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Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1923­1929

www.elsevier.com/locate/jastp

Global magnetic Úeld of the Sun and long-term variations of galactic cosmic rays
A.V. Belov, B.D. Shelting, R.T. Gushchina, V.N. Obridko , A.F. Kharshiladze, V.G. Yanke
IZMIRAN, Moscow Region, 142190 Troitsk, Russia Received 20 October 2000; received in revised form 20 June 2001; accepted 4 September 2001

Abstract The paper deals with the relation of long-term variations of 10 GV galactic cosmic rays (GCR) to the global solar magnetic Úeld and solar wind parameters. This study continues previous works, where the tilt of the heliospheric current sheet (HCS) and other solar-heliospheric parameters are successfully used to describe long-term variations of cosmic rays in the past two solar cycles. The novelty of the present work is the use of the HCS tilt and other parameters reconstructed from H observations of Úlaments for the period when direct global solar magnetic Úeld observations were unavailable. Thus, we could extend the GCR simulation interval back to 1953. The analysis of data for 1953­1999 revealed a good correlation (the correlation coe cient ¿ 0:88) between the solar-heliospheric parameters and GCR in di erent cycles of solar activity. Moreover, the approach applied makes it possible to describe the behavior of cosmic rays in the epochs of solar maxima, which could not be done before. This indicates both the adequacy of the model and the reliability of the reconstructed global solar magnetic Úeld parameters. c 2001 Elsevier Science Ltd. All rights reserved. Keywords: Solar activity; Solar cycle; Long-term variation of cosmic rays

1. Introduction Long-term variations of galactic cosmic rays were compared with the behavior of various solar-activity indices and heliospheric parameters many times by di erent authors. In doing so, special importance was attached to the solar magnetic Úeld calculated on the solar wind source surface (Hoeksema and Scherrer, 1986). The coronal magnetic Úeld is calculated from photospheric Úeld observations under potential approximation, i.e., in terms of a source surface (SSMF) model. Under this assumption and within the Parker model, the Úeld is radial at some height above the photosphere. This sphere is called the source surface and, for better
Corresponding author. Tel.: +7-095-334-0282; fax: +7-095334-0124. E-mail address: solter@izmiran.troitsk.ru (V.N. Obridko).

agreement with real measurements near the Earth, is placed at a distance of 2.5 solar radii (see, for example, Hoeksema and Scherrer, 1986). The complex Úeld structure in the photosphere simpliÚes with increasing height in the corona until a single line is left separating the two polarities at about 2.5 solar radii. SSMF determines the structure and properties of the solar magnetosphere; therefore, it is likely to bear a closer relationship to cosmic ray modulation than other solar parameters, such as the sunspot numbers or coronal emission intensity. It is no surprise that the amplitudes of the global solar magnetic Úeld spherical harmonics were successfully used by Mikhajlutsa (1990) and Nagashima et al. (1991) to simulate long-term modulation of cosmic rays. The basic equation of galactic cosmic rays (GCR) modulation describes (Parker, 1963) the di usion, convection and drift processes. Although drift e ects were formally included in

1364-6826/01/$ - see front matter c 2001 Elsevier Science Ltd. All rights reserved. PII: S1364-6826(01)00073-6


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A.V. Belov et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1923­1929

Fig. 1. HCS tilt (monthly mean data) as inferred from magnetic measurements (thick curve) and H optical observations (thin curve) -- top panel. Variations of 10 GV cosmic rays (thin curve) and their model representation (thick curves) based HCS tilt variations.

this transport equation, only in the past two decades the importance of GCR drift due to the gradients and curvatures of the interplanetary magnetic Úeld (IMF) as well as along the wavy HCS was proved. The current sheet separating the heliomagnetosphere into the northern and southern parts must favor the transport of CR in the radial and, at a signiÚcant tilt, in the latitudinal directions. It should be noted that the HCS tilt also determines the size of the low-latitude region of reduced mean solar wind speed and intensiÚed interaction of the wind streams of di erent velocity. This region seems to have a strong modifying e ect on cosmic rays. Finally, it is important that CME events originate mainly in the vicinity of the current sheet. A close relation of the HCS to the behavior of GCR was substantiated theoretically (Jokipii and Thomas, 1981; Kota and Jokipii, 1983). It was proved experimentally in numerous investigations (Smith and Thomas, 1986; Saito and Swinson, 1986; Webber and Lockwood, 1988; Smith, 1990; Webber et al., 1990; Belov et al., 1995, 1997; Bazilevskaya and Svirzhevskaya, 1998; Belov et al., 1999a, b). At present, it is clear that the details of GCR modulation could not be explained unless we invoke the HCS tilt and other magnetic Úeld parameters on the source surface. However, the uniform series of SSMF parameters are only available since 1976, and all studies referred to above are conÚned to a few latest solar cycles alone. Recent work appears to have removed these time limitations (Wang, 1993; Obridko and Shelting, 1999). Direct measurements of the magnetic Úeld in the photosphere are only available since 1976 (WSO data). There are also earlier data obtained at Mt-Wilson and Kitt Peak observatories from 1965 up to 1984, which were reduced to the Stanford system by Obridko and Shelting (1999). The problem is that this set of data is not uniform. Direct magnetic Úeld measurements for earlier periods do not exist.

