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A 22-yr variation of geomagnetic activity and interplanetary magnetic field
A 22-yr variation of geomagnetic activity and interplanetary magnetic field J. K.
CHAO,*
*Institute tGeophysical
H. H. CHEN,* A. J. CHEN* and L. C. LEE*+
of Space Science. National Central University. Taiwan; Instilutc. 1JniccrGly 01‘ Alaska. t.;llrhanks. Alaska. I1.S A
(Received in,final
form 22 June 1992
; accepplrd
22 June 1992)
variation in geomagnetic activity has been reported by CHEKNOSKY[(1966) J. It has been suggested that the observed 22-yr variation in the geomagnetic activity is related to the 22-yr cycle of the solar magnetic field. In order to provide a quantitative understanding of this relationship, we first calculate (B:),,,, the annual average of the z-component of the interplanetary magnetic fields (IMF) in GSEQ (Solar Equatorial) coordinates, observed at 1 A.U. from 1967 to 1988. It activity. We then calculate (B,),,,o, the is found that (E_)oSEo does not correlate with the geomagnetic _v-component of the IMF in GSEQ coordinates and (B_) oSM, the z-component of IMF in GSM coordinates and found both of them to correlate with the 22-yr variation of the geomagnetic activity. We then suggest that the cause for the 22-yr variation of the geomagnetic variation is because (B,&o, the y-component of the IMF in the solar equatorial plane, has a 22-yr variation. In comparison with the 22-yr variation of geomagnetic activity with the effective component of IMF for geomagnetic activity. we c.kulated (B ),,,, and found that southward of (B )c.s,, correlates with a higher geomagnetic activity. Then, adopting a simple model, we assume the IMF consists of a spiral magnetic field in the .P,V plane of the GSEQ coordinates with no z-component (i.e. (BZ)oSEo = 0). However, the effective (Bc)CiSM which derives mainly from (B,&o does give a (Br)oSM ranging from -0.08 to activity in which 0. I5 nT. This simple model assumes that the effective B_(oSMjis related to geomagnetic there is no geomagnetic activity for BT,GsM,> 0 and the geomagnetic activity is proportional to lB_l for < 0. It is found from this simple model that the calculated geomagnetic activity due to the 22-yr kshl, variation of (B,),,, can explain the phase and amplitude of the observed 22-yr variation of geomagnetic activity. Abstract-The
qeophys.
22.yr
Rcs. 71,964.
numbered cycles, signifying a 22-yr cycle in geomagnetic activity. Recently, NEWELL ef al. (I 989) subjected global and hemispheric marine night air and sea surface temperature for 1856-1986 to harmonic analysis. They found that shorter periods are dominated by a significant 22-yr period but without a significant 1I-yr period. STOKER and CHAO (199 1) pointed out that the solar magnetic field polarity reversals are correlated with the changes in hemisphere night marine air temperature, suggested by which a 22-yr variation may be imposed on the Earth’s surface. They propose that the enhanced precipitation of electrons into the atmosphere occurs when B, is negative and these energetic electron precipitation events can be the major cause’s for the 22-yr variation in sea surface temperature. RUSSELLand MCPHERRON (1973) studied the semiannual variation of geomagnetic activity and proposed that it is caused by a semi-annual variation in the effective southward component of the interplanetary magnetic field. The southward field arises because the interplanetary field is ordered in the solar equatorial coordinates whereas the interaction with the magnetosphere is controlled by the solar mag-
1. INTRODUCTION The 22-yr cycle in solar activity
is the period in which the normal longitudinal sequence of the magnetic polarity indications of bipolar sunspot groups completes a cycle of change. A bipolar sunspot group usually has its joining axis in an east-west direction. During one 1 I-yr cycle the eastern spot of a group in the northern solar hemisphere will be north-poleseeking and in the southern hemisphere south-poleseeking. During the alternate 1 I-yr cycle the eastern spot will be south-seeking in the northern hemisphere and north-seeking in the southern hemisphere. This polarity change indicating the 22-yr of the sunspotmagnetic cycle was first noted at the 1913 minimum. The 1 I-yr sunspot-number cycle is known to be accompanied by a similar period of variation in geomagnetic activity (CHAPMAN and BARTELS, 1940). CHERNOSKY (1966) has found a 22-yr cycle in geomagnetic activity using a superimposed epoch analysis of the Ci index from 1844 to 1963. He showed that in Zurich even-numbered cycles, in the last half of the sunspot cycle the geomagnetic activity is more active than the first half and the converse is true for odd959
960
J. K.
CHAO cl ul.
netospheric system. Hence, a component of IMF in the solar equatorial plane can give rise to an effective north-south component in the GSM coordinates. The purpose of this paper is to examine the possible cause of the 22-yr variation of the geomagnetic activity observed by CHERNOSKY (1966). First, we examine the IMF data for the period from 1967 to 1988 in order to find if there is any correlation with the 22-yr variation of the geomagnetic activity. Next, we calculate using a quantitative simple merging model (RUSSELL and MCPHERRON, 1973) the variation of geomagnetic activity index from the effective (B,) obtained from the IMF data. It is possible to compare the prediction of our model calculated value with the 22-yr geomagnetic activity variation given by CHERNOSKY(1966).
2.
