agreement between the predicted and observed lo-calization and inclination of the heliospheric current

sheet (HCS). Spatial and temporal parameters of thisgreatest structure in the heliosphere determine theentire picture of the IMF, but the HCS features arepoorly known. The HCS Parker’s angle at differentAU, large-scale HCS twisting as well as the south-north displacement are widely discussed questions,being of great importance for the IMF properties un-derstanding [14–16]. Meanwhile, as shown in [17]through the comparison of observations and calcula-



tions according to the Stanford source surface mag-netic field model, predictions of the HCS positionmeet with serious problems. The difference betweenthe calculated HCS azimuth angle and observationalvalues sometimes reaches 25◦. The best results canbe obtained using semi-empirical models, rather thanMHD-models [18, 19]. All discussed facts demon-strate insufficient understanding of processes of thesolar wind expansion into the heliosphere.

Therefore, the IMF behavior in the inner helio-sphere considerably differs from predictions of quasi-Parker models even under a rough approach, anddemands further study. On the one hand, Parker’smodel is very attractive in its simplicity and the pos-sibility of fast point-to-point recalculation of the solarwind parameters through elementary formulas. Onthe other hand, there is obvious necessity to un-derstand why those formulas work well for plasmaparameters, but do not work for the IMF, and todetermine the true law of the IMF radial decrease inthe inner heliosphere.

The current paper continues empirical investiga-tions of the large-scale IMF in light of the discussedproblems and previously obtained results. The mainidea is as follow: the revealed deviations of the ob-served IMF parameters from the predicted values aremainly not caused by non-stationary effects (such ascoronal mass ejections), but are related to misusedIMF recalculation according to r−2 law. Also, a-priori believing the IMF to be completely “frozen in”to the plasma may lead to the observed discrepancies.

The development of a new model is a future task.Meanwhile, there are several key dependencies whichmay be empirically found right now. For example:What is the law of the IMF decrease in the innerheliosphere? What is the main cause of the “fluxexcess” effect? Whether the IMF depends on thesolar wind speed and heliolatitude? These (as well asrelated) questions will be discussed below.

2. PECULIARITIESOF THE INTERPLANETARY MAGNETIC

FIELD RADIAL AND LATITUDINALDEPENDENCIES

2.1. The Radial IMF Component Changeswith Distance. The “Magnetic Flux Excess”

Problem

Let us check the results obtained in [13] by thecalculation of the Br curve slope through the alterna-tive spacecraft data analysis. The best candidate forthis purpose is the Ulysses spacecraft, which allowsconsideration both radial and latitudinal dependen-cies due to its unique orbit, which was nearly per-pendicular to the ecliptic plane. Hourly Ulysses data

were used in this work for 25.10.1990–30.09.2009(see http://cdaweb.gsfc.nasa.gov/).

For adequate comparison, let’s select the data forthe near-ecliptic Ulysses passages (±10◦ latitudinalvicinity around the ecliptic plane) . Then, the “〈|Br|〉or |〈Br〉|” problem arises (see [10]). The most rea-sonable and reconciling approach to the problem’ssolving was demonstrated in [11]. Meanwhile, inthe author’s subjective opinion, first-step averagingof a bimodally distributed parameter is unreasonable.For instance, averaging of any sinusoid gives zero.The modulus of the pre-averaged Br (|〈Br〉|) givesan analogical result. It is not zero for short-timeintervals of averaging. But the longer time intervalis considered, the closer the result is to zero (whichis the mean of the symmetrically distributed bimodalparameter Br). As a result, the longer time interval,the lesser the “flux excess,” but the physical senseof the results of such averaging is as disputable as asense of the averaged sinusoid.

To avoid the “averaging mistake,” the radial IMFcomponent module (|Br|) without averaging usedin [13] will be considered here. The result is shownin Fig. 1b, analogues to Fig. 1a. The white approx-imation curve has a slope of −1.614, which is closeto the value −5/3 found in [13], hence Br ∝ r−1.6.It is interesting that the used Ulysses data coveredmuch more long time interval in comparison with thedata taken for the previous analysis in [13]. Similarityof the results means stable deviations of the IMFbehavior from the theoretical expectations.

Let’s turn now to the physical meaning of thefactor x multiplying R in the approximation equation|Br| = x · R−y.

In the paper [13], x = 3.8 (see Fig. 1a), but x = 2.4in Fig. 1b. It is known that multiplying a function bya positive number leads to an increase in the upwardscale of the corresponding graph. In our case, theessential difference would be seen in rising of thegraph’s part corresponding to the small distancesfrom the Sun. According to a method of dimensions,x from x · R−y can be represented as x = B0, whereB0 is some reference field, and R = r/r0 (r is a he-liocentric distance, a variable; r0 is a distance fromthe Sun to the point where |Br| = B0). Therefore, theradial IMF component is:

|Br| = B0

(r

r0

)−5/3

. (2)

In [13] (see Fig. 1a), B0 = B1AU at r0 = 1 AU asobtained on the basis of measurements, starting fromthe heliocentric distance of 0.29 AU. In the case of theUlysses database (Fig. 1b), the IMF was measuredat distances greater than 1 AU, and B0 had a smallervalue. It is important to note that B0 varies with time


848 KHABAROVA

–4

0.2 0.4

r

, AU1.0 1.6 1.8 2.2

–3

–2

–1

0

1

2

3

4

Δ F

S

, 10

14

Wb

Observations [8]

Account of the dependence

B

r

~

r

–5/3

–50.6 0.8 1.2 1.4 2.0

Fig. 2. Illustration of the cause of the “magnetic excess” effect. Points represent the difference between the magnetic flux,according to distant spacecraft measurements and observations at the Earth’s orbit, ΔFS (from figure 5 in [8]). The curve isΔFS calculated on the basis of the formula (3), where the experimentally found dependence Br ∝ r−5/3 is used.

and solar cycle. Its measured values are also influ-enced by the spacecraft magnetometer’s characteris-tics. As an example of the IMF temporal variations,one can see the features of the IMF changing withsolar cycle at 1 AU in the first figure of the paper [20].Accordingly to B0 changes, the entire experimentalcurve correspondingly shifts up and down, but theslope very probably remains the same.

