CHAPTER V

STRUCTURE OF THE HELIOSPHERIC CURRENT SHEET

AND SOLAR WIND VELOCITY CHARACTERISTICS

IN HoW SECTORS

page

5.1.

5.2.

5.3.

5.4.

5.5.

Introduction

Symmetric HCS structure and solar

wind speed in IMF sectors

North-south asymmetry in the HCS and

characteristics of high speed solar

vdnd streans

Discussion

Sun~ary of results

110

113

118

127

133

110

CHAPTER V

STRUCTURE OF THE HELIOSPHERIC CURRENT SHEET AND

SOLAR WIND VELOCITY CHARACTERISTICS IN I~W SECTORS

5.1. Introduction

Spacecraft observations have revealed that solar

wind characteristics observed near 1 AU are well organised

~around I[1F sector boundaries (Wilcox and Ness, 1965~ Wilcox,

1968~ Rhodes and Smith, 1975). Sawyer (1976) showed that

solar wind velocity has a peak invariably in the middle of

each IflF sector observed near earth. It is also found that

even though high speed solar wind strea~s usually follow the

IMF sector boundaries, sectors without streams and Sectors

with more than one stream are also observed. One can also

find differences in the solar wind velocity distribution in

IMF sectors of opposite polarities during a solar rotation

period and this IMP polarity dependence of solar wind plasma

distribution change with ti~e and heliolatitude of

observation (Bame et al., 1977).

Svalgaard and Wilcox (1976a) introduced the

terminology of Hale sector boundaries in the Sun, by

defining the Hale (anti-Hale) boundary as the half of

sector boundary (northern or southern hemisphere) where

a

the

III

change in magnetic polarity across the boundary is the ~ame

as (opposite to) that from a preceding to a following

sunspot. They have also shown that the brightness of the

green corona and the strength of the photospheric magnetic

field are a maximum (minimum) above Hale (non-Hale) sector

boundaries. A study by Nayar (1979) and subsequently by

Lundstedt et a1. (1981) showed that there is a difference in

the change in geomagnetic activity around Hale and non-Hale

IMF sector boundaries. Solar flares are observed to occur

preferentially around Hale sector boundaries (Dittmer, 1975;

Levitskii, 1980).

Using solar \lind observations -near 1 AU Nayar and

Revathy (1982) showed a difference in the variations of

solar wind speed around Hale and anti-Hale sector

boundaries. According to them the velocity gradient

following a Hale sector boundary is higher than the same

after a non-Hale sector boundary. Sastry (1986) performed a

super epoch analysis of solar wind speed around Hale and

anti-Hale boundaries following Nayar and Revathy (1982)

separating the solar wind flows from transient solar events.

Sastry (1986) found that the solar wind velocity has a

higher gradient after non-Hale sector boundaries and

concluded that the zonal-sector solar magnetic

match/mismatch affects the high speed stream characteristics

near 1 AU.

112

Large scale features in the coronal expansion is

known to be controlled by the solar magnetic field. The

three dimensional nature of the solar corona and the

associated large scale solar magnetic field is responsible

for the solar wind and IMP variations near 1 AU (Svalgaa~d

and Wilcox, 1978; Hundhausen, 1977). The solar wind velocity

generally increase away fro~ the HCS and this heliomagnetic

latitude dependence of the solar wind speed change with the

phase of the solar cycle (Newkirk and Fisk, 1985; Hakamada

and Akasofu, 1981; Hakamada and Munakata, 1984; Zhao and

Hundhausen, 1981, 1983; Pry and Akasofu, 1987; Bruno et al.,

1986; Kotova et al., 1987). Limitations in expressing the

solar wind speed near 1 AU as a function of heliomagnetic

latitude are nainly due to the asymmetric solar uindspeed

distribution about the HCS (Suess et al., 1984; Pry and

Akasofu,

1986).