A
22-YR VARIATION OF GEOMAGNETICACTIVITY AND INTERPLANETARY MAGNETIC FIELD
CHERNOSKY(1966) found a double sunspot cycle of about 22 yr in the occurrence of geomagnetic activity. In his fig. 4 the annual mean daily index Ci and the annual number of magnetically disturbed days with Ci 2 1.Oare reported in the upper two panels of Fig. 1 in terms of the 22-yr solar magnetic cycle, starting the cycle when EI turns negative. The curves superimposed on these histograms in the upper two panels depict the 8-yr running means of the annual geomagnetic values. In the bottom panel the 8-yr running
2 4 6 8 10 12 14 16 18 20 Solar polar magnetic cycle year
22
Fig. 1. (a) The annual mean geomagnetic index Ci, (b) the number of geomagnetically disturbed days with Ci > 1.Oand (c) the sunspot numbers averaged for four even-numbered and four odd-numbered solar cycles between 1884 and 1963 are replotted from fig. 2 of STOKER and CHAO (1991).
mean of seasonally averaged Zurich sunspot numbers is shown. It is clearly shown in this figure that a higher level of activity is maintained during the years of negative Bz than during the period of positive B_, signifying a 22-yr cycle in geomagnetic activity. Since there is only one full cycle of interplanetary magnetic field data available starting from 1967 to 1988 for analysis (KING, 1989) it is not possible to deduce the 22-yr periodicity from the IMF data alone. Therefore, we have to assume the periodicity exists if there is a correlation between IMF and geomagnetic activity. The simplest description of the solar magnetic field is a dipole, orientated along the solar rotational axis with unipolar fields at the poles (SAITO et al., 1989; WEBB et al., 1984). The reversal in the sign of the magnetic field occurred during the maximum of the twenty-first solar activity cycle, starting around March 1980 in the north and about six months later in the south. The polarity of the z-component of IMF is also expected to follow the change of solar magnetic field. Before presenting the interplanetary magnetic field, two coordinate systems will be introduced (RUSSELL, 1971). The solar equatorial (GSEQ) coordinates and the solar magnetospheric (GSM) coordinates all have a common axis which points at the Sun, but they and _- axes differ by a rotation about the x-axis. However, the GSEQ y-axis is parallel to the Sun’s equatorial plane which is inclined to the ecliptic plane by about 7.25” and the z-axis is not necessarily parallel to the Sun’s axis of rotation. The Sun’s axis of rotation must lie in the x-z plane. Since the angle between the Sun’s axis of rotation and the GSEQ z-axis is less than 7.25”. we will approximate the z-component of IMF in GSEQ to be in the direcuon ol’thc Sun‘s axls ol ro[atlon. Furthermore, the interaction of the southward component of the interplanetary field with the magnetosphere is ordered in the solar magnetospheric (GSM) coordinates. The GSM y-axis is defined to be perpendicular to the Earth’s magnetic dipole so that the .X--Zplane contains the Earth’s dipole axis. We will approximate the z-component of IMF in GSM to be in the dipole direction. Now, the annual average of the z-component of IMF in GSEQ coordinates for the period from 1967 to I988 is calculated and shown in Fig. 2(a). Contrary to our expectation, the (Br)CSEQ does not show any correlation with the changes of the solar polar magnetic field polarity. It also does not correlate with the 22-yr variation of the geomagnetic activity shown in Fig. I. We then checked the (Bz)GSEo for those months near the winter and summer solstice and come to the same conclusion. Next, we computed the annual average of the =-component of IMF in
A 22-yr variation of geomagnetic activity
961
Yearly averaged
1’
-0.3i-0.41
I ’ ’ 68 70
’ 72
’ ’ 74 76
’ 70
’ 80
’ 82
’ 84
’ 86
I
1 88
1
I
I
’
I
I
1
’
I
I
I
I
I
I
I
I
I
I_
A Autumnal
Year
I
equinox
Fig. 2. (a) Annual average of the z-component of IMF data in GSEQ coordinates from 1967 to 1988. (b) Annual average of the z-component of IMF data in GSM coordinates from 1967 to 1988.
1’ GSM coordinates and looked for the same correlation. Figure 2(b) shows the (B;),,, which can be considered as the effective (B;) for geomagnetic activity (AKASOFU, 1980). From the figure, we find is predominately negative during the that
3. THE ORIGIN
OF THE 2%YR VARIATION
OF (Bz)CSM
It appears that (BJoSEQ is not the source for the 22-yr variation in ( BZ)oSM nor for the 22-yr variation in geomagnetic activity. Thus, the y-component of IMF in GSEQ coordinates was examined. First, the annual average of (BY)osFo was calculated [shown in Fig. 3(a)]. It appears that (By)osEQ does not correlate with the 22-yr variation of solar polar magnetic field polarity. However, the monthly average of (B,,)GSEo close to the vernal equinox is calculated and shown in Fig. 3(b). This result shows that good correlation
68
’
I
70
72
I
’
’
74 16
70
’ 80
‘Y
82
84
I
I 86 88
Year Fig. 3. (a) Annual average of the y-component of IMF data in GSEQ coordinates from 1967 to 1988. (b) 30 days average at vernal equinox of the y-component of IMF data in GSEQ coordinates from 1967 to 1988. (c) 30 days average at autumnal equinox of the y-component of IMF data in GSEQ coordinates from 1967 to 1988.
with (B_)oSM. When the monthly average of (BY)osEo close to autumnal equinox is calculated and shown in Fig. 3(c), it is found that this (B,),s,Q is anticorrelated with those values shown in Fig. 2(b). Since the ecliptic plane is inclined to the solar equatorial plane at an angle of about 7.25”, it is possible that a spatial variation of (B,),;,,Q in solar latitude exists. In order to simplify our analysis, we assume that the monthly variation of ( By)GSEQcan be recognized as the latitudinal spatial variation. Figure 4(a) shows the monthly average value of (BJ)ciSEQ averaged for the period from 1971 to 1979 corresponding to one polarity of the solar polar magnetic field. It can be seen that
962
J. K. CHAO et al.
’
-1.0
1.0
’
’
’
’
’
(b)
’
’
’
’
1981-1987
JPMAMJJASOND Month Fig. 4. (a) Monthly variation of (Br)GSEo where (B,)o,,o is the averaged y-component of IMF data from 1971 to 1979. (b) Monthly variation of (B,)oSsO where (B,)oSEP is the averaged y-component of IMF data from 1981 to 1987.
