N O R T H - S O U T H A S Y M M E T R Y IN THE H E L I O S P H E R I C
C U R R E N T S H E E T AND THE IMF S E C T O R S T R U C T U R E
T. E. G I R I S H and S. R. P R A B H A K A R A N N A Y A R
Department of Physics, University of Kerala, Kariavattom, Trivandrum, India
(Received 17 August, 1987; in revised form 24 March, 1988)
Abstract. It is shown that in a heliomagnetic field the presence of a magnetic quadrupole in addition to a magnetic dipole introduces a north-south asymmetry in the heliospheric current sheet (HCS) about the heliographic equator. The dominant polarity of the interplanetary magnetic field (IMF) for the above type of current sheet reverses sign at a transition latitude O r , which lies in a heliohemisphere opposite to the one in which the HCS has more heliolatitudinal extension. The position of Or in the heliosphere and the north-south asymmetry introduced in the HCS change with the relative phase of the dipole and quadrupole components present in the solar magnetic field. The effect of the above type of asymmetric HCS in the IMF 'mean sector width' is evaluated and the results are in agreement with the observations during the minima Of solar cycle 21.
1. Introduction
Interplanetary magnetic field (IMF) sector structure discovered first by Wilcox and Ness (1965) is now described in terms of a warped heliospheric current sheet (HCS) separating heliohemispheres of opposite magnetic polarity. The structure and evolution of the HCS have been studied by many authors (Newkirk and Fisk, 1985; Hoeksema, Wilcox, and Scherrer, 1982, 1983; Hoeksema, 1984; Korzhov, 1983; Akasofu and Fry, 1986). The heliospheric current sheet is often found to be placed asymmetric about the heliographic equator (Korzhov, 1983; Tritakis, 1984a, b). Several solar parameters and activity indices like sunspot area, sunspot groups, photospheric magnetic field, faculae, solar flares, green coronal line intensity, etc., have been found to show north-south asymmetry with respect to the heliographic equator (Waldmeier, 1971 ; Rene Roy, 1977; Howard, 1974; Fracastro and Marocchi, 1978; Newton and Milson, 1955). Osherovich, Tzur, and Gliner (1984) and Osherovich, Gliner, and Tzur (1985) explained the observed north-south asymmetry in the solar coronal structure during sunspot minimum as due to the presence of a magnetic quadrupole in the heliomagnetic field. Hundhausen (1977) and Thomas and Smith (1981) described the HCS in terms of a tilted dipole model. It is now known that the role of higher order solar magnetic multipoles cannot be neglected when interpreting the structure of the HCS during a solar cycle (Hoeksema, 1984; Saito and Swinson, 1986; Hakamada and Akasofu, 1981; Bruno, Burlaga, and Hundhausen, 1982).
The dominant polarity effect of the IMF (Rosenberg and Coleman, 1969) is based upon a model of the HCS represented by a simple sinusoidal curve, symmetric about the heliographic equator (Svalgaard and Wilcox, 1976). It is apparent from different studies that the heliographic latitudinal variation of the dominant polarity of the IMF at 1 AU cannot be explained in terms of a simple sinusoidal and symmetric HCS model
Solar Physics 116 (1988) 369-376. �9 1988 by Kluwer Academic Publishers.
370 T. E. GIRISH AND S. R. PRABHAKARAN NAYAR
(Moussas and Tritakis, 1982; Tritakis, 1984a; Xanthakis, Tritakis, and Zerefos, 1981; Neidner, 1982). Tritakis (1984a, b) suggested that the deviations from the Rosenberg and Coleman (1969) model can be understood in terms of a sinusoidal current sheet shifted northward or southward parallel to the heliographic equator during periods like sunspot minimum.
In the present study, we have investigated the effect of the presence of a magnetic quadrupole in addition to a magnetic dipole in the heliomagnetic field in shaping the HCS geometry and the resulting IMF variations near Earth. It is seen that the quadrupole moment introduces a north-south asymmetry in the HCS. This also causes interesting change in the heliographic latitude, where the reversal of the sign of the dominant polarity of the IMF takes place during a solar rotation period, depending on the relative phases of the dipole and quadrupole components in the solar magnetic field. The effect of the above type of HCS on the 'mean sector width' changes of the IMF Earth is also evaluated and found that the inequalities resulted from such a study is in agreement with HCS observations during 1974-1977 compared to the shifted sinusoidal HCS model (Tritakis, 1984a, b).
2. Transition Latitude and the Asymmetry in the Heliospheric Current Sheet
The HCS can be described in heliocentric coordinates by the relation
0 --- R 1 sin(q~) + R 2 sin(2q~ - b), (1)
where R~ and R 2 are the inclinations due to the dipolar and quadrupolar magnetic moments present in the heliomagnetic field, 0 and ~b are the heliographic latitude and longitude, and b is the phase lag between the maxima of the dipole and quadrupole moments (Hakamada and Akasofu, 1981; Saito and Swinson, 1986). The geometry of the heliospheric current sheet in the interplanetary medium is determined by the relative values of R 1, R2, and 8.
