Daejeon, UN/ESA/NASA/JAXA Workshop,

20-25 Sept 2009 On the Connection of Cosmic Ray Long-Term Variation with Sunspot Numbers:

Convection-Diffusion and Drift Modulations

in the Heliosphere

by Lev I. Dorman (1, 2)

(1) Israel Cosmic Ray & Space Weather Center and Emilio Segre’ Observatory, affiliated to Tel Aviv University, Technion

and Israel Space Agency, Qazrin 12900, Israel;

(2) Cosmic Ray Department of IZMIRAN, Russian Academy of Science, Troitsk 142092, Moscow Region, Russia;

2

CONTENTS• Introduction• 1. Hysteresis phenomenon and the problem for galactic cosmic ray (CR)

propagation and modulation in the Heliosphere: short history of development• 2. Hysteresis phenomenon and the model of CR global modulation in the

frame of convection-diffusion theory • 3. Even-odd solar cycle effect in CR and role of drifts for NM energies• 4. The problem for CR propagation and modulation during solar cycle 22 on

the basis of NM data• 5. Diffusion time lag for small energy particles• 6. Convection-diffusion modulation for small energy galactic CR particles • 7. Small energy CR long-term variation caused by drifts• 8. The satellite proton data and their corrections on solar CR increases • 9. Results for alpha-particles in the energy interval 330500 MeV• 10. Forecasting of CR intensity variations by integral F near solar activity

minimum• 11. Forecasting of CR intensity during the period of solar activity increasing• References

3

Introduction• The propagation and modulation of galactic CR (generated mostly during

Supernova explosions and in Supernova remnants in our Galaxy) in the Heliosphere are determined by their interactions with magnetic fields frozen in solar wind and in coronal mass ejections (CME) with accompanied shock waves (produced big magnetic storms during their interactions with the Earth’s Magnetosphere). The most difficult problem of monitoring and forecasting the modulation of galactic CR in the Heliosphere is that the CR intensity in some space-time 4D-point is determined not by the level of solar activity at this time-point of observations and electro-magnetic conditions in this space-point but by electromagnetic conditions in total Heliosphere. These conditions in total Heliosphere are determined by development of solar activity during many months before the time-point of observations. It is main cause of so called hysteresis phenomenon in connection galactic CR – solar activity. From other hand, detail investigations of this phenomenon give important possibility to estimate conditions in and dimension of Heliosphere. To solve described above problem of CR modulation in the Heliosphere, we considered as the first step behavior of high energy particles (more than several GeV, for which the diffusion time of propagation in Heliosphere is very small in comparison with characteristic time of modulation) on the basis of neutron monitor data in the frame of convection diffusion theory, and then take into account drift effects. For small energy galactic CR detected on satellites and space probes we need to take into account also additional time lag caused by diffusion in the Heliosphere. Then we consider the problem of CR modulation forecasting for several months and years ahead.

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1. Hysteresis phenomenon and the problem of galactic CR propagation and modulation in the Heliosphere: short

history of development• Main investigations of the connection between long-term variations in CR intensity observed at the Earth and