0.3
-(a)
0.2-
reverses sign from that of (B,,)GSEQin Fig. 4(a). Therefore. we suggest that the y-component of IMF has not only a spatial variation in solar latitude but also a 22-yr variation in time. RUSSELL (1974) has derived a heliographic latitude dependence of IMF from the 22-yr cycle of geomagnetic activity. Here, our analysis of IMF data confirms his result. To show that the ( B,)c;SEY is the source for the 22-yr variation of geomagnetic activity, we resolved the ( Bv)tiSEOand projected it onto the z-axis of the GSM coordinates. Figure 5(a) shows the (Br)GSM projected value of (B, )GSFQonto the z-axis of GSM which is the effective value for geomagnetic activity. It shows clearly that this value correlates with the 22-yr variation of geomagnetic activity. The annual average value of (B,),;s,~Q projecting onto the z-axis of GSM coordinates on the other hand does not correlate with the 22-yr variation of geomagnetic activity as shown in Fig. 5(b). Thus, we suggest that (B_)GSEO is not the source for the 22-yr variation of geomagnetic variation. Adding the values of Fig. 5(a) and 5(b). we obtain Fig. 2(a), the annual average of the :-component of the IMF in GSM coordinates. Note that the annual average of (Bv)c;sry does not contribute to (B.),;,, because by definition B,,,;,,o, is orthogonal to B;,,;,,,.
4. A QUANTITATIVEMODEL FOR THE 22-YR VARIATION IN GEOMAGNETIC ACTIVITY -0.3 -0.4- ’ ’ 0.4 0.3 (b)
-0.41 ’
’ 68 70
’
’
’
’
’
’
’
’
’
’
’
’
’
’
’
’
1
12 74 76 78 80 82 84 86 88 Year
(a) Annual average of y-component of IMF data, (B,),,,,, projecting onto the z-axis of the GSM coordinates from 1967 to 1988. (b) Annual average of z-component of IMF data, (B,)os,o onto the z-axis of the GSM coordinates from 1967 to 1988.
The geomagnetic activity has a 22-yr variation as first reported by CHERNOSKY(1966). The amplitude changes measured by the annual mean geomagnetic index Ci and the number of magnetically disturbed days with Ci > 1.0 have been discussed in Section 2 and shown in Fig. l(a) and l(b). During the period from 1969 to 1980 when the solar polar magnetic field is northward implying a southward B, in IMF, the averaged values of Ci and .fCi > 1.O/yr are 0.69 and 104, respectively. And during the period from 1980 to 1987. when the polarity of the solar magnetic field changes, the average value of Ci and ,fC’i b I.O/yr become 0.61 and 81, respectively. The percentage changes are 12.3 and 24.8%, respectively. In this section we will model the changes of the geomagnetic
Fig. 6. (a) A contour plot in gammas of the diurnal and annual variation of the effective average southward component in the GSM coordinates due to inward and outward fields of 5 nT along the ideal interplanetary spiral magnetic field in the GSEQ coordinates. The solar equatorial azimuthal angle of the spiral field has been taken to be 135 and 315 ‘_ This figure is fig. 5 of RUSSELL and MCPHERRON (1973). The averaged geomagnetic activity is -0.53. (b) Same as (a) but a constant value of -0.08 nT has been added to the Zcomponent of IMF, the effective average southward component in the GSM coordinates. The annual averaged geomagnetic activity value is -0.58. (c) Same as (a) and (b) but a constant value of 0.15 nT has been added to B. in GSM coordinates. The annual averaged geomagnetic value (G) is -0.45.
24
(a)
(Bz)GSM=O.OOnT
963
=-0.53
22 20 18 16 14 12 10 a 6 4 2 0
60
120
180
240
300
360
n,.,
24
(b)
(Bz)asM=-0.08nT
=-0.57
22 20 I8 I6 14 I2 10 a 6 4 2 0
60
180
240
300
360
300
360
Day
=-0.45 24 22 20 18 16 14 12 10 8 6 4 2 0
60
120
180 Day
240
964
J. K.
CHAO
activity following a simple merging model used by ARNODY (197 1) and RUSSELLand MCPHERRON (1973). In these calculations, the magnetosphere acts as a rectifier in which the interaction is linearly proportional to the z-component of IMF in GSM coordinates if the field is southward and zero otherwise. To obtain the averaged (B.)osM for the south and north solar magnetic field polarities. we averaged the (BZ)(;sM for the periods 196991980 and 1981-1988 and found that the averaged (BZ)oSM is -0.08 and 0.1 nT for these two periods, respectively. In the calculations, the field is assumed to be constant at a value of 5 nT inward and outward along the spiral angle in GSEQ coordinates. Then the fields are transformed into GSM coordinates. Figure 6(a) shows the contours of the constant southward component as a function of time of day and time of year. The resulting northward component in GSM coordinates of the two fields is set to zero and the two components of inward and outward fields are then averaged. The average field is plotted here. The yearly averaged value of this figure is taken as the annual average of geomagnetic activity for this year. In order to add the 22-yr variation of (BZ)oSM to this model we add the above averaged values of -0.08 and 0.15 nT to BZtoSMjrrespectively, and calculate the contours following the same procedure for Fig. 6(a), and we obtained Fig. 6(b) and 6(c). The average values of the geomagnetic activity (G) for Fig. 6(b) and 6(c) are -0.57 and -0.45, respectively. In Table 1, we show the calculated geomagnetic activity (G) for the two opposite solar magnetic field polarities and these values are compared with the averaged values of Ci and fCi > 1.O/yr. The percentage changes in (G) from our calculation agree with the observed value of fCi 3 I .O/yr.
