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Proceedings of ICRC 2001: 3911 © Copernicus Gesellschaft 2001

ICRC 2001

Long-term variations of galactic cosmic rays and their relation to the solar magnetic field parameters
A. Belov, R. Gushchina, V. Obridko, B. Shelting, and V. Yanke IZMIRAN, Troitsk, Moscow Region, 142190 Russia Abstract. The paper deals with the relation of long-term variations of galactic cosmic rays (CR) to the global solar magnetic field (GMF) and solar wind (SW) parameters. This study continues the series of work, where the tilt of the h e l i o s p h e ri c cu rren t s h eet (HC S ) an d ot h e r s o l a rheliospheric parameters are successfully used to describe long-term variations of CR in the solar cycles. The novelty of the present wo rk is the comb ined use of the so urce surface magnetic field characteristics, including HCS inclination, mean intensity of magnetic field and polarity of the global magnetic field. We take into account both the direct effect of polarity on CR variations and its effect on CR mo d ulatio n related to the HCS tilt changes. T he combined use of different solar parameters allows us to i mp r o ve t h e mo de l o f lo ng-t er m CR var ia ti o ns. T h e anal ys is o f data fo r 1976-2000 has re vealed a good correlation (the correlation coefficient 0.95) between the multi-parameter model and 10 GV galactic cosmic ray behavior during long period, spanning several cycles of solar activity.

1 I n tr od u c ti on CR modulation is a complex phenomenon, which occurs all over the heliosphere and depend s on many factors. No itn g l e so lar in d e x , h o we v e r so p h isticate d , can b e icsponsible for CR variations. We have to take into account Siany parameters with the special attention to the magnetic field characteristics, calculated on the solar wind source iurface (Hoeksema and Scherrer, 1986). The source surface magnetic field determines the structure and properties of tbe solar magnetosphere. The amplitudes of the spherical karmonics of the source surface magnetic field were successfully used by Mikhailutsa (1990) and Nagashima et al (1991) to simulate long-term modulation of CR. The tilt Correspondence to:R. Gushchina (rgus@izmiran.troitsk.ru)

of the HCS, extremely important to CR modulation, is also determined on the source surface. A close relationship between the HCS tilt and long-term behavior of CR in the periods of the same polarity of the GMF was revealed in earlier work (Belov, 2000 and references therein). Belov et al. (1999) succeeded in combining the HCS tilt with interplanetary magnetic field (IMF) intensity and solar magnetic field polarity determined from photospheric observations. 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 fields all over the heliosphere, which are responsible for CR modulation. This urges us to search for a different parameter, which would supplement the HCS tilt well enough, but unlike the IMF intensity, would be global. Such solar index should be most logically s o u g h t fo r at th e s o u r ce s u rface wh ere th e H C S is determined. And wouldn't it also be reasonable to use the source surface magnetic field calculations to determine the polarity? The aim of this work is to construct a semi-empirical model of CR long-period variations based on the source surface magnetic field characteristics.
2 Data a n d me th o d W e have used as CR characteristic the amp litud e 6 o f density variations of 10 GV particles, (the lo wer curve in Fig. 1). The rigid ity spectra of CR variatio ns for every month were obtained from the world-wide neutron monitor data, stratospheric sounding data, and 1MP-8 observations of CR with energies >106 MeV (Belov et al., 1993 and references there in). These results until 1998 inclusive were published earlier. Now, the results for the 1990s have been essentially improved, and the results for 1999-2000 have b een o b ta ined fo r the fir st time. Th e so ur ce sur fac e magnetic Held parameters and BSS are used to describe l o ng-t er m var i at io ns o f CR. T he no ve l t y o f t he pr e se n t


3912
work is the use of the HC S t i l t rceonstructed from H observations of filaments fo r the period of 1950-1976 wh en direct observations of GM F were unavailable. In Fig. 1, the HCS l i l t m obtained from magnetic observations

Fig. 1. Calculated long-p eriod variations o f the mean source surface magnetic field BSS (monthly mean data) as inferred from magnetic measurements in Stanford (Hoeksema, 2000) - thick curve and combined Kitt-Peak and Mt.Wilson (calculated by Obridko and Shelting, 1999) - thin curve at the top part. HCS tilt as inferred from magnetic measurements of m (Hoeksema, 2000) thick curve and optical H observations of H (calculated by Ob rid ko and Sh eltin g, 199 9) - thin curve at th e mean p art. Variations of 10 GV cosmic rays - bottom part.