variations of solar activity (SA), started about 50 years ago (Dorman, M1957; Forbush, 1958; Neher and Anderson, 1962; Simpson, 1963; Dorman, M1963a, M1963b). In the middle of 60-th many scientists came to conclusion that the dimension of modulation region (or Heliosphere) is about 5 AU, and not more than 10-15 AU (Quenby, 1965; Kudo and Wada, 1968; Charakhchyan and Charakhchyan, 1967, 1968; Stozhkov and Charakhchyan, 1969; Pathak and Sarabhai, 1970). It was supposed that the radius of CR modulation region is very small: either by analysis of the intensity of coronal green line in some helio-latitude regions (as controlled solar activity factor; in this case was obtain 5 AU), or by investigation the CR modulation as caused by sudden jumps in solar activity (10-15 AU). In Dorman and Dorman (1965, 1967a,b,c), Dorman (M1975) the hysteresis phenomenon was investigated on the basis of neutron monitor (NM) data for about one solar cycle in the frame of convection-diffusion model of CR global modulation in the Heliosphere with taking into account time lag of processes in the interplanetary space relative to processes on the Sun. It was shown that the dimension of the modulation region should be about 100 AU (much bigger than accepted in those time in literature, 5-15 AU). These investigations were continued on the basis of CR and SA monthly average data for about four solar cycles in Dorman et al. (1997, 1999). Let us note that many authors worked on this problem, used sunspot numbers or other parameters of solar activity for investigations of CR long-term variations, but they did not take into account time lag of processes in the interplanetary space relative to processes on the Sun as integral action (see review in Belov, 2000). The method, described below, takes into account that CR intensity observed on the Earth at moment t is caused by solar processes summarized for the long period started many months before t. In paper Dorman (2001) was considered again by this method CR and SA data for solar cycles 19-22, but with taking into account drift effects according to Burger and Potgieter (1999). It was shown that including drift effects (as depending from the sign of solar polar magnetic field, sign of parameter A, and determined by difference of total CR modulation at A > 0 and A < 0, and with amplitude proportional to the value of tilt angle between interplanetary neutral current sheet and equatorial plane) is very important: it became possible to explain the apparent great difference in time-lags between CR and SA in hysteresis phenomenon for even and odd solar cycles.

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2. Hysteresis phenomenon and the model of CR global

modulation in the frame of convection-diffusion mechanism

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max13

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max,,,

,1 , urXuAUXurX ooE

6

• Sunspot numbers and long-term CR variations (years 1953–1999) recorded by neutron monitors on the Earth, balloons in the stratosphere and the IMP-8 satellite in space. Black rectangles show the reversal periods between positive (+) and negative (-) polarities of the general solar magnetic field. From Belov (2000).

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• Long-term density variations of cosmic rays with 5, 10, 20 GV rigidity calculated from data of the neutron monitor network. From Belov (2000).

8

• The relation of 12-months running averaged sunspot numbers and cosmic ray (10 GV) variations for 4 successive solar cycles (19–22). From Belov (2000).

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3. Even-odd cycle effect in CR and role of drifts for NM energies

• We assume that observed long-term CR modulation is caused by two processes: the convection-diffusion mechanism (e.g., Parker, 1958, Dorman, 1959), which is independent of the sign of the solar magnetic field; and the drift mechanism (e.g., Jokipii and Davila, 1981; Burger and Potgieter, 1999; Ferreira et al., 1999), what gave opposite effects with changing sign of solar magnetic field. For the convection-diffusion mechanism we use the model described in detail in Dorman (2001), for drift effects we use results of Burger and Potgieter (1999), and assume that the drift effect is proportional to the value of the tilt angle with negative sign at A > 0 and positive sign at A < 0, and in the period of reversal we suppose linear transition through 0 from one polarity cycle to other

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• Dependences for Climax NM. The drift effect is about 2.0% for Climax NM and about 0.33% for Huancayo/Haleakala NM

5

10

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20

25

30

35

0 0.5 1 1.5 2 2.5 3 3.5 4Adr, %

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CY19 CY20 CY21 CY22

dro AX max

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4. The inverse problem for CR propagation and modulation during solar cycle 22 on the

basis of NM data

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0 5 10 15 20 25 30 35 40

Xo, av.month

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RR

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ION

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FIC

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T R

(Xo

, A

dr)

Adr=0% Adr=0.5% Adr=1% Adr=1.5%

Adr=2% Adr=2.5% Adr=3% Adr=4%

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Results for Climax NM data. Results for Kiel NM data. Results for Tyan-Shan NM data. Results for Huancayo/Haleakala NM data.