GO~SEQdoes not correlate with the 22-yr variation of geomagnetic activity. Therefore, we suggest that the 22-yr variations of the solar magnetic field do not imply the same variation of the z-component of IMF in GSEQ coordinates. The 22-yr variation of the solar activity may also be accompanied by the changes of the other components of IMF. We have checked the azimuthal component B., and found that (B,,)Gs,o is not only correlated with the 22-yr geomagnetic activity but also has a solar latitudinal variation of about 1.O nT. Thus, we suggest that the semi-annual variation of geomagnetic activity should include not only the tilt effects of the Earth’s rotation axis and the dipole axis (RUSSELL and MCPHERRON, 1973) but also the latitudinal effect as shown in Fig. 4(a) and 4(b). In our calculation, both the axis tilt effects and the latitudinal variation effect for B,.s in GSEQ coordinates are included to derive (B_)cISM, the z-component of IMF in GSM coordinates, and it was found that this correlates with the 22-yr variation of geo(B&s, magnetic variation. One find from Fig. 3(b) and 3(c) is that ( B,)ciSEO changes sign across the solar neutral sheet and when combined with the axis tilt effect it makes the (B_)c;SM stays in one sign. Thus, the correlates with the 22-yr variation of geo(B&M magnetic activity. It is always somewhat ambiguous to use one spacecraft measurement in space to deduce the time and spatial variations of IMF. Therefore. we have to assume that the 22-yr variation can be separated from the yearly variation of our IMF data. The 22-yr variation is attributed to time and the yearly variation is attributed to latitudinal spatial variation. Under this assumption, we derived the (B,),;,, which has a 22-yr variation implying that the cause for the 22-yr variation of geomagnetic variation is the IMF
5. DISCUSSJON AND SUMMARY Since the 22-yr variation of geomagnetic activity correlates with the solar polar magnetic field, we first check if the z-components of IMF in GSEQ coordinates also have a 22-yr variation. It is found that
Table 1. Comparison Geomagnetic activity index (G) (calculated) Ci (observed) ,jCi > 1.O/yr (observed)
of calculated
and observed
IMF southward (Bz)osM = -0.08 -0.57 0.69 104
et ul.
nT
geomagnetic
activity
IMF northward (B.)oSM = f0.15 -0.45 0.61 81
nT
Percentage change 21.5 12.3 24.8
A 22-yr variation the northern
hemisphere.
that the ecliptic in June
and December.
during the first six months, the Earth
the following
figures
solar cycle, the sunspot
it appears
(B,.),;,,o
show
that
ation of geomagnetic In summary,
the changes
changes
sheet. In polarity
sign. There-
in polarity
of the
cause for the 22-yr vari-
activity.
we found
activity
that
sheet and in the
also changes
group is the primary
geomagnetic
also
sheet
when (B,.)oSEQ is negative,
the Earth is above the neutral
and the observed sunspot
The
4(a) and 4(b) shows the solar neutral
is below the solar neutral
last six months
fore,
Figure
plane intersects
of geomagnetic
does show correlation
(B,)
variation
simple model that the calculated due to the 22-yr variation
phase and amplitude
in space.
geomagnetic
activity
of ( Br)cisM can explain
of the observed
the
22-yr variation
activity.
of
with the
in GSM coordinates. It was also found that the source for the 22-yr variation of (B;)C;,, is the (4 )GWQ which has not only a 22-yr variation in time but also a latitudinal
The changes in the amplitudes of (B_)GSM of the 22-yr variation are used to calculate the changes in geomagnetic activity from a simple model. This simple model assumes that B; is related to geomagnetic activity in which there is no geomagnetic activity for activity is proB:CGSM,> 0 and the geomagnetic portional to lBzl for B,,,;,,, < 0. It is found from this
of geomagnetic
that the 22-yr variation
965
activity
Ac,lino,~l~~~~~ments-The authors thank Dr J. H. Kmg of NSSDC/WDC-A for providing us with the magnetic field data used in our analysis. This work is an effort of the SOLTIP Project for the STEP activities.
REFERENCES AKASOFUS. 1. AKNODYR. L. CHAPMANS. and BARTELSJ.
1980 1971 1940
CHERNOSKYE. J. KING J. H.
1966 1989
NEWELL N. E.. NEWELL R. E., HSIUNGJ. and ZHONC;x. W. RUSSELL C. T. RUSSELL C. T. RUSSELL C. T. and MCPHERRONR. L. SAITOT., OKI K., OLMSTEADC. and AKASOFUS. I STOKEKP. H. and CHAOJ. K. WEBB D. F., DAVIS J. M. and MCINTOSHP. S.
1989
Planet. Space Sci. 28,495. J. ,geophys. Res. 76, 5189. Geomagnetism, ch. I I. Oxford University Press. New York. J. geoph)‘s. Res. 11, 965. Interplanetary Medium Data Book, NSSDC/WDC-A Rand S. 89-17. Geophys. Rex. Leti. 16, 3 I I
1971 1974 1973 1989 1991 1984
Cosmic EIec/rodvn. 2, 184. Geophys. Res. Lert. 1, I I, J. geophys. Res. 18, 92. J. geophys. Res. 94, 14.993. S. 41;. J. Sci. 87, 51. Solar phys. 92, 109.