Heliographic latitude of Earth varies annually between + 7.25 ~ The IMF sector structure properties at any fixed heliographic latitude of observation during a solar rotation period can be easily found from the geometry of the HCS given by Equation (1) (Hakamada and Akasofu, 1981). The dominant polarity of the IMF (Rosenberg and Coleman, 1969) observed during a solar rotation change with heliographic latitude of the observer and the heliolatitude of its sign reversal depends on the geometry of the HCS in the interplanetary medium. Let us define the transition latitude O r as the heliographic latitude at which the dominant polarity of the IMF observed during a solar rotation period just reverses the sign. The plane, given by 0 T = constant, separates regions of dominant IMF of opposite magnetic polarities in the heliosphere. For a sinusoidal HCS symmetric about the heliographic equator (R 2 = 0) this plane coincides with the plane of solar equator.
Let us investigate on what happens to a HCS given by the relation (1) with R 2 @ 0 and ~ va 0. In Figure 1, the variation in the geometry of the HCS with Rz/R 1 is depicted for a fixed value of b (20~ For such a system the transition latitude 0T has been
ASYMMETRY IN THE CURRENT SHEET AND SECTOR STRUCTURE 371
4G
r
t o
C / �9 \
/" \
/ B ]" t " \ ' \
i / .<---~:~ i , / / A - ~
/;//
/o ~'~
" , 1 . / / ~ " " , '` /,,;,
~,--~---~/ / \ ' . . . . . , / \ / ' \ /
\
I I I
0 ~ 120 ~ 240 ~ 360 ~
Fig. 1. H e l i o s p h e r i c c u r r e n t s h e e t g e o m e t r y for ~5 = 20 ~ a n d
(C) R2/R 1 = 1.0. (A) R2/R ~ = 0 .25, (B)R2/R 1 = 0.5,
evaluated and Figure 2 shows the variation of 0 r with R 2 for a fixed value of R 1 and
6. As the ratio of R2/RI is increased, 0r increases until Rz/R 1 = 0 . 5 , where it reaches a maximum and then decreases. We define the asymmetry factor A as the difference in
the maximum heliolatitudinal extention of the HCS in the northern and southern
heliospheres. For a HCS with either R 1 = 0 or R 2 -- 0, A = 0. From Figures 1 and 2 we find that a north-south asymmetry is introduced in the HCS due to the presence of the quadrupole term (R2) which has a phase lag with the dipole term (R~). In this case the asymmetry factor A is found to increase with increase in (Ra/R~) for a fixed value of
6. To find the dependence of 0r maximum on 6, the HCS geometry has been evaluated for different values of 6 as shown in Figure 3. The corresponding change in 0r with 6
is shown in Figure 4. It is interesting to note that 0r variation is symmetric about 6 = 0 ~ with maximum deviation from the heliographic equator at b = + 90 ~ From Figure 4 it is noticed that as the sign of the phase factor 6 is reversed, the transition latitude (Or) and the asymmetry in HCS (A) reverse sign.
We find that for a complete description of the north-south asymmetry in the HCS one has to calculate both 0 r and A, which depend on the relative values of R1, R 2 , and 6. It is interesting to observe that the transition latitude 0 T lies in a heliohemisphere
372 T.E. GIRISH AND S. R. PRABHAKARAN NAYAR
D
-1"
J , - 2 ~
OT_3o
_/4 ~
Fig. 2.
I I ! I I I |
0 4 8 12 16 20 24
)R 2
Variat ion o f O r wi th R2 for 6 = 20 ~ and RI = 20 ~
Fig. 3.
O
4d
,~o~. i~.7 ~--, \
2d "' : \ \ k\
///
-2(
-4( J ! t I I
0 ~ 40 ~ 120 ~ 200 ' 280 ~ 360"
Hel iospher ic current sheet geometry for R2/R 1 = 0.5 and (A) 6 = 0 ~ (B) 6 = 45 ~ (C) 8 = 90 ~
ASYMMETRY IN THE CURRENT SHEET AND SECTOR STRUCTURE 373
8 ~
P O
_ s o
9r
/ \ /
\ /" \ / /
\ \ / /
\ / / \ \ /
\ / \ /
\ / \ /
\ \ / /
A / / / / ~ \ \ \ / \ k / / \
/ \ / \
! \
i i \ \ l k
/ / \
/
o
16
0
I f I I
- 1 4 0 ~ - 6 0 ~ 0 ~ 6 0 ~
Fig . 4. V a r i a t i o n o f O r a n d ,4 w i t h ~ f o r R a / R 1 = 0.5.
140 ~
opposite to the one in which HCS has maximum heliolatitudinal extension, for the case R 2 # 0 and ~ # 0. This is in contrast to a simple sinusoidal current sheet shifted parallel to the heliographic equator (northward or southward) where 0r lies in the same heliohemisphere in which HCS has maximum extension (Tritakis, 1984a, b).