Main results for the solar cycle 22 on the basis of NM data. • The taking into account drift effects gives an important possibility, using data only for

solar cycle 22, to determine the most reliable drift amplitude (at W = 75) and the effective time of the solar wind moving with frozen magnetic fields from the Sun to the boundary of the modulation region). We found that with an increasing effective CR primary particle rigidity from 1015 GV (Climax NM and Kiel NM) up to 3540 GV (Huancayo/Haleakala NM) are decreased both the amplitude of drift effect (from about 1.5% to about 0.15%) and time-lag (from about 13 av. months to about 10 av. months). It means that in cycle 22, for the total long term modulation of CR with rigidity 10-15 GV, the relative role of the drift mechanism was 1/4 and the convection-diffusion mechanism about 3/4 (we take into account that observed total 11-year variation in Climax and Kiel NM is 25%, and the total change of CR intensity owed to drift effects is about 4 times more than the amplitude); for rigidity 35-40 GV these values were 1/10 for the drift mechanism, and about 9/10 for the convection-diffusion mechanism. If we assume that the average velocity of the solar wind in the modulation region was about the same as the observed average velocity near the Earth’s orbit in 1965-1990:u = 7.73 AU/(average month), the estimated dimension of modulation region in cycle 22 will be ~ 100 AU for CR with rigidity of 10-15 GV and about 80 AU for CR with rigidity of 35-40 GV. It means that at distances more than 80 AU the magnetic fields in solar wind and in inhomogeneities are too weak to influence intensity of 35-40 GV CR particles.

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5. Diffusion time lag for small energy particles

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X X X X XT R t X X X C R t

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14

6. Convection-diffusion modulation for

small energy galactic CR particles

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n R r t A X t t B X t t F t X W t X

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0 10 20 30 40 50 60 70 80 90

TILT ANGLE

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T C

(R,T

)

R=3 GVR=1.0 GVR=0.3 GV

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7. Small energy CR long-term variation caused by drifts

• Expected drift modulations for R = 3, 1, and 0.3 GV relative to the intensity out of the Heliosphere, in dependence of sunspot number W and derived from Burger and Potgieter (1999)

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SUNSPOT NUMBER, W

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R=3 GV

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R=0.3 GV

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8. The satellite proton data and their corrections on solar CR increases

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0 5 10 15 20 25 30 35 40 45 50

Xo, AVERAGE MONTHS

CO

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ION

CO

EF

FIC

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Adr=0 Adr=0.05 Adr=0.1 Adr=0.2 Adr=0.3

Adr=0.4 Adr=0.5 Adr=0.6 Adr=0.7 for GOES data of protons with energy 100kE MeV from Jan 1986 to Dec 1999

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9. Results for alpha-particles in the energy interval 330500 MeV

Xo, AVERAGE MONTHS

-0.985

-0.98

-0.975

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-0.965

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-0.955

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0 5 10 15 20 25 30 35 40

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FIC

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Adr=0, Adr=0.05, Adr=0.10, Adr=0.15,

Adr=0.20, Adr=0.25, Adr=0.30, Adr=0.40

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10. Forecasting of CR intensity variations by integral F near SA minimum

Comparison of integral F, calculated according to Eq. 5, with observations by the Climax NM CR intensity: LN(CL11M), correlation coefficient maxR = 0.993, and LN(CL1M), maxR = 0.930. The left ordinate scale between

two nearest horizontal lines shows 0.5% variation.

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11. Forecasting of CR intensity during the period of SA increasing.For effective 10 GV (Climax NM) drift amplitude 2% at W = 75, correl. coef. 0.988. For effective 30 GV (Huncayo/Haleakala NM) drift amplitude 0.25% at W = 75, correl. coef. 0.986

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References• 1. References for monographs and books• Dorman L.I., Cosmic Ray Variations. Gostekhteorizdat, Moscow, M1957 (in

Russian). English translation: US Department of Defense, Ohio Air-Force Base, M1958.

• Dorman L.I., Geophysical and Astrophysical Aspects of Cosmic Rays. North-Holland, Amsterdam, in series “Progress in Physics of Cosmic Ray and Elementary Particles”, ed. J.G. Wilson and S.A. Wouthuysen, Vol. 7, pp. 1-324, M1963a.