CHAO,*
*Institute tGeophysical
H. H. CHEN,* A. J. CHEN* and L. C. LEE*+
of Space Science. National Central University. Taiwan; Instilutc. 1JniccrGly 01‘ Alaska. t.;llrhanks. Alaska. I1.S A
(Received in,final
form 22 June 1992
; accepplrd
22 June 1992)
variation in geomagnetic activity has been reported by CHEKNOSKY[(1966) J. It has been suggested that the observed 22-yr variation in the geomagnetic activity is related to the 22-yr cycle of the solar magnetic field. In order to provide a quantitative understanding of this relationship, we first calculate (B:),,,, the annual average of the z-component of the interplanetary magnetic fields (IMF) in GSEQ (Solar Equatorial) coordinates, observed at 1 A.U. from 1967 to 1988. It activity. We then calculate (B,),,,o, the is found that (E_)oSEo does not correlate with the geomagnetic _v-component of the IMF in GSEQ coordinates and (B_) oSM, the z-component of IMF in GSM coordinates and found both of them to correlate with the 22-yr variation of the geomagnetic activity. We then suggest that the cause for the 22-yr variation of the geomagnetic variation is because (B,&o, the y-component of the IMF in the solar equatorial plane, has a 22-yr variation. In comparison with the 22-yr variation of geomagnetic activity with the effective component of IMF for geomagnetic activity. we c.kulated (B ),,,, and found that southward of (B )c.s,, correlates with a higher geomagnetic activity. Then, adopting a simple model, we assume the IMF consists of a spiral magnetic field in the .P,V plane of the GSEQ coordinates with no z-component (i.e. (BZ)oSEo = 0). However, the effective (Bc)CiSM which derives mainly from (B,&o does give a (Br)oSM ranging from -0.08 to activity in which 0. I5 nT. This simple model assumes that the effective B_(oSMjis related to geomagnetic there is no geomagnetic activity for BT,GsM,> 0 and the geomagnetic activity is proportional to lB_l for < 0. It is found from this simple model that the calculated geomagnetic activity due to the 22-yr kshl, variation of (B,),,, can explain the phase and amplitude of the observed 22-yr variation of geomagnetic activity. Abstract-The
qeophys.
22.yr
Rcs. 71,964.
numbered cycles, signifying a 22-yr cycle in geomagnetic activity. Recently, NEWELL ef al. (I 989) subjected global and hemispheric marine night air and sea surface temperature for 1856-1986 to harmonic analysis. They found that shorter periods are dominated by a significant 22-yr period but without a significant 1I-yr period. STOKER and CHAO (199 1) pointed out that the solar magnetic field polarity reversals are correlated with the changes in hemisphere night marine air temperature, suggested by which a 22-yr variation may be imposed on the Earth’s surface. They propose that the enhanced precipitation of electrons into the atmosphere occurs when B, is negative and these energetic electron precipitation events can be the major cause’s for the 22-yr variation in sea surface temperature. RUSSELLand MCPHERRON (1973) studied the semiannual variation of geomagnetic activity and proposed that it is caused by a semi-annual variation in the effective southward component of the interplanetary magnetic field. The southward field arises because the interplanetary field is ordered in the solar equatorial coordinates whereas the interaction with the magnetosphere is controlled by the solar mag-
1. INTRODUCTION The 22-yr cycle in solar activity
is the period in which the normal longitudinal sequence of the magnetic polarity indications of bipolar sunspot groups completes a cycle of change. A bipolar sunspot group usually has its joining axis in an east-west direction. During one 1 I-yr cycle the eastern spot of a group in the northern solar hemisphere will be north-poleseeking and in the southern hemisphere south-poleseeking. During the alternate 1 I-yr cycle the eastern spot will be south-seeking in the northern hemisphere and north-seeking in the southern hemisphere. This polarity change indicating the 22-yr of the sunspotmagnetic cycle was first noted at the 1913 minimum. The 1 I-yr sunspot-number cycle is known to be accompanied by a similar period of variation in geomagnetic activity (CHAPMAN and BARTELS, 1940). CHERNOSKY (1966) has found a 22-yr cycle in geomagnetic activity using a superimposed epoch analysis of the Ci index from 1844 to 1963. He showed that in Zurich even-numbered cycles, in the last half of the sunspot cycle the geomagnetic activity is more active than the first half and the converse is true for odd959
960
J. K.
CHAO cl ul.
netospheric system. Hence, a component of IMF in the solar equatorial plane can give rise to an effective north-south component in the GSM coordinates. The purpose of this paper is to examine the possible cause of the 22-yr variation of the geomagnetic activity observed by CHERNOSKY (1966). First, we examine the IMF data for the period from 1967 to 1988 in order to find if there is any correlation with the 22-yr variation of the geomagnetic activity. Next, we calculate using a quantitative simple merging model (RUSSELL and MCPHERRON, 1973) the variation of geomagnetic activity index from the effective (B,) obtained from the IMF data. It is possible to compare the prediction of our model calculated value with the 22-yr geomagnetic activity variation given by CHERNOSKY(1966).
2.
