Vol.3, No.2, 101-103 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.32014
Study of anisotropic variation of cosmic rays intensity
with solar activity
Chandra Mani Tiwari*, Devendra Sharma, Lalji Tiwari, Ajay Kumar Saxena, Dadan Prasad Tiwari
Department of Physics, A. P. S. University, Rewa (M.P.), India; *Corresponding Author:
Received 27 September 2010; revised 28 October 2010; accepted 20 November 2010.
ABSTRACT
The annual average values of amplitudes and
phases of first two harmonics of cosmic ray
anisotropy have been derived by using the
harmonic analysis technique for the period 1989
to 2004, which covers mostly the major period
of solar cycles 22 and 23. In this paper we have
taken the pressure corrected hourly data for Kiel
neutron monitor station (cut off rigidity ≈ 2.29
GV) to derive the harmonic component of cos-
mic ray daily variation and compared with the
data of Halekala neutron monitor (cut off rigidity
≈ 13.2 GV) for the period 1991 to 2004. From the
analysis it has been concluded that the diurnal
amplitude and phase of daily variation of cos-
mic rays have been found to be correlated with
solar activity. However, the semi-diurnal ampli-
tude and phase are inversely correlated with
solar activity for both the stations.
Keywords: Cosmic Ray, Anisotropic Variation,
Solar Parameter
1. INTRODUCTION
The anisotropic variations in cosmic ray intensity
which are observed only in the heliosphere can be easily
detected by the ground based detectors [1-6]. Among the
various cosmic ray intensity variations, 27-day varia-
tions, Forbush decreases and solar daily variations have
been widely investigated by number of researchers [6-8].
The large differences in the diurnal and semi-diurnal
variation of cosmic ray intensity indicate that large
changes occur in interplanetary space for continuous
periods, which are associated with the spatial distribu-
tion of cosmic ray intensity as well as geomagnetic dis-
turbances. The amplitudes and phases of first two har-
monics of cosmic ray daily variation and their average
characteristics have been particularly emphasized in a
series of papers [9-10]. Since the realization of “in situ”
observations; the convection-diffusion and the inter-
planetary magnetic field (IMF) gradient as well as cur-
vature drift phenomena in galactic cosmic ray particles;
all together manifest itself as a time variation in the
count rate of the monitor, a phenomena called solar daily
variation or cosmic ray anisotropies [11-15].
In this paper we have collected the data of diurnal and
semi-diurnal amplitudes and phases of cosmic ray ani-
sotropies for the period 1989-2004 of Kiel neutron mon-
itor (a high-latitude station) and for the period 1991-
2004 of Haleakala (a low-latitude) neutron monitor sta-
tion and correlated with sunspot number (Rz) covering
the previous solar cycle 22 and present solar cycle 23.
2. METHOD OF ANALYSIS
Generally, cosmic ray intensity shows significant ani-
sotropic variation on a day-to-day basis with most prob-
able amplitude of 0.4% to 0.5% at high and low latitude
neutron monitor stations. During the period 1989 to
2004, covering the major portion of solar cycles 22 and
23, the amplitudes and phases of the first two harmonics
of the daily variation of high energy cosmic rays have
been obtained on a day-to-day basis by using the pres-
sure corrected hourly data of neutron monitors, well dis-
tributed particularly in latitudes, to cover different cut-
off rigidities. Such data enable us to study the rigidity-
dependent variations. These observational results for
first and second (diurnal and semi-diurnal) harmonics
have been compared with the solar and geomagnetic
parameters. The hourly pressure corrected cosmic ray
neutron monitor data of Kiel (a high-latitude station with
low cut-off rigidity) and Haleakala (a low-latitude sta-
tion with high cut-off rigidity) neutron monitor stations
have been obtained from the website www.cosmic ray
neutron monitor data NGDC/WDC STP, Boulder-Cosmic
Rays. The amplitudes and Phases (time of maximum) of
the anisotropic variation of cosmic rays have been de-
rived from these data by simple harmonic analysis. The
annual average is calculated from individual daily vec-
tors after rejecting the days with universal time (UT)
associated cosmic ray variations. The daily values of

C. M. Tiwari et al. / Natural Science 3 (2011) 101-103
102
solar and geomagnetic parameters have been taken from
Solar Geophysical Data Books.
3. DISCUSSION AND CONCLUSIONS
The solar activities play a significant role in modulat-
ing the cosmic ray intensity. It modifies interplanetary
and geomagnetic parameters. The cosmic ray daily vari-
ations which are due to spinning motion of the earth, are
particularly described in this analysis. In fact, the largest
amplitudes are observed during the declining phase of
solar activity (Figures 1 and 2). In other words, we infer
that the semi-diurnal amplitude for Kiel and Haleakala
neutron monitor stations are negatively correlated with
sunspot numbers, (Figures 3 and 4) which is opposite to
that found for the diurnal amplitudes.
Nevertheless, the semi-diurnal phase i.e. the time of
maximum for Kiel and Haleakala is positively correlated
(Kiel r = 0.84, Haleakala r = 0.53) with sunspot number,
as was also the case for the diurnal phase. The results are
presented here for the recent periods.
Figure 1. The crossplot between the first harmonic (diurnal
variation) annual average amplitude (for Kiel as well as for
Haleakala in %) with sunspot numbers, for the interval
1989-2004 for Kiel and 1991-2004 for Haleakala. The best fit
lines are also shown.
Figure 2. The crossplot between the first harmonic (diurnal
variation) annual average phase values (in hours) for (Kiel/
Haleakala) neutron monitor with sunspot numbers for the in-
terval 1989-2004 for Kiel and 1991-2004 for Haleakala. The
best fit lines are also shown.
Figure 3. The crossplot between the second harmonic (semi-
diurnal variation) annual average amplitudes in (%) for Kiel/
Haleakala neutron monitor with sunspot numbers, for the in-
terval 1989-2004 for Kiel and 1991-2004 for Haleakala. The
best fit lines are also shown.
Figure 4. The crossplot between the second harmonic (semi-
diurnal variation) annual average phase values (in hours) for
Kiel as well as for Haleakala neutron monitor station with
sunspot numbers for the interval 1989-2004 for Kiel and
1991-2004 for Haleakala. The best fit lines are also shown.
1) Significant positive correlations of amplitudes
and phase for both the stations as well as for the
solar parameter (Rz) have been found for diurnal
variation. From the analysis, it is observed that
the diurnal amplitude and phase show a signifi-
cant correlation with sunspot activity.
2) The amplitude as well as the time of maximum
of the diurnal phase has been found to increase
with the increase of sunspot numbers, i.e. diurnal
amplitude as well as phase is generally high
during high solar activity period. The negative
correlations of the semi-diurnal amplitudes with
sunspot number signify that during maximum
sunspot activity periods, the semi-diurnal ampli-
tudes have least magnitudes.
3) The semi-diurnal amplitude for Kiel and Halea-
kala neutron monitor stations are negatively cor-
related with sunspot number, which is opposite
to that found for the diurnal amplitudes.
4) Nevertheless, the semi-diurnal phase i.e. the time
of maximum for Kiel and Haleakala is positively
correlated (Kiel r = 0.84, Haleakala r = 0.53)

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103
with sunspot number, as was also observed in
case of the diurnal phase.
4. ACKNOWLEDGEMENT
The authors are thankful to world Data Centers (ngdc and Omni web
centers) whose data have been used by the present investigators for the
analysis.
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