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Proceedings of the 30th International Cosmic Ray Conference Rogelio Caballero, Juan Carlos D'Olivo, Gustavo Medina-Tanco, Lukas Nellen, Federico A. SÀnchez, JosÈ F. ValdÈs-Galicia (eds.) Universidad Nacional AutÑnoma de MÈxico, Mexico City, Mexico, 2008 Vol. 1 (SH), pages 473­476

ID 225

30TH INTERNATIONAL COSMIC RAY CONFERENCE

Manifestation of the solar global field changes in the long-term cosmic rays modulation
R.T. GUSHCHINA1, A.V. BELOV1, V.N OBRIDKO1, B.D SHELTING1, YU. V. BALABIN
1 IZ M IR A N , 1 4 2 1 9 0 T ro itsk, M o sco w R eg io n , R u ssia
2 2

PGI, 184209 Apatity, Murmansk Region, Russia
Abstract: We discuss the improving of the semi-empirical model of cosmic ray (CR) modulation proposed by us previously. In order to describe the long-term variations with more complete reflection in the CR modulation of the complex interaction of global and local solar magnetic fields it has been proposed to introduce into the model the next characteristics: the solar magnetic field polarity, the integral index, the partial indexes as well the tilt of the current sheet and the flare index. The role of each index in the CR modulation is determined. For the multi-parameter description of long-term CR variations by using the integral index or one of four partial indexes the best fit for 1977-1999 periods is obtained for the integral index and the sector-odd index, characterizing an inclined dipole. It is proposed that decreasing of density CR in minima of the last solar activity (SA) cycles (from cycle to cycle) could be explained by decreasing of the zone-odd index. The discrepancy between the model and observations increases beginning from the beginning of 2000 therefore the problematic features of CR behavior and modeling during the 23rd cycle are discussed.

rgus@izmiran.ru

Introduction
The density of CR is modulated in the heliosphere by the solar wind thus providing a relatio n to th e s o la r m a g n e tic a c tiv ity . T h e d e n s ity of CR reflects the various solar cyclic variatio n s . T h e m o d e lin g o f th e C R m o d u la tio n b y e le c tro m a g n e tic f ie ld s in th e h e lio s p h e re is c a rrie d o u t to u n d e rs ta n d th e s e p ro c e s s e s . T h e present study of galactic CR modulation in the heliosphere through the 19-23 cycles is a cont i n u a t i o n o f o u r p r e v i o u s w o r k s [ 1- 4 ] a n d i s based on the long-term distribution of CR obta in e d b y th e n e u tro n m o n ito r n e tw o rk . W e d i s c u s s t h e i m p r o v i n g o f t h e s e m i- e m p i r i c a l model of CR modulation proposed by us previously. In order to describe the long-term variatio n s w ith m o re c om p le te re f le c tio n in th e C R m o d u la tio n o f th e c om p le x in te ra c tio n o f g lo b a l and local solar magnetic fields it has been prop o s e d to in tro d u c e into th e m o d e l th e s o la r m a g n e t i c f i e l d c h a r a c t er i s t i c s a s w e l l t h e f l a r e index. The role of each index in the CR modulatio n is d e te rm in e d w ith d e ta ile d ju s tif ic a tio n o f

s u c h a c h o ic e . T h e d is c re p a n c y b e tw e e n th e model and observations increases beginning from the beginning of 2000 therefore the problematic features of CR behavior and modeling during the 23rd cycle are discussed.