A
22-YR VARIATION OF GEOMAGNETICACTIVITY AND INTERPLANETARY MAGNETIC FIELD
CHERNOSKY(1966) found a double sunspot cycle of about 22 yr in the occurrence of geomagnetic activity. In his fig. 4 the annual mean daily index Ci and the annual number of magnetically disturbed days with Ci 2 1.Oare reported in the upper two panels of Fig. 1 in terms of the 22-yr solar magnetic cycle, starting the cycle when EI turns negative. The curves superimposed on these histograms in the upper two panels depict the 8-yr running means of the annual geomagnetic values. In the bottom panel the 8-yr running
2 4 6 8 10 12 14 16 18 20 Solar polar magnetic cycle year
22
Fig. 1. (a) The annual mean geomagnetic index Ci, (b) the number of geomagnetically disturbed days with Ci > 1.Oand (c) the sunspot numbers averaged for four even-numbered and four odd-numbered solar cycles between 1884 and 1963 are replotted from fig. 2 of STOKER and CHAO (1991).
mean of seasonally averaged Zurich sunspot numbers is shown. It is clearly shown in this figure that a higher level of activity is maintained during the years of negative Bz than during the period of positive B_, signifying a 22-yr cycle in geomagnetic activity. Since there is only one full cycle of interplanetary magnetic field data available starting from 1967 to 1988 for analysis (KING, 1989) it is not possible to deduce the 22-yr periodicity from the IMF data alone. Therefore, we have to assume the periodicity exists if there is a correlation between IMF and geomagnetic activity. The simplest description of the solar magnetic field is a dipole, orientated along the solar rotational axis with unipolar fields at the poles (SAITO et al., 1989; WEBB et al., 1984). The reversal in the sign of the magnetic field occurred during the maximum of the twenty-first solar activity cycle, starting around March 1980 in the north and about six months later in the south. The polarity of the z-component of IMF is also expected to follow the change of solar magnetic field. Before presenting the interplanetary magnetic field, two coordinate systems will be introduced (RUSSELL, 1971). The solar equatorial (GSEQ) coordinates and the solar magnetospheric (GSM) coordinates all have a common axis which points at the Sun, but they and _- axes differ by a rotation about the x-axis. However, the GSEQ y-axis is parallel to the Sun’s equatorial plane which is inclined to the ecliptic plane by about 7.25” and the z-axis is not necessarily parallel to the Sun’s axis of rotation. The Sun’s axis of rotation must lie in the x-z plane. Since the angle between the Sun’s axis of rotation and the GSEQ z-axis is less than 7.25”. we will approximate the z-component of IMF in GSEQ to be in the direcuon ol’thc Sun‘s axls ol ro[atlon. Furthermore, the interaction of the southward component of the interplanetary field with the magnetosphere is ordered in the solar magnetospheric (GSM) coordinates. The GSM y-axis is defined to be perpendicular to the Earth’s magnetic dipole so that the .X--Zplane contains the Earth’s dipole axis. We will approximate the z-component of IMF in GSM to be in the dipole direction. Now, the annual average of the z-component of IMF in GSEQ coordinates for the period from 1967 to I988 is calculated and shown in Fig. 2(a). Contrary to our expectation, the (Br)CSEQ does not show any correlation with the changes of the solar polar magnetic field polarity. It also does not correlate with the 22-yr variation of the geomagnetic activity shown in Fig. I. We then checked the (Bz)GSEo for those months near the winter and summer solstice and come to the same conclusion. Next, we computed the annual average of the =-component of IMF in
A 22-yr variation of geomagnetic activity
961
Yearly averaged
1’
-0.3i-0.41
I ’ ’ 68 70
’ 72
’ ’ 74 76
’ 70
’ 80
’ 82
’ 84
’ 86
I
1 88
1
I
I
’
I
I
1
’
I
I
I
I
I
I
I
I
I
I_
A Autumnal
Year
I
equinox
Fig. 2. (a) Annual average of the z-component of IMF data in GSEQ coordinates from 1967 to 1988. (b) Annual average of the z-component of IMF data in GSM coordinates from 1967 to 1988.
1’ GSM coordinates and looked for the same correlation. Figure 2(b) shows the (B;),,, which can be considered as the effective (B;) for geomagnetic activity (AKASOFU, 1980). From the figure, we find is predominately negative during the that
3. THE ORIGIN
OF THE 2%YR VARIATION
OF (Bz)CSM
It appears that (BJoSEQ is not the source for the 22-yr variation in ( BZ)oSM nor for the 22-yr variation in geomagnetic activity. Thus, the y-component of IMF in GSEQ coordinates was examined. First, the annual average of (BY)osFo was calculated [shown in Fig. 3(a)]. It appears that (By)osEQ does not correlate with the 22-yr variation of solar polar magnetic field polarity. However, the monthly average of (B,,)GSEo close to the vernal equinox is calculated and shown in Fig. 3(b). This result shows that good correlation
68
’
I
70
72
I
’
’
74 16
70
’ 80
‘Y
82
84
I
I 86 88
Year Fig. 3. (a) Annual average of the y-component of IMF data in GSEQ coordinates from 1967 to 1988. (b) 30 days average at vernal equinox of the y-component of IMF data in GSEQ coordinates from 1967 to 1988. (c) 30 days average at autumnal equinox of the y-component of IMF data in GSEQ coordinates from 1967 to 1988.
with (B_)oSM. When the monthly average of (BY)osEo close to autumnal equinox is calculated and shown in Fig. 3(c), it is found that this (B,),s,Q is anticorrelated with those values shown in Fig. 2(b). Since the ecliptic plane is inclined to the solar equatorial plane at an angle of about 7.25”, it is possible that a spatial variation of (B,),;,,Q in solar latitude exists. In order to simplify our analysis, we assume that the monthly variation of ( By)GSEQcan be recognized as the latitudinal spatial variation. Figure 4(a) shows the monthly average value of (BJ)ciSEQ averaged for the period from 1971 to 1979 corresponding to one polarity of the solar polar magnetic field. It can be seen that
962
J. K. CHAO et al.
’
-1.0
1.0
’
’
’
’
’
(b)
’
’
’
’
1981-1987
JPMAMJJASOND Month Fig. 4. (a) Monthly variation of (Br)GSEo where (B,)o,,o is the averaged y-component of IMF data from 1971 to 1979. (b) Monthly variation of (B,)oSsO where (B,)oSEP is the averaged y-component of IMF data from 1981 to 1987.