Let’s take as a basis that the Br ∝ r−2 statementis true only in a first approximation. Deviations of yfrom ‘2’ may lead to serious mistakes of Br point-to-point recalculations. The “flux excess” effect isjust a confirmation of this statement. Theoretically,FS should be an invariant over the entire heliosphere,at any distances. As was mentioned above, a con-sistent increase of FS with heliocentric distance isobserved: distantly measured FS increasingly differsfrom FS calculated on the basis of measurements atthe Earth’s orbit. This deviation from the theory canbe neglected (as many other discrepancies) if one isinterested only in order of magnitudes, but, undoubt-edly, such intriguing inconsistency is worthy to be asubject of keen interest.

The assurance that Br decreases as r−2 leads tothe situation, when among different assumptions onthe nature of the effect, a hypothesis about the inap-plicability of the theory due to non-ideality of spaceplasma was not seriously considered. Meanwhile,one can see that the observed effect may be explainedeasily using this hypothesis. Let’s calculate the dif-ference between the magnetic flux FS(r) at some

heliocentric distance r and FS 1 AU at 1 AU, takinginto account (2):

ΔFS = FS(r) − FS_1 AU (3)

= 4π[|Br|r2 − B1 AU(1 AU)2

]

= 4π[B1 AU

( r

1 AU

)−5/3r2 − B1 AU(1 AU)2

]

= 4πB1 AU

(1 AU)−5/3

[r2−5/3 − (1 AU)2−5/3

].

In some studies (see, for example, [11, 12, 20])the factor of 2π is used instead of 4π, as half ofthe flux is directed away from the Sun and half issunward, but it does not change the matter of theeffect. This dependence is graphically represented asa black curve in Fig. 2. The points are ΔFS valuestaken from [8]. In [8] ΔFS was calculated on the basisof several spacecraft data and averaged over 0.1 AU(the corresponding deviations can be found in Fig. 5from [8]). The standard assumption that |Br| variesas r−2 was used in [8] for the ΔFS calculations.

Figure 2 demonstrates rather good agreementbetween the data of [8] and the curve (3). Forexample, theoretical curves in [9] calculated in as-sumption of kinematic effects show the upward trend.It is remarkable that the calculations according to (3)do not require anything but heliocentric distance.Moreover, the suggested approach explains easily themysterious “separating point” of ΔFS (on either sideof which ΔFS is negative and positive). It is easyto see from (3) that this point, shown by light-grey



lines in Fig. 2, is 1 AU at the axis of abscises. Thisis a natural consequence of the fact that ΔFS wascalculated in [8, 9] on the basis of practically thesame data as taken in [13] for derivation of the |Br| =

B1 AU ·(

r

[1 AU]

)−5/3

dependence. Therefore, B0

in [8, 9] and in [13] coincide: B0 = B1 AU. Obviously,this point may slightly shift if another database isused, as B0 changes correspondingly.

Of course, the effects discussed in [9–12, 20] alsoexist and amplify the revealed trend. Among otherthings, the flux excess effect can be additionally in-fluenced by the latitudinal dependence of Br, whichwill be discussed below. Note that the differencebetween the calculated and observed flux (dependingon distance as R−y) appears for any y �= 2. Hence,there is a need for further study of the Br behavior inthe inner heliosphere as seen by different spacecraftand at different phases of solar cycle.

2.2. Latitudinal and Solar Cycle Dependences of Br

To answer the question about the dependency orindependency of Br on latitude, look at the entirepicture of the solar wind parameters’ change providedby Ulysses. Hourly data for the entire period ofmeasurements are shown in Fig. 3. The spacecrafttrajectory is presented in panel (а), where the latitudeis shown in white and the heliocentric distance r—in black. Referring to it, three areas of the increasedamplitudes and disturbances of all parameters areseen in the other panels. They correspond to relativelysmall distances from the Sun (r ≤ 2 AU) and thefast change in heliolatitude. The maximum of theparameters’ change occurs at crossings of the eclipticplane.

Guided by morphological data analysis, investi-gators made conclusions that the solar wind speeddecreases and density increases around ±30◦ of theecliptic plane (see, for example, [20, 21], http://ulysses.jpl.nasa.gov/science/mission_primary.htmland http://ulysses.jpl.nasa.gov/2005-Proposal/UlsProp05.pdf). At the same time, it is believed thatthe radial component of the IMF has no latitudinaldependence at any certain heliocentric distance. Thisstatement forms the basis for many studies ([8–12,20–23]).

The recent paper [23] gives typical views on thissubject: Br does not depend on latitude, as “the mag-netic flux density (referred to 1 AU) tends to be uni-form, at least in the fast, polar solar wind > · · · > themagnetic flux density measured at a single point isa representative sample of the absolute value of themagnetic flux density everywhere in the heliosphere”([23]). As was mentioned above, such an approach

gives gratifying results at the first approximation, butmore detailed analysis can give a key to the explana-tion of many inconsistencies between the theory andobservations.

