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Solar rotation and solar wind–magnetosphere coupling
ARTICLE IN PRESS
Planetary and Space Science 53 (2005) 197–207 www.elsevier.com/locate/pss
Solar rotation and solar wind–magnetosphere coupling K. Georgievaa,, B. Kirova, J. Javaraiahb,c, R. Krastevad a
Solar-Terrestrial Influences Laboratory at the Bulgarian Academy of Sciences, Bl.3 Academy G. Bonchev str., 1113 Sofia, Bulgaria b Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India c Department of Physics and Astronomy, 8371 MS, University of California, Los Angeles, CA 90095, USA d Central Laboratory of Mechatronics and Instrumentations at the Bulgarian Academy of Sciences, Bl.5 Academy G. Bonchev str., 1113 Sofia, Bulgaria Accepted 12 September 2004
Abstract This paper deals with three characteristics of the interplanetary magnetic field (IMF), important for solar wind–magnetosphere coupling and related to solar rotation: the IMF azimuthal component, the IMF total magnitude, and the handedness or the sense of rotation of magnetic clouds. The IMF configuration is described by Parker’s Archimedian spiral model (Astrophys. J. 128 (1958) 664) under the assumptions of a purely radial solar wind with a constant velocity emanating from a uniformly rotating Sun. In situ measurements confirmed this general picture, but a systematic deviation from the predicted IMF winding angle was found, supposedly exhibiting a 11-year periodicity. We account for the non-uniform solar rotation and compare the observed IMF azimuthal component to the one calculated from Parker’s formula with the measured equatorial solar rotation rate. We find that the differences between the calculated and measured IMF azimuthal component and the winding angle have a clear 22-year dependence on the solar polarity cycle, matching the 22-year periodicity in solar rotation rate rather than on the 11-year sunspot cycle. Our results are an observational confirmation of the validity of the model of Fisk (J. Geophys. Res. 101 (1996) 15547) for heliospheric magnetic field with footpoint motions due to solar differential rotation. Solar differential rotation is also an important element of the solar dynamo which is responsible for the generation of the solar magnetic field. We compare the different periodicities in the variations in the latitudinal rotation gradient of the two solar hemispheres and show that the IMF which is an extension of the solar coronal field, is related to the differential rotation in the more active solar hemisphere. Another feature related to solar differential rotation that is persistently different in the two solar hemispheres is the prevailing magnetic helicity, which is carried to the Earth by magnetic clouds preserving the helicity of the source region of their origin. The reaction of the magnetosphere to magnetic clouds is determined mainly by the presence or absence of a prolonged period of southward IMF component. We show that it also depends on the helicity of the clouds, and compare the effects of right- and left-handed magnetic clouds on geomagnetic activity. r 2004 Elsevier Ltd. All rights reserved. Keywords: Solar rotation; Interplanetary magnetic field; Magnetic cloud; Helicity; Geomagnetic disturbance
1. Introduction Though sunspots had been observed since ancient times, only when the telescope came into use it was noticed that they turn with the Sun, and thus the period of the solar rotation could be defined. Since these early studies of Galileo, Carrington, Scheiner, Fabricius, Hale, Sacchi and many others (Abetti, 1965), it has Corresponding author. Tel.: +359 2 979 3432; fax: +359 2 870 0178. E-mail address: [email protected] (K. Georgieva).
0032-0633/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2004.09.045
been known that the Sun is not a solid body and that it rotates faster near the equator than near the poles—an effect known as ‘‘differential rotation’’. This differential rotation is described by the formula XðlÞ ¼ a þ b sin2 l; where XðlÞ is the rotation rate at latitude l; a is the equatorial rotation rate, and b is the latitudinal gradient of the rotation rate. St. John (1918) was the first one who summarized the published solar rotation rates, and concluded that the differences in series measured in
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different years can hardly be attributed to personal equation or to local disturbances on the Sun, and are probably due to time variations in the rate of rotation, and Hubrecht (1915) was the first one to find that the two solar hemispheres rotate differently. Now the time variations in the solar equatorial rotation rate and in the latitudinal gradient of the rotation rate are a wellestablished fact (Balthasar and Woehl, 1980; Arevalo et al., 1982; Balthasar et al., 1986; Hathaway and Wilson, 1990; Pulkkinen and Tuominen, 1998, among others). Even earlier attempts were made to connect the solar dynamics with the terrestrial magnetism (i.e. Secchi, 1854). However, to the best of our knowledge, no analysis has been made of the effects of the time variations and of the north–south differences in the solar rotation rate on the way in which the solar wind interacts with the Earth’s magnetosphere. In the present paper, we study three features of the interplanetary magnetic field (IMF) related to solar rotation, which are important for the solar wind–magnetosphere interaction: the azimuthal IMF components (By and Blong ), related to the solar equatorial rotation rate, the IMF total magnitude (B), related to the solar differential rotation, and the handedness (i.e. sense of rotation) of rotating magnetic field structures, also related to the solar differential rotation and a manifestation of the differences between the northern and southern solar hemispheres. The components of the IMF at the Earth’s orbit are given by Parker’s Archimedian spiral model which assumes a purely radial solar wind with a constant velocity emanating from a uniformly rotating Sun, with the magnetic field frozen in the flow (Parker, 1958). This general picture has been confirmed by in situ measurements but some deviations from the model have been registered. Smith and Bieber (1991), based on data between 1965 and 1987, found that from 0.7 to 16 AU, the measured winding angle of the heliospheric magnetic field is always greater than the predicted one, with a 10 variation between solar minimum and solar maximum. They suggested that this variation may be, in part, a direct result of the solar cycle variations in solar wind speed. Bruno and Bavassano (1997) confirmed this result for 0.3–1 AU and found a definite dependence of the winding angle on the solar wind speed. However, even after taking into account the measured solar wind speed, they found that the winding angle still remained overwound by several degrees beyond the theoretical value. Here, we recalculate the IMF azimuthal components from Parker’s formula with the actually measured solar wind parameters and solar rotation rate, and compare the results with the observations. It is well known that the IMF at the Earth’s orbit is the extension of the large-scale solar magnetic field. Solar magnetic fields are believed to be generated jointly by differential rotation (Babcock, 1961) and turbulent
convection described by kinetic helicity in the thin transition region between solar convection and radiation zones, somewhere about 200,000 km below the visible solar surface (Pevtsov et al., 1994). After the pioneering work of Hubrecht (1915), the north–south asymmetry in the differential rotation of the Sun and its long-term and solar-cycle variations have been a subject of intense survey (i.e., Arevalo et al., 1982; Howard and Labonte, 1983; Balthasar et al., 1986; Hathaway and Wilson, 1990; Javaraiah, 2003; Gigolashvili et al., 2003; Temmer et al., 2003). The differences in the rotational properties should imply differences in the magnetic field generated by the differential rotation in the two solar hemispheres. Antonucci et al. (1990) analyzed photospheric synoptic charts obtained at the Wilcox Solar Observatory for solar cycles 20 and 21, and pointed out the different behaviors of the solar photospheric magnetic field originating from the northern and southern solar hemispheres, suggesting only a weak magnetic coupling between the two. Temmer et al. (2002), based upon fulldisc averages of the daily line-of-sight component of the unsigned magnetic field strength measurements from the Kitt Peak National Solar Observatory, confirmed this conclusion for cycles 21 and 22, and the current part of cycle 23. In the present study, we compare the periodicities in IMF magnitude at the Earth’s orbit to the periodicities in the latitudinal rotation gradient in the two solar hemispheres since 1881. While the differential rotation has been investigated observationally in great details, the kinetic helicity is still the subject of numerical modeling. Generally speaking, the helicity describes the rotation of the flow, and its sign determines the handedness, that is, the sense of rotation—positive for right-handed or clockwise rotation, and negative for left-handed or counter-clockwise rotation (i.e., Zeldovich et al., 1983). The solar helicity, responsible together with the differential rotation for the generation of the solar magnetic field, is thought itself to be generated by the solar differential rotation (DeVore, 2000). It has been observed that left-handed magnetic forms predominate in the northern solar hemisphere while right-hand ones predominate in the south, and this hemispheric preference is the same for both even and odd-numbered solar cycles (Rust and Kumar, 1994). This is the only feature known so far which is persistently different in the two solar hemispheres, so it may be the key to understanding why the two solar hemispheres affect the Earth in a different way (Georgieva and Kirov, 2000; Georgieva et al., 2000; Georgieva, 2002). The magnetic field rotation is carried to the Earth by the interplanetary magnetic clouds caused by erupting filaments. The magnetic clouds are observed at the Earth’s orbit as regions in the solar wind with higher than average magnetic field strength and smooth rotation of the magnetic field (Burlaga et al., 1981), and they have the same helical field structure and
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hemispherical preference for handedness as the filaments (Kumar and Rust, 1996). In the present study we compare the geoeffectiveness of left- and right-handed magnetic clouds. The paper is organized as follows: The data and methods used are described in Section 2. Looking for the sources of discrepancies between Parker’s formula and observations, in Section 3 we calculate the azimuthal components of the IMF at the Earth’s orbit using Parker’s formula with not only the actually measured solar wind speed and magnetic field magnitude, but also with the measured solar rotation rate, and compare the calculated and the observed values. In Section 4, we compare the periodicities in IMF magnitude at the Earth’s orbit to the periodicities in the latitudinal gradient of the rotation rate in the two solar hemispheres since 1881 to the end to check the role of the solar differential rotation in the generation of the IMF. In the search of the reasons for the different terrestrial response to solar activity originating from the two solar hemispheres, in Section 5 we compare the geoeffectiveness of left- and right-handed magnetic clouds originating predominantly from the northern and southern solar hemispheres, respectively. We summarize our results in Section 6.