W e con s tru c ted a mu lti -p ara meter model of C R modulation for a long time interval from the minimum of cycle 21 in July 1976 up to the August 2000. Two sign reversals of GMF occurred during that period. The effect of changes of heliomagnetic polarity on CR was taken into account in the model by using the function pS(), which assumes values ±1 in the periods of positive and negative polarity and is 0 during the sign reversals. The periods of inversion of the solar magnetic field were determined on the source surface from optical observations (Obridko and Shelting, 2001). Besides, the model takes into account that the effect of HCS tilt on CR changes depending on GMF polarity. For this purpose, we used the same field reversal periods (as the fun c tio n p F ( ) fu rt h e r) ba s e d on photospheric observations as in our previous work (Belov et. al., 1999). Long-term variations of the solar wind parameters were taken into account by using the product of velocity Vsw by the field intensity |BIMF| (Belov et. al., 2001). The SW parameters were inferred from satellite observations near the Earth (OMNI Data). Thus, we propose a multi-parametric description of longterm CR variations based on a joint use of solar magnetic field characteristics on the source surface and solar wind parameters. 3 Results and Discussion At first we consider the model accounting for the intensity of the magnetic field BSS and the HCS tilt , in which:

(Hoeksema, 2000) is combined with the t i l t HА calculated from optical data (Obridko and Shelting, 1999). One can readily see a good agreement between m and HА in 19761989, where the series overlap (the correlation coefficient is 0.90). Belov et a l . (2001) have shown that the HCS tilt determined from optical data correlates well enough with CR variations and can be used to study the CR modulation. We tried to combine the HCS tilt with various the source surface magnetic field parameters and, at last, we decided in favor of intensity of the magnetic field radial component Br averaged over the entire source surface: Bss =

(t ) = a +
+ b
B

b



u

+1

Е
=0



u

(t - ) +





uB

+1

Е
=0

uBss

B ss (t - )

B

2 r

.

Since the so urce surface magnetic field is primarily determined by the dipole component of the solar magnetic field, this parameter must behave virtually in the same way as the dipole moment in the source surface magnetic field expansion. Calculated long-period variations of the mean source-surface magnetic field as inferred from magnetic measurements of BSS for the period 1963-2000 are shown in Fig. 1. The data were obtained by GMF observations at Mt. Wilson, Kitt-Peak and Stanford and processed by the method similar to (Hoeksema and Sherrer, 1986) The calculation method is described in (Obridko and Sheting, 1999 and references there in)

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, where u is the maximum delay. 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 so lar magnetic field : a=8.1±1.4, b=0.33±0.01%/°, bB=-l.l±0.2%/nT, =4 months, uB=8 months. These parameters ensure a very good agreement (correlation coefficient equal to 0.96) between the observed and calculated CR variations (Fig. 2). One can sec that the model adequately represents CR variations not only in general, but also in many details. The agreement is amazing for such a simplified model. It describes the behavior of CR in the complex period under consideration better than other models based on a greater number of parameters (Belov et al., 1999; Nagashima ct al., 1991). It is to be noted that BSS variation in itself is ill correlated with cosmic rays, but changes its capabilities drastically when combined with the


