1. Long-term variations of vector and tensor anisotropies of cosmic rays
P.Yu. Gololobov, G.F. Krymsky, P.A. Krivoshapkin
Yu. G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS, Yakutsk, Russia

2. NAGOYA MULTI-DIRECTIONAL MUON TELESCOPE
Introduction 2
NAGOYA MULTI-DIRECTIONAL MUON TELESCOPE
Operates since 1970 till nowadays
Provides the data of 17 direction
COSMIC-RAY RESEARCH SECTION
SOLAR-TERRESTRIAL ENVIRONMENT LABORATORY
NAGOYA UNIVERSITY, NAGOYA JAPAN

3. CR anisotropy 3 𝑅 0 0 𝑅 1 1 𝑅 2 1 𝑅 2 2 Isotropic intensity
𝐼 𝜃,𝜑 = 𝑛=0 ∞ 𝑚=0 𝑛 𝑎 𝑛 𝑚 cos 𝑚𝜑 + 𝑏 𝑛 𝑚 𝑚𝜑 𝑃 𝑛 𝑚 ( sin 𝜃 )
𝐴 =( 𝑎 0 0 , 𝑎 1 0 , 𝑎 1 1 , 𝑏 1 1 , 𝑎 2 0 , 𝑎 2 1 , 𝑏 2 1 , 𝑎 2 2 , 𝑏 2 2 )
𝑅 𝑛 𝑚 =( 𝑎 𝑛 𝑚 , 𝑏 𝑛 𝑚 )
𝑅 isotropic intensity
𝑅 1 1 ={ 𝑎 1 1 , 𝑏 1 1 }- symmetric diurnal variations
𝑅 2 1 ={ 𝑎 2 1 , 𝑏 2 1 } - anti-symmetric diurnal variations
𝑅 2 2 ={ 𝑎 2 2 , 𝑏 2 2 } - semidiurnal variations
Isotropic intensity
Vector anisotropy
Tensor anisotropy
𝑅 0 0
𝑅 1 1
𝑅 2 1
𝑅 2 2

4. Method of VA and TA decomposition4
𝐴 =( 𝑎 0 0 , 𝑎 1 0 , 𝑎 1 1 , 𝑏 1 1 , 𝑎 2 0 , 𝑎 2 1 , 𝑏 2 1 , 𝑎 2 2 , 𝑏 2 2 )
𝐴 =( 𝑎 𝑛 𝑚 , 𝑏 𝑛 𝑚 )
𝑍 =( 𝑥 𝑛 𝑚 , 𝑦 𝑛 𝑚 )
Receiving vectors (Fujimoto et al., 1984)
𝐼= 𝐴 ∙ 𝑍
𝑨 1,𝑜𝑏𝑠 = 𝑎 1,1 𝑏 1,1 ⋮ 𝑎 1,𝑗 𝑏 1,𝑗
𝑨 2,𝑜𝑏𝑠 = 𝑎 2,1 𝑏 2,1 ⋮ 𝑎 2,𝑗 𝑏 2,𝑗
𝑴 1 = 𝑥 1,1 1 𝑦 1,1 1 𝑥 2,1 1 𝑦 2,1 1 −𝑦 1,1 1 𝑥 1,1 1 −𝑦 2,1 1 𝑥 2,1 1 ⋮ ⋮ ⋮ ⋮ 𝑥 1,𝑗 1 𝑦 1,𝑗 1 𝑥 2,𝑗 1 𝑦 2,𝑗 1 −𝑦 1,𝑗 1 𝑥 1,𝑗 1 −𝑦 2,𝑗 1 𝑥 2,𝑗 1
𝑴 2 = 𝑥 2,1 2 𝑦 2,1 2 −𝑦 2,1 2 𝑥 2,1 2 ⋮ ⋮ 𝑥 2,𝑗 2 𝑦 2,𝑗 2 −𝑦 2,𝑗 2 𝑥 2,𝑗 2
𝑨 1,𝑒𝑥𝑝 = 𝑴 1 𝑨 1,𝑜𝑏𝑠
𝑴 1 𝑇 𝑴 1 −1 𝑴 1 𝑇 𝑨 1,𝑜𝑏𝑠 = 𝑨 1,𝑒𝑥𝑝
𝑨 2,𝑒𝑥𝑝 = 𝑴 2 𝑨 2,𝑜𝑏𝑠
𝑴 2 𝑇 𝑴 2 −1 𝑴 2 𝑇 𝑨 2,𝑜𝑏𝑠 = 𝑨 2,𝑒𝑥𝑝
𝑨 1,𝑒𝑥𝑝 = 𝑎 𝑏 𝑎 𝑏 2 1
𝑨 2,𝑒𝑥𝑝 = 𝑎 𝑏 2 2
Errors:
∆ 1 = 𝑨 1,𝑜𝑏𝑠 − 𝑴 1 𝑨 1,𝑒𝑥𝑝
𝜎 1 = ∆ 1 𝑇 ∆ 1 𝑇 ( 𝑵 1 − 𝒏 1 )
∆ 2 = 𝑨 2,𝑜𝑏𝑠 − 𝑴 2 𝑨 2,𝑒𝑥𝑝
𝜎 2 = ∆ 2 𝑇 ∆ 2 𝑇 ( 𝑵 2 − 𝒏 2 )
K. Fujimoto, A. Inoue, K. Murakami et al. Coupling coefficients of cosmic ray daily variations for meson telescopes. Report of cosmic ray research laboratory 9, 1984.

