S H O R T - T I M E V A R I A T I O N S OF SOLAR N E U T R I N O S AND

SOLAR ACTIVITY CYCLE

(Research Note)

P R O B H A S R A Y C H A U D H U R I

Department of Applied Mathematics, Calcutta University, Calcutta 700009, lndia

(Received 30 December, 1985; in revised form 27 June, 1986)

Abstract. It is shown from the statistical analysis of the sunspot data and solar neutrino data that both the data exhibits 5, 10, 15, 20, 25, and 30 months period and these periods may be g-mode oscillation of the core associated with the solar activity,

In this note we wish to point out the short-time variations of the solar neutrino data and its relation with the sunspot data. For this we smooth the solar neutrino data (Rowley et aL, 1984) by weighted moving average of order 5 by

O = ZOett , (1) 2;t i

where Q; is the value of Q (37mr) in the ith run and t i is the duration of the session (see Figure 1).

Fig, I.

2.0

1"5 E o

o

LtJ

i '0

Z 0

u 0.~ 0 0

42 49

~ " :~ I t I "~

10.0

8,0 tO F--

5.0 ~ O Z

4.0 ~- uJ Z

r~ 2.0

0 cn

0"0

I I I I 1 I I I 1 I I 1 I

1970 71 72 7:5 7'4 75 76 7'7 78 79 80 81 82 37Ar production rate observed in the solar neutrino experiment 1970-1982 and the weighted moving

average data (dashed curve).

Solar Physics 106 (1986) 421-424. �9 1986 by D. Reidel Publishing Company

I

'9~ t 1 7 o ~

422 PROBHAS RAYCHAUDHURI

n" LU OO

Z

I.- 0 13- co Z

o')

b.l

_3 W n~

150

IlO

9 0

7 0

5 0

3 0

Fig. 2.

'o F I I I i I I I I I I i I

I g 7 0 71 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 8 0 81 Ig82

The monthly mean values of the relative sunspot numbers for the year 1970-1982. The moving average for 5 months is indicated by the dot (o) points.

Similarly we smooth the relative sunspot data from 1970-1982 by moving averages of order 5 and is plotted in Figure 2.

From Figure 1 of solar neutrino data its appears that solar neutrino data from 1970-1976 are varying approximately with a period of about 30 months (if we consider the troughs), the length of solar neutrino data from 1976-1978 is about 25 months and that from 1978-1979 is about 20 months. Thus within the 11-yr period (Rauchaudhuri, 1984a) the solar neutrino detector pulses also with the period of 20, 25, and 30 months. Using superposed epoch analysis we have studied the solar neutrino data. Regions of minimum and maximum 37At production rate were selected for every superposing and the parameter t is calculated according to the formula (Kenney and Keeping, 1951)

t = e \N1 + N 2 / ' (2)

SHORT-TIME VARIATIONS OF SOLAR NEUTRINOS AND SOLAR ACTIVITY CYCLE 423

where

~2 _ N1 S~ + N2 S~

N I + N 2 - 2

The behaviour of t reveals peaks with maximum at 15, 20, 25, and 30 months where tma • > 3 and thus 15, 20, 25, and 30 months variation of (solar neutrino) flux is statistically meaningful. The maximum value of t implies that at a confidence level not less than 99.5~o, the 37Ar production rate in the detector pulsate with periods 15, 20, 25, and 30 months with depth of modulation 0.06, 0.13, 0.14, 0.05, respectively. Since 15, 20, 25, and 30 months periods are commensurable there will be numbers, in particular a smallest number, 5 months period which is an exact multiple of all the periods. This should be the period of the series. Here also we have used superposed epoch analysis to study statistically the variation of solar neutrino flux with 5 and 10 months and have found t = 3.82 and t = 3.20 with depth of modulation 0.03 and 0.036, respectively. Haubold and Gerth (1983) have found also periods of 6.3, 8.8, 15.2, 19.6, 25.6, 35.7, 58.8, 100 months in the solar neutrino flux data by power spectrum analysis. Gavrin et al. (1982) have found 20, 25 months variation in solar neutrino flux data by superposed epoch analysis. Sukurai (1979) has shown only 25 months period both in sunspot data and in solar neutrino data.

