Using Galactic Cosmic Ray Observations for Determination
of the Heliosphere Structure During Different Solar Cycles
Lev I. Dorman
Israel Cosmic Ray Center and Emilio Segre’ Observatory, affiliated to Tel Aviv University, Technion and Israel Space
Agency, Israel; IZMIRAN, Russian Academy of Science, Troitsk, Russia;
Abstract. Our studies of the neutron and muon components data from many observatories with different cut-off rigidities
during solar cycles 19-22 have made it possible to investigate the hysteresis character of the relationships between the
variations in solar activity and in galactic cosmic ray intensity. We use here a special model described the connection between
solar activity and CR convection-diffusion global modulation with taking into account time-lag of plasma processes in the
Heliosphere relative to the active processes on the Sun. We supposed different dimension of the modulation region and for
each dimension was determined the correlation coefficient between variations of expected and observed CR intensities. We
found that the maximum of correlation coefficient occurred for even cycles for about two-three times in the shorter time than
for odd cycles. We came to conclusion that this difference is caused by CR drift effects: during even cycle drift effect from
minimum to maximum of SA produced the small increasing of CR global modulation additional to the caused by convectiondiffusion mechanism, and after maximum of SA - about the same decreasing of CR modulation. This gives sufficient
decreasing of observed time-lag between CR and SA in even solar cycles. For odd solar cycles we have inverse situation: drift
effect from minimum to maximum of SA produced the additional decreasing of CR global modulation caused mainly by
convection-diffusion mechanism, and after maximum of SA - increasing of CR modulation. This gives sufficient increasing of
observed time-lag between CR and SA in odd solar cycles. By comparison of expected results with observed for particles of
different energy we determine the relative role of convection-diffusion and drift mechanisms in formation of CR global
modulation in the Heliosphere.
COSMIC RAY LONG-TERM
MODULATION, TIME-LAG AND
CONVECTION-DIFFUSION
MECHANISM
it is now known) is about 5 AU, and not more than 10-15
AU [7-11]. The radius ro of the CR modulation region
was found to be very small both by analysis of the
intensity of coronal green line in some helio-latitude
regions ( ro ≈ 5 AU), or by investigation the CR
Short Historical Information on the
Problem of CR Long-Term Modulation
modulation as caused by sudden jumps in solar activity
( ro ≈ 10-15 AU). In [12-15] the hysteresis phenomenon
The investigation of the hysteresis phenomenon in the
connection between long-term variations in cosmic ray
(CR) intensity observed at the Earth and solar activity
(SA), started about 40 years ago [1-6]. In the middle of
sixties many scientists came to conclusion that the:
dimension of the modulation region (or Heliosphere, as
was investigated on the basis of neutron monitor (NM)
data for about one solar cycle in the frame of convectiondiffusion model of CR global modulation in the
Heliosphere taking into account the 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 much bigger, about 100 AU. These
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
148
where W (t − r u ) is the sunspot number in the time
t − r u . By the comparison with observation data it was
determined in [13, 14] that parameter 0 ≤ β ≤ 1 and
α ≈ 1 3 in the period of high solar activity
and α ≈ 1 near solar minimum
W t ≈W
investigations were continued on the basis of CR and SA
monthly average data for about four solar cycles in [16,
17]. Though many authors have worked on this problem,
the time lag of processes in the interplanetary space
relative to processes on the Sun has not been taken into
account (see review in [18]). The method, described
below, considers that CR intensity observed on the Earth
at moment t is caused by solar processes occurring for
many months before t. In a recent paper [19] CR and SA
data for solar cycles 19-22 was considered again taking
into account drift effects according to [20]. It was shown
that including drift effects (depending on the sign of
solar polar magnetic field 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 great
difference in time-lags between CR and SA in hysteresis
phenomena for even and odd solar cycles.
( () )
(W(t )<< W ).
max
with [15], that
((
) )= A(R, X , β ,t ,t )−
− B(R, X , β ,t ,t )× F(t, X , β ,W(t − X )
ln n R,r ,t
(3)
o
obs
1
2
1
2
o
Xo
XE
)
(4)
where
(
(
F t, X , β ,W t − X
o
 W (t − X )

= ∫ 

W


Xo
XE
)
(
Xo
XE
1 2
+
1− W
3 3
)=
( t− X )
(5)
W max
)
−β
X dX
max
X = r u , X E = 1AU u , X o = ro u ( X E and X o are
in units of average month). Let us note that regression
coefficient A(R, X o , β , t1 , t 2 ) determined the CR
intensity out of the Heliosphere, and B(R, X o , β , t1 , t 2 )
characterized the effective diffusion coefficient in the
interplanetary space; these coefficients can be determined
by correlation between observed values ln n(R, rE , t )obs
( ) 
n (R, r , t ) n (R) ≈ exp −a ∫
D (R, r, t)

(
o
robs
E
o
It was shown in [12] that the time of propagation
through the Heliosphere of particles with rigidity bigger
than 10 GV (to whom NM are sensitive) is not longer
one month. This time is at least about one order of
magnitude smaller than the observed time-lag in the
hysteresis phenomenon. It means that the hysteresis
phenomenon on the basis of NM data can be considered
as quasi-stationary problem with parameters of CR
propagation changing in time. In this case according to
[20, 21]
 r u r,t dr  ,
(1)
o
α (t ) = 1 3 + (2 3)(1 − W (t ) Wmax ) ,
where Wmax is the sunspot number in the maximum of
solar activity cycle.