An unbiased look at the picture of the radial (b),tangential (c) IMF components and the IMF strength(d) in Fig. 3 may put in doubt the statement of latitu-dinal independence of Br, because the IMF growth(as well as all its components’ increase), occurringsimultaneously with the solar wind speed decreaseand density increase, is rather obvious. However,taking into account the double Br dependence (onboth latitude and distance), an additional statisti-cal analysis must be performed. It is reasonableto separate variables and investigate how the radialIMF component varies with latitude and heliocentricdistance. Then, a least-square 3-D surface “Br—latitude—distance” can be plotted (see Fig. 4).

The radial IMF component in the subspace “Br—heliolatitude” (Fig. 4a) displays two trends: Br in-creases toward the ecliptic plane, and there is someless-expressed Br enhancement in the polar lati-tudes. Fig. 4b represents Br changing with distance.The |Br| radial decrease was partially studied in theSection 2.1. The combined pattern of these twodependencies is shown in Fig. 4c as a 3-D surface.

The same kind of surface for the IMF strengthB is given for comparison (Fig. 4d). Both panelsdemonstrate very similar behavior for Br and B: themagnetic field decreases with distance, and it hasmaximum at the ecliptic plane (this increase is mostclearly expressed at small distances from the Sun).The slight increase of Br and B in polar regions is aninteresting feature which may be related to peculiar-ities of the solar magnetic field generation (dynamowaves effect) as was predicted in [24].

The found effect of the IMF strength increase atthe ecliptic plane may be demonstrated in anotherway. Let us analyze Ulysses data for three selecteddistance ranges from the Sun (1–2 AU, 2–3 AU,and 3–4 AU) and separate them by latitude (aboveand below 40◦). The radial component distribution fordifferent latitudes and heliocentric distances is shownin Fig. 5ab. One can see that at the same distance rfrom the Sun, the high-latitude Br values are alwayssmaller in comparison with low-latitudes values. Thisis a plain evidence of the found effect. Therefore, theradial IMF component can not be considered as in-dependent of heliolatitude because of its pronouncedincrease it the ecliptic plane vicinity, especially atsmall heliocentric distances.

Continuing the analysis of the Br histogram, itis necessary to mention the Br “bimodality effect”(see Introduction), which became an object of specialinterest during the last years. It is known that atthe Earth’s orbit, the horizontal IMF components


850 KHABAROVA

10

1990Year

200

400

600

800

92 94 96 98 2000 02 04 06 08 20100

20

30

40

50

Den

sity

, cm

–3

Vel

oci

ty, km

/s

5

0

10

15

20

25

–20

–10

0

10

B

, nT

B

t

, nT

10

–10

–15

–5

0

5

B

r

, nT

Dis

tance

to S

un, A

U

2

3

4

5

6

Hel

iola

titu

de,

deg

–100

–50

0

50

100(a)

(b)

(c)

(d)

(e)

(f)

Fig. 3. The IMF and solar wind data, provided by the Ulysses spacecraft for the entire period of measurements (1990–2009).(a) the Ulysses’ trajectory, (b) the radial component of the IMF, (c) the tangential IMF component, (d) the IMF strength,(e) the solar wind speed, (f) the solar wind density.

(the GSE coordinate system) or radial and tangentialcomponents (RTN, in the ecliptic plane) have a two-humped form. First, variations of the histograms’view with solar cycle was investigated in [25]. Then,the work discussing the histograms’ change withdistance followed [26] (this preprint’s results werepartially published in [13]). The question about thedependence of the magnetic flux density (Br · r2) his-togram’s shape on the solar wind flow type (high-

speed, low-speed and CME) as well as on the solarcycle was discussed in [23].

Figure 5 shows that the effect of fast Br his-togram’s bimodality disappearance found in [13, 26]for the IMF in-ecliptic measurements looks signifi-cantly smoothed at high latitudes. Two peaks trans-formation into one peak with increasing r is clearlyseen at low latitudes (Fig. 5b), but histogram’s bi-modality is still apparent at 3–4 AU at high latitudes



–4

1 2

B

r

, nT

r

, AU3 4 5 6

–2

0

2

4(b)

–4

–60

B

r

, nT

Heliolatitude, deg–30 0 30 90

–2

0

2

4(a)

–90 60

(c)

(d)

3

2

1

12

34

5

|

B

r

|

, nT

r

, AU

9060

30

–90–60

–300

Heliolatitu

de, deg

3

2

1

12

34

5

B

, nT

r

, AU

9060 30

–90–60–300

Heliolatitude, deg

4

5

6

Fig. 4. The IMF behavior in the inner heliosphere as measured by Ulysses: (a) the latitudinal dependence of Br ; (b) the radialBr dependence; (c) 3-D representation of (a) and (b); (d) the same as (c), but for the IMF strength B.

(Fig. 5a). Obviously, at high latitudes, the bimodalitydisappears farther from the Sun. Possible reasons forthis phenomenon are discussed below.

It would be interesting to trace changes in the Br

histogram at high and low latitudes at different solarcycle phases. One can analyze histograms of thehorizontal IMF (GSE) components at 1 AU in theecliptic plane, using many spacecraft’s data collectedin the OMNI long-time database (see. Figs. 6a and6b). The histograms become broader at solar activitymaxima, their peaks are reduced, but the bimodalitydoes not disappear. It is useful to note for furthercomparisons that the Bx IMF component in GSE co-ordinate system equals to −Br in the RTN coordinatesystem.