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several sources: Fenrich and Luhmann (1998), Leamon et al. (2002), Vilmer et al. (2003), SOHO LASCO CME catalog (http://cdaw.gsfc.nasa.gov/CME_list/), WIND MFI magnetic cloud list (http://sprg.ssl.berkeley.edu/ davin/clouds/cloud_list.html). For our investigation we are mainly interested in magnetic field rotation; so the cases without clear rotation in the Y –Z plane have been omitted, and our final list of magnetic clouds includes a total of 88 events—48 with left-handed helicity, and 40 with right-handed helicity. The final list of magnetic clouds used in this survey has been compiled in Table 1.
3. Interplanetary magnetic field azimuthal component As already mentioned, Parker’s formula for the IMF components is derived for radial solar wind with a constant velocity emanating from a uniformly rotating Sun. To take into account the actually measured solar wind velocity and solar rotation rate, we use a generalization of this formula provided by Giacalone (2001). For the IMF azimuthal component By the expression is r r X sin y þ V ðy; f0 ; t0 Þ 0 f 0 By ðr; y; j; tÞ ¼ Br ðr0 Þ ; Vo r
2. Data
2 r Br ðr0 Þ ¼ Br ðrÞ ; r0
As we are interested in how solar rotation affects the IMF, we begin by examining the solar rotation data. Two sources of data for the solar rotation have been utilized: Mt. Wilson Doppler shift measurements of photospheric line (Howard et al., 1984) providing daily values for the period 1967–1994, and yearly values calculated from Greenwich Photoheliospheric Results (Javaraiah and Gokhale, 1995) complemented by SOON/NOAA data on sunspot groups since 1977 (Javaraiah, 2003). Greenwich data cover the years 1874–1976, however, because of the large uncertainties in 1878, the data for the years 1874–1878 has been omitted. The equatorial rotation rate and the latitudinal gradient of the rotation rate have been calculated for moving time intervals of five years successively shifted by one year. As pointed out by Javaraiah and Gokhale (1997), yearly values are inadequate to determine periodicities; therefore, we use five-year averages, placing the beginning of our data-set in 1881. For IMF and solar wind parameters, daily average values were obtained from the OMNI database through the National Space Science Data Center web-site (http:// nssdc.gsfc.nasa.gov/omniweb/). The geomagnetic indices Kp, aa-N and aa-S are from the National Geophysical Data Center, ftp://ftp.ngdc.noaa.gov/STP/. The list of magnetic clouds used in this study, covering the period 1992–2002, was compiled from
where By is the azimuthal, and Br ðrÞ the radial IMF component at the Earth orbit r ¼ 1 AU, r0 is the solar radius (according to Parker; or, according to later works—the radius of the source surface defined as a sphere around the Sun, inside which no currents flow and on which and outside it, currents restrict the field to being radial, and then stretch toward a spiral—Schatten et al., 1969), X is the solar rotation rate, Vo is the solar wind radial velocity and Vy the azimuthal velocity at the source surface r ¼ r0 ; and t0 ¼ t ðr r0 Þ=V o : Following Parker (1958), we assume a zero velocity azimuthal component Vf ¼ 0; but we introduce a non-constant solar rotation rate, X ¼ Oðy0 ; t0 Þ: Further, we confine our study to the ecliptic plane, so cos y ¼ 1; and Xðy0 ; t0 Þ ¼ Oðt0 Þ is the solar equatorial rotation rate. We now denote the measured in situ values of the azimuthal and radial components of the solar wind magnetic field by By and Bx ; respectively, to distinguish from the calculated ones Bf and Bo ; and calculate the difference between the observed and the calculated IMF azimuthal component, dBy ¼ By By : The yearly averages of dBy (five-year running means) are presented in the middle panel of Fig. 1, and in the top panel—the sunspot cycle. Unlike the measured IMF winding angle which has been found by Smith and Bieber (1991) to be always ‘‘overwound’’ with respect to the theory predictions, the measured IMF azimuthal component can be both bigger
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Table 1 List of magnetic clouds in the period 1992–2000 (R ¼ right-handed, L ¼ left-handed) 09 21 01 14 10 09 27 08 04 03 08 04 07 22 10 16 27 01 07 24 10 11 21
February March April April May October October May August December February March April August October December May July August October January April April
1992 1992 1992 1992 1992 1992 1992 1993 1993 1993 1995 1995 1995 1995 1995 1995 1996 1996 1996 1996 1997 1997 1997
R R L R R R R L L L L L L R R L L L R R R R R
15 20 26 09 19 15 03 03 18 22 01 11 24 27 04 07 22 10 04 07 22 30 04
May May May June June July August September September April October October October October November November November December January January January January February
1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1998 1998 1998 1998 1998
L R R R R L L R R R L R R L L R R L R L L R L
Fig. 1. Top panel—sunspot numbers; middle panel—yearly averages of the difference between the observed and the calculated IMF azimuthal component, dBy (5-year running means); bottom panel— difference between the measured and predicted IMF winding angle dBlong :
17 04 02 16 04 06 24 20 25 19 09 13 18 17 09 22 21 15 28 12 18 14 28
February March April April May June June August September October November November February April August September February July July August September October October
1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1999 1999 1999 1999 2000 2000 2000 2000 2000 2000 2000
R L L R L L L R L L L R L L L L L L L L L L L
07 04 19 31 04 12 18 22 29 28 10 17 30 21 24 19 24 19 23 01
November March March March April April April April April May July August September October November March March May May August
2000 2001 2001 2001 2001 2001 2001 2000 2001 2001 2001 2001 2001 2001 2001 2002 2002 2002 2002 2002
L R L L L R L L L L R R L R L R R R R R
or smaller than the calculated one, that is, the difference dBy can be both positive and negative. Moreover, the sign of this difference changes shortly after sunspot maximum—in the moments of the solar polarity reversals (the vertical lines in Fig. 1). In positive (negative) polarity cycles, By is larger (smaller) than predicted. Therefore, the difference between the measured and calculated IMF azimuthal component is governed by the solar polarity cycle rather than by the sunspot cycle as suggested by Smith and Bieber (1991) and Bruno and Bavassano (1997) for the IMF winding angle. The conclusion of Smith and Bieber (1991) about the sunspot cycle dependence of the difference between the measured and predicted IMF winding angle has been drawn on the basis of data from 1965 to 1987, and using a constant solar rotation rate. We have recalculated this difference dBlong until 2000 taking into account the measured solar rotation rate, and it is presented in the lower panel of Fig. 1. It is clearly seen that the difference between the measured and predicted IMF winding angle dBlong also demonstrates a 22-year dependence, matching the 22-year solar magnetic polarity cycle: dBlong is bigger (more ‘‘overwound’’) in positive polarity cycles, and smaller (less ‘‘overwound’’) in negative polarity cycles. The systematic variation of the differences between the measured and calculated IMF azimuthal components means that Parker’s formula does not properly account for all factors determining them. The neglected or underestimated factor we are looking for should obviously have a 22-year periodicity. To identify it, we have compared the mean values in negative and positive
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Table 2 Mean values and standard deviations in positive and negative polarity solar cycles (PPSC and NPSC, respectively), of IMF magnitude B; solar wind velocity V; solar equatorial rotation rate in microrads per second and latitudinal gradient for the whole sphere (a and b) and for the northern and southern hemispheres (an ; as ; bn and bs ; respectively)
Mean in PPSC Sigma in PPSC Mean in NPSC Sigma in NPSC
B
V
a
an
as
b
bn
bs
5.823 1.071 6.096 1.136
442.33 45.359 442.52 54.967
2.933 0.001 2.931 0.001
2.932 0.001 2.928 0.002
2.934 0.002 2.934 0.002
0.564 0.011 0. 499 0.013
0.570 0.014 0.502 0.017
0.557 0.015 0.498 0.019
the IMF azimuthal component is greater than calculated, the IMF winding angle is more overwound.
