E V O L U T I O N A N D N A T U R E O F N O R T H - S O U T H A S Y M M E T R Y

I N T H E H E L I O S P H E R I C C U R R E N T S H E E T

T. E. G I R I S H and S. R. PRABHAKARAN NAYAR

Department of Physics, University of Kerala, Kariavattom, Trivandrum, India 695 581

(Received in revised form 25 September, 1989)

Abstract. The nature and evolution of north-south asymmetry in the heliospheric current sheet (HCS) has been investigated using solar and interplanetary magnetic field (IMF) observations for the past few solar cycles. The mean heliographic latitude of the HCS (averaged over the solar longitude) '%' is found to be non-zero during many solar rotations indicating that the large-scale solar magnetic field is more ordered in a system where the origin is shifted away from the centre of the Sun. We have shown that the asymmetry in HCS manifests in different forms depending on the transition heliographic latitude of the reversal of dominant polarity of the IMF (Or) and the difference in the maximum latitudinal extension of the HCS in the two solar hemispheres (A). The classification of the observed asymmetry during 1971-1985 and its effect on IMF observations near Earth has been studied. We have also inferred the sign of Or during 1947-1971 using inferred IMF polarity data. The observed sign reversals of O r suggest the importance of periodicities less than the solar cycle period to be associated with the evolution of asymmetry in HCS. Asymmetry in sunspot activity about the solar equator does not seem to relate consistently well with the asymmetry in HCS about the heliographic equator.

I. In troduc t ion

The heliospheric current sheet (HCS), observed near 1 A U as the interplanetary mag-

netic field ( IMF) sector boundary, shows a wide variety of structural changes, often

complex, during the course of the solar cycle (Akasofu and Fry, 1986; Hoeksema, 1984;

Hoeksema and Scherrer, 1986; Newkirk and Fisk, 1985; Tritakis, 1984a; Korzhov,

1983; Behannon et al., 1988). The multipole heliomagnetic structure responsible for the

geometry of the H C S also shows characteristic changes during the solar cycle

(Hoeksema, 1984; Levine, 1980). Like many other solar phenomena, H C S is also found

to show nor th-south asymmetry about heliographic equator (Burlaga, Hundhausen, and

Zhao, 1981; Tritakis, 1984a; Korzhov, 1983). A relationship existing between the

asymmetry in H C S and asymmetry in solar activity has been suggested earlier (Saito

eta l . , 1977; Tritakis, 1984a, b). Girish and Nayar (1988) explained the observed

nor th-south asymmetry in HCS in terms of the higher-order solar magnetic dipoles, viz.,

a magnetic quadrupole in addition to a solar magnetic dipole and also studied the effect

of an asymmetric HCS on the I M F mean sector widths observed near Earth modifying the earlier model of Tritakis (1984a).

In this work the nature and evolution of H C S for the past few solar cycles have been

studied using solar and I M F observations. It is seen that one could classify the observed

asymmetry in H C S about the solar equator into different types depending on the relative

values of the three asymmetry parameters Or, ao, and A defined to characterize the

nor th-south asymmetry in HCS. It is also shown that the yearly average sign of O r could

also be guessed from inferred I M F polarity data. Several sign reversals observed in

Solar Physics 125: 399-407, 1990. �9 1990 Kluwer Academic Publishers. Printed in Belgium.

400 T. E. GIRISH AND S. R. PRABHAKARAN NAYAR

asymmetry parameters of the HCS especially the 0 T suggests the existence of periodici- ties less than 11 years to be associated with the evolution of asymmetry in the HCS and the later when compared with the asymmetry in sunspot activity does not show a consistent relationship between each other.

2. 'Mean' Heliographic Latitude and Different Forms of Asymmetry in HCS

To study the evolution of north-south asymmetry in the HCS during 1971-1985 the following data have been used. For the period 1971-1975 the HCS data inferred from synoptic K corona brightness observations of Korzhov (1982) have been used. For the period 1976-1985 the HCS data of Hoeksema and Scherrer (1986) which is inferred from potential field modelling of the photospheric magnetic field have been used. The data gaps in 1975 and 1976 have been supplemented by the HCS data inferred using K-corona synoptic maps of High Altitude Observatory (Sime, 1988) using the MBC method of inference (Burlaga, Hundhausen, and Zhao, 1981) and from Bruno, Burlaga, and Hundhausen (1984).