According to (1) the value of the natural logarithm of
observed CR intensity global modulation at the Earth’s
orbit, taking into account (2) and. (3), will be
Hysteresis Phenomenon and Model of CR
Global Modulation in the Frame of
Convection-Diffusion Mechanism
obs
Here we suppose, in accordance
max
r
)
and the values of F, calculated according to (5) for
different values of X o and β . In [16] three values of
β = 0; 0.5; 1 have been considered; it was shown that
β = 1 strongly contradicts CR and SA observation data,
and that β = 0 is the most reliable value. Therefore, we
will consider here only this value.
where n(R, robs , t ) is the differential rigidity CR density,
no (R ) is the differential rigidity density spectrum in the
local interstellar medium out of the Heliosphere,
a ≈1.5, u (r , t ) is the effective solar wind velocity
(taking into account also shock waves and high speed
solar wind streams), and Dr (R, r , t ) is the radial
diffusion coefficient in dependence of the distance r
from the Sun of particles with rigidity R at the time t .
According to [13, 14] the connection between Dr (R, r , t )
and solar activity can be described by the relation
D (R, r , t ) ∝ r β (W (t − r u ))−α ,
(2)
EVEN-ODD CYCLE EFFECT AND ROLE
OF DRIFTS
Cosmic Ray Time-Lags in Odd and Even
Solar Cycles
r
149
1976- September 1993), we found that there are very
good relation between T and W; for 11 months smoothed
data T = 0.349W + 13.5° with correlation coefficient
0.955. We used 11 months smoothed data of W (shown
in Figure 1) and determined the amplitude Adr of drift
To determine X o max , corresponding to the
maximum value of the correlation coefficient for (4), we
compare 11 months moving averages of the Climax NM
(H = 3400 m, cut-off rigidity Rc = 2.99 GV ) for solar
cycles 19-22 and onset of cycle 23 with expectation
according to (4) and. (5). For each time-lag,
X o = ro u =1, 2, 3, … 60 av. months, we determined the
correlation between observed and expected CR
intensities. The Climax NM data correspond to an
effective rigidity of primary CR of about 10-15 GV. For
higher energy particles (about 30-40 GV) we used
Huancayo ( Rc = 12.92 GV , H = 3400m ) and Haleakala
( Rc = 12.91 GV , H = 3030m ) NM data from January
1953 to August 2000. A big difference in X o max for odd
and even solar cycles was found.
effects as drift modulation at W11M = 75 (average value
of W11M for 1953-1999). The reversal periods were:
August 1949 ± 9 months, December 1958 ± 12 months,
December 1969 ± 8 months, March 1981 ± 5 months,
and June 1991 ± 7 months. We determined correlation
coefficients between the expected integrals F for
different values of X o = 1, 2, 3, … 60 av months with
the observed LN(CL11M) and LN(HU/HAL11M), as
well as with corrected for the drift effects according to
the 1-st, 2-nd and 3-rd Approaches with Adr from
0.15% up to 4%. An example for correction of observed
CR intensity on the drift effects (to obtain only
convection-diffusion modulation) is shown for period
January 1953-November 2000 in Figure 1.
We assume that observed long-term CR modulation
is caused by two processes: the convection-diffusion
mechanism (e.g. [21-23]) independent of the sign of the
solar magnetic field, and the drift mechanism (e.g. [20,
24-25]) what gave opposite effects with changing sign of
solar magnetic field. For the convection-diffusion
mechanism we use the model described in detail in [19],
shortly given above by (1)-(5). We considered three
Approaches of drift effects: First, we assume a constant
value of drift modulation between two reversals of solar
magnetic field with negative sign at A>0 and positive
sign at A<0, and in the short period of reversal we
suppose linear transition through 0 from one polarity
cycle to other (in this case for convection-diffusion part
of CR modulation we obtained sufficient differences in
CR maximums near SA minimums in contradiction with
observations); Second, we correct the first by reducing
the value of drift modulation near SA minimums; Third,
we assume that the drift effect is proportional to the
value of the tilt-angle T with negative sign at A>0 and
positive sign at A<0, and in the period of reversal we
again suppose linear transition through 0 from one
polarity cycle to other (see Figures 1-4 in [20]; we
assume that average of curves for A>0 and A<0 in these
figures characterized convection-diffusion modulation,
and difference of these curves – double drift
modulation). Data on tilt-angles for solar cycles 19 and
20 are not available. We used relation between sunspot
numbers W and T to made homogeneous analysis of the
period 1953-2000. Based on data for 18 years (May
8.4
225
A>0 19 SC A<0 20 SC A>0
21 SC A<0 22 SC A>0 23 SC
200
LN(CL11M), LN(CLCOR3_DR2%)
8.35
175
8.3
150
8.25
125
8.2
100
75
8.15
50
8.1
8.05
1950
SUNSPOT NUMBERS W11M
How Drift Effects Influenced on the TimeLag in Odd and Even Cycles?
