Study of High Energy Cosmic Ray Anisotropies with Solar and Geomagnetic Disturbance Index

An inter-comparison of the first two harmonics has been made so as to understand the basic reason for the occurrence of cosmic ray anisotropies during the period 1989-2004 and 1991 – 2004 using the Neutron monitor data from Kiel and Haleakala Neutron Monitoring Stations. The annual average values of the first two (daily) harmonic amplitudes and phases for neutron monitor data due to the change in the annual average magnitudes of the sunspot number and Ap index. Significant positive correlations among diurnal amplitude of both stations with Rz and Ap index have been found. The largest amplitudes are observed during the declin ing phase of solar activ ity. The semi-d iurnal amplitude for Kiel and Haleakala neutron monitor stations have been found negatively correlated with sunspot number and Ap index, while the semi-diurnal phase is positively correlated with sunspot number and Ap index. Examinations and analysis of simultaneous variations in cosmic ray anisotropies along with solar and geomagnetic disturbance index has lead us to identify possible mechanis m in producing significant correlat ions.


Introduction
The anisotropic variations in cosmic ray intensity which are observed only in the helio-sphere can be easily detected by the ground based detectors, [1][2][3][4][5][6][7][8]. The short-term as well as long-term cosmic ray modulat ion studies which have been continuing for almost more than eight decades were widely investigated by number of researchers [9][10][11][12][13]. The short-term periodic variations (diurnal and semi-diurnal) of cos mic rays intensity indicate that large changes occur in interplanetary space for continuous periods, which are associated with the spat ial d ist ribut ion o f cos mic ray in tens ity as well as geomagnet ic d isturbances. The amp litudes and phases of first two harmonics of cosmic ray daily variation and their average characteristics have been particularly emphasized by researchers [14][15][16]. The observed diurnal variations, even on a day-to-day basis, have been successfully exp lained (for more than 80% of the days) [17][18][19][20].. Since the realization of "in situ" observat ions; the convect ion -d iffusion and the interp lanet ary magnet ic field (IM F) g rad ient as well as curvature 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 an isotropies [21][22]. The geo magnetic field is usually disturbed when the magnetized solar p lasma with specific characterist ics flo ws through the v icinity of the earth. These are usually represented by various indices derived fro m the continuous records of the geomagnetic components. One such disturbance index representing the mid-latitude geomagnetic disturbances is Ap or Kp index. Ap is based on linear scale. In fact, Ap index has been found to be a good proxy for the interp lanetary disturbances, which should also be reflected in the daily variation of cosmic rays. Since it has been already seen within heleo-sphere, by earlier researchers, that solar variab ility parameters are responsible to affect directly or indirect ly the interplanetary and geomagnetic activit ies. Thus in the light of recent data and literature further analysis is needed to review this work.
In this paper we have collected the data of diurnal and semi-diurnal amp litudes and phases of cosmic ray anisotropies for the period 1989 -2004 of Kiel neutron monitor (a mid-lat itude) station and for the period 1991 -2004 of Haleakala (a low latitude) neutron monitor stations and correlated with solar index (Rz) and geo magnetic index (Ap) covering the previous solar cycle 22 and solar cycle 23.

Data and Plots
During the period 1989 to 2004, covering the major portion of solar cycles 22 and 23, the amp litudes 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 pressure corrected hourly data of neutron monitors, well distributed particularly in latitudes, to cover different cut-off rigid ities. Such data enable us to study the rig idity dependent variations. These observational results for first and second (diurnal and semi-diurnal) harmon ics have been compared with the solar and geomagnetic disturbance parameters. The hourly pressure corrected cosmic ray neutron monitor data of Kiel (a high latitude station with low cut-off rig idity)and Haleakala (a low lat itude station with high cut-off rig idity)neutron monitoring stations have been obtained from the website www.cosmic ray neutron monitor data NGDC/WDC STP, Boulder-Cosmic Rays. The amp litudes and Phases (time of maximu m) of the anisotropic variation of cosmic rays have been derived from these data by simple harmonic analysis. The annual average is calculated fro m individual daily vectors after reject ing the days with universal t ime (UT) associated cosmic ray variations. The daily values of solar and geo magnetic disturbance parameters have been taken fro m Solar Geophysical Data Books.
The (Correlation coefficient r = 0.60 for Kiel station, and r = 0.65 for Haleakala neutron monitor stations respectively. These two sets of figures very clearly show, which are also in support of our earlier findings, that both the amplitude and phase are significantly smaller during low sunspot activity period as well as during lo w Ap (quiet) periods.
In a similar manner, the correlations for the semi-d iurnal amp litude and phase with sunspot number have been depicted in figure 5 and 6 for the period 1989 -2004 fo r Kiel and 1991 to 2004 for Haleakala neutron monitors. Here again a significant positive correlation is evident for the semi-diurnal phase with sunspot number (Fig. 6, correlation coefficient r = 0.84 for Kiel station and r = 0.53 for Haleakala station). However, an indication of negative correlat ion is observed in case of semi-diurnal amplitude (Fig. 5). In figure  6 the semi-diurnal phase scale is from 8 to 15 hours, whereas the maximu m value is expected to be only 12 hours (in 360°). Since the semi-diurnal variation is distributed on both sides of the zero hour, of the lower values has been added by 12 to better represent their correlations. The negative correlations of the semi-d iurnal amp litudes with sunspot number (Kiel r = -0.57 and for Haleakala r = -0.31) signify that during maximu m sunspot activity periods the semi-diurnal amp litudes have least magnitudes.      For the case of semi-diu rnal variation of cos mic rays, figure 7 reveals that the semi-diurnal amplitude is somewhat negatively correlated with annual Ap index values. (The correlation coefficient r = -0.23 for Kiel station and r = -0.31 for Haleakala station are not very significant). Similar correspondence has been found for the phase changes, though of reverse nature. The semi-diurnal phase (time of maximu m) has been observed to shift to earlier hours during low sunspot activity periods, whereas the correlation with Ap index is also positive and quite satisfactory at least for Kiel station (figure 8; correlation coefficient r = 0.68 for Kiel station, and r = 0.34 for Haleakala station). The correlation coefficient of Kiel station is observed to be quite large as compared to low values fo r the Haleakala station. The best fit line (trend line) fo r station Kiel also reveals similar behavior as compared to only moderate increase seen at Haleakala station.