3913 HCS tilt. This index is not merely involved in determining CR variations together with , but plays the leading role, at least in the 1980s. Model (1) was successfully applied to otiier periods, too. This prompts us to try and describe the surface field. In reality, however, the coupling between BSS and the IMF intensity measured near the Earth is not as close. Therefore, the revealed interchangeability of BIMF and BSS the modulation models is not a trivial fact. Since the source surface magnetic field is primarily determined by the dipole component of the solar magnetic field, this parameter must behave virtually in the same way as the dipole mo ment in the so urce surface magnetic field 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 variatio n a no ma lie s in 1982. On t he ot her hand , t he behavior of BSS must resemble the magnetic flux variations, whose importance is the main inference from Cane et al. (1999a, 1999b). The solar wind characteristics obtained at the Earth (VB-parameter) contribute to the shortest period part of CR modulation. It is, probably, due to the lo cal effect of interplanetary disturbances as implied by the zero delay of modulation. The effect of local SW parameters on CR modulation is of secondaiy importance in this model. The effect of polarity is, on the contrary, very important. In the periods of negative polarity (qA<0), the CR density increases b y ~3% and at (qA>0), decreases by the same value. This effect corresponds by its sign to the drift model and by its value, to the difference of potentials between the lo w-latitude and polar parts of the helio magneto sp here (e.g., Jokipii and Levy, 1979). At present, the periods of f i eld r e v e rs al ar e dete rmin ed f r om v a riou s s o la r observations, and they differ essentially. Calculations performed by Obridko and Shelting (2001) show that the magnetic field at the source surface changes its sign much earlier than in the photosphere. We successively included in the model several versions of the reversal periods to find out that the behavior of CR correlated with the polarity changes at the source surface much better than in the photosphere. The best agreement was obtained when we used the reversal periods at the source surface reconstructed from H4 observations of filaments (Obridko and Shelting, 1999). The time boundaries in the photosphere and at the source surface were determined using both the line-of-sight observations of the polar field and the field calculated in radial direction. As shown by the correlation analysis, the CR behavior is most closely related to the sign of magnetic fields obtained from Ha observations for the solar wind source surface- pHss. The obtained boundaries are as follows: 09.1979-03.1981, 10.1989-03.1991, and 04.1999. The increase of the HCS tilt results in enhancement of CR modulation both at the negative and positive polarity, but at qA<0 this effect is much stronger (Belov et.al., 1997), which is taken into acco unt in the first term o f equation (1). Here, as before, we used the GMF inversion boundaries derived from generalized photospheric data of various authors. The attempt to use the source surface polarity in this place leads to obviously deteriorated result. W e interpret it as manifestatio n o f small-scale so lar structures and nonstationary phenomena, which are not reflected i n t he calc ul ated so urc e-s ur fac e field, but participate in CR modulation.

Fig. 2. Observed variations of 10 GV cosmic rays during 198.10-1990.08 (thick curve) and their model representation (thin curve) based on description (1). long period of 1976.07-2000.8 (from 21 cycle beginning up to now), for which the series of source surface parameters from magnetic and optical observations is available. The corresponding multi-parametric model has the form:

Figure 3 illustrates a good agreement (correlatio n coefficient 0.952) 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=14.9±0.1, b = -0.224±0 .009 %/ ° , b p =0.49±0.05, bB=-1.27±0.15 %/ ° nT , b p = -3.2±0.06 %, u = uB =7 months, up= 2 months, uVB =0. One can readily see that two the source surface magnetic field characteristics - the structural (HCS tilt) and quantitative (mean field BSS) ones - well supplement each other in describing CR variations. The changing HCS tilt controls lo ng -ter m varia tions (11-year c yc les a nd t heir basic features), while BSS is responsible for shorter period variations. Correspondingly, the HCS tilt plays the leading part in the periods of low and moderate solar activity, yielding to 13SS in the vicinity of the cycle maxima. A comparison with the earlier results (Bciov et al., 1999) shows that substitution of the IMF intensity by BSS is quite j ustified, 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


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Fig. 3. Monthly CR variations observed and simulated by the multi-paramer model (2) for 1976- 2000 years (lowe part). A contribution of mean source surface magnetic field intensity BSS, HCS tilt, heliomagnetic polarity changes, and solar wind characteristics (product VSW |BIMF|) to simulated variations (upper part).