In negative polarity solar cycles,
Fig. 2. Solar rotation rate averaged over the two solar hemispheres in cycles with positive (solid line) and negative (dotted line) magnetic polarity.
polarity solar cycles (NPSC and PPSC, respectively) of the IMF magnetic field (B) and solar wind speed (V) from OMNI data-base, and the solar rotation parameters: the equatorial rotation rate a and the latitudinal rotation rate gradient b for the whole sphere, and separately for the northern and southern hemispheres, an ; bn ; as and bs ; respectively, from Greenwich data (Table 2). Of the parameters studied, only the solar rotation is significantly different in positive and negative polarity cycles reflecting a 22-year cyclicity. Fig. 2 illustrates the average (over the two hemispheres) solar rotation for PPSC, and NPSC. In PPSC, solar equatorial rotation is faster (at a significance level of 2 sigma) and the latitudinal gradient of the rotation rate is greater (at 4 sigma) than in NPSC. To summarize: In positive polarity solar cycles,
the solar rotation rate is faster, the latitudinal gradient of the rotation rate is greater,
the solar rotation rate is slower, the latitudinal gradient of the rotation rate is smaller, the IMF azimuthal component is smaller than calculated, the IMF winding angle is less overwound.
The solar rotation rate is included in Parker’s formula. What is neglected in it are the solar wind and magnetic field non-radial components. One of the possible reasons for the 22-year periodicity in the difference between Parker’s formula and the measured By may be the presence of a non-zero azimuthal solar wind component at the source surface, proportional to the solar rotation rate. This probably has some effect, as not only the difference dBy ; but By itself show a clear 22-year dependence; however, it cannot explain the negative differences. Another reason for the 22-year periodicity in the deviations of the IMF azimuthal components from the theoretical predictions can be the presence of a small azimuthal magnetic field component on the source surface, as suggested by Smith and Bieber (1991). Such azimuthal component is forecasted by the model of Fisk (1996) of the heliospheric magnetic field. According to this model, the differential rotation of the photosphere and the non-radial expansion of the magnetic field and solar wind from the polar coronal holes which are the main sources of the open magnetic flux and hence of the IMF at solar minimum, will lead to magnetic field footpoint motions at low latitude on the source surface. These footpoint motions can be in the direction of the solar rotation or opposite to it and, as discussed by Zurbuchen et al. (1998), will lead to systematic overwinding or underwinding of the heliospheric magnetic field, depending on the magnetic polarity. If this hypothesis is true, the result must be a 22-year dependence of the difference between the Parker spiral and the actual heliospheric field, with the biggest deviations occurring in solar minimum. This is exactly what we observe, so our results can be considered the
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direct observational evidence for the validity of the model sought by Fisk (2000).
4. Periodicities in solar rotation parameters As seen in Table 2, the rotation parameters are different in the northern and southern solar hemispheres—a result demonstrated earlier for the last three and a half sunspot cycles (Antonucci et al., 1990; Temmer et al., 2003). Table 2 summarizes data since 1881; there is a lack of good correspondence in the entire period between the rotation in the two solar hemispheres. Fig. 3 presents the relation between the rotation parameters in the two hemispheres, with the values for the northern hemisphere plotted along the x-axis of the scatter plots, and the ones for the southern hemisphere—along the y-axis. The solid lines show the linear fit regression functions. While there is some weak though statistically significant correlation between the equatorial rotation rates an and as ; r ¼ 0:36 with po0:05 (the upper panel of Fig. 3), there is no correlation at all between the latitudinal gradients in the two hemispheres, bn and bs : the correlation coefficient is only 0.06 (the lower panel of Fig. 3).
Fig. 3. Dependence between the equatorial rotation rates an and as (upper panel), and latitudinal gradients of the rotation rate bn and bs (lower panel) in the northern and southern solar hemispheres. The solid lines represent the linear regression fit.
Periodicities for the period covered by Greenwich data, 1881–1974, in the solar equatorial rotation rate and the rotation rate latitudinal gradient averaged over the whole solar sphere, a and b; respectively, as well as in the solar rotation asymmetry, aa ¼ ðan as Þ=ðan þ as Þ; have been investigated by Javaraiah and Gokhale (1995, 1997) and Javaraiah (2003). Here, we are comparing the periodicities in the equatorial rotation rate and in the latitudinal rotation rate gradient in the two hemispheres. In the upper and lower panels of Fig. 4, the FFT spectra of the equatorial rotation rates in the northern and southern solar hemispheres an and as are presented, respectively. Both show pronounced periodicities at 94 years, the length of the data series, and this is their only common periodicity. A 47-year periodicity which is also the dominant periodicity in the Earth’s rotation fluctuations (Georgieva, 2002), in the Earth’s electromagnetic core–mantle coupling torques (e.g., GreinerMai, 1987), considered one of the possible mechanisms for the excitation of the Earth’s rotation fluctuations (Hide, 1995), in the inertial movement of the Sun around the baricenter of the solar system (Bucha et al., 1985), as well as in the asymmetry in solar equatorial rotation (Javaraiah and Gokhale, 1997), is observed in an but not in as : Another periodicity evident only in an and not in as is the 18.8-year periodicity found
Fig. 4. FFT spectra of the equatorial rotation rates an and as in the northern (upper panel) and southern (lower panel) solar hemispheres, respectively.
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in b (Javaraiah and Gokhale, 1995) and matching the 17-year one in the IMF directions and coronal holes asymmetries (Juckett, 1998). On the other hand, a 10.4year periodicity corresponding to the 11-year solar cycle period, and a 23.5-year periodicity corresponding to the 22-year Hale cycle are only found in as and not in an : In Fig. 5, the FFT spectra of bn and bs are presented. The 47-year and the10.4-year periodicities found by Javaraiah and Gokhale (1997) in the asymmetry of the latitudinal rotation rate gradient, ba ¼ ðbn bs Þ=ðbn þ bs Þ; are seen only in the northern hemisphere, while the dominant 18.8-year periodicity found in b (Javaraiah and Gokhale, 1995) and the 13.3-year periodicity in ba (Javaraiah and Gokhale, 1997) are much weaker in the southern one. The behavior of the b coefficient of the solar differential rotation is particularly important with relation to the dynamo theory of the solar magnetic field (Babcock, 1961). The IMF, being an extension of the coronal field, results from this large-scale solar field. IMF has been measured directly since the beginning of the satellite era. For the period 1967–1994, we have data for both bn and bs coefficients of the solar differential rotation derived by Mt. Wilson Doppler shift measurements, and IMF parameters compiled in OMNI database of the National Space Science Data Center.
