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.