Long-term behavior of the CR and modulating parameters
In itia l d a ta f o r m o d e lin g o f C R v a ria tio n s a re lo n g - te rm o b s e rv a tio n s o f C R in te n s ity , th e c h a ra c te ris tic s o f th e s o la r g lo b a l m a g n e tic f ie ld and data of solar x-rays flares (importance M1). The rigidity spectrum of CR variations for each month was obtained from the data of neutro n m o n ito rs o f th e e n tire g lo b a l n e tw o rk o f C R stations, stratospheric sounding data for 1976­ 2 0 0 6 . H e re w e s tu d y a m p litu d e v a ria tio n s o f C R with 10 GV rigidity, excluding variations assoc ia te d w ith g ro u n d le v e l e n h a n c e m e n ts o f s o la r C R . N o te th a t a v a lu e o f th is e f f e c t is g re a te r th a n 3 % e v e n f o r m o n th ly a v e ra g e d a m p litu d e values for some events and particular CR stat i o n s u s e d i n o u r a n a l y s i s . T h u s , i n t h i s c a se

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a m p litu d e o f lo n g te rm C R v a ria tio n s w ith 1 0 G V rig id ity o b ta in e d b y u s in g th e m e th o d o f g lo b a l s u rv e y b e c o m e s a v a lu e o f p u re g a la c tic origin and free from influence of solar particles. C a l c u l a t i o n s o f C R m o du l a t i o n h a v e s h o w n t h a t such amplitude improves the proposed modulation model. The structural and quantitative chara c t e r is t i c s o f t h e s o l a r g l o b a l m a g n e t i c f i e l d a s : a h e l io s p h e r i c c u r r e n t s h e e t t i l t - , t h e s o l a r polar field - Hpol and the average magnetic field intensity Bss are calculated on the surface of solar wind source. Along with using of the average of solar magnetic field Bss index, the partial in d e x e s h a v e b e e n d e te rm in e d f ro m d a ta o f th e S ta n f o rd o b s e rv a to ry ( W S O ) f o r 5 .1 9 7 6 ­ 12.2006. (zone-even ZE, zone-odd ZO, sectoreven SE and sector-odd SO). Here we used data of measurements of the large - scale photosphere magnetic field with magnetometer resolution of (3) performed in the Wilcox solar o b s e rv a to ry ( W S O ) in 1 9 7 6 ­ 2 0 0 6 [ 5 ] a n d p ro c e s s e d b y th e o rig in a l m e th o d d e s c rib e d in [ 6 ,7 ]. T h e re is a p ro b le m o f th e m a g n e to m e te r s e n s itiv ity in re s u lts o f s o la r f ie ld o b s e rv a tio n s in 2000-2002 and, possibly, after recalibration th e d a ta s e t is n o t u n if o rm . In o rd e r to u n d e rs ta n d a m o d u la tin g in f lu e n c e o f lo c a l s o la r a c tiv ity o n C R it is p ro p o s e d to u s e F x , a s p e c ia lly c a lc u la te d in d e x o f s o la r f la re s . The flare index Fx empirically determined depends on maximum x-ray intensity (events of 1 h a v e b e e n s e le c te d ) d u rin g th e f la re a n d its lo n g itu d in a l lo c a tio n re la tiv e ly to th e E a rth , where Fx = 0, if IX < IC (IX ­ the maximum flux of x-ray event, IC = 10-5 W/m2), = E for <0; = W for >0. It is supposed W = E /2. The evaluation of Fx is performed for longitudes 0 = -18, -14, -10, -6, -2° and = 55, 60, 6 5 , 7 0 , 7 5 ° . G iv e n v a lu e s o f th e p a ra m e te r a re . F ig u re 1 s h o w s the behavior modulating characteristics in 19762 0 0 6 . A ll in d ic e s o f th e g lo b a l f ie ld in th e p h a s e o f S A m in im u m f lu c tu a te n e a rly to z e ro e x c e p t o f q u a s i- d i p o l e Z O , w h i c h h a s a m a x i m u m

value. The ZO cycles are ahead of 11-years of W o lf n u m b e rs ( W ) b y a h a lf o f c y c le .