3. Influence of Solar Magnetic Quadrupole on 'Mean Sector Width' Variations of IMF
Tritakis (1984a, b) and Moussas and Tritakis (1982) studied the mean sector width changes of IMF sectors observed when Earth is in northern or southern heliolatitudes separately. Tritakis (1984a, b) assumed an asymmetric current sheet model to explain
374 T. E. GIRISH AND S. R. PRABHAKARAN NAYAR
the mean sector width variations during sunspot minimum in which a sinusoidal HCS
is simply displaced parallel to the solar equator. During solar maximum, Tritakis
assumed a symmetric HCS model to explain the corresponding IMF sector variations near Earth. Let us evaluate the mean sector width of IMF observed near Earth, when
a quadrupole component in the solar magnetic field is also taken into consideration to
describe the HCS. For simplicity let us assume that the 'mean IMF sector width' as the width of the IMF sector at a mean heliographic latitude _+ 7.25 (2/n) ~ in the northern
and southern heliospheres. One can evaluate separately the 'mean sector width' for
positive sector ( = XA) and negative sector (= Xr) at the mean heliographic latitudes _+ 7.25 (2/re) ~ in the northern and sourthern heliosphere. We have evaluated these
parameters of HCS corresponding to different values of R1, R 2 and b and obtained the
valid inequalities between 'mean IMF sector width differences' in the northern and
southern heliospheres as observed near Earth following Tritakis (1984a, b). The
inequalities resulted from such a model of asymmetric HCS due to the presence of the magnetic quadrupole component is compared with the model of Tritakis (1984a, b) as
given in Table I, where
Ibll = 12A -XTI north, Ib2l = ]-~A - X r ] south. (2)
TABLE I
ComparisonofvalidinequalitiesofmeanlMFsectorwidthsinthetwomodelsofasymmetric HCS
Type of Shifted sinusoidal Non-sinusoidal current current sheet current sheet model sheet model with
(Tritakis, 1984a) quadrupole contribution
Northward depressed Ibll < Ib2l Ibl[ > ]b21 (A> o)
Southward depressed Ibl[> [b2] Ibll<lb21 (A<O)
For any current sheet model cyclic every 360 ~
XA north + Xr north = XA south + 2 r south
and
(3)
lall = IXA n o r t h - XA southl = ] X r n o r t h - XTSOUth] = la2l. (4)
So the inequalities mentioned in Tritakis (1984) between l a, I and l a21 are not valid for a cyclic current sheet and we have considered only the inequalities between I bll and [b21.
Let us test the validity of the present model describing the mean sector width variations of IMF using the IMF and solar observations for the minimum of solar
ASYMMETRY IN THE CURRENT SHEET AND SECTOR STRUCTURE 375
cycle21. Between 1971-1977, the HCS is found to be on an average depressed southward as evident from different inferences of HCS during that period (Korzhov, 1983: Smith and Thomas, 1986). According to the observed IMF data near Earth during 1974-1977 the valid mean sector width inequality as reported by Tritakis (1984a, b) is given by
Ibll < Ib~] (5)
From Table I, the above inequality in (5) corresponds to a southward depressed HCS according to the present model in agreement with HCS observations during that period, where as Tritakis (1984a) suggested a northward depressed HCS model. This result indicates the presence of a quadrupole component in the solar magnetic field during this period. The presence of a quadrupole moment in the heliomagnetic field during the same period is also evident from different studies (Hoeksema, 1984; Saito and Swinson, 1986; Hakamada and Akasofu, 1981; Bruno, Burlaga, and Hundhausen, 1982).
4. Discussion
The north-south asymmetry in the HCS has been explained as due to a north-south asymmetric distribution of solar activity or solar wind streams (Saito etal., 1977; Tritakis, 1984a, b). The geometry of the HCS is basically determined by the large scale solar magnetic field (Hoeksema, 1984). In this work we have shown that the presence of a quadrupolar component in the solar magnetic field modifies the geometry of the HCS and can introduce a north-south asymmetry in the HCS about the heliographic equator. For such a heliospheric current sheet resulting due to the presence of both dipole and quadrupole components of the solar magnetic field (with their maxima out of phase), the transition latitude Or, where the dominant polarity of IMF near 1 AU reverses sign, lies in a heliohemisphere opposite to the one in which the HCS maximum heliolatitudinal extension. So, for the above type of HCS geometry, suppose the current sheet is extended more in northern heliosphere, the transition latitude 0r is in the southern heliosphere, causing an excess of IMF with the magnetic polarity identical to that of solar north pole near the solar equator.
HCS observations during 1974-1977 support the present study concerning the effect of an asymmetric HCS on IMF sector widths observed near Earth in comparison with that of Tritakis (1984a, b). Using the above concept one can evaluate the quadrupole contribution in the solar magnetic field from IMF mean sector width data for the past few solar cycles.
Acknowledgements
The authors wishes to thank Dr N. P. Korzhov, Sib. Izmiran, U.S.S.R. and Dr J. T. Hoeksema, Stanford University, U.S.A. for providing necessary heliospheric current sheet data. The authors are also thankful to the referee for useful suggestions.
376 T. E. GIRISH AND S. R. PRABHAKARAN NAYAR
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