1987; Kojima and Kakinuma, 1987; Bruno et al.,

In this study we seek to explain the observed

characteristics of solar wind velocity associated with IMP

sectors of opposite polarity and Hale/anti-Hale sector

boundaries, in ter~s of the structure of the HCS and the

associated heliomagnetic latitude dependence of solar wind

(HakaE1ada and Akasofu, 1981). He have studied helio~agnetic

lati tude changes in H1F sectors associated with symmetric

and asymmetric RCS structures to explain the difference in

solar wind velocity

113

characteristics in them. The

characteristics of high speed streams were studied during

some years during solar cycle 20 and 21. This study shows

that the north-south asymmetry in HCS influences the

amplitude and duration of high speed streams observed near 1

AU.

5.2. Symmetric HCS structure and solar wind speed

in ItW sectors

The heliolatitudinal variation of solar wind speed

. for a dipole solar Qagnetic field configuration has been

studied extensively (Pnuemann 1976, Pnuemann and Orrall,

1986; Steinolfsen, 1982; Hhang, 1983; Hundhausen, 1978; Fry

and Akasofu, 1987). Let us consider a tilted dipole solar

magnetic field. For this type of heliomagnetic field the

position of the heliomagnetic equator with respect to the

heliographic equator is sinusoidal. The resulting HCS

geometry is a sinusoidal curve symmetric about the solar

equator.

Consider a sinusoidal HCS structure symmetric

about the heliographic equator with a dominant positive

magnetic polarity above HCS. Figure 5.1 shows a typical

heliospheric current sheet with an amplitude p (8 = P sin¢).

The dashed line ABC and AIBIC I shows positions of earth in

114

the northern and southern heliolatitudes (+ &ejduring the

autumnal and vernal months. In this system, within a solar

rotation, earth re~ains above the current sheet for 27/2

days and below the current sheet for 27/2 days, when the

• • Iearth lies in the heliographlc equator. Conslder the earths'

position in the northern heliographic latitude shown by

ABC in figure 5.1. Earth will be in, a negative sector

within points A and B (heliolongitudes) and in a positive

sector within points Band C. Within the sector AB, as we

move from A to B the heliomagnetic latitude (angular

distance from the current sheet) goes on changing, attaining

a peak value at the mid point Ql of the sector AB,

corresponding to a heliomagnetic latitude ~e- p. Since the

solar wind velocity has a positive gradient from the

heliomagnetic equator, the solar wind velocity within the

sector AB solar wind shows a similar variation with a peak

value at the point Ql. Similarly in the positive sector BC,

the solar wind velocity has a magnetic latitudinal

dependence attaining a peak value at the point Q2 (= P ~ ~ e

) at the middle of this sector. The heliomagnetic latitudes

of the points Ql and Q2 are given in table 5.1.

Now let us consider the sector boundaries at

points A and B. At point A, earth experiences a sector

boundary crossing from a negative sector AB to a positive

sector BC (-/+ sector boundary). Here the change is from a

QJ'U::l.j..J0,"".j..J

+~eraH

U0,""

..c: a0..ra>-l -&3tJl0

0,""HQJ:c:

A'

- --)t- -..--

Ql

- - - - - - - - -k- - - --

IQl

Heliographic longitude

+

~ ­Q2

- - - - ~--,

Q2

f-'f-'U1

Fig.S.l. Schematic rep~esentation of a sy~etric heliospheric current sheet

116

Table 5.1

t1~imum valu~ of heliomagnetic latitude in IMF

sectors for a symmetr"ic HCS

Type of sectorstructure

+

Northernheliosphere

6e + ~

6e - ~

Southernheliosphere

-6e + f3

-6e - 0

117

sector with a peak value V+. Here V+ corresponds to the

velocity at magnetic latitudes oe + ~. Similarly at point B,

which is a +/- sector boundary, the type of change is from a

sector with peak value in velocity V: So in this example we

find that, when the dominant polarity of the northern

heliosphere is positive, the change in the solar wind

velocity around the -/+ sector boundary is higher compared

to that around the +/- sector boundary. Similarly one can

evaluate the solar \1ind changes within sectors of southern

heliolatitude (-6e) shown by A'B'C' in figure 1. In this

case Ql' and Q2' are the points of maximum heliomagnetic

latitude in the negative and positive sectors given by table

5.1. One can see that the passage of the +/- sector boundary

in the southern heliosphere causes a higher increase in

solar wind velocity compared to the -/+ sector boundary

passage.