F ig u re 1 : to 1 9 7 6 ), a v e ra g e v index Bss (µ T )

T e m p o ra l c h a n g e s o f C R f la re in d e x F x , s u n s p o t a lu e s o f s o la r m a g n e tic f ie a n d p a rtia l in d e x e s Z O ,

in te n s ity n u m b e rs ld s tre n g t ZE, SO ,

(% W, h­ SE

The index ZO accounts for part of the magnetic field with the odd zonal symmetry (analog of the vertical dipole). The index ZE is small as a result of the Hale law. The sectorial-odd index SO characterizes the tilted dipole and reflects an i n f l u e n c e o f t h e S A a t l o w a n d m i d d l e l a t i t u d e s. The sectorial-even index SE is usually manifested in the 4-sector structure. The features Fx variations during the decay phase of 23 solar cycles are considered in [4].

Discussion results of CR modulation
A c c o u n tin g c o rre c te d in te g ra l in d e x e s o f th e solar field, which allow describing the longte rm C R v a ria tio n s ; th e m o d e l h a s b e e n tu n e d for reliable presentation of short - term variations. The multi- parametric regression analysis h a s s h o w n th a t m o d e l d e s c rip tio n o f C R n e e d s a jo in t c o n s id e ra tio n o f f o llo w in g m o d u la tin g parameters: above-mentioned , Bss, (or one of the partial indexes) Hpol as well the flare index Fx. The description of flare influence on CR modulation with the Fx index provides the best result for effective range of longitudinal distrib u tio n =55°-75° for all parameters 0 and >65°. The introducing of Fx allows improvin g re p re s e n ta tio n o f o b s e rv e d C R v a ria tio n s . In

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30TH INTERNATIONAL COSMIC RAY CONFERENCE 2007 th e p e rio d 1 .1 9 7 7- 1 2 .1 9 9 9 th e m o d e l p ro v id e s the result for 4-parameter case with the correlation coefficient = 0.96. The performed modeling allows estimating a relative impact of temp o ra l c h a n g e s o f e a c h p a ra m e te r w ith its o w n tim e d e la y to th e to ta l m o d u la tio n . T h e d e la y tim e o f C R m o d u la tio n re la tiv e th e f la re a c tiv ity o b ta in e d in o u r m o d e l o f lo n g - te rm m o d u la tio n shows that the flare influence is rather prolo n g e d in th e h e lio s p h e re . It is s h o w n th a t f o r th e lo n g - te rm m o d u la tio n o f C R a lo n g itu d in a l dependence of the flare index is not so importa n t, b u t th e re is a s tro n g d e p e n d e n c e f ro m f la re intensity, this is characteristic for long- term CR variations. However description of short-term CR phenomena (like Forbush-decreases (FD), includes the longitudinal dependence. The amp litu d e a n d o th e r c h a ra c te ris tic s o f F D s tro n g ly depend on flare intensity and longitude of the solar source of interplanetary disturbance. T h e m u ltip a ra m e te r m o d e l o f C R m o d u la tio n , w h ic h a d d itio n a lly a c c o u n ts th e f la re in d e x F x im p ro v e s th e p ic tu re o f o b s e rv e d v a ria tio n s , b u t o n c e a g a in u p to th e y e a r o f 2 0 0 0 o n ly . A f te r th e year of 2000 a discrepancy between calculated a n d o b s e rv e d v a ria tio n s in c re a s e s . It is v e ry d if f ic u lt to d e s c rib e th e s e p a ra te p e rio d o f 1 2 .1 9 9 9 - 1 2 .2 0 0 6 w ith in th e p ro p o s e d m o d e l with a high accuracy. Such a picture of modulatio n is o b s e rv e d f o r a ll p a rtia l in d ic e s u n d e r their use in turns as the forth modulation para m e te r. F o r a ll lis te d p a ra m e te rs th e m o d e l d e s c rip tio n o f C R v a ria tio n s w a s p ro v id e d f o r th e w h o le p e rio d o f 1 9 7 6 - 2 0 0 6 . D u rin g th is period we have =0.93 and = 2.05% and = 0.96 during the period of 1.1977-12.1999. Figure 2 shows the impacts the changes of the different indexes to the CR modulation. The behaviour of the parameters ZE and SE in cycle 23 is anomalous. The increase a contribution from cyclical variations of these indices may be rela te d w ith tw o re a s o n s . T h e y a re e ith e r s tro n g ly d e v e lo p e d f ro m s e c to r s tru c tu re o r a n e rro r in th e W S O d a ta . T h e c o n trib u tio n f ro m Z O in d e x d e c re a s e s d u rin g th e s e c y c le s .