The relation of the Br histogram shape at high lat-itudes to the solar activity cycle is shown in Figs. 6cand 6d, which represents parts of Fig. 5a for selectedcycle phases. The Ulysses observations at the lati-tudes above ±40◦ covered two minima and one max-imum of sunspot numbers. At solar activity minima,the histograms’ bimodality is expressed clearlier thanat the solar maximum. Dominance of one or anotherhistogram’s hump in Figs. 6c and 6d is related to sta-tistical prevailing of positive/negative polarity activeregions on the Sun. As a whole, the bimodality effectdisappears neither in minimum, nor in maximum ofsolar activity at high latitudes.

During the solar activity maximum, the his-tograms’ spreading is observed at all distances from


852 KHABAROVA

10

0–4

(b)

B

r

, nT

5

15

25

20

30

–3 –2 –1 0 1 2 3 4

1–2 AU

2–3 AU

3–4 AU

Low latitudes (below ±40°)

10

0–2.0

(a)

B

r

, nT

5

15

25

20

30

–1.6 –1.2 –0.8 0 0.4 0.8 1.2 1.6

1–2 AU

2–3 AU

3–4 AU

High latitudes (above ±40°)

–0.4

Num

ber

in i

nte

rval

, %

Fig. 5. The latitudinal dependence of the Br histogram seen at different heliocentric distances: (a) high latitudes, (b) lowlatitudes. The grey curve corresponds to 1–2 AU; the thick black curve—to 2–3 AU; the thin black curve—to 3–4 AU.

the Sun. This effect is known in the ecliptic plane,1 AU (see Figs. 6a, 6b), where it is usually explainedby the impact of CMEs, most frequently occurringat solar activity maxima. Hence, the observed high-latitude histograms’ broadering indirectly indicatesthat CMEs fill the significant part of the inner helio-sphere.

Temporal (solar cycle) changes of the interval be-tween the positive/negative histogram peaks seen inFigs. 6a and 6b were investigated in [25], where theIMF strength along the Parker spiral BL was calcu-lated on the basis of OMNI data. It was found thatthe variations of the distance ΔBL from one peak toanother have the same tendency as was demonstratedin Fig. 6: ΔBL reaches maximum in maxima of solaractivity and minimum in solar activity minima. Onecan see that the distance Δ between the humps ofthe histogram correlates with the peaks’ height. Ifthe histogram spreads, the peaks’ height decreases.This helps to fill the gap in our knowledge of theIMF behavior at high latitudes. There is no sufficientinformation from Ulysses on the IMF there duringsolar maxima, but as the solar cycle dependenciesof the BL bimodality are same at any latitudes, itis possible to expect that ΔBr varies with cycle atthe latitudes above ±40◦ in the same way as at lowlatitudes.

2.3. Whether the Radial IMF Component Dependson the Solar Wind Speed? The Solar Wind Speed

Changes with Latitude and Solar Cycle

This is remarkable that Figs. 5 and 6 are con-sistent with some results of [23]. The magnetic fluxdensity (Br · r2) bimodality is expressed in the “fast”solar wind rather than in the “slow” solar wind asfollows from figure 1 in [23]. The solar wind speed Vmeasured by Ulysses has a two-peaked distribution,so separation of the “fast/slow” solar wind was madein [23] according to this fact. Having in mind thatV has only one-peak distribution at the Earth’s orbit,let’s puzzle out why the Ulysses data give these twopeaks. What does the “fast” or “slow” solar windmean when we use Ulysses measurements?

V is believed to be approximately independent oflatitude and longitude in [23]. The solar wind typesare divided according to the Ulysses-measured Vdistribution peaks: the “slow wind” has velocitiesV < 400 km/s and the “fast wind” flows faster than600 km/s independently of latitude or heliocentricdistance. Meanwhile, more detailed analysis does notconfirm that the Br (and, consequently, the magneticflux density) is determined anyhow by V . A thesisabout the latitudinal independency of V is not con-firmed either. As one can see below, the found in [23]



–10 –6 –2 2 6 10

B

y

, nT

25

20

15

10

5

0

(b)

Num

ber

in i

nte

rval

, %

–10 –6 –2 2 6 10

B

x

, nT

25

20

15

10

5

0

(a)

Solar-activitymaximum

Solar-activityminimum

1 AU, the ecliptic plane

–2.0 –1.6 –1.2 –0.8 –0.4 0 0.4 0.8 1.2 1.6 2.0

B

r

, nT

(d)

(c)

25

20

15

10

5

0

25

20

15

10

5

0

1–2 AU2–3 AU3–4 AU

1–2 AU2–3 AU3–4 AU

Solar-activity minimum

Solar-activity maximum

Latitudes above ±40°

Fig. 6. The solar cycle dependence of the Br histogram: (a, b) the horizontal IMF components Bx and By in the GSEcoordinate system at different phases of the solar cycle. The hourly OMNI2 data for 1977–2009 are used (1 AU, the eclipticplane). (c, d) the high-latitude Br histogram’s view (Fig. 5а) during two minima (1994–1997, 2006–2009) and one maximum(1999–2002) of solar activity as measured by Ulysses. The colors are as in Fig. 5.

–60

r

, A

U

Latitude, deg–30 0 30 90

2

4

(b)

–90 60

3

5

1

6

400

B

r

, nT

Velocity, km/s600 800

–4

4

(a)

200 1000

–2

2

6

0

Fig. 7. (a) The radial IMF component Br and the solar wind speed V scatterplot. (b) The Ulysses’ trajectory (the “latitude—distance” dependence). All available Ulysses data are used.

dependence of Br on the fast/slow solar wind, in fact,is a latitudinal dependence.

