Study of Galactic Cosmic Rays at high cut- off rigidity during solar cycle 23 Partha Chowdhury 1 and B.N. Dwivedi 2 1 Department of Physics, University of Calcutta & 2 DEPARTMENT of Applied Physics, Institute of Technology, Banaras Hindu University

Layout of the Talk :  Study of the time– lag between galactic cosmic rays and some solar and geomagnetic parameters during solar cycle 23 ( May, December, 2008)  We have divided solar cycle 23 into two phases viz.1] May, 1996 – december,2000 ( A > 0 epoch ) and 2] Jan December, 2008( A < 0 epoch).Then studied the time-lag between GCRs and solar parameters in both the phases Then studied the time evolution of short and intermediate –term periodicities of Galactic cosmic ray time series for complete cycle 23  Then studied the time evolution of short and intermediate –term periodicities of Galactic cosmic ray time series for complete cycle 23

 Cosmic rays (CRs) are energetic charged particles having extra solar origin and filter through our atmosphere. The portion of the CRs spectrum that reaches the Earth’s atmosphere is controlled by geomagnetic cut-off (goes to zero at the magnetic poles & ~15 GV in the equatorial region) and atmospheric cut-off (defined by altitude).  The CRs intensity, as is observed from Earth, exhibits a ~11 year variation, anti- correlated with sunspot numbers.  Galactic cosmic rays arrive at Earth after a long journey in the heliosphere, during which they are affected by the magnetic field of the solar wind. At different distances from the Sun they interact with the solar wind plasma emitted at different times in the past. Thus, current cosmic ray observations are conditioned not only by the Sun today, but yesterday and last year. Therefore, we observe a time lag between changes in solar activity and CR variations, the so-called cosmic ray hysteresis.  The amplitude of CRs modulation varies during different solar cycles depending on the strength of the solar magnetic field.  Although the study of CRs modulation within the heliosphere is advancing rapidly, yet it is a subject of intense research to assess the continuously changing behavior of the Sun and its influence on CRs propagation during odd/even solar cycles.

Data and Methods :  GCRs data : Monthly and 27-day averaged values of CRs intensity obtained from Beijing neutron monitor station (cut-off rigidity 10 GV; altitude 48 m; N; E)  The solar and geomagnetic parameters used in this study are : 1] sunspot numbers (SSN), 2] 10.7 cm solar flux & 3] Geomagnetic A p index.  We have divided cycle 23 in two parts viz. May 1996 – December 2000 (A > 0 state: solar magnetic field polarity is outward in northern hemisphere) and January 2001 – December 2008 (A < 0; solar magnetic field is outward in Polar Regions).  We have calculated the cross- correlation coefficients (CC) between solar/ geomagnetic parameters and CRs data with various time-lags (0, + 1, + 2…, months) and determined the time-lag (L) corresponding to optimum correlation in both epochs, namely A > 0 and A < 0.  The time-evolution of the main, short and intermediate term quasi-periodicities (16 – 500 days) using Morlet wavelet technique setting ω 0 = 12 and considering a red- noise background

Figure 1. Solar modulation of galactic cosmic rays, monthly sunspot number and tilt angle α of the heliospheric current sheet. Marked by A+ (A−) are times when the solar magnetic field is directed inward (outward) from the Sun in the northern polar and outward (inward) in the southern polar region, as sketched on top (Scherer et al., 2004). A gradual increase of GCRs after 2004, when the Sun was its descending phase

Sunspot no. gradually falls down after 2004 and abnormal low value during

Cross-correlation and time –lag between monthly Beijing GCRs and sunspot numbers for A > 0 phase of cycle 23.Lag varies from 0 to 10 months.GCRs are lagging behind the SSN.

Solar polarity A < 0 ; CC :0.604 – ; Lag = -1 – ( -6) months GCRs are leading in A < 0 phase.

Complete solar cycle 23, CC : Lag = -1 month; CC : L= 4 months Time –lag is small.

Solar polarity A > 0 ; CC : 0.60 – ; Lag = months GCRs are lagging behind 10.7 cm solar flux during A >0 phase.

Solar polarity A < 0 ; CC : – ; Lag = -1 to (- 4) months. GCRs are leading than 10.7 cm solar flux during A <0 phase.

Complete solar cycle 23, CC : – ; Time Lag = 2- 4 months; Time – lag is small.

Solar polarity A > 0 ; CC : ; ; Lag = 0 months GCRs and Ap are in same phase during A >0 epoch.

Solar polarity A < 0 ; CC : ; Time Lag = 0 months GCRs and Ap are in same phase during A < 0 epoch

Complete solar cycle 23, CC : 0.899; Time Lag = 0 month; Time –lag is zero.

Results and Discussion  We have detected that during solar cycle 23, the time lag between Beijing GCRs data and solar and geomagnetic indices is small. This result is contradiction to the result of Mavromichalaki et al. ( 2007 ) and Kane ( 2011) who detected a high time-lag between GCRs of low cut-off rigidity ( Moscow NM station) during this cycle. However, our result support the earlier findings of zero time –lag between Ap and GCRs ( Mavromichalaki et al. 2007)  We have detected for SSN and 10.7 cm. solar flux, the lag is –ve for A < 0 state of the heliosphere, which implies that GCRs are leading.  The current sunspot minimum, which we have seen at the end of Cycle 23, has been one of the deepest minima that we have experienced in recent times with roughly 71–73% of the days in 2008 and 2009, respectively, being entirely spotless. Apart from this, Cycle 23 has shown several other peculiarities, such as a second maximum during the declining phase that is unusual for odd- numbered cycles, a slower rise to maximum than other odd numbered cycles, and a slower than average polar reversal. During cycle 23, polar fields have been at their lowest compared to cycles 21 and 22.Perhaps the weak solar magnetic has created low barrier to the propagation of GCRs and due to these reason GCRs was leading. More observational analysis is required to explain this time –lag.

Wavelet spectrum of Beijing NM data for complete solar cycle 23 ( May, december,2008 ). Considering W 0 = 6 and lag-1 correlation coefficient is ~ 0.95.

Wavelet spectrum of Beijing NM data for complete solar cycle 23 ( May, december,2008 ). Considering W 0 = 12 and lag-1 correlation coefficient is ~ 0.95.

Observed Quasi –periodicities in Beijing NM data for cycle 23 A number of short & mid-term periodicities were detected through wavelet analysis and most of the periods are time variable. The significant periods are :  ~27 –day period is detected during different phases of cycle 23 which is similar to the solar rotational periodicities.  The periods ~9 days are also detected which is considered as the 3 rd harmonic of 27 – day period ( Sabbah & Kudela, 2011)  Other periods ~40 days, ~60 days and ~100 days were also detected. These are also detected in the data of daily sunspot number and coronal index data during cycle 23 ( Chowdhury & Dwivedi, 2011)  Rieger and near Rieger period of days.  year period. This period was found in the data of solar wind speed, sunspot area as well as in the rotation rate of tachocline.  A detailed answer about these periodicities would be available when the complete modulation mechanism of GCRs within the heliosphere would be known.