The geometry of the HCS in the interplanetary medium is basically determined by the various magnetic multipoles present in the solar magnetic field (Hoeksema, 1984; S aito and Swifison, 1986). The locus of the HCS on the source surface could be approximated by a combination of harmonic functions (Hakamada and Akasofu, 1981)given by

0 = R a sin(q~ - 61) + R 2 sin(2~p - b2) + . . . + R n sin(nq5 - 6n), (1)

where R1, R 2, R 3 . . . . are different terms contributed by heliomagnetic multipoles, viz., dipole, quadrupole, octupole, etc.; 61, 62, 63, ... are the phase shift of the maxima of the corresponding magnetic moments; 0 and ~p are the heliographic latitude and longitude of HCS, respectively. The 'mean' heliolatitude of HCS can be defined as

1 2~

a o = - ~ O(qS). (2) 2re ~=o

Using the HCS data, the mean heliographic latitudes ao, for the Carrington rotations 1580-1765 during the period 1971-1985 have been calculated and depicted in Figure 1. For the rotations 1676-1702, during the solar maximum the HCS geometry is very complex and the a o values are equated to zero. Now the expressions for HCS, Equation (1), must be modified to the form

O= a o + ~ Risin(iO- 60. (3) i = l

For a good approximation n can be taken to be 6. The value of n can change with a phase of the solar cycle, e.g., during solar minimum, n = 2 (Girish and Nayar, 1988). Saito and Swinson (1986) have also used as 'a o' term in their analysis of inferred HCS data.

For a given heliospheric current sheet the transition heliographic latitude 0 T (Girish and Nayar, 1988) is defined as the heliographic latitude where the predominant polarity

E V O L U T I O N OF A S Y M M E T R Y IN C U R R E N T S H E E T 401

15 ~

i0 q

5 c

o 0 c

-5'

-i0'

-15 c

Fig. 1.

I

I I i I [ I | I 1600 1620 1 6 4 0 1 6 6 0 1680 1700 172 0 1 7 2 0

C/~RRINGTON ROTATIONS

Mean heliographie latitude 'a o' of HCS for the Carrington rotations 1580-1765 during 1971-1985.

of IMF observed during the corresponding solar rotation reverses sign. For a simple sinusoidal HCS symmetric about the heliographic equator 0 r lies in the solar equatorial

plane (Figure 2) depicts the variation of 0 r during the Carrington rotations 1580-1765. The third asymmetry parameter A is defined as the difference in the maximum

latitudinal extension of the HCS (Girish and Nayar, 1988) in the northern and southern

heliohemispheres. A > 0 corresponds to a current sheet extended more in the northern heliohemisphere and A < 0 corresponds to a HCS extended more in the southern heliohemisphere. Figure 3 depicts the variation of A during the solar rotations 1580-1765. Let (0 ~ A ~ be the asymmetry parameters for a HCS geometry given by (1). When the geometry is modified to that of (3), i.e. when a o r 0, then we will observe the asymmetry parameters of HCS in the modified geometry as

0 r = 0 ~ A--A ~ o. (4)

For any HCS ao = 0, the only type of asymmetric geometry about the heliographic equator possible is that of when Or and A are of opposite sign, i.e., Or is situated in a heliohenfisphere opposite to the one in which the HCS has maximum heliolatitudinal extension (Girish and Nayar, 1988). Let this form of asymmetric HCS be labelled as case (A). When a o r 0, different types of asymmetric HCS systems are possible depend- ing on the values of parameters in (3) such as R1, R2, R 3 , . . . and b l , b2, b3, . . . . They can be of following cases: case (B) O r and A are of same sign, i.e., 0 r is in the same

402 T. E. G I R I S H A N D S. R. P R A B H A K A R A N N A Y A R

,0el 30o[

0 ~

-i0 ~

-20 O

-30 ~

-40 O

i

' ? t~ j,I I

Fig. 2.

1600 1620 1640 1660 1680 1700 1720 1740

CARRINGTON ROTATIONS

Transition heliolatitude O r of HCS for the Carrington rotations 1580-1765 during 1971-1985.