Conclusions and Discussion
The solar activities play the significant role in modulat ing the cosmic ray intensity. It modifies interplanetary and geomagnetic parameters. The cosmic ray daily variations which are due to spinning motion of the earth are particularly described in this analysis. In fact, the largest amp litudes are observed during the declin ing phase of solar activ ity. In other words, in general we infer that the semi-d iurnal amp litude for Kiel and Haleakala neutron monitor stations are negatively correlated with sunspot numbers, which is opposite to that found for the diurnal amplitudes. Nevertheless, the semi-diurnal phase i.e. the time of maximu m 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 d iurnal phase, [20] and [15]. Earlier investigators have also used the criteria that the disturbances in the interplanetary magnetic field can be generally represented by the geomagnetic disturbance index Ap. They have reported that the intensity of such a disturbance is largely associated with the changes in cosmic ray diurnal variation, [6, 7, 11and 20] the results which are in support of our results presented here for the most recent periods. There are various ways to derive the standard error of the mean. One easy and accurate method for the standard error of the mean is to derive it separately for the amplitude and phase of the harmonics of the daily variation. In fact, if the derived standard errors of the mean is also plotted for each of these observed annual average values, one would find that the standard error of the mean is quite large in the later sets of cases (about 10% of the actual vector for the semi-diurnal and about 25% for the tri-diu rnal cases). In other words, it is a pertinent way to judge the significance of the average; or it is a way out to assess the low scatter of the daily vectors of the observed amp litudes and/or the phase values. We have found that the typical values of the standard error of the mean for the diurnal variat ion calculated fro m the observed daily vectors are of the order of 0.02% but many a t imes the error has extreme values in between 0.01% to 0.04% for the diurnal variat ion during the eleven year period. Nevertheless, instead of considering vectors, if only each day values of the diurnal amp litudes are considered, then the standard error of the annual mean diurnal amp litude is observed to be ≈ 0.01% only for most of the years. That is why one can easily conclude that the annual average diurnal vectors are always significant even with more than ten-sigma level. We have also found that the semi-d iurnal annual averages are significant at five to six sig ma levels. 2. Significant positive correlations of amplitudes and phase for both the stations as well as for both the parameters (Rz and Ap) have been found for diurnal variation. Moreover, it is observed that the diurnal amplitude and phase show a significant correlation with sunspot activity and geomagnetic disturbance index Ap. The first harmonic o f daily variation was found to be maxima in the year 1989 while the minimu m values of these parameters were ach ieved in the years 1986 and 1997.
3. The amp litude as well as the time of maximu m o f the diurnal wave has been found to increase with the increase of sunspot numbers, i.e. diurnal amp litude as well as phase is generally h igh during high solar act ivity period. The negative correlations of the semi-diu rnal amp litudes with sunspot number and Ap (Kiel r = -0.57 and for Haleakala r = -0.31) signify that during maximu m sunspot activity periods the semi-d iurnal amp litudes have least magnitudes.
4. The se mi-diurnal amp litude for Kiel and Haleakala neutron monitor stations are negatively correlated with sunspot number and Ap index, which is opposite to that found for the diurnal amp litudes.
5. Nevertheless, the semi-diu rnal phase i.e. the time of maximu m for Kiel and Haleakala is positively correlated (Kiel r = 0.84, Haleakala r = 0.53) with sunspot number, as was also seen in the case 0f the diurnal phase.
6. The amp litude and phase of diurnal variat ion remain constant for the year 1992 to 1995 wh ile the amplitude and phase of semi-d iurnal variation show maxima in the years 1993 and 1994. Thus the amplitude and phase are found significantly smaller during low sunspot activity period as well as during low Ap (quiet) periods.
7. The semi-diurnal amplitude is negatively correlated with annual value of geo magnetic d isturbance index Ap (the correlation coefficient r = -0.23 for Kiel station and r = -0.31 for Haleakala station.
8. Even though the semi-diurnal time of maximu m shifts to earlier hours during low sunspot activity periods, whereas the correlation with Ap index is found positive during the period 1989 -2004, at both the stations. 9.
In the year of minimu m solar activ ity period, the diurnal amp litude as well as phase, show deep min ima on long-term basis. The amplitude of diurnal variation remains constant during the period 1992 to 1995. The amp litude of semi-diurnal variation shows maxima in the years 1993 and 1994. On a long-term basis, the semi-d iurnal amp litude shows min ima in the years 1990 and 1991while, the diurnal phase is seen to be progressively decreasing since 1989 with some recovery during the years 1989 to 2000. The phase of the semi-diurnal variation pract ically remains constant from the period 1985 to 1989. After 1991 the phase of the semi-diurnal variat ion decreases.
Based on convection-diffusion theory, the theoretical explanations for the observed changes may co me out fro m the careful examination of the solar wind parameters, which include fluctuations in the interplanetary magnetic field. For this purpose, the years 2005 and 2006 may be considered for detailed investigations, on short-term basis, as these years larger ano malies are expected.