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The dominant periodicity in the average IMF magnitude B in this period is 9.3 years coinciding with the dominant periodicity in bs ; while the dominant periodicity in bn is 14 years (Fig. 6c). In this period, predominantly more active is the southern solar hemisphere, i.e., the dominant periodicity in the IMF matches the dominant periodicity in the differential rotation of the more active solar hemisphere. The solar rotation data considered for this study date back to 1881. For this period there are no direct measurements of the IMF, so as a proxy for its magnitude we use the aa index of geomagnetic activity. We use this index rather than the sunspot numbers as geomagnetic activity is related to the interplanetary magnetic field which is the extension of the coronal open magnetic field while sunspots are regions of closed magnetic field, and their long-term evolution has been shown to be quite different (Wang et al., 2000). The southern solar hemisphere was more active during the period 1881–1912. The dominant periodicity in bs is 16 years, and the same is the dominant periodicity in aa ; while bn varies with a period of 10.8 years (Fig. 6a). During the second period, from 1913 to 1966, the northern hemisphere was more active. The dominant periodicity in aa is 10.8 years. A strong peak at this periodicity is seen in bn ; and no peak in bs (Fig. 6b). Two conclusions can be made from the data summarized in Figs. 5 and 6. First, the rotation parameters vary and are different in the northern and southern solar hemispheres for the whole period covered by solar rotation data, from 1881 to 2000, or 12 sunspot cycles which confirms the weak magnetic coupling between the two solar hemispheres. Second, the solar rotation exhibits long-term changes, matching the longterm changes in the IMF. The IMF, the extension of the solar coronal magnetic field, is influenced by the differential rotation in the solar hemisphere with dominant activity.
5. Geomagnetic response to magnetic clouds with different helicity
Fig. 5. FFT spectra of rotation rate latitudinal gradients bn and bs ; in the northern (upper panel) and southern (lower panel) solar hemispheres, respectively.
One of the most powerful manifestations of the solar wind–magnetosphere coupling is the reaction of the magnetosphere to magnetic clouds (Burlaga et al., 1987). The smooth rotation of the magnetic field inside the cloud and its handedness representing the helicity of the cloud’s source region at the Sun relates the magnetic clouds to the solar differential rotation. The geoeffectiveness of magnetic clouds is considered to be determined by the strong long-lasting southward fields (Wu and Lepping, 2002) under which reconnection of the interplanetary and geomagnetic field lines partially opens Earth’s magnetic field to the solar wind (Dungey,
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In the upper panel of Fig. 7, the reaction of K p index of geomagnetic activity is compared for the cases of encounter of right-handed (solid line) and left-handed (broken line) magnetic clouds. K p index reaches higher values in the cases of left-handed clouds, and this difference is significant at 2.5 sigma. The difference in geomagnetic response is in the same direction in the northern and southern hemispheres. Fig. 8 presents the changes in aa-N and aa-S indices—the aa indices of geomagnetic activity calculated only from stations in the northern and southern hemisphere, respectively. In both hemispheres, stronger geomagnetic disturbances are registered for left-handed magnetic clouds. Cid et al. (2003) have approached the problem from the opposite side. They have selected all major geomagnetic storms ðDst o 70Þ in the period 1995–2000, and have searched WIND data for possible magnetic clouds related to each storm event. They have found a close relationship between the helicity of geoeffective magnetic clouds and the longitude angle
Fig. 6. (a) Periodicities in the aa-index of geomagnetic activity aa (solid line), and the rotation rate latitudinal gradients in the northern solar hemisphere bn (broken line) and in the southern solar hemisphere bs (dotted line) in the period 1881–1912; (b) Periodicities in the aaindex of geomagnetic activity aa (solid line), and the rotation rate latitudinal gradients in the northern solar hemisphere bn (broken line) and in the southern solar hemisphere bs (dotted line) in the period 1913–1966; (c) Periodicities in IMF magnitude B (solid line), and the rotation rate latitudinal gradients in the northern solar hemisphere bn (broken line) and in the southern solar hemisphere bs (dotted line) in the period 1967–2000.
1961). This study aims to determine whether the geoeffectiveness of the cloud is also determined by its helicity.
Fig. 7. Upper panel—superposed method analysis of the variations of K p index of geomagnetic activity for the cases of arrival of righthanded (solid line) and left-handed (broken line) magnetic clouds. Lower panel—the same with the cases without Bz o0 excluded. Day 0 corresponds to the day of encounter of the magnetic cloud.
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Fig. 8. Superposed method analysis of the variations of the aa indices of geomagnetic activity calculated only from stations in the northern (aa-N—upper panel) and southern hemisphere (aa-S—lower panel). Day 0 corresponds to the day of encounter of the magnetic cloud.
of the axis of the cloud, determining the presence of a southward magnetic field component. However, we find that the presence of a southward magnetic field component is not the only factor for the geoeffectiveness of a magnetic cloud. In the lower panel of Fig. 7, only the magnetic clouds with Bz o0 are included, while the upper panel includes all clouds. It can be seen that the difference between left- and right-handed clouds does not vanish. Moreover, there is no difference between right- and left-handed clouds in the prevailing direction of the IMF vertical component (Fig. 9a), as there is no difference in the magnetic field magnitude (Fig. 9b) or the solar wind pressure (Fig. 9c). Clearly, the problem of the dependence of the geoeffectiveness of magnetic clouds on their helicity requires further study. The importance of this question arises from the fact that solar activity originating from the northern and southern hemispheres has been found to have different effect on the Earth, and magnetic helicity is the only feature known so far which is persistently different in the two solar hemispheres.
Fig. 9. Superposed method analysis of the variations of the IMF Bz component (a), total magnitude B (b) and solar wind pressure (c) for right-handed (solid line) and left-handed (broken line) magnetic clouds. Day 0 corresponds to the day of encounter of the magnetic cloud.
6. Summary (1) We have studied the deviations of the measured IMF azimuthal component and IMF winding angle from Parker’s formula taking into account the irregular solar rotation rate, and have found that these deviations
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follow the 22-year solar magnetic cycle rather than the 11-year sunspot cycle as previously suggested. The deviations are the same as predicted by Fisk’s model of the heliospheric magnetic field, and the presented results are a confirmation of the validity of the model. (2) For the last four solar cycles, it has been known that the rotation parameters of the two solar hemispheres differ. We have shown this to be true for the last 12 sunspot cycles, which proves the weak magnetic coupling between the hemispheres. We have compared the periodicities in solar rotation parameters in the two hemispheres to the periodicities in IMF magnitude at the Earth’s orbit and have shown that the IMF which is an extension of the large-scale coronal field, has the same periodicities as the differential rotation in the more active solar hemisphere. (3) We have compared the geomagnetic response to magnetic clouds with left- and right-handed helicity, originating predominantly from the northern and southern solar hemispheres, respectively, and have shown it to be different depending on the magnetic cloud helicity, which confirms the different effect of the solar hemispheres on the Earth.