0.3
-(a)
0.2-
reverses sign from that of (B,,)GSEQin Fig. 4(a). Therefore. we suggest that the y-component of IMF has not only a spatial variation in solar latitude but also a 22-yr variation in time. RUSSELL (1974) has derived a heliographic latitude dependence of IMF from the 22-yr cycle of geomagnetic activity. Here, our analysis of IMF data confirms his result. To show that the ( B,)c;SEY is the source for the 22-yr variation of geomagnetic activity, we resolved the ( Bv)tiSEOand projected it onto the z-axis of the GSM coordinates. Figure 5(a) shows the (Br)GSM projected value of (B, )GSFQonto the z-axis of GSM which is the effective value for geomagnetic activity. It shows clearly that this value correlates with the 22-yr variation of geomagnetic activity. The annual average value of (B,),;s,~Q projecting onto the z-axis of GSM coordinates on the other hand does not correlate with the 22-yr variation of geomagnetic activity as shown in Fig. 5(b). Thus, we suggest that (B_)GSEO is not the source for the 22-yr variation of geomagnetic variation. Adding the values of Fig. 5(a) and 5(b). we obtain Fig. 2(a), the annual average of the :-component of the IMF in GSM coordinates. Note that the annual average of (Bv)c;sry does not contribute to (B.),;,, because by definition B,,,;,,o, is orthogonal to B;,,;,,,.
4. A QUANTITATIVEMODEL FOR THE 22-YR VARIATION IN GEOMAGNETIC ACTIVITY -0.3 -0.4- ’ ’ 0.4 0.3 (b)
-0.41 ’
’ 68 70
’
’
’
’
’
’
’
’
’
’
’
’
’
’
’
’
1
12 74 76 78 80 82 84 86 88 Year
(a) Annual average of y-component of IMF data, (B,),,,,, projecting onto the z-axis of the GSM coordinates from 1967 to 1988. (b) Annual average of z-component of IMF data, (B,)os,o onto the z-axis of the GSM coordinates from 1967 to 1988.
The geomagnetic activity has a 22-yr variation as first reported by CHERNOSKY(1966). The amplitude changes measured by the annual mean geomagnetic index Ci and the number of magnetically disturbed days with Ci > 1.0 have been discussed in Section 2 and shown in Fig. l(a) and l(b). During the period from 1969 to 1980 when the solar polar magnetic field is northward implying a southward B, in IMF, the averaged values of Ci and .fCi > 1.O/yr are 0.69 and 104, respectively. And during the period from 1980 to 1987. when the polarity of the solar magnetic field changes, the average value of Ci and ,fC’i b I.O/yr become 0.61 and 81, respectively. The percentage changes are 12.3 and 24.8%, respectively. In this section we will model the changes of the geomagnetic
Fig. 6. (a) A contour plot in gammas of the diurnal and annual variation of the effective average southward component in the GSM coordinates due to inward and outward fields of 5 nT along the ideal interplanetary spiral magnetic field in the GSEQ coordinates. The solar equatorial azimuthal angle of the spiral field has been taken to be 135 and 315 ‘_ This figure is fig. 5 of RUSSELL and MCPHERRON (1973). The averaged geomagnetic activity is -0.53. (b) Same as (a) but a constant value of -0.08 nT has been added to the Zcomponent of IMF, the effective average southward component in the GSM coordinates. The annual averaged geomagnetic activity value is -0.58. (c) Same as (a) and (b) but a constant value of 0.15 nT has been added to B. in GSM coordinates. The annual averaged geomagnetic value (G) is -0.45.
24
(a)
(Bz)GSM=O.OOnT
963
22 20 18 16 14 12 10 a 6 4 2 0
60
120
180
240
300
360
n,.,
24
(b)
(Bz)asM=-0.08nT
22 20 I8 I6 14 I2 10 a 6 4 2 0
60
180
240
300
360
300
360
Day
60
120
180 Day
240
964
J. K.
CHAO
activity following a simple merging model used by ARNODY (197 1) and RUSSELLand MCPHERRON (1973). In these calculations, the magnetosphere acts as a rectifier in which the interaction is linearly proportional to the z-component of IMF in GSM coordinates if the field is southward and zero otherwise. To obtain the averaged (B.)osM for the south and north solar magnetic field polarities. we averaged the (BZ)(;sM for the periods 196991980 and 1981-1988 and found that the averaged (BZ)oSM is -0.08 and 0.1 nT for these two periods, respectively. In the calculations, the field is assumed to be constant at a value of 5 nT inward and outward along the spiral angle in GSEQ coordinates. Then the fields are transformed into GSM coordinates. Figure 6(a) shows the contours of the constant southward component as a function of time of day and time of year. The resulting northward component in GSM coordinates of the two fields is set to zero and the two components of inward and outward fields are then averaged. The average field is plotted here. The yearly averaged value of this figure is taken as the annual average of geomagnetic activity for this year. In order to add the 22-yr variation of (BZ)oSM to this model we add the above averaged values of -0.08 and 0.15 nT to BZtoSMjrrespectively, and calculate the contours following the same procedure for Fig. 6(a), and we obtained Fig. 6(b) and 6(c). The average values of the geomagnetic activity (G) for Fig. 6(b) and 6(c) are -0.57 and -0.45, respectively. In Table 1, we show the calculated geomagnetic activity (G) for the two opposite solar magnetic field polarities and these values are compared with the averaged values of Ci and fCi > 1.O/yr. The percentage changes in (G) from our calculation agree with the observed value of fCi 3 I .O/yr.
