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Periodic variations of the cosmic radiation—III. The 27-day variation
Planet. Space Sci. 1973, Vol. 21, pp. 1141 to 1150. Pergmxm Press. Printed in Northern Iceland
PERIODIC
VARIATIONS OF THE COSMIC THE 27-DAY VARIATION
RADIATION-III.
W. MESSERSCHMIDT Sektion Physik der Martin-Luther-Universitlt in Halle &ale), G.D.R.
(Received inear
form 14 l)ece&er 1972)
Abstract-The relation between the 27-day variation of the cosmic radiation and of the terrestrial horizontal magnetic intensity has been investigated by means of the data recorded from 1957 to 1968. The periods have a correiation of about t0.5. The cosmic radiation is undoubtedly modulated by the Sun. A persistent wave with a periodicity of approximately 27.2 days could be proved from the data of several ion chamber and neutron monitor stations, but not underground (14m w.e.). The frequency of the daily period of the cosmic radiation shows a 27.3 day variation, too. The sum total of the relative sunspot numbers has a period length of 27.4 days. Their ~onn~ion with the cosmic radiation is discussed. 1. INTRODUCTION
The 27-day variation of the cosmic radiation is directly related to the solar activity. It influences the cosmic radiation as well as the terrestrial magnetic field. According to the report by Forbush (1966), the cosmic rays have opposite phase with respect to the magnetic character figures, and correspondingly, equal phase with the horizontal intensity. Dyring et al. (1970) investigated the k, values from 1932 to 1968 and the cosmic radiation data of the neutron monitor Deep River from 1962 to 1968. They proved a well defined repetitive effect of the 27-day period with its phase and size varying every year. The k, values showed marked overtones, in contrast to the cosmic radiation. Forbush (1966) takes the view that a statistically real persistent 27-day wave does not exist at a period length of 27-O days. Zwanzig (1961, 1965) found that from 1936 to 1956 a real persistent wave with a periodicity of 27.3 days occurred at the ion chamber stations of Huancayo, Cheltenham and Christchurch (data of Beach, Lange and Forbush, 1948,1957,1961). It is the aim of the present paper to investigate the existence of a persistent 27-day wave for the following time and the relation between the cosmic radiation, the terrestrial magnetism and the solar activity. Dorman (1963) gives a summarizing report on the 27-day period of the cosmic radiation. 2. COSMIC RAYS AND TERRRSTRIAL MAGNETISM
The data available for the time from 1957 to 1968 were the measurements of the ion chambers at Huancayo and Frederiksburg (Beach and Forbush, I969), the two ion chambers Kl at Halle at sea level, the two underground ion chambers K4 at Halle (14m w.e.) and the neutron monitors at Lindau and Halle. A list of the positions of the stations is contained in Messerschmidt (1970, 1971). First, the data were classified according to Bartels’ rotation numbers (rot. no. 1961 . . . 1852). In order to eliminate the yearly course of the ion chamber measurements, yearly means of the 27”day variation were formed with each year containing 13 or 14 Bartels’ rotations, respectively. The values of the horizontal intensity of the terrestrial magnetic field (data of the Adolf-Schmidt-Obse~ato~, Niemegk, G.D.R.) were treated the same way with regard to Bartels rotations. Since among the different cosmic ray stations, the variations obtained of the yearly means of the 27-day period agreed well, the measurements of the ion chambers as well as those of the neutron monitors were summarized, The correlation coefficients among the different cosmic ray stations are about +0+8. The correlation coefficients of the yearly means of the 27-day variation between the 1141
1142
W. MESSERSCHMIDT
cosmic radiation and the horizontal magnetic intensity are shown in Table 1. The values of the single years show a great scattering. With a mean correlation of r = +05, the ratio between the variation of the cosmic ray intensity and of the horizontal intensity of the terrestrial magnetism amounts to approximately 2*2%,/1Oy in the case of the ion chambers, and to about S%,,/lOy in the case of the neutron monitors. The extent of the effects corresponds to the ratio of the variations of both the instrument types. This ratio amounts to NM/IC = 3. The question arises whether there exists a causal relationship between the 27-day period of the cosmic radiation and the geomagnetic data, or not. The positive correlation contradicts the terrestrial latitude dependence of the cosmic rays. This dependence is a genuine TABLE 1. CORRELATION COEFFICIENTS BETWEEN THEYEARLYMEANS OF THE 27-DAY