Acknowledgements The authors are grateful to the referees for the helpful comments. This study has made use of NASA Astrophysical Data System. References Abetti, G., 1965. Sunspots from Galileo to Hale, vol. 432, Astronomical Society of the Pasific, Leaflet, pp. 257–266. Antonucci, E., Hoeksema, J.T., Scherrer, P.H., 1990. Rotation of the photospheric magnetic field: a north–south asymmetry. Astrophys. J. 360, 296–304. Arevalo, M.J., Gomez, R., Vazquez, M., Balthasar, H., Wo¨hl, H., 1982. Differential rotation and meridional motions of sunspots from 1874 to 1902. Astronom. Astrophys. 111 (2), 266–271. Babcock, H.W., 1961. The topology of the sun’s magnetic field and the 22-year Cycle. Astrophys. J. 133, 572–587. Balthasar, H., Woehl, H., 1980. Differential rotation and meridional motions of sunspots in the years 1940–1968. Astronom. Astrophys. 92 (1–2), 111–116. Balthasar, H., Vazquez, M., Woehl, H., 1986. Differential rotation of sunspot groups in the period from 1874 through 1976 and changes of the rotation velocity within the solar cycle. Astronom. Astrophys. 155 (1), 87–98. Bruno, R., Bavassano, B., 1997. On the winding of the IMF spiral for slow and fast wind within the inner heliosphere. Geophys. Res. Lett. 24 (18), 2267–2270. Bucha, V., Jakubcova, I., Pick, M., 1985. Resonance frequencies in the sun’s motion. Studia Geophys. Geod. 85 (2), 107–111. Burlaga, L.F., Sittler, E., Mariani, F., Schwenn, R., 1981. Magnetic loop behind an interplanetary shock: Voyager, Helios and IMP-8 observations. J. Geophys. Res. 86, 6673–6684. Burlaga, L.F., Behannon, K.W., Klein, L.W., 1987. Compound streams, magnetic clouds, and major geomagnetic storms. J. Geophys. Res. 92 (1), 5725–5734.
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Planetary and Space Science 53 (2005) 197–207 www.elsevier.com/locate/pss
Solar rotation and solar wind–magnetosphere coupling K. Georgievaa,, B. Kirova, J. Javaraiahb,c, R. Krastevad a
Solar-Terrestrial Influences Laboratory at the Bulgarian Academy of Sciences, Bl.3 Academy G. Bonchev str., 1113 Sofia, Bulgaria b Indian Institute of Astrophysics, Koramangala, Bangalore 560034, India c Department of Physics and Astronomy, 8371 MS, University of California, Los Angeles, CA 90095, USA d Central Laboratory of Mechatronics and Instrumentations at the Bulgarian Academy of Sciences, Bl.5 Academy G. Bonchev str., 1113 Sofia, Bulgaria Accepted 12 September 2004
Abstract This paper deals with three characteristics of the interplanetary magnetic field (IMF), important for solar wind–magnetosphere coupling and related to solar rotation: the IMF azimuthal component, the IMF total magnitude, and the handedness or the sense of rotation of magnetic clouds. The IMF configuration is described by Parker’s Archimedian spiral model (Astrophys. J. 128 (1958) 664) under the assumptions of a purely radial solar wind with a constant velocity emanating from a uniformly rotating Sun. In situ measurements confirmed this general picture, but a systematic deviation from the predicted IMF winding angle was found, supposedly exhibiting a 11-year periodicity. We account for the non-uniform solar rotation and compare the observed IMF azimuthal component to the one calculated from Parker’s formula with the measured equatorial solar rotation rate. We find that the differences between the calculated and measured IMF azimuthal component and the winding angle have a clear 22-year dependence on the solar polarity cycle, matching the 22-year periodicity in solar rotation rate rather than on the 11-year sunspot cycle. Our results are an observational confirmation of the validity of the model of Fisk (J. Geophys. Res. 101 (1996) 15547) for heliospheric magnetic field with footpoint motions due to solar differential rotation. Solar differential rotation is also an important element of the solar dynamo which is responsible for the generation of the solar magnetic field. We compare the different periodicities in the variations in the latitudinal rotation gradient of the two solar hemispheres and show that the IMF which is an extension of the solar coronal field, is related to the differential rotation in the more active solar hemisphere. Another feature related to solar differential rotation that is persistently different in the two solar hemispheres is the prevailing magnetic helicity, which is carried to the Earth by magnetic clouds preserving the helicity of the source region of their origin. The reaction of the magnetosphere to magnetic clouds is determined mainly by the presence or absence of a prolonged period of southward IMF component. We show that it also depends on the helicity of the clouds, and compare the effects of right- and left-handed magnetic clouds on geomagnetic activity. r 2004 Elsevier Ltd. All rights reserved. Keywords: Solar rotation; Interplanetary magnetic field; Magnetic cloud; Helicity; Geomagnetic disturbance
1. Introduction Though sunspots had been observed since ancient times, only when the telescope came into use it was noticed that they turn with the Sun, and thus the period of the solar rotation could be defined. Since these early studies of Galileo, Carrington, Scheiner, Fabricius, Hale, Sacchi and many others (Abetti, 1965), it has Corresponding author. Tel.: +359 2 979 3432; fax: +359 2 870 0178. E-mail address: [email protected] (K. Georgieva).
0032-0633/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2004.09.045
been known that the Sun is not a solid body and that it rotates faster near the equator than near the poles—an effect known as ‘‘differential rotation’’. This differential rotation is described by the formula XðlÞ ¼ a þ b sin2 l; where XðlÞ is the rotation rate at latitude l; a is the equatorial rotation rate, and b is the latitudinal gradient of the rotation rate. St. John (1918) was the first one who summarized the published solar rotation rates, and concluded that the differences in series measured in
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different years can hardly be attributed to personal equation or to local disturbances on the Sun, and are probably due to time variations in the rate of rotation, and Hubrecht (1915) was the first one to find that the two solar hemispheres rotate differently. Now the time variations in the solar equatorial rotation rate and in the latitudinal gradient of the rotation rate are a wellestablished fact (Balthasar and Woehl, 1980; Arevalo et al., 1982; Balthasar et al., 1986; Hathaway and Wilson, 1990; Pulkkinen and Tuominen, 1998, among others). Even earlier attempts were made to connect the solar dynamics with the terrestrial magnetism (i.e. Secchi, 1854). However, to the best of our knowledge, no analysis has been made of the effects of the time variations and of the north–south differences in the solar rotation rate on the way in which the solar wind interacts with the Earth’s magnetosphere. In the present paper, we study three features of the interplanetary magnetic field (IMF) related to solar rotation, which are important for the solar wind–magnetosphere interaction: the azimuthal IMF components (By and Blong ), related to the solar equatorial rotation rate, the IMF total magnitude (B), related to the solar differential rotation, and the handedness (i.e. sense of rotation) of rotating magnetic field structures, also related to the solar differential rotation and a manifestation of the differences between the northern and southern solar hemispheres. The components of the IMF at the Earth’s orbit are given by Parker’s Archimedian spiral model which assumes a purely radial solar wind with a constant velocity emanating from a uniformly rotating Sun, with the magnetic field frozen in the flow (Parker, 1958). This general picture has been confirmed by in situ measurements but some deviations from the model have been registered. Smith and Bieber (1991), based on data between 1965 and 1987, found that from 0.7 to 16 AU, the measured winding angle of the heliospheric magnetic field is always greater than the predicted one, with a 10 variation between solar minimum and solar maximum. They suggested that this variation may be, in part, a direct result of the solar cycle variations in solar wind speed. Bruno and Bavassano (1997) confirmed this result for 0.3–1 AU and found a definite dependence of the winding angle on the solar wind speed. However, even after taking into account the measured solar wind speed, they found that the winding angle still remained overwound by several degrees beyond the theoretical value. Here, we recalculate the IMF azimuthal components from Parker’s formula with the actually measured solar wind parameters and solar rotation rate, and compare the results with the observations. It is well known that the IMF at the Earth’s orbit is the extension of the large-scale solar magnetic field. Solar magnetic fields are believed to be generated jointly by differential rotation (Babcock, 1961) and turbulent