5. Obtained results 5
Fig. 2. The observed mean annual values of amplitudes of symmetric diurnal 𝑅 1 1 , antisymmetric diurnal 𝑅 2 1 , semidiurnal 𝑅 Also the maximum times of symmetric diurnal 𝑇 1,𝑚𝑎𝑥 1 and semidiurnal 𝑇 2,𝑚𝑎𝑥 2 variations. The solar sunspot number and the average solar field of the Northern and Southern Hemispheres , that is taken by measurements from the Wilcox Solar Observatory ,are shown

6. Obtained results 6
FFT
Fig. Observed mean monthly values of the component of diurnal ( 𝑎 1 1 , 𝑏 1 1 ), antisymmetric ( 𝑎 2 1 , 𝑏 2 1 ) and semidiurnal ( 𝑎 2 2 , 𝑏 2 2 ) variations of CR which are obtained by the data of 17 directions of the multidirectional muon telescope st. Nagoya for the time period

7. Obtained results 7
- the annual oscillations of TA are of solar origin!
- the reason of such behavior is that coordinate systems which was used in the method and the mechanisms don’t match!
P.A. Krivoshapkin, G.F. Krymsky, A.I. Kuzmin et al. The second spherical harmonics in the distribution of cosmic rays. Acta Physics Academiae Scientiarum Hungaricae. V. 29, P. 147, 1970.
E.G. Berezhko. Acceleration of charged particles in a cosmic-phase shear flow. JETP Letters. V. 33, P. 399, 1981.

8. The possible mechanisms that create TA are:
Obtained results 7
The possible mechanisms that create TA are:
Screening of CR by IMF
(Krivoshapkin et al., 1970)
𝐴 1 = , 0, 0, cos2𝜑 sin2𝜑
Shear flow of SW
(Berezhko, 1981)
𝐴 2 ={ 0, cos𝜃, sin𝜃, 0, 0 }
P.A. Krivoshapkin, G.F. Krymsky, A.I. Kuzmin et al. The second spherical harmonics in the distribution of cosmic rays. Acta Physics Academiae Scientiarum Hungaricae. V. 29, P. 147, 1970.
E.G. Berezhko. Acceleration of charged particles in a cosmic-phase shear flow. JETP Letters. V. 33, P. 399, 1981.

9. Obtained results 8 ℎ 𝑡 =1− 𝑘 1 sin𝑡 − 𝑘 2 ( sin 2 𝑡− 1 2 )
Latitudinal distribution of Screening mechanism
ℎ 𝑡 =1− 𝑘 1 sin𝑡 − 𝑘 2 ( sin 2 𝑡− 1 2 )
The resulting TA from both mechanisms in GSE coordinate system
𝐴 =ℎ 𝑡 𝐴 1 + 𝑘 3 𝐴 2
𝑴 𝑙𝑜𝑛𝑔 (𝛼)= cos𝛼 sin𝛼 −sin𝛼 cos𝛼 cos2𝛼 sin2𝛼 −sin2𝛼 cos2𝛼
𝑴 𝑙𝑎𝑡 (𝛽)= 1− 3 2 sin 2 𝛽 0 − sin2𝛽 − sin 2 𝛽 0 0 cos𝛽 0 0 −sin𝛽 − sin2𝛽 0 cos2𝛽 1 2 sin2𝛽 0 − sin 2 𝛽 0 − 1 2 sin2𝛽 1 2 (1+ cos 2 β) 0 0 sin𝛽 0 0 cos𝛽
𝑴 𝑙𝑜𝑛𝑔 (𝛼) 𝑴 𝑙𝑜𝑛𝑔 (𝛽) 𝑴 𝑙𝑜𝑛𝑔 (𝛾) 𝐴

10. Obtained results 9
Experiment vs Model
The existence of NS asymmetry (Krymsky et al., 2007, 2010)
The IMF tilted to the south of helioequator ≈6.3°
𝑘 1 =0.2
𝑘 2 =0.12
𝑘 3 =0.05
𝜑=50°
𝜃=−40°

11. Conclusions 10
By the data of multidirectional muon telescope st. Nagoya for the period using the method of receiving vectors the decomposition of the observed diurnal variations into the vector and tensor anisotropies of CR is made.
It is shown that the vector anisotropy of CR experiences changes with the solar magnetic cycle and solar activity. The main mechanism of the generation of this anisotropy is convective-diffusive and drift motion of CR.
It is shown that the components of tensor anisotropy( 𝑎 2 1 , 𝑏 2 1 , 𝑎 2 2 , 𝑏 2 2 ) experience stable annual and semiannual oscillation during the whole investigated time period, which are generated mainly by the CR screening mechanism. The mechanism of CR shear flow has a small contribution to this variations. Comparison of the model and experiment indicates that there is a shift of interplanetary magnetic field to the south of the solar equator on ≈6.3°.

12. Thank you for attention!
The work was supported by the grants RFBR Nos r_vostok_a, r_vostok_a and the program of Presidium of SB RAS No. 23. We acknowledge Cosmic Ray Section, Solar-Terrestrial Environment Laboratory, Nagoya University and Wilcox Solar Observatory for providing the data.