Obridko and Shelting (1999) used the data on the polarity of large-scale magnetic Úelds obtained by systematic H observations of solar Úlaments. A special calibration method was developed to calculate the Úeld at the source surface in the Stanford system of units (see Obridko and Shelting, 1999). The SSMF parameters can be determined in that way for a long time interval covering the entire series of CR observations. In an earlier work (Belov et al., 1997), the modulation of cosmic rays was studied using an alternative method of reconstructing HCS tilt from geomagnetic data (Vanyarkha, 1995). The disadvantage of this method is its being inapplicable under high solar activity. The aim of the present study is to simulate long-term modulations of cosmic rays over a longer time interval than using the source surface magnetic Úeld parameters and to check the reliability of the SSMF parameters inferred from indirect optical observations.

2. Cosmic ray data We have used as CR characteristic the amplitude of density variations of 10 GV particles (the lower curve in Fig. 1). The rigidity spectra of CR variations for every month were obtained by the method proposed by Belov and co-authors from the world-wide neutron monitor data, stratospheric sounding data, and IMP-8 observations of CR with energies ¿ 106 MeV (see Belov et al., 1993 and references therein). These results until 1998 inclusive were published earlier. Now, the results for the 1950s and 1990s have been essentially improved, and the results for 1999 have been obtained for the Úrst time. The latter should be considered preliminary, since the neutron monitor data are incomplete.


A.V. Belov et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1923­1929 Table 1 Regression coupling parameters Period 53.07­59.06 61.02­70.01 73.05 ­80.05 81.09 ­91.09 92.03­99.12 a (%) 2 2 4 4 4 : : : : : 7 2 3 6 0 ± ± ± ± ± 0 0 0 0 0 : : : : : 2 1 2 2 1

1925

and à for Eq. (1) b (%= ) - - - - - 0 0 0 0 0 : : : : : 24 16 15 33 20 ± ± ± ± ± 0: 0: 0: 0: 0: 01 01 02 01 01


u

(months) 0.93 0.92 0.88 0.95 0.93

(%) 2.26 1.32 1.51 2.23 1.04

26 23 4 5 25

3. CR modulation and HCS tilt In Fig. 1, the HCS tilt àm , obtained from magnetic observations (Hoeksema, 2000) is combined with the tilt àH calculated from optical data (Obridko and Shelting, 1999). One can readily see a good agreement between àm and àH during 1976 ­1989, where the series overlap (the correlation coe cient is 0.89). A close relationship between the HCS tilt and long-term behavior of cosmic rays in the periods of the same polarity of the global solar magnetic Úeld was revealed in earlier work (e.g., Belov et al., 1995, 1999a, b; Belov, 2000). To Únd out whether such a relationship exists at longer time scales, we have taken a combined data series à, which comprises àH up to April 1976 and àm since May 1976. Using linear regression analysis, we isolated the intervals approximately coinciding with the periods of equal heliomagnetospheric polarity, when CR variations were described reasonably well by the expression (t )= a +
u

b +1

u

à(t - );
=0

(1)

into account that a simpliÚed model (1), based on a single solar-heliospheric parameter, was used. Thus, the HCS tilt derived from indirect optical data correlates with CR variations well enough and can, obviously, be used instead of the traditional tilt values obtained from magnetic measurements. To what degree is such substitution justiÚed? The results for the last two periods look more convincing than the others, and it is, most probably, no mere chance. Separately, we analyzed in the same way the period of 1981.04 ­ 1989.12, when the HCS tilt data obtained by di erent methods overlapped. The correlation with CR variations proved to be deÚnitely higher for àm than for àH , though the latter also provided quite a satisfactory result ( =0:93 at =2:37 and =0:89 at =2:93, respectively). The results obtained above imply that optical observations can be an adequate and well-justiÚed substitute for HCS tilt data and can be successfully used in analyzing CR modulation in the periods when direct magnetic observations are unavailable. Our analysis corroborates a good correlation between the long-term behavior of cosmic rays and the HCS tilt both under negative (1960s and 1980s) and positive polarity of the global solar magnetic Úeld (Belov et al., 1995).