convection described by kinetic helicity in the thin transition region between solar convection and radiation zones, somewhere about 200,000 km below the visible solar surface (Pevtsov et al., 1994). After the pioneering work of Hubrecht (1915), the north–south asymmetry in the differential rotation of the Sun and its long-term and solar-cycle variations have been a subject of intense survey (i.e., Arevalo et al., 1982; Howard and Labonte, 1983; Balthasar et al., 1986; Hathaway and Wilson, 1990; Javaraiah, 2003; Gigolashvili et al., 2003; Temmer et al., 2003). The differences in the rotational properties should imply differences in the magnetic field generated by the differential rotation in the two solar hemispheres. Antonucci et al. (1990) analyzed photospheric synoptic charts obtained at the Wilcox Solar Observatory for solar cycles 20 and 21, and pointed out the different behaviors of the solar photospheric magnetic field originating from the northern and southern solar hemispheres, suggesting only a weak magnetic coupling between the two. Temmer et al. (2002), based upon fulldisc averages of the daily line-of-sight component of the unsigned magnetic field strength measurements from the Kitt Peak National Solar Observatory, confirmed this conclusion for cycles 21 and 22, and the current part of cycle 23. In the present study, we compare the periodicities in IMF magnitude at the Earth’s orbit to the periodicities in the latitudinal rotation gradient in the two solar hemispheres since 1881. While the differential rotation has been investigated observationally in great details, the kinetic helicity is still the subject of numerical modeling. Generally speaking, the helicity describes the rotation of the flow, and its sign determines the handedness, that is, the sense of rotation—positive for right-handed or clockwise rotation, and negative for left-handed or counter-clockwise rotation (i.e., Zeldovich et al., 1983). The solar helicity, responsible together with the differential rotation for the generation of the solar magnetic field, is thought itself to be generated by the solar differential rotation (DeVore, 2000). It has been observed that left-handed magnetic forms predominate in the northern solar hemisphere while right-hand ones predominate in the south, and this hemispheric preference is the same for both even and odd-numbered solar cycles (Rust and Kumar, 1994). This is the only feature known so far which is persistently different in the two solar hemispheres, so it may be the key to understanding why the two solar hemispheres affect the Earth in a different way (Georgieva and Kirov, 2000; Georgieva et al., 2000; Georgieva, 2002). The magnetic field rotation is carried to the Earth by the interplanetary magnetic clouds caused by erupting filaments. The magnetic clouds are observed at the Earth’s orbit as regions in the solar wind with higher than average magnetic field strength and smooth rotation of the magnetic field (Burlaga et al., 1981), and they have the same helical field structure and
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hemispherical preference for handedness as the filaments (Kumar and Rust, 1996). In the present study we compare the geoeffectiveness of left- and right-handed magnetic clouds. The paper is organized as follows: The data and methods used are described in Section 2. Looking for the sources of discrepancies between Parker’s formula and observations, in Section 3 we calculate the azimuthal components of the IMF at the Earth’s orbit using Parker’s formula with not only the actually measured solar wind speed and magnetic field magnitude, but also with the measured solar rotation rate, and compare the calculated and the observed values. In Section 4, we compare the periodicities in IMF magnitude at the Earth’s orbit to the periodicities in the latitudinal gradient of the rotation rate in the two solar hemispheres since 1881 to the end to check the role of the solar differential rotation in the generation of the IMF. In the search of the reasons for the different terrestrial response to solar activity originating from the two solar hemispheres, in Section 5 we compare the geoeffectiveness of left- and right-handed magnetic clouds originating predominantly from the northern and southern solar hemispheres, respectively. We summarize our results in Section 6.
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several sources: Fenrich and Luhmann (1998), Leamon et al. (2002), Vilmer et al. (2003), SOHO LASCO CME catalog (http://cdaw.gsfc.nasa.gov/CME_list/), WIND MFI magnetic cloud list (http://sprg.ssl.berkeley.edu/ davin/clouds/cloud_list.html). For our investigation we are mainly interested in magnetic field rotation; so the cases without clear rotation in the Y –Z plane have been omitted, and our final list of magnetic clouds includes a total of 88 events—48 with left-handed helicity, and 40 with right-handed helicity. The final list of magnetic clouds used in this survey has been compiled in Table 1.
3. Interplanetary magnetic field azimuthal component As already mentioned, Parker’s formula for the IMF components is derived for radial solar wind with a constant velocity emanating from a uniformly rotating Sun. To take into account the actually measured solar wind velocity and solar rotation rate, we use a generalization of this formula provided by Giacalone (2001). For the IMF azimuthal component By the expression is r r X sin y þ V ðy; f0 ; t0 Þ 0 f 0 By ðr; y; j; tÞ ¼ Br ðr0 Þ ; Vo r
2. Data
2 r Br ðr0 Þ ¼ Br ðrÞ ; r0
As we are interested in how solar rotation affects the IMF, we begin by examining the solar rotation data. Two sources of data for the solar rotation have been utilized: Mt. Wilson Doppler shift measurements of photospheric line (Howard et al., 1984) providing daily values for the period 1967–1994, and yearly values calculated from Greenwich Photoheliospheric Results (Javaraiah and Gokhale, 1995) complemented by SOON/NOAA data on sunspot groups since 1977 (Javaraiah, 2003). Greenwich data cover the years 1874–1976, however, because of the large uncertainties in 1878, the data for the years 1874–1878 has been omitted. The equatorial rotation rate and the latitudinal gradient of the rotation rate have been calculated for moving time intervals of five years successively shifted by one year. As pointed out by Javaraiah and Gokhale (1997), yearly values are inadequate to determine periodicities; therefore, we use five-year averages, placing the beginning of our data-set in 1881. For IMF and solar wind parameters, daily average values were obtained from the OMNI database through the National Space Science Data Center web-site (http:// nssdc.gsfc.nasa.gov/omniweb/). The geomagnetic indices Kp, aa-N and aa-S are from the National Geophysical Data Center, ftp://ftp.ngdc.noaa.gov/STP/. The list of magnetic clouds used in this study, covering the period 1992–2002, was compiled from
where By is the azimuthal, and Br ðrÞ the radial IMF component at the Earth orbit r ¼ 1 AU, r0 is the solar radius (according to Parker; or, according to later works—the radius of the source surface defined as a sphere around the Sun, inside which no currents flow and on which and outside it, currents restrict the field to being radial, and then stretch toward a spiral—Schatten et al., 1969), X is the solar rotation rate, Vo is the solar wind radial velocity and Vy the azimuthal velocity at the source surface r ¼ r0 ; and t0 ¼ t ðr r0 Þ=V o : Following Parker (1958), we assume a zero velocity azimuthal component Vf ¼ 0; but we introduce a non-constant solar rotation rate, X ¼ Oðy0 ; t0 Þ: Further, we confine our study to the ecliptic plane, so cos y ¼ 1; and Xðy0 ; t0 Þ ¼ Oðt0 Þ is the solar equatorial rotation rate. We now denote the measured in situ values of the azimuthal and radial components of the solar wind magnetic field by By and Bx ; respectively, to distinguish from the calculated ones Bf and Bo ; and calculate the difference between the observed and the calculated IMF azimuthal component, dBy ¼ By By : The yearly averages of dBy (five-year running means) are presented in the middle panel of Fig. 1, and in the top panel—the sunspot cycle. Unlike the measured IMF winding angle which has been found by Smith and Bieber (1991) to be always ‘‘overwound’’ with respect to the theory predictions, the measured IMF azimuthal component can be both bigger
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Table 1 List of magnetic clouds in the period 1992–2000 (R ¼ right-handed, L ¼ left-handed) 09 21 01 14 10 09 27 08 04 03 08 04 07 22 10 16 27 01 07 24 10 11 21
February March April April May October October May August December February March April August October December May July August October January April April
1992 1992 1992 1992 1992 1992 1992 1993 1993 1993 1995 1995 1995 1995 1995 1995 1996 1996 1996 1996 1997 1997 1997
R R L R R R R L L L L L L R R L L L R R R R R
15 20 26 09 19 15 03 03 18 22 01 11 24 27 04 07 22 10 04 07 22 30 04
May May May June June July August September September April October October October October November November November December January January January January February
1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1998 1998 1998 1998 1998
L R R R R L L R R R L R R L L R R L R L L R L
Fig. 1. Top panel—sunspot numbers; middle panel—yearly averages of the difference between the observed and the calculated IMF azimuthal component, dBy (5-year running means); bottom panel— difference between the measured and predicted IMF winding angle dBlong :