We have considered here an idealistic current

sheet to explain the observed differences associated with

+/- and -/+ sector boundaries originating from northern or

southern heliolatitudes. It is seen that the velocity

distribution within positive and negative sectors show

different features due to difference in the change in

heliomagnetic latitude. By definition Ir1F polarity change

around Hale sector boundaries in the northern and southern

heliosphere remains unaltered during the course of a solar

:t18

cycle while dominant polarity of the IMF in a given

heliohemisphere reverses sign during the declining phase of

the sunspot activity. So for a symmetric HCS geometry and

associated heliomagnetic latitude dependence of solar wind,

one can observe a higher gradient in solar wind velocity

after Hale sector boundaries during the descending phase of

a solar

sector

cycle as compared with the same

boundaries. The reverse will be

after non-Hale

true during the

ascending phase of the sunspot cycle.

5.3. North-south asymmetry in the ReS and characteristics

of high speed solar wind streams

Heliomagnetic latitude chanses for an asymmetric HCS

It is known from chapters II and III that the

presence of non-dipolar solar magnetic field components

(e.g., quadrupole) introduces an asymmetry in the HCS

geometry about the solar equator. For illustrating the

heliomagnetic latitude changes in IMF sectors for an

asymr~etric Res, one has to rClainly consider the asymmetry in

the heliolatitudinal extension of the HCS in the opposite

heliohe!l1ispheres (6.). This is because 6. is important in

determining the angular distance from the current sheet

comoared to 8 T or a .~ 0

119

Let us consider the case of a non-dipolar solar

magnetic field and related asymriletric RCS with 6 t- 0 . If PH

and f3 s are the maximum heliographic latitude of RCS in the

northern and southern heliohemispheres respectively then we

have

asymmetry factor 6 = lPN' - l~sl

In figure 5.2 we schematically represent such an asymmetric

current sheet. For any heliolatitude of observation +de(position ABC) in the northern heliosphere or -oe in the

I ' I

southern heliosphere (positionABC) during a solar rotation

period the maximum value of heliomagnetic latitude in IMF

sectors of opposite polarity is shown in table 5.2 If the

maximum value of heliornagnetic latitude in the positive IMF

sector is +represented by A and the same in negative IMF

sector is by A-, we define the heliolatitude of observation

at which IA+I = lA-I during a solar rotation period as 9 .e

For a symmetric sinusoidal RCS (6. =0) \le have ee

coincides with heliographic equator. For any asymmetric RCS

with ~ t-O we have

For e.g. let f3N

=

e = ~/2e .

+8 0 and f3 s

i.e., when 6 t- 0, e 'I- o.e

o= -12

A 0 _2 0Here u = -4 and ee =

Thus at e we calculate A+ and A using table 5.2. So thate

=

=

2 1008 + =

12 - 2 = 100 i.e.,

---..;----4<--- -----

f--'NC

c----------X­

Q2

IQ

l

-~

Q1

-- - --~- -----

A

~

~N

Wrc;;::l.jJ.~

.jJ

+deco~

().~

.c 00..co\..l

-<£eUl0.~

~

(J)

::c

Heliographic longitude

Fig.5.2. Schematic representation of an asynmetric heliospheric current sheet

121

Table 5.2

r1~imum value of heliomagnetic latitude in IMF

sectors for an asymmetric HCS

-------------------------------------Type of sectorstructure'