being the delay between solar indices and cosmic rays. Here, we take into account that CR modulation is controlled by the solar events both in the current month ( = 0) and in the nearest past beginning with moment t - u . Three parameters (a, b, and the maximum delay u ) were determined for each period by the least square method. The obtained values are tabulated together with the correlation coe cient and the standard r.m.s. deviation in Table 1. Cosmic ray variations in the time intervals under consideration derived from Eq. (1) are represented in Fig. 1. The values of àm alone were used for the last two periods, and the values of àH , for the Úrst two ones. In the third period (1971­1981), various data were combined. The relationship between CR variations and the HCS tilt was often analyzed in the 1980s. Recently, this analysis has been extended to cover 5 half-periods of the solar magnetic cycle (i.e., the total of 47 years). One can see that the current sheet and cosmic rays usually behave in a similar way, except for relatively short periods during and immediately after the Úeld reversal. In all selected periods, the correlation coe cient proved to range from 0.88 to 0.95, and the r.m.s. deviation was ¡ 2:3%. Such correlation can be considered quite satisfactory, taking

4. Multi-parameter model and CR modulation under high solar activity Our description of actual cosmic ray variations is rather approximate, and it could not be otherwise. CR modulation is a complex phenomenon, which occurs all over the heliosphere and depends on many factors. No single solar index, however, sophisticated, can account for CR variations. Belov et al. (1999b) proposed a multi-parametric description of long-term CR variations, based on a joint use of the HCS tilt and intensity variations of the IMF. The effect of IMF intensity variations on cosmic ray modulation is even easier to substantiate theoretically than the e ect of the HCS tilt. The main determining parameter of particle transport--gyroradius--is inversely proportional to IMF module (H ). According to theoretical reasons (e.g. Parker, 1963) an increase of H should lead to a decrease of transport path and the di usion coe cient and, consequently, to an increase of the CR modulation. The relationship between the IMF modulus and long-period variations of CR was corroborated experimentally (Cane et al., 1998; Belov et al.,


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A.V. Belov et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1923­1929

Fig. 2. Observed variations of 10 GV cosmic rays during 1981.10 ­1990.08 (thick curve) and their model representation (thin curve) based on description (2).

1998) when long data series of solar wind measurements were built up. Indeed, these parameters--the HCS tilt and the IMF intensity--successfully supplement each other. The point is that the HCS tilt manifests the structure of the heliosphere, while the IMF intensity characterizes quantitatively its e ect on cosmic rays. However, at least one doubt is always present when IMF data are used. It is whether the IMF parameters measured in the Earth's environment are able to fully characterize the magnetic Úelds all over the heliosphere, which are responsible for CR modulation. This urges us to search for a di erent parameter, which would supplement the HCS tilt well enough, but unlike the IMF intensity, would be more global. Such solar index might be the magnetic Úeld of the Sun as a star or, more logically, it should be sought at the source surface, where the HCS is determined. We tried to combine various SSMF parameters with the HCS tilt, and, at last, we decided in favor of intensity of the magnetic Úeld radial component Br averaged over the entire 2 source surface: Bss = Br . Since the SSMF is primarily determined by the dipole component of the solar magnetic Úeld, this parameter must behave virtually in the same way as the dipole moment in the SSMF expansion. It is appropriate to recall here the work by Bazilevskaya et al. (1990) and Nagashima et al. (1991), where the solar dipole was invoked to account for the CR variation anomalies in 1982. On the other hand, the behavior of BSS must resemble the magnetic ux variations, whose importance is the main inference from Cane et al. (1999a, b). Now, let us modify Eq. (1) as follows: (t )= a + bà à +1
uà

u

à(t - )+
=0

u

bB B +1

uB

Bss (t - ):
=0

(2)