20 ~ I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i ti , i 10 o i~ I~11 s II , i

-i0 (

- 2 0 ~

Fig. 3.

1600 1620 1640 1660 1680 1700 1720 1740

CARRINGTON ROTATIONS

Asymmetry in HCS extension Z for the Carrington rotations 1580-1765 during 1971-1985.

EVOLUTION OF ASYMMETRY IN CURRENT SHEET 403

heliohemisphere where HCS has maximum extension in latitude. Case (C)A = 0, O r ~a 0 and case (D) O r = 0, A r 0.

The computations of O r and A for the period 1971-1985, supports such a classifi- cation of asymmetry in HCS as defined above. During 1971-1985 the occurrence of asymmetric HCS cases (A) and (B) are most common and that of(C) and (D) are rare. Out of 186 solar rotations between Carrington rotations 1580-1765 we have only 159 solar rotations where O r and A could be determined accurately since for solar rotations 1673-1699 the HCS geometry is too complex to allow such determination. During the above period the relative percentile distribution is as follows. Case (A) 49.6 70 (79 solar rotations), case (B) 3770 (59 solar rotations), case (C) 6.370 (10 solar rota- tions), and case (D) 6.9~/o (11 solar rotations).

3. Effect on IMF Observations near 1 A U

Girish and Nayar (1988) studied the effect of the asymmetric HCS type (A) on the IMF sector structure observed near 1 AU. The effect of the other asymmetric HCS types, viz., (B), (C), and (D) on the IMF observations near Earth can also be similarly investigated. For the asymmetric HCS geometries (A), (B), and (C) the sign of Or is the basic parameter which will determine the dominant polarity of IMF observed near Earth's orbit. Suppose the Or is in the northern heliosphere (0r > 0), then the IMF with magnetic polarity identical to the solar south pole will be found to be in excess near heliographic equator. The interesting case is that of an HCS type (D). In the case Or = 0 and when A is greater than/less than zero, the magnetic polarity of IMF that could be found in excess at Earth's orbit will be identical to that of solar south/north pole. Let L n and L~ denote the yearly average IMF sector widths observed near Earth with magnetic polarity identical with solar north pole and south pole, respectively. The yearly average of sign of Or could be inferred as

0 T>Of or L n < L , and O r < 0 for L n > L ~ .

Such an inference of 0 v is done for the period during 1972-1985 using IMF observations near Earth's orbit. In Table I we give a schematic representation of the sign of the yearly average values of 0 r calculated from inferred HCS data (Hoeksema and Scherrer, 1986; Korzhov, 1982). We also give the O r signs inferred from IMF observations and the sign of average A obtained using inferred HCS observations. The symbol 'O ' means no asymmetry or the sign is indeterminable.

Except during 1975-1977 and 1983-1985 the average configuration of HCS is that of system (A). During 1977 the average picture is ambiguous due to the fact that for some solar rotations during that period HCS configuration resembles that of (D). During 1983-1985 the system resembles configuration (B). It is seen from Table I that sign of 0 T inferred from IMF observations agree well with the yearly average sign of O r obtained from HCS data. This implies that one could infer the sign of O r using IMF observations for the past few solar cycles. Such an attempt is made as shown in Table II for the period 1947-1971 using the catalogue of inferred IMF polarities of Svalgaard (1976). For years

404 T. E. GIRISH AND S. R. PRABHAKARAN NAYAR

TABLE I

Schematic representation of yearly average sign of 0 r from HCS observa- tions and from IMF observations, A from HCS observations and asym-

metric in sunspot activity As for the period 1972-1985

Year Or Or A As (HCS) (IMF) (HCS) (sunspot)

1972 + + - - 1973 + + - - 1974 + + - - 1975 - + - + 1976 - - - + 1977 O O - + 1978 - - + + 1979 �9 0 0 + 1980 0 0 0 - 1981 + + - - 1982 + + - - 1983 . . . . 1984 . . . . 1985 - - -

b e t w e e n s o l a r m a x i m a a n d s o l a r p o l a r r e v e r s a l p e r i o d ( 1 9 4 7 - 1 9 4 9 , 1 9 5 7 - 1 9 5 8 , a n d

1 9 6 9 - 1 9 7 0 ) O r h a s b e e n a s s i g n e d ' O ' s i g n in T a b l e I I .