+

Northernheliosphere

68 + (1s

68 - (~N

Souther-nhel i ospher- e

-e58 + (1s

-68 - (iN

122

Heliographic latitude of earth varies between

+7.25 0 during an year. Assuming a stable RCS structure let

~av+ and ~av represent the mean value of the maxima in

heliolatitude observed in positive and negative IMF sectors

respectively during an year. For an RCS structure with ~<O

and assuming positive polarity above the HCS as in figure

5.2, one can evaluate the average value of the heliornagnetic

latitude

sectors

maxima

during

in positive (A + .-av ) and negatlve (\av )

an year. For simplicity we can assume

H1F

that

A +av and Aav correspond to the value of the heliomagnetic

latitude maxima ill"t positive andnegative H1F sectors

respectively at the mean heliographic latitude of earth

during an year. Since earth has equal excursion of +7.250

from heliographic equator the mean heliographic latitude of

earth during an year can be taken as Oo~ At the heliographic

equator VJe have

Let

+For ~ < 0 and f3 s > f3N

; we have Aav > Aav

+V represent the observed mean value of the solar wind

velocity maxima observed in IMF sectors of positive polarity

during an year and V- in IMF sectors of negative polarity.

Then we have for a positive magnetic polarity above the RCS- +

with 6 <0, V+>V-. Similarly for an RCS with 6 >0, V >V . The

above

123

inequalities reverse with reversal in dominant

polarity above/below the HCS. Here we have, assumed a

positive gradient in solar wind velocitY,with heliomagnetic

latitude (Hakamada and Akasofu, 1981).

Amplitude and width of high speed streams and

asy~~etry parameters of HCS

To illustrate the effect of an asymmetric HCS

structure in solar wind velocity characteristics near 1 AU,

we make use of the published catalogues of high speed

streams (Lindbald and Lundstedt, 1981, 1983; Havromichalaki

et al., 1988). Data gaps are often present in the solar Hind

velocity observations near earth. Since these data gaps

affect the calculation of the parametedassociated with high

speed streams, vie have selected periods where at least 80%

data coverage is available (Couzens and King, 1986). During

1967, 1974, 1975, 1976, 1978 and 1982 there is good coverage

of solar wind plasma observations and the present study is

restricted to these periods. For the above years we have

studied the relationship betueen the amplitude and duration

of corotating high speed streams of opposite polarity near 1

AU and asymmetry parameters 6 and 8 T of HCS investigated in

the earlier chapters. Information on the above high speed

stream characteristics is derived from Lundstedt and

124

Lindblad (1981, 1983) for 1967, 1974 and 1975 and for the

years 1976, 1978, 1982, from Havromichalaki et ale (1988).

Let V+ and V represent the mean amplitude (velocity

maximum) of corotating high speed streams in positive and

negative IMF sectors respectively during an year. Similarly

\Je define + -Wand W as the mean width of corotating high

speed streams in positive and negative IMF sectors during an

+ - + -year. The parameters V , V , ~'/ and H were calculated for

the yean 1967, 1974, 1975, 1978 and 1982 and the results are

depicted in table 5.3. The nunber of positive and negative

high speed solar wind streams observed during an year are

also shown in the same table.

To compare this result with aSyffiQetry in RCS weDb-

make useAthe yearly average signs of 6 and eT

given in table

4.2 and 4.3 in chapter IV. From tables 5.3 and 4.2, and 4.3

we have constructed the valid inequalities related to the

parameters err' 6. , v+, V , v/+ and \"1- dan the results are

depicted in table 5.4. We find from table 5.4 that the

inequalities between V+ and V for the years under

consideration correspond with the sign of 6 of HCS implying

the role of asymmetry in heliomagnetic latitudinal

organisation of solar wind velocity in IMF sectors. We find

that the inequalities connecting Vl+ and ~1 are in agreeI:1ent

with + - d t IMFthe inequalities connecting 1 and 1 relate 0

sectors. These ineaualities are in agreement with the sign.1

125

Table 5.3

Yearly mean value of amplitude and duration of

corotating high speed solar wind streams

Year V+ V No.of posi- No.of nega- v/ H

-1 -1 tive streams tive streams (days) (days)(kms ) (kms )

------------------------------------------------------------

1967 585 575 5 15 6.4 7..