The following parameters were obtained by the least square method for the period of 1981.10 ­1990.08, approximately coinciding with negative polarity of the global solar magnetic Úeld: a =7:9 ± 1:5, bà = - 0:35 ± 0:01%= , bB = - 1:3 ± 0:2%= nT, uà = 4 months uB = 11 months. These parameters ensure a very good agreement (correlation coe cient equal to 0.97) between the observed and calculated CR variations (Fig. 2). Such agreement cannot be any longer regarded as "rough". One can see that the model adequately represents CR variations not only in general, but also in many details. The agreement is amazing for such a simpliÚed model. It describes the behavior of cosmic rays in the complex period under consideration better than other models based on a greater number of parameters (Belov et al., 1999; Nagashima et al., 1991). It is to be noted that BSS variation is ill-correlated with cosmic rays in itself, but changes its capabilities drastically when combined with the HCS tilt. This index is not merely involved in determining CR variations together with à, but plays a leading role, at least in the 1980s. Model (2) was successfully applied to other periods, too. This prompts us to try and describe the entire period of 1977.01­1999.10, for which a uniform series of SSMF parameters is available. We leave out 1976 because of the lag, which must be taken into account. Since two Úeld reversals occurred during the period under examination, the model must include index p, which characterizes polarity variations of the global solar magnetic Úeld. Polarity of the global magnetic Úeld is determined as function p( ), which can only adopt three values: ±1 in the periods of positive and negative polarity and 0 in the Úeld reversal periods. Following Belov et al. (1999b), we take into account both the direct e ect of polarity on CR variations and its e ect on CR modulation as the HCS tilt changes. The corresponding


A.V. Belov et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1923­1929

1927

Fig. 3. Monthly CR variations observed and simulated by the multi-parametric model (3) for 1977­1999 years (lower part). A contribution of mean source surface magnetic Úeld intensity BSS , HCS tilt and heliomagnetic polarity changes p to simulated variations (upper part).

supplemented model has the form (t )= a + +
u

bà à +1

uà

(1 + bàp p(t - ))à(t - )
=0
uB

bB uB +1

Bss (t - )+
=0

bp up +1

up

p(t - ):
=0

(3)

This description di ers from the model proposed by Belov et al. (1999b) by the absence of the solar wind velocity parameter and by using BSS instead of the IMF intensity. Fig. 3 illustrates a good agreement (correlation coe cient 0.945) of the observed and calculated variations both in general and in many details. The calculations were performed for the following values of the parameters involved: a =7:7 ± 0:7, bà = - 0:242 ± 0:007%= , bàp = - 0:52, bB = - 1:25 ± 0:10%= nT, bp = - 3:5 ± 0:2%, uà = 9 months, and uB = up = 4 months. A comparison with the earlier results (Belov et al., 1999a) shows that substitution of the IMF intensity by BSS is quite justiÚed, and it even improves the model as far as the periods of high solar activity are concerned. From general reasons, it is obvious that IMF must be related to the source surface Úeld. In reality, however, the coupling between BSS and the IMF modulus measured near the Earth (Fig. 4) is not as close (correlation coe cient for the period of 1976.05 ­1999.10 is 0.52). Therefore, the revealed interchangeability of BIMF and BSS in the modulation models is not a trivial fact. One can readily see that two SSMF characteristics-- the structural (HCS tilt) and quantitative (mean Úeld BSS ) ones--well supplement each other in describing CR variations. The changing HCS tilt controls long-term variations (11-year cycles and their basic features), while BSS is responsible for shorter period variations. Correspondingly, the HCS tilt plays a leading role in the periods of low and

moderate solar activity, yielding to BSS in the vicinity of the cycle maxima. The e ect of polarity is, on the contrary, very important. In the periods of negative polarity (qA ¡ 0), the CR density increases by 3% and at (qA ¿ 0), decreases by the same value. This e ect corresponds by its sign to the drift model and by its value, to the di erence of potentials between the low-latitude and polar parts of the heliomagnetosphere (e.g., Jokipii and Levy, 1979). An alternative mechanism of in uence of the GMF polarity on CR modulation was suggested by Burger et al. (1997). Theoretical estimates given in that work qualitatively agree with our results. At present, it is commonly believed (McDonald, 1998) that CR modulation under high solar activity is mainly determined by expanding magnetic shells in the solar wind (the global merged interaction regions--GMIRs (Burlaga et al., 1993). We do not think that the close correlation between the source surface magnetic Úeld and cosmic ray modulation, revealed above, contradicts the traditional concept. The coupling of solar and interplanetary Úelds, including major solar wind disturbances, is still poorly investigated; the clue to its understanding is, obviously, to be sought for at the source surface. We have made an attempt to apply the same approach to an earlier period, using (BSS )H --the magnetic Úeld inferred from indirect optical data and averaged over the source surface. However, no explicit relationship between this parameter and CR modulation was revealed. The fact is that (BSS )m and (BSS )H (Fig. 4) di er substantially in the physical sense. The local components and sector structure of the solar magnetic Úeld contribute signiÚcantly to (BSS )m , whereas (BSS )H describes mainly the global Úeld and its zonal components (Obridko and Shelting, 1999). Fig. 4 shows that the long-term behavior of (BSS )m and (BSS )H , coinciding in some features (e.g., in 1982), di ers