The solar wind speed dependencies are shown inFigs. 7–9. Fig. 7a is illustrative of a scatter of pointsin the “radial IMF component—solar wind speed”subspace, where two clouds of points are seen. Thereis no Br dependency of V inside each cloud. Asone can see below, these two clouds correspond to

two humps of the V distribution. To answer thequestion about the nature of the V distribution’s bi-modality, it is necessary to plot the Ulysses “latitude-distance” curve (Fig. 7b), as well as to reveal the“speed-latitude” and “speed-distance” dependencies(Fig. 8).

As seen in Fig. 8, the V distribution’s bimodality(Fig. 8a) is a consequence of the solar wind speed


854 KHABAROVA

1 2

r

, AU3 4 5 6

400

600

800

1000

(c)

–60Latitude, deg

–30 0 30 90

(b)

–90 60

(d)

12

34

5

r

, AU

9060

30

–90–60

–300

Latitude, d

eg

900

200

Vel

oci

ty, km

/s

800700600500400300200

Vel

oci

ty, km

/s

400

600

800

Vel

oci

ty, km

/s

1000

20080

Number in interval60 40 20

(a)

100 0

400

600

800

1000

200

Fig. 8. The solar wind speed V as seen by Ulysses: (a) the V histogram; (b) the latitudinal dependence; (c) the radialdependence; (d) 3-D representation of (b) and (c).

complex latitudinal (Fig. 8b) and radial (Fig. 8c) de-pendencies. Fig. 8b resembles a flying eagle withtwo wings and two legs (one leg, corresponding tonegative latitudes, is more expressed). The radialsolar wind speed dependence is shown in Fig. 8c.It is also degenerate, as there are both lower andupper branches of the curve. Fig. 8d was built in thesame manner as Figs. 4c and 4d. One can see there“wings” of Fig. 8b and some V increase at 2–3 AU ofFig. 8c, as well as well-known strong V decrease inthe area of zero latitude (the ecliptic plane).

The V -“wings” and “legs” in Fig. 8b are relatedto both the Ulysses’ trajectory features and the solarcycle. “Legs” represent V in high latitudes in thesolar activity maximum, and “wings” correspond to V

measurements in high latitudes during solar activityminima. This follows from Fig. 9 where V was plottedseparately for the latitudes above ±40◦ (Fig. 9a) andlatitudes of ±10◦ around the ecliptic plane (Fig. 9b) incomparison with the solar cycle. Fig. 9a shows thatthe solar wind speed has minimum in the maximum ofsolar activity and maximum during the solar activityminima.

Therefore, the high-latitude solar wind is fast (asit often believed) at solar activity minima only. Com-parison of Fig. 9a and Fig. 9b indicates that V valuesat high latitudes during the solar maximum are closeto low-latitudes values of the solar wind speed. It isinteresting that variations of the near-ecliptic solarwind speed have a ∼2 years outstripping shift regard-



1990 1995 2000 2005 2010Year

250

200

150

100

50

Num

ber

of

sunsp

ots

(c)

300

700

600

500

400

Vel

oci

ty, km

/s

(b)

300

700

600

500

400

800

900(a)

Vel

oci

ty, km

/s

Fig. 9. The solar cycle dependence of the solar wind speed V on the basis of the Ulysses data: (a) the annual mean of V at theheliolatitudes above ±40◦, (b) the annual mean of V near the ecliptic plane (±10◦ around), (c) the sunspot numbers (27-daysaveraging, the OMNI database).

ing the solar cycle maxima/minima. There is a peakduring 2002–2005, a period known for its anomalies.As it was shown in [27], the large-scale magneticfield of the Sun unexpectedly dominated during thatperiod, and this is seen in the solar wind too. The solarwind speed relation with the solar cycle is obvious justin high latitudes. Near the ecliptic plane, it is stilldoubtful.

Summarizing, one can see that a bright solarcycle dependence of V is the main source of the Vdistribution bimodality. The central part of Fig. 8b(the “eagle’s body”) is V in low latitudes; the high-latitudinal solar wind in solar activity minima formstwo upper branches (“wings” of V > 700 km/s). Be-

sides, the high-latitude solar wind in the maximumof solar activity is characterized by V values approx-imately from 400 km/s to 600 km/s (see the “legs”in Fig. 8b). Weakness of this branch is explainedmerely by insufficiency of measurements in the solarmaximum (Ulysses provided high-latitude measure-ments for two minima and for one maximum of solaractivity only). A hypothetical continuation of theUlysses measurements would lead to enhancement ofthe “legs,” and the whole picture of the solar windspeed latitudinal dependence would be completed.The “wings” in Fig. 8b form the 650–850 km/s peakof the V distribution (Fig. 8a). The “legs” and the


856 KHABAROVA

1

Vel

oci

ty, km

/s

r

, AU2 3 4 6

200

600

(b)

5

400

800

0

1000

Low latitudes

1 2 3 4 6

(a)

50

High latitudes at solar-activity minimum

Vel

oci

ty, km

/s

200

600

400

800

1000

Fig. 10. The radial dependence of the solar wind speed V on the basis of the Ulysses data: (a) the high latitudes (above ±40◦),solar activity minima; (b) in the ±10◦ vicinity of the ecliptic plane, all data.

“eagle’s body” give the second peak of the V distri-bution with values of 250–550 km/s. Thus, the Vdistribution bimodality is determined by changing ofthe Ulysses’ latitude and solar cycle.