1974 707 680 17 17 7.07 9.63

1975 666 627 18 13 6.1 7.3

1976 642 625 15 9 5.7 5.35

1978 578 585 8 11 8.3 6.3

1982 654 679 12 13 8.33 8

126

Table 5.4

Valid inequalities connecting yearly mean amplitude and

width of high speed plasma streams, IMF sector

widths, ~nd sign of 8T and ~ of RCS

Year Amplitude of high 6. vHdth of high H1F sector 8 T

speed streams (RCS) speed streams widths (HCS)

------------------------------------------------------ --~-----

v+ v'1+ - 1+1967 > V ? \'1 > l > gT<O,...;

1974 V+ > V ~<O VI > \"1+ 1 > 1+ gT>O.~ -

1975 v+ > V ~<O H > v/ 1 > 1+ 8T>0,-v

1976 v+ > V 6<0 v/ > VI 1+ > 1 8T<O''V ""'

1978 V > v+ 6>0 vl+ > \'1 1+ > 1 gT<O,-..J ""

1982 V > V+ 6<0 vl+ > H 1+ > 1 gT>O.-V ,..,

of of

127

HCS except for the year 1975. l+Here _ and

represent the yearly average width of IMF sectors of

positive and negative polarity which is also shown for each

year in table 5.4. Thus the above results suggests the

influence of asymmetry in RCS structure in solar wind

velocity characteristics near 1 AU. For the year 1967 we

- + + -have 1 >1 and 8 T>0. Also V >V . If we assume here ~ ~O and

heliomagnetic latitude organisation of solar wind velocity

for a dominant negative polarity above the HCS we infer the

yearly average sign of A as positive i.e., 6 > o.

5.4. Discussion

We have shown that one could explain the observed

differences in solar wind velocity characteristics in IMP

sectors of opposite polarity in terms of the structure of

the heliospheric current sheet and heliomagnetic latitude

organisation of solar wind velocity. We have investigated

the above case for symmetric and asymr,1etric HCS structures.

Comparing observed characteristics of high speed solar wind

streams with the asymmetry parameters of RCS during some

years in solar cycle 20 and 21 we have found that the north-

south asymmetry in HCS, influence not only the HIF

observations (as investigated in chapter IV) but also the

solar wind velocity variations near 1 AU. High speed streams

128

with an IMF polarity opposite to that of the sign of ~

during an year is observed to possess relatively larger

amplitudes compared to the same with anIMF polarity same as

the sign of 6 . Using this concept we have inferred the sign

of the asymmetry in latitudinal extension of the

heliospheric current sheet (6) fro~ observations of high

speed stream amplitudes during 1967. Similarly high speed

solar wind streams with IMF polarity opposite to the sign of

8T

has relatively larger width compared to the sa~e with an

IMF polarity same as the sign of 8T

. This implies that

relatively, larger IMF sectors will be associated with high

velocity solar wind streams of longer duration. It is found

+that the difference in the Dean values between V and V and

between w+ and W given in Table 5.3 are not statistically

significant when a two tail student It' test of significance

is used (Spiegel, 1981). The low statistical significance of

the above analysis can be ascribed due to temporal changes

in solar wind spatial structure during an year (Suess et

al., 1984) or due to the possible association of coronal

.mass ejections (CHE) with the coronal holes (Verma, 1989).

So for further clarification that the asymmetry in HCS

influence high speed solar wind stream characteristics near

1 AU, the average values of the high speed streams in

positive (v+) and negative (V ) IMF sectois are calculated

separately for the periods when earth is in the northern

129

helioshpere of observation (June 7 to December 6) and in

southern heliosphere (Deceober 7 to June 6) during each year

of this study. The results are shown in Table 5.5. In that

table the difference Iv+-v-I in the northern and southern

heliosphere is also shown. For an HCS with 6 < 0 we expect

that

Iv+-v-I northern heliosphere > Iv+-v-I southern heliosphere

Similarly for an HCS with ~ > 0 the opposite of the above

inequality is t~e. Comparing Tables 5.5 and 5.4 one can

find that the inequalities between Iv+-v-I in the northern

and southern heliosphere is in agreement with the sign of 6

of HCS during different years of observation.