• Dorman L.I., Cosmic Ray Variations and Space Research. Nauka, Moscow, M1963b (in Russian).

• Dorman L.I., Variations of Galactic Cosmic Rays. Moscow State University Press, Moscow, M1975 (in Russian).

• Dorman L.I., Cosmic Rays in the Earth’s Atmosphere and Underground, Kluwer Academic Publishers, Dordrecht/Boston/London, M2004.

• Dorman L.I., Cosmic Ray Interactions, Propagation, and Acceleration in Space Plasmas, Springer, Dordrecht, M2006.

• Dorman L.I., Cosmic Rays in Magnetospheres of the Earth and other Planets, Springer, M2009.

• Parker E.N., Interplanetary Dynamical Processes, John Wiley and Suns, New York-London, M1963. In Russian (ed. L.I. Dorman; transl. L.I. Miroshnichenko): Inostrannaja Literatura, Moscow, M1965.

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• 2. References for papers• Belov A.V., LARGE SCALE MODULATION: VIEW FROM THE EARTH, Space Sci. Rev, 93, 79-105 (2000).• Burger R.A. and M.S. Potgieter “The Effect of Large Heliospheric Current Sheet Tilt Angles in Numerical Modulation Models: A Theoretical Assessment”, Proc. 26-th

Intern. Cosmic Ray Conf., 7, 13-16 (1999).• Charakhchyan A.N. and T.N. Charakhchyan “Secular cosmic ray modulation in interplanetary space”, Izvestia Academy of Sci. of USSR, Series Phys., 31, No. 8, 1313-

1318 (1967).• Charakhchyan A.N. and T.N. Charakhchyan “Eleven-year modulation of galactic cosmic rays in interplanetary space”, Canad. Journ. of Phys., 46, No. 10, part 4, S879-

S882 (1968).• Dorman L.I. “To the theory of cosmic ray modulation by solar wind”, Proc. 6-th Intern. Cosmic Ray Conf., Moscow, 4, 328-334 (1959).• Dorman L.I. “Galactic and solar cosmic rays in interplanetary space”, Proc. 9th Intern. Cosmic Ray Conf., London, 1, 292-295 (1965).• Dorman L.I. “Cosmic ray long-term variation: even-odd cycle effect, role of drifts, and the onset of cycle 23”, Adv. Space Res., 27, No. 3, 601-606 (2001).• Dorman L.I. “Using galactic cosmic ray observations for determination of the Heliosphere structure during different solar cycles”, Solar Wind Ten (ed. M. Velli et al.), AIP

Conf. Proc., Melville, New York,148-151 (2003a).• Dorman L.I. “Changing of the modulation region structure with particle rigidities according to data of hysteresis phenomena”, Solar Wind Ten (ed. M. Velli et al.), AIP

Conf. Proc., Melville, New York, 164-167 (2003b).• Dorman Lev I. “Estimation of Radiation Hazard for Aircrafts from Galactic Cosmic Rays: Monitoring and Forecasting”, Proc. 3-rd Ankara Intern. Aerospace Conf., Ankara,

Paper Track # 1098, 1-7, in DVD (2005).• Dorman I.V. and L.I. Dorman “Investigation of 11-year cosmic ray variations (on the base of sea-level observations)”, Cosmic Rays, NAUKA, Moscow, 7, 5-17 (1965).• Dorman I.V. and L.I. Dorman “Solar wind properties obtained from the study of the 11-year cosmic ray cycle. 1”, J. Geophys. Res., 72, No. 5, 1513-l520 (1967a).• Dorman I.V. and L.I. Dorman “Propagation of energetic particles through interplanetary space according to the data of 11-year cosmic ray variations”, J. Atmosph. and