GO~SEQdoes not correlate with the 22-yr variation of geomagnetic activity. Therefore, we suggest that the 22-yr variations of the solar magnetic field do not imply the same variation of the z-component of IMF in GSEQ coordinates. The 22-yr variation of the solar activity may also be accompanied by the changes of the other components of IMF. We have checked the azimuthal component B., and found that (B,,)Gs,o is not only correlated with the 22-yr geomagnetic activity but also has a solar latitudinal variation of about 1.O nT. Thus, we suggest that the semi-annual variation of geomagnetic activity should include not only the tilt effects of the Earth’s rotation axis and the dipole axis (RUSSELL and MCPHERRON, 1973) but also the latitudinal effect as shown in Fig. 4(a) and 4(b). In our calculation, both the axis tilt effects and the latitudinal variation effect for B,.s in GSEQ coordinates are included to derive (B_)cISM, the z-component of IMF in GSM coordinates, and it was found that this correlates with the 22-yr variation of geo(B&s, magnetic variation. One find from Fig. 3(b) and 3(c) is that ( B,)ciSEO changes sign across the solar neutral sheet and when combined with the axis tilt effect it makes the (B_)c;SM stays in one sign. Thus, the correlates with the 22-yr variation of geo(B&M magnetic activity. It is always somewhat ambiguous to use one spacecraft measurement in space to deduce the time and spatial variations of IMF. Therefore. we have to assume that the 22-yr variation can be separated from the yearly variation of our IMF data. The 22-yr variation is attributed to time and the yearly variation is attributed to latitudinal spatial variation. Under this assumption, we derived the (B,),;,, which has a 22-yr variation implying that the cause for the 22-yr variation of geomagnetic variation is the IMF
5. DISCUSSJON AND SUMMARY Since the 22-yr variation of geomagnetic activity correlates with the solar polar magnetic field, we first check if the z-components of IMF in GSEQ coordinates also have a 22-yr variation. It is found that
Table 1. Comparison Geomagnetic activity index (G) (calculated) Ci (observed) ,jCi > 1.O/yr (observed)
of calculated
and observed
IMF southward (Bz)osM = -0.08 -0.57 0.69 104
et ul.
nT
geomagnetic
activity
IMF northward (B.)oSM = f0.15 -0.45 0.61 81
nT
Percentage change 21.5 12.3 24.8
A 22-yr variation the northern
hemisphere.
that the ecliptic in June
and December.
during the first six months, the Earth
the following
figures
solar cycle, the sunspot
it appears
(B,.),;,,o
show
that
ation of geomagnetic In summary,
the changes
changes
sheet. In polarity
sign. There-
in polarity
of the
cause for the 22-yr vari-
activity.
we found
activity
that
sheet and in the
also changes
group is the primary
geomagnetic
also
sheet
when (B,.)oSEQ is negative,
the Earth is above the neutral
and the observed sunspot
The
4(a) and 4(b) shows the solar neutral
is below the solar neutral
last six months
fore,
Figure
plane intersects
of geomagnetic
does show correlation
(B,)
variation
simple model that the calculated due to the 22-yr variation
phase and amplitude
in space.
geomagnetic
activity
of ( Br)cisM can explain
of the observed
the
22-yr variation
activity.
of
with the
in GSM coordinates. It was also found that the source for the 22-yr variation of (B;)C;,, is the (4 )GWQ which has not only a 22-yr variation in time but also a latitudinal
The changes in the amplitudes of (B_)GSM of the 22-yr variation are used to calculate the changes in geomagnetic activity from a simple model. This simple model assumes that B; is related to geomagnetic activity in which there is no geomagnetic activity for activity is proB:CGSM,> 0 and the geomagnetic portional to lBzl for B,,,;,,, < 0. It is found from this
of geomagnetic
that the 22-yr variation
965
activity
Ac,lino,~l~~~~~ments-The authors thank Dr J. H. Kmg of NSSDC/WDC-A for providing us with the magnetic field data used in our analysis. This work is an effort of the SOLTIP Project for the STEP activities.
REFERENCES AKASOFUS. 1. AKNODYR. L. CHAPMANS. and BARTELSJ.
1980 1971 1940
CHERNOSKYE. J. KING J. H.
1966 1989
NEWELL N. E.. NEWELL R. E., HSIUNGJ. and ZHONC;x. W. RUSSELL C. T. RUSSELL C. T. RUSSELL C. T. and MCPHERRONR. L. SAITOT., OKI K., OLMSTEADC. and AKASOFUS. I STOKEKP. H. and CHAOJ. K. WEBB D. F., DAVIS J. M. and MCINTOSHP. S.
1989
Planet. Space Sci. 28,495. J. ,geophys. Res. 76, 5189. Geomagnetism, ch. I I. Oxford University Press. New York. J. geoph)‘s. Res. 11, 965. Interplanetary Medium Data Book, NSSDC/WDC-A Rand S. 89-17. Geophys. Rex. Leti. 16, 3 I I
1971 1974 1973 1989 1991 1984
Cosmic EIec/rodvn. 2, 184. Geophys. Res. Lert. 1, I I, J. geophys. Res. 18, 92. J. geophys. Res. 94, 14.993. S. 41;. J. Sci. 87, 51. Solar phys. 92, 109.