17 04 02 16 04 06 24 20 25 19 09 13 18 17 09 22 21 15 28 12 18 14 28
February March April April May June June August September October November November February April August September February July July August September October October
1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1999 1999 1999 1999 2000 2000 2000 2000 2000 2000 2000
R L L R L L L R L L L R L L L L L L L L L L L
07 04 19 31 04 12 18 22 29 28 10 17 30 21 24 19 24 19 23 01
November March March March April April April April April May July August September October November March March May May August
2000 2001 2001 2001 2001 2001 2001 2000 2001 2001 2001 2001 2001 2001 2001 2002 2002 2002 2002 2002
L R L L L R L L L L R R L R L R R R R R
or smaller than the calculated one, that is, the difference dBy can be both positive and negative. Moreover, the sign of this difference changes shortly after sunspot maximum—in the moments of the solar polarity reversals (the vertical lines in Fig. 1). In positive (negative) polarity cycles, By is larger (smaller) than predicted. Therefore, the difference between the measured and calculated IMF azimuthal component is governed by the solar polarity cycle rather than by the sunspot cycle as suggested by Smith and Bieber (1991) and Bruno and Bavassano (1997) for the IMF winding angle. The conclusion of Smith and Bieber (1991) about the sunspot cycle dependence of the difference between the measured and predicted IMF winding angle has been drawn on the basis of data from 1965 to 1987, and using a constant solar rotation rate. We have recalculated this difference dBlong until 2000 taking into account the measured solar rotation rate, and it is presented in the lower panel of Fig. 1. It is clearly seen that the difference between the measured and predicted IMF winding angle dBlong also demonstrates a 22-year dependence, matching the 22-year solar magnetic polarity cycle: dBlong is bigger (more ‘‘overwound’’) in positive polarity cycles, and smaller (less ‘‘overwound’’) in negative polarity cycles. The systematic variation of the differences between the measured and calculated IMF azimuthal components means that Parker’s formula does not properly account for all factors determining them. The neglected or underestimated factor we are looking for should obviously have a 22-year periodicity. To identify it, we have compared the mean values in negative and positive
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Table 2 Mean values and standard deviations in positive and negative polarity solar cycles (PPSC and NPSC, respectively), of IMF magnitude B; solar wind velocity V; solar equatorial rotation rate in microrads per second and latitudinal gradient for the whole sphere (a and b) and for the northern and southern hemispheres (an ; as ; bn and bs ; respectively)
Mean in PPSC Sigma in PPSC Mean in NPSC Sigma in NPSC
B
V
a
an
as
b
bn
bs
5.823 1.071 6.096 1.136
442.33 45.359 442.52 54.967
2.933 0.001 2.931 0.001
2.932 0.001 2.928 0.002
2.934 0.002 2.934 0.002
0.564 0.011 0. 499 0.013
0.570 0.014 0.502 0.017
0.557 0.015 0.498 0.019
the IMF azimuthal component is greater than calculated, the IMF winding angle is more overwound.
In negative polarity solar cycles,
Fig. 2. Solar rotation rate averaged over the two solar hemispheres in cycles with positive (solid line) and negative (dotted line) magnetic polarity.
polarity solar cycles (NPSC and PPSC, respectively) of the IMF magnetic field (B) and solar wind speed (V) from OMNI data-base, and the solar rotation parameters: the equatorial rotation rate a and the latitudinal rotation rate gradient b for the whole sphere, and separately for the northern and southern hemispheres, an ; bn ; as and bs ; respectively, from Greenwich data (Table 2). Of the parameters studied, only the solar rotation is significantly different in positive and negative polarity cycles reflecting a 22-year cyclicity. Fig. 2 illustrates the average (over the two hemispheres) solar rotation for PPSC, and NPSC. In PPSC, solar equatorial rotation is faster (at a significance level of 2 sigma) and the latitudinal gradient of the rotation rate is greater (at 4 sigma) than in NPSC. To summarize: In positive polarity solar cycles,
the solar rotation rate is faster, the latitudinal gradient of the rotation rate is greater,
the solar rotation rate is slower, the latitudinal gradient of the rotation rate is smaller, the IMF azimuthal component is smaller than calculated, the IMF winding angle is less overwound.
The solar rotation rate is included in Parker’s formula. What is neglected in it are the solar wind and magnetic field non-radial components. One of the possible reasons for the 22-year periodicity in the difference between Parker’s formula and the measured By may be the presence of a non-zero azimuthal solar wind component at the source surface, proportional to the solar rotation rate. This probably has some effect, as not only the difference dBy ; but By itself show a clear 22-year dependence; however, it cannot explain the negative differences. Another reason for the 22-year periodicity in the deviations of the IMF azimuthal components from the theoretical predictions can be the presence of a small azimuthal magnetic field component on the source surface, as suggested by Smith and Bieber (1991). Such azimuthal component is forecasted by the model of Fisk (1996) of the heliospheric magnetic field. According to this model, the differential rotation of the photosphere and the non-radial expansion of the magnetic field and solar wind from the polar coronal holes which are the main sources of the open magnetic flux and hence of the IMF at solar minimum, will lead to magnetic field footpoint motions at low latitude on the source surface. These footpoint motions can be in the direction of the solar rotation or opposite to it and, as discussed by Zurbuchen et al. (1998), will lead to systematic overwinding or underwinding of the heliospheric magnetic field, depending on the magnetic polarity. If this hypothesis is true, the result must be a 22-year dependence of the difference between the Parker spiral and the actual heliospheric field, with the biggest deviations occurring in solar minimum. This is exactly what we observe, so our results can be considered the
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direct observational evidence for the validity of the model sought by Fisk (2000).
4. Periodicities in solar rotation parameters As seen in Table 2, the rotation parameters are different in the northern and southern solar hemispheres—a result demonstrated earlier for the last three and a half sunspot cycles (Antonucci et al., 1990; Temmer et al., 2003). Table 2 summarizes data since 1881; there is a lack of good correspondence in the entire period between the rotation in the two solar hemispheres. Fig. 3 presents the relation between the rotation parameters in the two hemispheres, with the values for the northern hemisphere plotted along the x-axis of the scatter plots, and the ones for the southern hemisphere—along the y-axis. The solid lines show the linear fit regression functions. While there is some weak though statistically significant correlation between the equatorial rotation rates an and as ; r ¼ 0:36 with po0:05 (the upper panel of Fig. 3), there is no correlation at all between the latitudinal gradients in the two hemispheres, bn and bs : the correlation coefficient is only 0.06 (the lower panel of Fig. 3).
Fig. 3. Dependence between the equatorial rotation rates an and as (upper panel), and latitudinal gradients of the rotation rate bn and bs (lower panel) in the northern and southern solar hemispheres. The solid lines represent the linear regression fit.
Periodicities for the period covered by Greenwich data, 1881–1974, in the solar equatorial rotation rate and the rotation rate latitudinal gradient averaged over the whole solar sphere, a and b; respectively, as well as in the solar rotation asymmetry, aa ¼ ðan as Þ=ðan þ as Þ; have been investigated by Javaraiah and Gokhale (1995, 1997) and Javaraiah (2003). Here, we are comparing the periodicities in the equatorial rotation rate and in the latitudinal rotation rate gradient in the two hemispheres. In the upper and lower panels of Fig. 4, the FFT spectra of the equatorial rotation rates in the northern and southern solar hemispheres an and as are presented, respectively. Both show pronounced periodicities at 94 years, the length of the data series, and this is their only common periodicity. A 47-year periodicity which is also the dominant periodicity in the Earth’s rotation fluctuations (Georgieva, 2002), in the Earth’s electromagnetic core–mantle coupling torques (e.g., GreinerMai, 1987), considered one of the possible mechanisms for the excitation of the Earth’s rotation fluctuations (Hide, 1995), in the inertial movement of the Sun around the baricenter of the solar system (Bucha et al., 1985), as well as in the asymmetry in solar equatorial rotation (Javaraiah and Gokhale, 1997), is observed in an but not in as : Another periodicity evident only in an and not in as is the 18.8-year periodicity found
Fig. 4. FFT spectra of the equatorial rotation rates an and as in the northern (upper panel) and southern (lower panel) solar hemispheres, respectively.