Terr. Phys., 29, No. 4, 429-449 (1967b).• Dorman et al., 1997: Dorman L.I., G. Villoresi, I.V. Dorman, N. Iucci, and M. Parisi “High rigidity CR-SA hysteresis phenomenon and dimension of modulation region in

the Heliosphere in dependence of particle rigidity”, Proc. 25th Intern. Cosmic Ray Conf., Durban (South Africa), 2, 69-72 (1997).• Dorman et al., 2001a: Dorman L.I., I.V. Dorman, N. Iucci, M. Parisi and G. Villoresi “Hysteresis between solar activity and cosmic rays during cycle 22: the role of drifts,

and the modulation region”, Adv. Space Res., 27, No. 3, 589-594 (2001a).• Dorman et al., 2001b: Dorman L.I., N. Iucci and G. Villoresi “Time lag between cosmic rays and solar activity; solar minimum of 1994-1996 and residual modulation”, Adv.

Space Res., 27, No. 3, 595-600 (2001b).• Dorman et al., 2005: Dorman L.I., N. Iucci, M. Parisi, and G. Villoresi “The role of drift and convection-diffusion mechanisms in small energy global cosmic ray

modulation: application to the hysteresis phenomenon of proton and alpha particle satellite data”, Adv. Space Res., 35, No. 4, 569-578 (2005).• Ferreira et al., 1999: Ferreira S.E.S., M.S. Potgieter and R.A. Burger “Comparison of a Two- and Three-Dimensional Drift Model”, Proc. 26-th Intern.Cosmic Ray Conf., 7,

77-80 (1999)• Forbush S.E. “Cosmic-Ray Intensity Variations during Two Solar Cycles”, J. Geophys. Res., 63, No. 4, 651-669 (1958).• Jokipii J.R. and J.M. Davila “Effects of Particle Drift on the Transport of Cosmic Rays. IV. More Realistic Diffusion Coefficients”, Astrophys.J., Part 1, 248, 1156-1161

(1981)• Jokipii J.R. and B. Thomas “Effects of drift on the transport of cosmic rays, IV. Modulation by a wavy interplanetary current sheet”, Astrophys.J., Part 1, 243, 1115-1122

(1981).• Kόta J. and J.R. Jokipii “Cosmic-ray modulation and the structure of the Heliospheric magnetic field”, Proc. 26th Intern. Cosmic Ray Conf., Salt Lake City, 7, 9-12 (1999). • Kudo S. and M. Wada “Eleven-year variation of cosmic ray intensity and heliolatitudes of sunspots”, Report of Ionosp. and Space Res. in Japan, 22, No. 3, 137-147

(1968).• Lee M.A. and L.A. Fisk “The Role of Particle Drifts in Solar Modulation”, Astrophys.J., 248, No. 2, part 1, 836-844 (1981).• Le Roux J.A. and H. Fichtner “The influence of pickup, anomalous, and galactic cosmic-ray protons on the structure of the heliospheric shock: a self-consistent

approach”, Astrophys. J., 477, No. 2, part 2, L115-L118 (1997)• Neher H.V. and Anderson H.R. “Cosmic Rays at Balloon Altitudes and the Solar Cycle”, J. Geophys. Res., 67, 1309-1315 (1962).• Parker E.N. “Cosmic-Ray Modulation by Solar Wind”, Phys. Rev., 110, No. 6, 1445-1449 (1958).• Pathak P.N. and V. Sarabhai “A study of the long-term modulation of galactic cosmic ray intensity”, Planet.. Space Sci., 18, Issue 1, 81-94 (1970).• Quenby J.J. “Cosmic rays and the interplanetary field”, Proc. 9th Intern. Cosmic Ray Conf, London, 1, 3-13 (1965).• Simpson J.A. “Recent Investigations of the Low Energy Cosmic and Solar Radiation”, Semaine d’Etude sur le Probleme du rayonnement cosmique dans l’espace

interplanetaire, Pontifical Academy of Sciences, Vatican City, 323-352 (1963).• Stozhkov Yu.I. and T.N Gharakhchyan “11-year modulation of cosmic ray intensity relevant to heliolatitudinal distribution of sunspots”, Geomagn. and Aeron., 9, No. 5,

803-808 (1969).