This effect may lead to some misunderstandings.For example, the authors of [23], in fact, did notstudy the magnetic field of the “fast” solar wind, butrevealed the high-latitude solar wind properties atsolar activity minima. This fact does not diminishthe results [23], but demands a correct approach totheir interpretation. It is obvious from Fig. 8b that thelower threshold of the “fast” solar wind (600 km/s), asselected in [23], corresponds to a super-fast stream atlow latitudes, but at high latitudes such a stream issuper-slow. This also should be taken into accountin further investigations. Most reasonable “fast/slowwind” separation has been already performed in [28],where the threshold of 450 km/s was used, and itsphysical causality was confirmed.

Regarding the radial dependence of V , the lowerbranch in Fig. 8c, rising with distance accordingto theoretical expectations, mainly belongs to theUlysses measurements in low latitudes, and thebranch, decreasing after 3 AU, primarily correspondsto the measurements in high latitudes. The “pri-marily” word is used here because there is also thesolar cycle V dependence. Furthermore, Ulyssesregistered fast streams in high latitudes even during

the solar activity maximum (mainly in 2001–2002).Meanwhile, overall, the solar wind speed radiallydecreases in high latitudes at solar activity minima,and V radially growth in low latitudes independentlyof solar activity cycle (see Fig. 10). Two solaractivity minima data were selected for high latitudes(Fig. 10a), and all available data for near-eclipticmeasurements (±10◦ of heliolatitude) were used(Fig. 10b).

A “noisy” part of the data in Fig. 10b is a conse-quence of the Ulysses orbital rotation, as a spacecrafthas a minimal velocity in its apogee, so the r intervalof > 5 AU contains more points and the curve isnoised by non-stationary effects such as CME. Thesame effect is seen in Figs. 1b and 4b.

According to Figs. 7–10, the solar wind speed de-pends on heliolatitude and solar cycle phase in a highdegree. At the same time, the radial IMF componentdoes not depend on the solar wind speed.

3. CONCLUSIONS AND DISCUSSION

Several problems important for understanding ofthe large-scale picture of the magnetic field in theinner heliosphere were discussed in the paper:

1. What is the law of the radial IMF component(Br) decrease with heliocentric distance?



2. What is the cause of the “magnetic fluxexcess”—the enhancement of the open solar fluxcalculated from distant spacecraft measurementsover the flux measured 1 AU?

3. Whether Br depends on heliolatitude?4. How does the Br distribution’s bimodality vary

with latitude and solar cycle?5. Is there the Br dependence of the solar wind

speed V ?6. How does V depend on heliolatitude, heliocen-

tric distance and solar activity?The results of the analysis of the Ulysses and

OMNI data show that listed above problems are re-lated. For example, the deviation of the Br(r) lawfrom the classical dependence used in Parker-likemodels is one of the main causes of the “magneticflux excess.” The latitudinal Br dependence also con-tributes to this effect. At the same time, the depen-dence of the magnetic flux density on the solar windspeed reported in [23], in fact, is the Br dependenceon latitude and solar cycle.

Correspondingly to the listed above questions 1–6, it was found out that:

1. The radial IMF component Br decreasesas r−5/3, but not as r−2.

This conclusion was based on the Ulysses da-ta analysis for the entire period of measurements.The Br module approximation was used to avoid the“module of the mean or mean of the module” problem(see Section 2.1). The same result was obtainedin [13] from the five spacecraft data analysis.

The phenomenon’s nature may be not only in thefact that Parker’s model is stationary, but also inpoor applicability of the “frozen-in” magnetic fieldassumption to the non-ideal space plasma condi-tions. Indeed, the “frozen-in” IMF conditions’ breakoccurs in the solar wind very often, for example, insome vicinity of current sheets. As was shown [13],zero IMF lines, corresponding to current sheets, areobserved in the solar wind inside the IMF sectorsmore frequently than it was supposed earlier (zerolines were expected to be mainly an attribute of theheliospheric current sheet).

A magnetic reconnection recurrently occurs at thelarge-scale heliospheric current sheet as well as atsmaller-scale current sheets during the solar windexpansion. As a result, current sheets are subjectsof a multiplication (bifurcation) process. A significantpart of the heliosphere is filled with secondary currentsheets and other products of the magnetic reconnec-tion. Under averaging, it looks as a radial increase ofturbulence and intermittency of the solar wind plasma(especially in low latitudes), and, finally, as a breakof the expected IMF radial dependence law. It isworthy to remark that the solar wind plasma obeys

the Parker’s theory much better than the IMF does.This is also a confirmation that the IMF is not fullyfrozen into the solar wind plasma.

2. The “magnetic flux (FS) excess” is mainly aconsequence of the previous conclusion.

Accepting that the Br decreases as r−5/3, it is easyto explain the calculated values of the excess ΔFS—i.e. the difference between FS obtained through dis-tant spacecraft data and the measurements at theEarth’s orbit. Obviously, any deviation of the reallaw of the Br radial decrease from the theoreticallyexpected leads to unavoidable dissimilarities at thepoint-to-point recalculations using Br · r2 formula.Thus, experimental studies of the radial IMF depen-dence observed by different spacecraft seems to bea perspective way of future investigations. The lati-tudinal IMF dependence as well as effects discussedin [11, 12, 20] contribute to the “flux excess” effect.

3. The radial IMF component depends on theheliolatitude. Br as well as the magnetic flux canbe considered as independent of heliolatitude just in arough approximation. More detailed analysis showsthat the radial IMF component and the IMF strengthincrease toward the ecliptic plane. Additionally, someIMF enhancement is observed in the polar solar wind.The result is checked by different methods, includingthe analysis of the Br histograms at different helio-centric distances.