25
1960
1970
LN(CLCOR3_DR2%)
1980
1990
LN(CL11M)
0
2000 YEAR 2010
W11M
FIGURE 1. An example of CR data correction on drift effects
in 1953-2000 (19-22 cycles and onset of 23 cycle): LN(CL11M)
– observed natural logarithm of Climax NM counting rate
smoothed for 11 months, LN(CLCOR3_DR2%) – corrected on
assumed drift effect according to the 3-rd Approach with
Adr =2% at W11M=75. Interval between two horizontal lines
corresponds 5% of CR intensity variation.
.
Estimation of Role of Drift Effects in LongTerm Modulation and Dimension of CR
Modulation Region (Heliosphere)
In Fig. 2 the dependences of X o max on Adr are shown
for Climax NM.
150
Xomax, av. months
35
6. Dorman, L. I., Cosmic Ray Variations and Space Research,
Moscow, Nauka, 1963.
30
7. Quenby, J. J., Proc. 9th ICRC. 1, 3-13 (1965).
25
8. Charakhchyan, A. N., and Charakhchyan, T. N., Canad.
Journ. of Phys., 46, No. 10, part 4, 879-882 (1968).
20
9. Charakhchyan, A. N., and Charakhchyan, T. N., Proc. 12th
ICRC, 5, 1984-1991 (1971).
15
10. Stozhkov, Yu. I. and Charakhchyan, T. N., Geomagnetism
and Aeronomy, 9, 803-808 (1969).
10
11. Pathak, P. N. and Sarabhai V., Planet.. Space Sci., 18, 8194 (1970).
5
0
0.5
1
CY19
1.5
CY20
2
2.5
CY21
3
3.5Adr, %4
CY22
12. Dorman, I. V. and Dorman, L. I., Cosmic Rays, 7, 5-17
(1965).
FIGURE 2. Dependences X o max ( Adr ) for Climax NM.
13. Dorman, I. V. and Dorman, L. I., J. Geophys. Res., 72,
1513-1520 (1967).
From Figure 2 it can be seen that the region of crossings
of X o max ( Adr ) for odd and even cycles is:
13 ≤ X o max ≤ 16.5 ,
1.7% ≤ Adr ≤ 2.3% .
For
Huancayo/Haleakala
NM
this
region
is:
13 ≤ X o max ≤ 18, 0.23% ≤ Adr ≤ 0.43% , Thus we came
to conclusion that the amplitude of the drift effect is
about 2.0% for Climax NM and about 0.33% for
Huancayo/Haleakala NM. We came also to conclusion
that for primary CR with rigidity 10-15 GV a relative
contribution of drift effects is about 20-25%. For CR
with rigidity 35-40 GV a relative role of drift effects is
about 2-3 times smaller. For X o max we obtained for
both 10-15 and 35-40 GV about 15 av. months, what
corresponds ro ≈ 100 AU (with an average solar wind
14. Dorman, I. V. and Dorman, L. I., J. Atmosph. and Terr.
Phys., 29, 429-449 (1967).
15. Dorman, L. I., Variations of Galactic Cosmic Rays,
Moscow, Moscow State University Press, 1975.
16. Dorman, L. I. et al, Proc. 25 th ICRC, 2, 69-72 (1997).
17. Dorman, L. I. et al., Proc 26th ICRC, 7, 194-197 (1999).
18. Belov, A., Space Sci. Reviews, 93, 79-105 (2000).
19. Dorman, L. I., Adv. Space Res., 27, 601-606 (2001).
20. Burger, R. A., and Potgieter, M. S., Proc. 26th ICRC, 7,
13-16 (1999).
21. Dorman, L. I., Proc. 6th ICRC, 4, 328-334 (1959).
22. Parker, E. N., Interplanetary Dynamical Processes . New
York, Interscience. Publ., 1963.
speed 400 km/s).
23. Dorman, L. I., Proc. 9-th ICRC, 1, 292-295 (1965).
ACKNOWLEDGEMENTS
24. Jokipii, J.R., and Davila J.M., Astrophys. J., 248, Part 1,
1156-1161 (1981).
This research is partly supported by INTAS grant 0810.
25. Ferreira, S. E. et al., Proc. 26th ICRC, 7, 77-80 (1999).
REFERENCES
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Gostekhteorizdat, 1957.
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151