Figure 2: A contribution of BSS, ZO, ZE, SO, SE, W in d e x e s to s im u la te d C R v a ria tio n s T h e m o d e l re s u lts re p re s e n ts o n It is s h o w n , th a t th e c u rre n t c h a n g e s o f th e f la re in d e x a lo n g odd index SO are most effective tio n ( f ig .3 a ). th e F ig u re 3 a ,b . s h e e t tilt a n d with the sectorfor the modula-

F ig u re 3 a ,b : M o n th ly C R v a ria tio n s o b s e rv e d a n d s im u la te d b y th e m u ltip a ra m e te r m o d e l f o r a) Fx, Hpol, SO, and b) Fx, Hpol, ZO, F o r t h e m u l t i p a r a m e t e r d e s c r i p t i o n o f l o n g- t e r m C R v a ria tio n s b y u s in g th e a v e ra g e o f s o la r m a g n e tic f ie ld o r o n e o f f o u r p a rtia l in d e x e s d u r i n g t h e p e r i o d o f 1 . 1 9 7 7- 1 2 . 1 9 9 9 t h e b e s t f i t is o b ta in e d f o r th e a v e ra g e o f s o la r m a g n e tic field Bss and the sector-odd index SO, the minim u m v a lu e o f th e rm s d e v ia tio n is = 1 .7 3 % ( = 1 . 8 0 - 1 . 8 6 % f o r o t h e r s i n d e x e s ). The cyclic variations of SO index are well ref le c te d in th e C R m o d u la tio n , e s p e c ia lly c le a rly i n t h e m a x i m u m o f c y c l e s. I n 2 0 0 3 t h e y g a v e th e la rg e s t c o n trib u tio n o v e r th e w h o le p e rio d u n d e r c o n s id e ra tio n , th e n a s h a rp d ro p o f S O followed and consequently, a decrease of con-

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tribution in the CR modulation. Cyclical variations of ZO index are in the phase with CR v a ria tio n s . It is n o te w o rth y th a t c o n trib u tio n in th e m o d u la tio n f ro m th is p a ra m e te r is m u c h le s s after the maximum of cycle 23 as compared with the other cycles. It is assumed that a phen o m e n o n o f C R d e c re a s in g in m in im a o f S A c y c le s (f ro m c y c le to c y c le ) d is c u s s e d n o w in space physics could be described by corresponding a significant decrease maximum values of the zone-odd ZO index and similar dec re a s e o f th e v e rtic a l c o m p o n e n t o f th e d ip o le m a g n e tic m o m e n t re c e n tly f o u n d [8 ]. T h e m a in ro le in a d e f in itio n o f th e b a s ic a lly p o in ts o f C R cycles play average of solar magnetic field Bss and index ZO because a cyclical variation of the total solar magnetic field is conditioned by a c o n trib u tio n o f c y c lic a l v a ria tio n s o f th e lo c a l f ie ld s in to th e a v e ra g e o f s o la r m a g n e tic f ie ld Bss and by the global field, which defines ZO, especially on the source surface. A model des c r i p t i o n o f m o d u l a t i o n b y m e an s o f t h e i n d i c e s ZO and SO together with Fx and gives not w o rs e re s u lt th a n m o d e lin g w ith th e a v e ra g e o f solar magnetic field Bss index and the value of polar magnetic field Hpol.

tio n o f lo n g d e c re a s in g in to c y c le ) c o u d e c re a s in g o f

te rm C R v a ria tio n s th a t th e C R m in im a o f S A c y c le s ( f ro m c y c le ld b e d e s c rib e d b y c o rre s p o n d in g the zone-odd ZO index.