Most probably, the discussed underestimation ofthe IMF latitudinal dependence comes from historicaldevelopment of views on the large-scale solar mag-netic field. Before the Ulysses mission, the dominantopinion was that the magnetic field of the Sun shouldbe similar to the Earth’s magnetic field, which isvery close to a classical magnetic dipole. The polarmagnetic field strength was expected to be twice ofthe equatorial value. The Ulysses data did not confirmthat. Against the background of the expected dif-ference between the polar and low-latitude IMF, thepicture observed by Ulysses looked as any absence ofthe latitudinal dependence of the IMF.

It is necessary to remark that the statement of theBr latitudinal independence seems very strange fromthe point of view of specialists who investigate solarprocesses, since the zonality and difference of the so-lar magnetic field properties at low and high latitudesare obvious and proved by long-term observations. Itseems very unlikely that all observed differences takeplace only at distances of less than ten solar radiiand then disappear (the open magnetic flux uniformitydemands such an assumption).

Discarding of the Br and B increase in low he-liolatitudes inevitably reduces a quality of even verycompetent models (such as [29] and [30]), since they


858 KHABAROVA

are based on slightly simplified views on the large-scale IMF picture in the inner heliosphere, assuminga constant Br at any latitude with a sharp [29] ormore gradual [30] change of the Br sign at the eclipticplane.

4. (a) The Br histogram’s bimodality is ex-pressed at high heliolatitudes (above ±40◦)rather than in low latitudes. It is observed at highlatitudes at the heliocentric distances, where ithas already vanished near the ecliptic plane.

This fact may bear evidence of radial increasing ofturbulence and intermittency in the solar wind due tomentioned above processes in current sheets (mostnotably, in the heliospheric current sheet). Indeed,unimodality of the Br histogram means an absenceof any clear sector structure. Most possibly, mixing ofstructures occurs in low latitudes at 3–4 AU, but inhigh latitudes the solar wind remains well-structuredat the same distances.

(b) At high heliolatitudes, the Br histogram’sview has the same solar cycle dependence as atlow latitudes: the distribution spreads and itspeaks are reduced at the solar maximum.

This means that both Br and the Br internal scat-ter increase at solar activity maximum. Most possibly,this is a consequence of the CME impact on the high-latitude solar wind. Therefore, this result confirms theobservers’ conclusion that CMEs fill a significant partof the inner heliosphere [31].

5. Br is independent of the solar wind speed.6. (a) The solar wind speed significantly de-

pends on heliolatitude. In high latitudes, itstrongly depends on solar activity.

The solar wind speed increase at high latitudes (incomparison with its values near the ecliptic plane) hasbeen known since the first Ulysses flyby. After that,the solar wind above ±40◦ has been mostly believedto be fast.

The current investigation revealed that aforesaidis true only for solar activity minima. During a solaractivity maximum, the high-latitude solar wind speeddecreases to values, typical for low heliolatitudes. Thedifference between the yearly mean high-latitude V inmaximum and minimum is 200–300 km/s.

The latitudinal dependence of V has four branchesresembling “an eagle with outspread wings.” Thesolar wind flows above ±40◦ form the high-speed“wings” during solar activity minima. At the solaractivity maximum, lower high-latitude branches areformed (the “legs” with V ∼ 270−500 km/s). Thelow-latitude solar wind speed is characterized by val-ues of 300–550 km/s well-known through the databy in-ecliptic spacecraft.

(b) The solar wind speed depends on distancedifferently at high and low latitudes.

There are two branches of the radial V depen-dence. The lower one is mainly formed by V measure-ments in low latitudes, when V expectedly growthswith distance. This branch also contains a significantpart of data obtained at high latitudes during the solaractivity maximum.

The upper branch mainly corresponds to high-latitudinal V measurements at solar activity minima.It looks like an arch having maximum at ∼2−3 AU.Overall, V in high latitudes decreases with heliocen-tric distance. Further investigations should be carriedout to find why the coronal hole’s plasma propagateswith decreasing speed.

Therefore, using the solar wind speed data byUlysses, it is necessary to take into account the fol-lowing:

—the high-latitude solar wind is not permanentlyfast;

—the V histogram’s bimodality is a consequenceof the latitude and solar cycle dependencies of thesolar wind speed;

—the solar wind speed increases with distance atlow latitudes as well as at high latitudes during solaractivity maximum, but the high-latitude V radiallydecreases in solar activity minima.

All found peculiarities of the solar wind plasmapropagation may be used in advanced models suchas [32].

All the discussed effects together demonstrate thatthe observed solar magnetic field and plasma prop-erties are clearly seen in the solar wind at rather fardistances from the Sun, beyond the Earth’s orbit. TheUlysses measurements have revealed both solar windzoning and distinctions of the solar wind propagationat different phases of the solar cycle.

Keeping in mind all above said, one can see asubstantial input of high-latitude missions into ourunderstanding of the magnetic field properties in theheliosphere. The Ulysses mission provides nutrimentfor long-time investigations, although statistical datainsufficiency does not allow detailed analysis of thesolar cycle dependencies, and, in some measure, thereis no enough information on the radial IMF variationin heliosphere. Many hopes are anchored now on thefuture Russian Interheliozond mission. Meantime,the obtained here results will be verified and supple-mented through the analysis of available data of pastmissions.

The Ulysses data were taken from the Coordi-nated Data Analysis (Workshop) Web-site: http://cdaweb.gsfc.nasa.gov/ (the magnetic field andplasma data were provided by Prof. A. Balogh andDr. John L. Phillips, Imperial College, London, UK).