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A.V. Belov et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1923­1929

Fig. 4. Long-period variations of the mean source surface magnetic Úeld as inferred from magnetic measurements of (BSS )m (thick curve) and optical H observations of (BSS )H (thin curve). Variations of the monthly mean IMF intensity near the Earth (OMNI Data) are given at the top.

essentially. The obtained negative result is likely to suggest an important conclusion: The formation of the heliomagnetosphere is controlled not only by global magnetic Úeld but by local solar magnetic Úelds, too. It means that local Úelds also play an important part in long-term modulation of cosmic rays.

References
Bazilevskaya, G.A., Svirzhevskaya, A.K., 1998. On the stratospheric measurements of the cosmic rays. Space Science Review 85, 431­521. Bazilevskaya, G.A., Svirzhevsky, N.S., Stozhkov, Yu.I., Gorchakov, E.V., Okhlopkov, V.P., Okhlopkova, L.S., 1990. Modulation features of galactic cosmic rays in 1982. Proceedings of the 21st ICRC, Vol. 6, pp. 29 ­32. Belov, A.V., 2000. Large-scale modulation: view from Earth. Space Science Reviews 93, 79­107. Belov, A.V., Gushchina, R.T., Sirotina, I.V., 1993. The spectrum of cosmic rays variations during 19 ­22 solar cycles. Proceedings of the 23rd ICRC, Calgary, Vol. 3. pp. 605 ­608. Belov, A.V., Gushchina, R.T., Sirotina, I.V., 1995. Long term cosmic ray variations and their relation with solar activity parameters. Proceedings of the 24th ICRC, Vol. 4. pp. 542­545. Belov, A.V., Gushchina, R.T., Yanke, V.G., 1997. Long-term cosmic ray variations: spectrum and relation with solar activity. Proceedings of the 25th ICRC, Vol. 2. pp. 61­64. Belov, A.V., Gushchina, R.T., Yanke, V.G., et al., 1999a. Relation of long-term variations of cosmic rays to the magnetic Úeld in the Sun and solar wind. Izvestiya RAN, Series Physics 63 (8) 1606. Belov, A.V., Gushchina, R.T., Yanke, V.G., 1999b. On connection of cosmic ray long term variations with solar-heliospheric parameters. Proceedings of the 26th ICRC, Vol. 7. pp. 175 ­178. Burger, R.A., et al., 1997. The e ect of magnetic helicity on the propagation of galactic cosmic rays. Advanced Space Research 19, 897­900. Burlaga, L.F., McDonald, F.B., Ness, R., 1993. Cosmic ray modulation and the distant heliomagnetic Úeld: Voyager 1 and 2 observations from 1986 to 1989. Journal of Geophysical Research 98, 1­11. Cane, H.V., Wibberenz, G., Richardson, I.G., von Rosenvinge, T.T., 1999a. Cosmic ray modulation and the solar magnetic Úeld. Geophysical Research Letters 26, 565. Cane, H.V., Wibberenz, G., Richardson, I.G., 1999b. Modulation of galactic cosmic rays and changes in the solar magnetic Úeld. Proceedings of the 26th ICRC, Vol. 7. p. 111.

5. Basic conclusions (1) The HCS tilt derived from optical data can be used, with some reservations, to study the modulation of cosmic rays. (2) A good agreement between long-term cosmic ray variations and the tilt of the heliospheric current sheet exists in all periods of the same heliomagnetospheric polarity, since 1953 (i.e. during the whole history of ground-based CR observations with neutron monitors). (3) The HCS tilt and BSS mean intensity successfully supplement each other, providing the structural and quantitative characteristic of the source surface magnetic Úeld. Therefore, the combined use of these parameters in describing CR modulation allows us to improve semi-empirical models of CR long-term variations, particularly, in the periods of high solar activity. (4) The local components and sector structure of the solar magnetic Úeld take part in the formation of the heliomagnetosphere and play an important role in CR modulation.

Acknowledgements The work was sponsored by the Federal Research Program on Astronomy and the Russian Foundation for Basic Research (grants 99-02-18003, 99-02-18346 and 01-02-17580).


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