T o c o m p a r e t h e y e a r l y a v e r a g e s i g n o f 07 - w i t h t h e s i g n o f a s y m m e t r y in s u n s p o t

a c t i v i t y f o r t h e p e r i o d 1 9 4 7 - 1 9 8 4 t h e p a r a m e t e r As = R n / ( R n + Rs) h a s b e e n u s e d ,

w h e r e As d e n o t e s t h e a s y m m e t r y i n t h e s u n s p o t a c t i v i t y a b o u t t h e h e l i o g r a p h i c e q u a t o r ,

R n a n d R s a r e t h e a n n u a l m e a n s u n s p o t n u m b e r s in t h e n o r t h e r n a n d s o u t h e r n h e l i o -

h e m i s p h e r e s , r e s p e c t i v e l y ( K o y a m a , 1985 ; S w i n s o n , K o y a m a , a n d S a i t o , 1986) . T h e

TABLE II

Schematic representations of yearly average sign of 0 T from inferred IMF data and asymmetry in sunspot activity As for the period 1947-1971

Year 0 T AS Year 0 T As (IMF) (sunspot) (IMF) (sunspot)

1947 O - 1960 + + 1948 O - 1961 + + 1949 O + 1962 + + 1950 + + 1963 + + 1951 + + 1964 + + 1952 + + 1965 - + 1953 - + 1966 - + 1954 - + 1967 - + 1955 - + 1968 - + 1956 + + 1969 O + 1957 O + 1970 O + 1958 O + 1971 + + 1959 + +

EVOLUTION OF ASYMMETRY tN CURRENT SHEET 405

parameter As is assigned + sign if As > 0.5, - sign if As < 0.5, and it is assigned 'O ' sign if As = 0.5. The sign of As for the period 1972-1985 is shown in Table I and for the

period 1947-1971 is shown in Table II. From Table II we find that between 1949-1971 the sign of As remained positive while Or has several sign reversals during this period. During 1972-1982 it is interesting to observe that the sign of As is predominantly opposite to that of Or. But this relation breaks down during 1983-1984 where O r and As are of the same sign.

4. Discussion

It is well known that the geometry of the HCS is basically determined by the nature of the large-scale solar magnetic field which is subjected to significant spatial and temporal variations. We have shown from observations that the north-south asymmetry in HCS is not simple in form such as displacements from solar equator (Tritakis, 1984a; Korzhov, 1983), but manifests itself in different geometrical configurations depending on the parameters O r and A. Long-term changes in the north-south asymmetry in HCS is evident from the present study using solar and IMF observations. Swinson, Koyama, and Saito (1986) from an analysis of long-term data on the asymmetric sunspot activity suggested its relation with the 22-year magnetic solar cycle. Tritakis (1984a, b) also have associated the asymmetry in HCS with 22-year heliomagnetic cycle. From Figures 1-3 we can find several sign reversals in the asymmetry parameters of HCS especially Or during the course of a solar cycle. The inferred O r signs during 1947-1971 given in Table II also show sign reversals within a sunspot cycle. The above observations suggest the existence of periodicities less than the eleven-year solar cycle period to be associated with the evolution of the north-south asymmetry in HCS. The study of Gonzales and Gonzales (1987) also suggest the importance of short-term periodicities in the evolution of dominant structure of the IMF related to the geometry of HCS. The mean helio- graphic latitude 'a o' (averaged over the solar longitude) of the observed HCS is found to be non-zero in many solar rotations between 1580-1876. The possibility of solar origin of 'ao' due to the evolution in the large-scale solar magnetic field within a solar rotation period has yet to be investigated in detail. The non-zero value of a o suggest that the large-scale solar magnetic field is more ordered in a system where the origin is shifted away from the centre of the Sun to a point northward or southward of the heliographic equator.