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in b (Javaraiah and Gokhale, 1995) and matching the 17-year one in the IMF directions and coronal holes asymmetries (Juckett, 1998). On the other hand, a 10.4year periodicity corresponding to the 11-year solar cycle period, and a 23.5-year periodicity corresponding to the 22-year Hale cycle are only found in as and not in an : In Fig. 5, the FFT spectra of bn and bs are presented. The 47-year and the10.4-year periodicities found by Javaraiah and Gokhale (1997) in the asymmetry of the latitudinal rotation rate gradient, ba ¼ ðbn bs Þ=ðbn þ bs Þ; are seen only in the northern hemisphere, while the dominant 18.8-year periodicity found in b (Javaraiah and Gokhale, 1995) and the 13.3-year periodicity in ba (Javaraiah and Gokhale, 1997) are much weaker in the southern one. The behavior of the b coefficient of the solar differential rotation is particularly important with relation to the dynamo theory of the solar magnetic field (Babcock, 1961). The IMF, being an extension of the coronal field, results from this large-scale solar field. IMF has been measured directly since the beginning of the satellite era. For the period 1967–1994, we have data for both bn and bs coefficients of the solar differential rotation derived by Mt. Wilson Doppler shift measurements, and IMF parameters compiled in OMNI database of the National Space Science Data Center.
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The dominant periodicity in the average IMF magnitude B in this period is 9.3 years coinciding with the dominant periodicity in bs ; while the dominant periodicity in bn is 14 years (Fig. 6c). In this period, predominantly more active is the southern solar hemisphere, i.e., the dominant periodicity in the IMF matches the dominant periodicity in the differential rotation of the more active solar hemisphere. The solar rotation data considered for this study date back to 1881. For this period there are no direct measurements of the IMF, so as a proxy for its magnitude we use the aa index of geomagnetic activity. We use this index rather than the sunspot numbers as geomagnetic activity is related to the interplanetary magnetic field which is the extension of the coronal open magnetic field while sunspots are regions of closed magnetic field, and their long-term evolution has been shown to be quite different (Wang et al., 2000). The southern solar hemisphere was more active during the period 1881–1912. The dominant periodicity in bs is 16 years, and the same is the dominant periodicity in aa ; while bn varies with a period of 10.8 years (Fig. 6a). During the second period, from 1913 to 1966, the northern hemisphere was more active. The dominant periodicity in aa is 10.8 years. A strong peak at this periodicity is seen in bn ; and no peak in bs (Fig. 6b). Two conclusions can be made from the data summarized in Figs. 5 and 6. First, the rotation parameters vary and are different in the northern and southern solar hemispheres for the whole period covered by solar rotation data, from 1881 to 2000, or 12 sunspot cycles which confirms the weak magnetic coupling between the two solar hemispheres. Second, the solar rotation exhibits long-term changes, matching the longterm changes in the IMF. The IMF, the extension of the solar coronal magnetic field, is influenced by the differential rotation in the solar hemisphere with dominant activity.
5. Geomagnetic response to magnetic clouds with different helicity
Fig. 5. FFT spectra of rotation rate latitudinal gradients bn and bs ; in the northern (upper panel) and southern (lower panel) solar hemispheres, respectively.
One of the most powerful manifestations of the solar wind–magnetosphere coupling is the reaction of the magnetosphere to magnetic clouds (Burlaga et al., 1987). The smooth rotation of the magnetic field inside the cloud and its handedness representing the helicity of the cloud’s source region at the Sun relates the magnetic clouds to the solar differential rotation. The geoeffectiveness of magnetic clouds is considered to be determined by the strong long-lasting southward fields (Wu and Lepping, 2002) under which reconnection of the interplanetary and geomagnetic field lines partially opens Earth’s magnetic field to the solar wind (Dungey,
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In the upper panel of Fig. 7, the reaction of K p index of geomagnetic activity is compared for the cases of encounter of right-handed (solid line) and left-handed (broken line) magnetic clouds. K p index reaches higher values in the cases of left-handed clouds, and this difference is significant at 2.5 sigma. The difference in geomagnetic response is in the same direction in the northern and southern hemispheres. Fig. 8 presents the changes in aa-N and aa-S indices—the aa indices of geomagnetic activity calculated only from stations in the northern and southern hemisphere, respectively. In both hemispheres, stronger geomagnetic disturbances are registered for left-handed magnetic clouds. Cid et al. (2003) have approached the problem from the opposite side. They have selected all major geomagnetic storms ðDst o 70Þ in the period 1995–2000, and have searched WIND data for possible magnetic clouds related to each storm event. They have found a close relationship between the helicity of geoeffective magnetic clouds and the longitude angle
Fig. 6. (a) Periodicities in the aa-index of geomagnetic activity aa (solid line), and the rotation rate latitudinal gradients in the northern solar hemisphere bn (broken line) and in the southern solar hemisphere bs (dotted line) in the period 1881–1912; (b) Periodicities in the aaindex of geomagnetic activity aa (solid line), and the rotation rate latitudinal gradients in the northern solar hemisphere bn (broken line) and in the southern solar hemisphere bs (dotted line) in the period 1913–1966; (c) Periodicities in IMF magnitude B (solid line), and the rotation rate latitudinal gradients in the northern solar hemisphere bn (broken line) and in the southern solar hemisphere bs (dotted line) in the period 1967–2000.
1961). This study aims to determine whether the geoeffectiveness of the cloud is also determined by its helicity.
Fig. 7. Upper panel—superposed method analysis of the variations of K p index of geomagnetic activity for the cases of arrival of righthanded (solid line) and left-handed (broken line) magnetic clouds. Lower panel—the same with the cases without Bz o0 excluded. Day 0 corresponds to the day of encounter of the magnetic cloud.
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Fig. 8. Superposed method analysis of the variations of the aa indices of geomagnetic activity calculated only from stations in the northern (aa-N—upper panel) and southern hemisphere (aa-S—lower panel). Day 0 corresponds to the day of encounter of the magnetic cloud.
of the axis of the cloud, determining the presence of a southward magnetic field component. However, we find that the presence of a southward magnetic field component is not the only factor for the geoeffectiveness of a magnetic cloud. In the lower panel of Fig. 7, only the magnetic clouds with Bz o0 are included, while the upper panel includes all clouds. It can be seen that the difference between left- and right-handed clouds does not vanish. Moreover, there is no difference between right- and left-handed clouds in the prevailing direction of the IMF vertical component (Fig. 9a), as there is no difference in the magnetic field magnitude (Fig. 9b) or the solar wind pressure (Fig. 9c). Clearly, the problem of the dependence of the geoeffectiveness of magnetic clouds on their helicity requires further study. The importance of this question arises from the fact that solar activity originating from the northern and southern hemispheres has been found to have different effect on the Earth, and magnetic helicity is the only feature known so far which is persistently different in the two solar hemispheres.
Fig. 9. Superposed method analysis of the variations of the IMF Bz component (a), total magnitude B (b) and solar wind pressure (c) for right-handed (solid line) and left-handed (broken line) magnetic clouds. Day 0 corresponds to the day of encounter of the magnetic cloud.
6. Summary (1) We have studied the deviations of the measured IMF azimuthal component and IMF winding angle from Parker’s formula taking into account the irregular solar rotation rate, and have found that these deviations
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follow the 22-year solar magnetic cycle rather than the 11-year sunspot cycle as previously suggested. The deviations are the same as predicted by Fisk’s model of the heliospheric magnetic field, and the presented results are a confirmation of the validity of the model. (2) For the last four solar cycles, it has been known that the rotation parameters of the two solar hemispheres differ. We have shown this to be true for the last 12 sunspot cycles, which proves the weak magnetic coupling between the hemispheres. We have compared the periodicities in solar rotation parameters in the two hemispheres to the periodicities in IMF magnitude at the Earth’s orbit and have shown that the IMF which is an extension of the large-scale coronal field, has the same periodicities as the differential rotation in the more active solar hemisphere. (3) We have compared the geomagnetic response to magnetic clouds with left- and right-handed helicity, originating predominantly from the northern and southern solar hemispheres, respectively, and have shown it to be different depending on the magnetic cloud helicity, which confirms the different effect of the solar hemispheres on the Earth.
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