The 5, 10, 15, 20, 25, and 30 months variation of solar neutrino flux data must be related to some features of solar phenomena, because such variations with periods may produce some phenomena on the solar photosphere which are casually connected with those taking place in the core of the Sun. One of these must be the variation of the sunspot numbers because these are produced by instability of the solar core (Raychaudhuri, 1971, 1972). It was clear from Raychaudhuri's (1971, 1972)work that apart from temperature fluctuation in the core, p-mode (Raychaudhuri, 1984b, 1985) and g-mode oscillations of the solar core are also active in the sunspot cycle.

We expect that in the moving average sunspot data (Figure 2) there may also be 5, 10, 15, 20, 25, and 30 months variation. We used here also superposed epoch analysis to the moving average for relative sunspot numbers. Regions of minimum and maximum sunspot numbers were selected for every superposing and parameter t was calculated by formula (2). The behaviour oft reveals peaks at 5, 10, 15, 20, 25, and 30 months where tma x > 3 with depth of modulation 0.004, 0.008, 0.023, 0.033, 0.047, and 0.04, respec- tively, and thus 5, 10, 15, 20, 25, and 30 months variations of sunspot numbers are statistically meaningful. Specially, 5 and 10 months variations of relative sunspot numbers are very clear from April 1975 to June 1979. Thus 5 months period is clearly a period of the series in both solar neutrino data and sunspot data. So 5, 10, 15, 20, 25, and 30 months periods exist in both the sunspot data and the solar neutrino flux data. The pulsation periods of 5, 10, 15, 20, 25, and 30 months in the solar neutrino data and sunspot data are due to the g-mode oscillation of the core of the Sun during the solar activity cycle (Gavrin et aL, 1982; Haubold and Gerth, 1983).

It may be mentioned here that Wolff (1983) has also indicated the possibility of periods 5, 10.44, 15.71, 18.95 months in his extensive analysis of monthly mean sunspot data.

424 PROBHAS RAYCHAUDHURI

Rieger et al. (1984) observed a 5 months periodicity in the occurrence of hard solar flares during February 1980-September 1983. They have suggested that this type of energetic solar flares may have its origin in the deeper layer of the Sun. Recently, Ichimoto et aL (1985) studied the solar flare data from January 1965 to February, 1984 and have found 5 and 17 months periodicities in the solar flare activity. This period may be related to the time-scale for the storage and/or the escape of the magnetic field in the solar convection zone. From our analysis of 1970-1982 solar neutrino data it appears that solar neutrino data pulsate with almost a 5-month period, therefore, we suggest 5-month core oscillation (g-mode) of the Sun may be responsible for the occurrence of hard solar flares. Thus the solar neutrino data may also provide important information of solar flare production (Raychaudhuri, 1971).

References

Gavrin, V. N., Kopysov, Yu. S., and Hakeev, N. T.: 1982, JETP Letters 35, 491. Haubold, H. J. and Gerth, E.: 1983, Proc. 18th ICRC, SP6-2, Bangalore, India. Ichimoto, K., Kubota, J., Suzuki, M., Toshimura, I., and Kurokawa, H.: 1985, Nature 316, 422. Kenney, J. F. and Keeping, E. S.: 1951, Mathematics of Statistics, Vol. 11, 2nded., D. Van Nostrand

Company, Ind., New York. Raychaudhuri, P.: 1971, Astrophys. Space Sci 13, 231. Raychaudhuri, P.: 1972, Astrophys. Space Sci 18, 425. Raychandhuri, P.: 1984a, Solar Phys. 93, 397. Raychaudhuri, P.: 1984b, Astrophys. Space Sci 119, 000. Raychaudhuri, P.: 1985a, Phys. Teacher 27, 20. Rieger, E., Share, G. H., Forrest, D. J., KanBach, G., Reppin, C., and Chupp. E. L.: 1984, Nature 312, 623. Rowley, J. K., Cleveland, B., and Davis, R.: 1985, Am. lnst. Phys. Conf. Proc. 126, 1. Sakurai, K.: 1979, Nature 279, 146. Wolff, C. L.: 1983, Astrophys. J. 264, 667.