The effect of the a o term on IMF observations near Earth especially during 1983-1984 is significant. During the period, A < 0 as known from HCS inferences (Hoeksema and Scherrer, 1986) which is also supplemented by the IPS observations of a southward depression of minimum solar wind speed belt during 1983-1984 (Kojima and Kakinuma, 1987). The O r inferred from IMF data agrees well with that from solar observations during the same period. So solar and IMF observations during 1983-1984 suggest existence of an asymmetric HCS configuration with A < 0 and O r < 0 which is only possible due to non-zero a o values during CR 1730-1756 (1983-1984) from Figure 1. It is interesting to compare the Tritakis model (Tritakis, 1984a) of asymmetry

406 T. E. GIRISH AND S. R. PRABHAKARAN NAYAR

in HCS equivalently represented as 0 = ao + R1 sin~p, with the HCS observations during 1983-1984. For this type of HCS geometry, we expect Or = ao and A = 2ao given by Equation (4). But during 1983-1984 the observed values of 0 r # a o and A # 2a o as seen from Figures 1, 2, and 3 due to the effect of higher-order magnetic multipoles on HCS. So even though Tritakis (1984a) model of asymmetry in HCS could predict the sign of 0 T and A during 1983-1984, it cannot predict the magnitude of the asymmetry accurately. It is also worth mentioning that during solar maximum and during near-solar polar reversal year the HCS geometry is too complex to be described by Equation (3) and, hence, the asymmetry parameters like 0 T and A cannot be determined during that period. Tritakis (1984a) assumed a symmetric HCS model during solar maxima to explain IMF sector width variations near Earth which is not in agreement with the HCS observations during the maximum of solar cycle 21 (Hoeksema and Scherrer, 1986). The complexity of the HCS, represented by the variation of two- or four-sector structure with heliographic latitude is found to be asymmetric about the heliographic equator during several Carrington rotations during 1979-1980 as seen from a recent study by Behannon et al. (1989).

The sign of asymmetry in HCS (0r) is compared with the sign of asymmetry in sunspot activity (As) about the solar equator for the period 1947-1984. It is found that the two asymmetric phenomena does not have a consistent relationship. This result is in contrast to earlier studies (Saito etaI., 1977; Tritakis, 1984a, b) suggesting a one-to-one relationship between the asymmetry in sunspot activity about the solar equator and the asymmetry in HCS placement about the heliographic equator.

Various heliographic multipoles can exhibit different periodicities, e.g., the 22-year periodicity is exhibited by the north-south dipole harmonic. The amplitude or the intensity of the solar magnetic multipoles is a time-varying quantity. So the super- position of different magnetic modes existing in the Sun with different phases and amplitudes can determine the nature and evolution of various asymmetric phenomena about the solar equator such as sunspot activity and HCS. The investigations of Stenflo and Vogel (1986) and Stenflo and Gt~del (1988) will be helpful for a detailed study in the similar direction.

5. Conclusions

(1) Using solar and IMF observations it is shown that three key parameters, viz. the transition heliographic latitude of reversal of dominant polarity of IMF (Or), the dif- ference in the latitudinal extension of HCS between the two solar hemispheres (A), and the mean heliographic latitude of HCS averaged over heliolongitudes (%) are important in determining the nature of the north-south asymmetry in the HCS and its effect on IMF sector structure near 1 AU. The non-zero values of ao observed during several solar rotations suggest that the large-scale solar magnetic field is more ordered in a system where the origin is shifted away from the centre of the Sun.

(2) The observation of several reversals of 0 r for the past few solar cycles suggest the importance of periodicities less than 11 years to be associated with the evolution of

EVOLUTION OF ASYMMETRY IN CURRENT SHEET 407

a s y m m e t r y in the H C S . A s y m m e t r y in the sunspo t act ivi ty abou t the solar equa to r does

no t seem to re la te cons i s ten t ly well wi th the a s y m m e t r y in the H C S abou t the helio-

graphic equator .

Acknowledgements

We would like to thank Dr J. T. Hoeksema, Stanford Univesity, U.S.A. and Dr N. P. Korzhov, SibIzmiran, U.S.S.R. for providing us with the necessary helio- spheric current sheet data. The authors are grateful to Dr D. G. Sime, High Altitude Observatory, Boulder, Colorado for providing unpublished K-corona synoptic charts. We would also like to thank Dr K. W. Behannon and Dr L. F. Burlaga, NASA, Goddard Centre, U.S.A. for helpful comments.

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