The method of calculating energy losses along regular particle trajectories is applied to obtain the predicted cosmic ray anisotropies from 200 to 500 GV. The tilt angle of the interplanetary neutral sheet varies to simulate a 22-year cycle magnetic cycle. The calculated values of solar diurnal and semidiurnal, and sidereal diurnal intensity waves are compared with observations

Erdos, G.

Kota, J.

Merenyi, E.

English

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22-YEAR CYCLE OF THE UPPER LIMITING RIGIDITY OF DALY WAVES
| ,
G. Erd_s, J. K_ta and E. Merenyl
Central Research Institute for Physics, Budapest, Hungary
Abstract. The method of calculating energy losses along regular particle
trajectories is applied to obtain the predicted cosmic ray anisotropies
from 200 to 500 GV. The tilt angle of the interplanetary neutral sheet
varies to simulate a 22-year cycle magnetic cycle. The calculated values
of solar diurnal and semidiurnal, and siderial diurnal intensity waves
are compared with observations.
I___.Introduction. Earlier we suggested (Erd_s and K_a 1979, 1980) that the
cosmic ray anisotropies observed at underground energies can be interpre-
ted in terms of regular particle motion in the Interplanetary Magnetic
Field (IMF) incorporating a wavy neutral sheet. At high rigidities, the
effects of small-scale irregularities should be negligible and, being the
dominant large-scale feature of the IMF, the wavy neutral sheet plays the
decisive role.
In this paper we investigate how cosmic ray anisotropies change
during a 22-year magnetic cycle. We consider the 200 - 500 GV range which
represents the high rigidity tail of the modulation spectrum. The state
of the heliosphere changes in a complex way during a solar cycle. From
this complexity, the only feature we consider here is the variation of
the inclination of the tilted heliospheric neutral sheet. The tilt angle
is minimal around solar minimum and increases with increasing solar
activity (Thomas and Smith 1981). As a crude approximation, we simulate
the 22-year cycle by simply changing the tilt angle.
2. The Model. The IMF model and the method of calculation are described
in detail elsewhere (Erd_s and K_a 1979, 1980, 1981). Briefly, a conven-
tional Parker spiral field is applied with a 5 gamma field strength at
the earth. The wavy neutral sheet dividing the opposite polarities is
given by
sin e = sin_- . cos(? + r) (I)
where e and _ are heliographic latitude and longitude, respectively, r
is heliocentric distance in units of AU. The tilt angle, o_, gives the
" maximum latitudinal excursion of the neutral sheet. The configuration of
away polarity above the sheet and toward polarity below the sheet will be
referred to as A > 0.
We note that equation (I) does not exactly correspond to a tilted
plane at the sun. Calculations were also carried out for a tilted plane
of 90° inclination. This case of indefinite A, where the two configura-
tions merge, will be labelled with 90*.
The theoretical results to be presented always give the full free-
space anisotropy that would he observed by an equatorial observer in the
absence of geomagnetic deflection. Calculations do not include the Com-
pton-Getting effect due to the orbital motion of the earth.
https://ntrs.nasa.gov/search.jsp?R=19850026710 2020-03-20T16:52:47+00:00Z
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3__._.Results. In this paragraph we briefly report on the daily intensity
waves predicted for 200, 300 and 500 GV at various values of the tilt
angle, eC.
The harmonic dial of the solar daily variation calculated for 200 GV
is shown in Figure 1. For comparision, Figure 2 (taken from Benko eto