OMNI data were obtained from the GoddardSpace Flight Center OMNIweb plus web-site:http://omniweb.gsfc.nasa.gov/.

The author cordially thanks Prof. Vladimir Obridkoand Dr. Kirill Kuzanyan for fruitful discussions.

This study was supported by the RFBR grant nos.11-02-00259 and 13-02-92613.

REFERENCES1. R. L. Rosenberg, J. Geophys. Res.: Space Phys. 75,

5310 (1970).2. A. V. Belov, V. N. Obridko, and B. D. Shelting, Geo-

magn. Aeron. 46, 430 (2006).3. E. J. Smith, J. Geophys. Res.: Space Phys. 118, 58

(2013); doi:10.1002/jgra.50098.4. M. M. Echim, J. Lemaire, and �. Lie-Svendsen,

Surv. Geophys. 32, 1 (2011).5. V. N. Obridko, A. F. Kharshiladze, and B. D. Shelting,

Astron. Astrophys. Trans. 11, 65 (1996).6. P. Riley, Astrophys. J. Lett. 667, L97 (2007);

doi:10.1086/522001.7. M. J. Owens, H. E. Spence, S. McGregor,

et al., Space Weather 6, S08001 (2008);doi:10.1029/2007SW000380.

8. M. J. Owens, C. N. Arge, N. U. Crooker,et al., J. Geophys. Res. 113, A12103 (2008);doi:10.1029/2008JA013677.

9. M. Lockwood, M. Owens, and A. P. Rouillard,J. Geophys. Res. 114, A11104 (2009);doi:10.1029/2009JA014450.

10. E. J. Smith, J. Geophys. Res.: Space Phys. 116, A12(2011); doi:10.1029/2011JA016521.

11. M. Lockwood and M. Owens, J. Geoph. Res.: SpacePhys. 118, 5 (2013); doi:10.1002/jgra.50223 (2013).

12. M. Lockwood and M. Owens, Astrophys. J. 701, 964(2009); doi:10.1088/0004-637X/701/2/964.

13. O. Khabarova and V. Obridko, Astrophys. J. 761, 82(2012); doi:10.1088/0004-637X/761/2/82.

14. P. Riley, J. A. Linker, and Z. Mikic, J. Geophys. Res.107, A7 (2002); doi:10.1029/2001ja000299.

15. N. A. Schwadron and D. J. McComas,Geophys. Res. Lett. 32, L03112 (2005);doi:10.1029/2004GL021579.

16. K. Mursula and I. I. Virtanen, J. Geophys. Res. (2013,in press); doi:10.1029/2011JA017197.

17. C. M. Ho, B. T. Tsurutani, J. K. Arballo,et al., Geophys. Res. Lett. 24, 915 (1997);doi:10.1029/97GL00806.

18. M. Neugebauer, R. J. Forsyth, A. B. Galvin,et al., J. Geophys. Res. 103, 14587 (1998);doi:10.1029/98JA00798.

19. X. P. Zhao, J. T. Hoeksema, Y. Liu, andP. H. Scherrer, J. Geophys. Res. 111, A10108(2006); doi:10.1029/2005JA011576.

20. M. Lockwood, R. B. Forsyth, A. Balogh, andD. J. McComas, Ann. Geophys. 22, 1395 (2004).

21. E. J. Smith, A. Balogh, R. F. Forsyth, et al., Adv.Space Res. 26, 823 (2000); doi:10.1016/S0273-1177(00)00014-4.

22. A. Balogh, E. J. Smith, B. T. Tsuru-tani, et al., Science 268, 1007 (1995);doi:10.1126/science.268.5213.1007.

23. G. Erdos and A. Balogh, Astrophys. J. 753, 130(2012); doi:10.1088/0004-637X/753/2/130.

24. K. M. Kuzanyan and D. D. Sokoloff, Geophys.Astrophys. Fluid Dyn. 81, 113 (1995);doi:10.1080/03091929508229073.

25. A. B. Asgarov and V. N. Obridko, Sun Geosphere 2,29 (2007).

26. O. Khabarova and V. Obridko, Preprint Inst.Terrestr. Magn. (IZMIRAN, Troitsk, Moscow, 2011).http://arxiv.org/ftp/arxiv/papers/1102/1102.1176.pdf

27. V. N. Obridko, E. V. Ivanov, A. Ozguc, et al., SolarPhys. 281, 779 (2013).

28. Yu. I. Ermolaev, N. S. Nikolaeva, I. G. Lodkina, andM. Yu. Ermolaev, Kosmich. Issled. 47, 1 (2009).

29. I. S. Veselovskii and A. T. Lukashenko, Solar Syst.Res. 46, 149 (2012).

30. A. V. Usmanov, W. H. Matthaeus, B. A. Breech,and M. L. Goldstein, Astrophys. J. 727, 84 (2011);doi:10.1088/0004-637X/727/2/84.

31. D. F. Webb, T. A. Howard, C. D. Fry, et al., SolarPhys. 256, 239 (2009); doi: 10.1007/s11307-009-9351-8.

32. A. V. Usmanov, M. L. Goldstein, andW. H. Matthaeus, Astrophys. J. 754, 40 (2013);doi:10.1088/0004-637X/754/1/40.

Translated by O. Khabarova


Date post:	28-Nov-2023
Category:	Documents
Upload:	independent
View:	0 times
Download:	0 times

The interplanetary magnetic field: Radial and latitudinal dependences

Documents