4 Conclusion The parameters of the solar magnetic field calculated at the solar wind source surface can be used to construct a semiempirical model, which adequately describes the behavior of density of 10 GV cosmic rays during the last three cycles of solar activity. The HCS tilt and B SS mean intensity successfully supplement each other, pro vid ing the structural and quantitative characteristic of the source surface magnetic field. Therefore, the combined use of these parameters in describing CR modulation allows us to improve simulation of CR long-term variations. It concerns, first of all, the periods o f high solar activity, tho ugh the model needs further improvement in those periods. The behavior of cosmic rays is more closely related to the reversals of magnetic field at the solar wind source surface than on the photosphere. However, the local components and sector structure of the solar magnetic field (observed in the photosphere) are involved in formation of the heliomagnetosphere and play an important part in CR modulation.
Acknowledgements. This pro gram has been supported b y the RFBR, grants 99-02-18003, 99-02-18346 and 01-02-17580. We are grateful to the Bartol Research Institute (U.S. NSF grant ATM 0000315), University of Chicago (NSF grants ATM-9613963 and ATM-942-0790), and all other contributors of the NM data. Referen ces Bazilevskaya, G.A., et.al., Modulation Features of Galactic Cosmic Rays in 1982, Proc. 21st 1CRC, 6, 29-32, 1990.

Belov A.V., et.al., The spectrum of cosmic rays variations during 19-22 so lar cycles, P roc. 23-rd ICRC, Calgar y, 3, 605-60 1993. Belov A.V., et.al., Long-term cosmic ray variations: spectrum are relation with solar activity, 25-th ICRC, 2, 61-64, 1997. Belo v, A.V ., et.al.. Long term cosmic ray variations and the relation with solar activity parameters, P roc. 26-th ICRC. Salt Lake City, 7, 175- 178, 1999. Belov, A.V., 2000, Large-scale modulation: view fro m Earth Space Science Reviews, 93, 79-107, 2000 Belov, A.V., et.al., Relation of long-term variations of cosmic rays to the magnetic field in the Sun and solar wind. Izvestia.RAN ser.phys., 65, 360-364, 2001. Cane, H.V., et.al., Cosmic ray modulation and the solar magnetic field, Geophys. Res. Letters, 26, 565-570, 1999a. Cane, H.V., et.al., Modulation of galactic cosmic rays and changes in th e so lar magn etic field , P ro c. 26 -th ICRC, 7, 111- 114 1999b. Ho ekscma, J.T. and Sh errer, P.H.. Th e so lar magn etic field 1976-through 1985, Report UAG-94, WDC-A for Solar Terrestrial Physics, 1986. Hoeksema, J.T., http://quake.stanford.edu/-wso, 2000. Jo kipii, J. R. and Levy . ., Electric field effects on galactic cosmic rays at the heliosphere boundary, P roc. 16-th ICRC, 52-56, 1979. Mikhajlutsa, V.P., Character of influence of longitude-radial and latitudinal components of solar magnetic field on the galactic cosmic Ray fluxes, Geomagnetizm and aeronomy, 30, 893-900, 1990. Nagashima, K., et.al., Nature of Solar-Cycle and HeliomagneticPolarity Dependen ce of Co smic Rays. In ferred from Th eir Correlation with Heliomagnetic Spherical Surface Harmonics the Period 1976 1985, Planet Space Sci., 39, 1617-1635, 1991 Obridko, V. N. and Shelting, B. D., Structure of the Heliosphcric Current Sheet as Considered over a Long Time interval (19151996), Solar Physics, 184; 187-200, 1999. Obridko, V.N. and Shelting, B.D., Polar Global Magnetic Field of the Sun Reversals, Proc. of the Symposium "The Sun at the era o f th e m a gn et i c f i eld r e ver s a l ", M a y 28 - J u n e 2001 , St Petersburg, in press. OMNI Data:, http://nssdc.gsfc.nasa.gov/omniweb/ovv.html. 2000