al., 1984) shows the year-to-year daily vectors observed by the Budapest
underground telescopes (median energy: 180 GeV) in the period of 1976
(A>0, low solar activity) to 1983 (A<0). We find a remarkable agreement
if correction is made to the 1.5 hr geomagnetic deflection, the Compton-
Getting effect due to the earth's orbital motion, and the cos 47° = 0.68
attenuation factor due to the 47° N geografical latitude of the station.
The amplitudes of the solar daily waves calculated for 200, 300 and
500 GV are shown in Figure 3.
The predicted harmonic dial of the semidiurnal variation of 200 GV
cosmic rays is shown in Figure 4, while the calculated amplitudes are
given in Figure 5. A charge asymmetry can clearly be seen: for A > 0, an
earlier phase and a smaller amplitude is to be expected. These findings
are in general agreement with numerous observations (see, for example,
Morishita et. al., 1984).
As expected, the phase of the sidereal daily wave was always found to
be close to either 6 hr or 8 hr, depending on the polarity of the
magnetic sector. Figure 6 gives the calculated sidereal amplitudes. Our
theoretical results suggest a hard energy spectrum; the spectrum of the
sidereal variation turns out markedly harder than the solar diurnal and
semidiurnal spectra. This finding also suggests that a sidereal variation
of solar origin may still be present at rigidities where solar diurnal
and semidiurnal waves already diminish. Thus, in searching for a genuine
galactic anisotropy of cosmic rays one should be cautious in establishing
the upper rigidity limit of the heliospheric effects.
References:
' K_tao J. Somogyi, A., Varga_ A., 1984:Benk_, G., Kecskemetyj K.,
Proc. Int. Syrup.on CR Modulation, Morioka, p104
F r ,,I Iaos, G. and Kota. J., 1979: Proc. 16th ICRC, Kyoto, 4, 45
If
Erdos, G. and K_ta, J., 1980: Astrophys. Space Sci., 6_]_7,45
l! !
Erdos, G. and Kota, J., 1981: Proc. 17th ICRC, Paris, 1._O0,I05
Morishita, I.. Ueno, H., Fujii, Z., Mori, S. and Nagashima, K., 1984:
Proc. Int. Symp. on CR Modulation, Morioka, Japan, p130o
Thomas, B. T. and Smith, E. J., 1981: J. Geophys. Res., 86, 11105
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113
30tAR ]ST
200 GVj [QIJATOR
0 hr
O. -eo i 6 h"IRhr -,.
"J°l "_ Figure 1. Calculated hat-
/"
• monic dial of the solar
/_,_ daily waves of 200 GV
,_\ // cosmic rays. Numbers stand
'__ for the tilt angle, o_,
-4S ,30 * 0
in degrees (negative
- o.I
values refer to A < 0 ).
oh
sh _ lh
Figure 2. The Budapest
@_ solar daily vectors with-
_ out geomagnetic correc-
./ W tion. Numbers stand for
,/ the year of observation.
79r.._-°" _e Results are grouped
I./. according to the polarity
I_DA_ST,40_ w.[. state (triangles and
12h dashed lines refer toA>0).
_P J(%) 30tAR 2ND HARMONIC
3.0 2DO GV 7
o-----_,----'*-'*_,l
" /./ Figure 3. Calculated
// Jroosv./P _ amplitudes of the solar
- ////-- "\ : dailyvectorsof200,
.02 _/ , *_x 300 and 500 CV cosmic
/ *_ rays vs the tilt angle,
.0! oc , in degrees.
(Negative values of
., i , ' i i i" , . . , , refer to A < 0.)
30 GO 90 -00 -SO -30 e<
8H4.5-5
114
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0 hi" EQUATORIAL
,20,_ "4[,JO/ ,--,.
"_ i I \ .,_ I $ hr
• ,_ mO° .20
• -tO -_o .._"".- -so
-4$
0.05
ehr Figure 4. Same as Fig. 1.,
for semidiurnal vectors.
omp SOLAR 1ST HARI'IOtWC
f "/o;
.20 200BV
.,o / %I ....,-----."\ aoo 6v
.DE
.O2
.o/ Figure 5. Same as Fig. 3.,
I0 30 60 00 -90 ..60 -30 .10 for semidiurnal vectors.
amp l JID£REAL JUT EIARMONIC
f%)
.20
2006V
.o2 Figure 6. Same as Fig. 3.,
, , , , , , I , , . ' . -' for sidereal daily vec-
I0 30 60 00 "00 -$0 -30 ._0
,_ I:OrS.


Twenty-two-year cycle of the upper limiting rigidity of Daly waves

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