Acknowledgements
The authors are grateful to the Russian Foundation for Basic Research (grants 05-02-17251, 06-02-17346, 06-02-39028-CFNS -a) and the P re s id iu m o f R A S ( th e p ro g ra m " N e u trin o physics") for supporting this theme.

References
[ 1 ] B e lo v A .V . e t a l. " G lo b a l m a g n e tic f ie ld o f th e s u n a n d lo n g - te rm v a ria tio n s o f g a la c tic c o s m ic ra y s " , J . A tm o s . T e rr. P h y s ., 6 3 , N 1 8 , 1923 ­ 1929, 2001. [2] Belov A.V. et al. "Relation of the long-term m o d u la tio n o f c o s m ic ra y s to th e c h a ra c te ris tic s of the global solar magnetic field," Geomagnetis m a n d A e ro n o m iy a , 4 2 , N 6 , 6 9 3 ­ 7 0 0 , 2 0 0 2 . [ 3 ] B e lo v A .V . e t a l. " L o n g te rm v a ria tio n s o f g a la c tic c o s m ic ra y s in th e p a s t a n d f u tu re f ro m observations of various solar activity characteris tic s " , J . A tm o s . T e rr. P h y s , 6 8 , N 1 1 , 1 1 6 1 ­ 1166, 2006. [ 4 ] B e lo v A .V . e t a l. T h e re la tio n o f th e g lo b a l m a g n e tic s o la r f ie ld in d ic e s a n d th e s o la r w in d characteristics with the long-term variations of galactic cosmic rays", Proc. 29th ICRC, 2, 239 ­ 243, 2005. [5] http://quake.stanford.edu/~wso [ 6 ] O b rid k o V .N ., B . D . S h e ltin g " S tru c tu re o f th e h e lio s p h e ric c u rre n t s h e e t a s c o n s id e re d o v e r a long time interval (19151996)", Solar Phys. 184, 187 ­ 200, 1999. [7 ] O b rid k o V .N ., B . D . S h e ltin g " G lo b a l s o la r magnetology and solar cycle reference points", Proc. of Intern. Conf. on solar phys., S.- Peterb u rg , 3 3 9 - 3 4 2 , 2 0 0 3 . [ 8 ] L iv s h its I.M ., O b rid k o V .N . V a ria tio n s o f the dipole magnetic moment of the Sun during th e s o la r a c tiv ity c y c le . A s tro n o m y R e p o rts , 5 0 , N 11, 926- 935, 2006.

Conclusion
1. The multiparameter model of CR modulation, w h ic h a d d itio n a lly a c c o u n ts th e f la re in d e x F x improves the description of the observed variatio n s . It is p o s s ib le to u s e th e p a rtia l in d e x e s a lo n g w ith th e a v e ra g e o f s o la r m a g n e tic f ie ld in the model of CR modulation. 2. The features b e h a v i o r o f p r o p o s e d i n d i c e s o f s o l a r m ag n e t i c field and their contribution in the CR modulatio n a re s h o w n a n d a n a ly z e d . D u rin g th e p e rio d of 1977-1999 the best fit is obtained for the a v e r a g e o f s o l a r m a g n e t i c f i e l d a n d t h e s e c t o ro d d in d e x . T h e m o d e l f o r a ll a n a ly z e d in d e x e s shows a large discrepancy with observations in the beginning of 2000. It is possible that it connected with the anomalous behaviour of the parameters ZE and SE and the significant decrease of the ZO in cycle 23. 3. The longitudinal d e p e n d e n c e o f t h e f l a r e i n d e x f o r t h e l o n g- t e r m m o d u la tio n o f C R is n o t im p o rta n t, b u t th e re is a strong dependence on flare intensity, this is c h a ra c te ris tic f o r th is ty p e v a ria tio n . 4 . T h e propose is made on the basis of model descrip-

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