The above results suggest that high speed solar

wind characteristics in IMF sectors show north-south

asymmetry about the solar equator due to heliomagnetic

latitudinal organisation of solar \vind around an asymmetric

HCS. Studies of Bame et ale (1977) and DZhapiashvilli et ale

(1979) using solar wind observations during cycle 20 also

provide evidence for an asymmetry in solar wind velocity

characteristics depending on the IMF polarity about the

heliographic equator. Gringauz et ale (1987) provides the

observed characteris:tics of high speed streams (amplitude

and duration) during 1983-84 using PROGNOZ-9 observations

130

Table 5.5

Mean, value of amplitude of high speed streams

in northern and southern heliosphere

near 1 AU

Year

Northern heliosphere

v+ V Iv+-v-I

(Kms-1 )(Kms-1 ) (Kms-1 )

Southern helioshpere

v+ V Iv+-v-I

(Kms-1 ) (Kms-1 ) (~ms-l)

----------------------------------------~-------------------

1967 544 614 70 702 526 176

1974 739 676 63 685 686 1

1975 673 585 88 721 766 45

1976 628 586 42 662 636 26

1978 588 559 29 514 606 102

1982 633 679 46 675 678 3

131

and Kotova et al. (1987) observed a good heliomagnetic

latitudinal organisation of solar wind speed during the same

period. FroQ the above studies (Gringauz et al., 1987;

Kotova et al., 1987) one can find that for the period July

1983 to February 1984 the high speed solar wind streams with

negative IMF polarity is observed to possess relatively

larger averge amplitude and duration sompared to the same of

high speed streams with positive IMF polarity (During this

period dominant polarity of IMF above the HCS was negative).

Since earth covers ~7.25° during this period the above

result can be observed to be in agreement with the average

sign of the asymmetry parameters 6 and 8T

of HCS during the

same period (Fig. 3 of chapter III) i.e., 6 < 0 and 8T < O.

In this study we have assumed the concept of

continuous solar wind velocity distribution associated with

the heliomagnetic latitude similar to that of Hakamada and

(1981)Akasofu

characteristics

in explaining solar wind stream

in IMF sectors. There are also velocity

heliomagnetic latitude relationships derived by some authors

which assumes a plateau in the solar wind velocity

distribution beyond the increase of a critical heliomagnetic

latitude value (Hakamada and Nunakata, 1984; Newkirk and

Fisk, 1985). One must be also aware of the fact that solar

wind velocity distribution is sometimes asymmetric about the

HCS (Fry ad Akasofu, 1987; Bruno et al., 1986).

132

The amplitude of the high speed streams is related

to the size, magnetic field strength and magnetic flux tube

divergence associated with coronal holes present in the low

and mid solar latitudes (Nolte et al., 1976; Eslevich and

Filippov, 1988; Levine et al., 1977). In factJcoronal hol~s

formed above and below the RCS is observed to possess

opposite magnetic polarity (Stewart, 1985). Thus any

asymnetry in HCS structure will also reflected in the

heliolatitudinal distribution of low latitude coronal holes

(Hoeksema, 1984; Simon and Legrand, 1987) influencing the

solar wind stream characteristics near 1 AU. The observed

characteristics of solar wind in IMF sectors is basically

controlled by three dimensional coronal magnetic field

geometry vvhich defines the structure of the RCS and coronal

hole forrnation in the Sun. So the observed differences in

solar wind plasma distribution within IMF sectors of

opposite polarity can be better understood in terms of the

law of distribution of solar wind velocity (heliomagnetic

latitude dependence) around the HCS which often changeS with

the phase of the sunspot cycle (Fry and Akasofu, 1987;

Newkirk and Fisk, 1985).

133

5.5. Summary of results

i) It is shown that one could understand the observed

differences in solar wind velocity distribution in

IMP sectors of opposite polarity or associated

with Hale/anti-Hale sector boundaries near 1 AU in

terms of the structure of heliospheric current

sheet and associated heliomagnetic latitude

dependence of solar wind speed.

ii) Observations during some of years in solar cycle

20 and 21 suggest that the north-south asymmetry

in HCS influence the yearly mean amplitude and

width of corotating high speed solar wind streams

observed in IMP sectors of opposite polarity near

1 AU.