VARIATION
OF THE COSMIC
HORIZONTAL
Year 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
MAONFTIC
RADIATION
ILH +0*33 +0.47 +0.90 +0.48 t-O.63 +0.22 +0.72 +0*10 -0.41 $0.70 to.66 +0*41 i = t-o.44
AND
OF THE
INTENSITY
N&H
f f f f f f & & f f f *
o-11 0.10 0.02 0.10 0.08 0.13 0.06 0.12 0.11 0.06 0.07 0.11
+0.02 $0.91 $0.54 +0.71 $0.20 +0.76 $0.48 -0.13 +0.52 +0.82 +0*62
f
0.1
+0*50 * 0.1
f f * f f f f f * f f
0.13 0.02 0.09 0.06 0.13 0.05 0.10 0.13 0.09 0.04 0.08
magnetic effect with the maximum of the horizontal magnetic intensity coinciding with the minimum of the cosmic radiation. On the other hand the variations of both quantities of the 27-day period are most certainly caused by the solar activity by a modulation in the interplanetary space between the Sun and the Earth. On account of the scattering of the correlation coefficients in Table 1, for comparison the correlation of the single daily means has been investigated for the years with extreme correlation coefficients of the 27-day period by means of the corrected data of the IC Kl (1959 with r = +0*9 and 1965 with r = -0.4, respectively). In both cases r amounted to the small value with equal sign r = +0*31 f 0.03 with the average slope being about 1*5%,/1Oy. 3. PERSISTENCE
ANALYSIS
According to Zwanzig (1961,1965) the 27-day variation showed a persistent wave of 27.3 days with an amplitude of O-S%,during the years from 1936 to 1965. At this, the values of the three ion chamber stations investigated-Huancayo, Christchurch and Cheltenhamagreed well with each other. The statistical foundation of such results has also been discussed by Zwanzig (1965). It is the aim of the present paper to follow the existence of the persistent wave also in the following years. Zwanzig showed the continuation in the ion chamber measurements at Halle till 1961. As mentioned above the summed daily means
PERIODIC VARIATIONS
OF THE! COSMIC RADIATION
1143
of the ion chamber stations of Huancayo, Frederiksburg and Halle, and of the neutron monitors at Lindau and Halle were classified according to Bartels’ rotation numbers, and then summarized to yearly means. Those were subjected to a harmonic analysis up to the 4th harmonic. The amplitudes of the 3rd and 4th harmonics are small, whereas those of the 2nd sometimes exceed those of the 1st one. But since the phase of the 2nd harmonic is not stable, a persistent wave of 13.5 days cannot be proved. At a period of 27.0 days, the first harmonics of the different instruments show a progressing phase shift (Fig. la). This is more clearly expressed in the summary of Fig. l(b). The slope of the calculated straight line corresponds to a period length of 27.2 days. The phase obviously varies so that a period of 27.3 days might also be attributed to the time interval from 1957 to 1963. There is a regression, however, in 1964 and 1965. The whole time is best represented by a period length of 27.2 days (exactly 27.17 days). The variations of the horizontal intensity of the terrestrial magnetism have been investigated in the same way (Fig. 2). The calculated straight line points to a periodicity of 27.2 days, too. Additionally, the phase stability of the 27-day variation of the cosmic radiation was investigated for single rotations of several years. Figure 3 shows an example of the time of the quiet Sun (ion chambers Kl during 1964) with the yearly variation, caused by the temperature effect, being eliminated. The individual amplitudes are essentially greater than those of the yearly means. Most maxima are situated near the mean (dashed line), thus pointing to the fact that the individual periods show a certain phase stability.
FIG. l(a).PLOT OF THE MEANS OF THEIONCIIAMBERSTATIONSOFHUANCAYO,FREDERIKSBURG ANDHALLE(FULLL~NE),THEMEANSOFTHEIGYNECITRONMON~TORSAT LMDAUANDHALLE (DASHEDLINE)ANDTHEIONCHAMBERSK~ ATHALLE,CORRECTED BYTHEII-YEARPERIOD AND THE SEASONAL VARIATION (DOTTED LINE). FIG. l(b). MEANS OF ALL STATIONS,THE CALCULATEDDASHEDLINECORRESWNDSTOAPERIOD LENGTH OF 27.2 DAYS.
W. MESSERSCHMIDT
1144
1957
\ \
1958
‘\
1 \
1959
\\ \\ \
I
1980
1961
‘.
hv 1 1
1963 1964
1.965 1966 1967 1969 1
18
9
27days
FIG. 2. THE~STHARMONICSOPTHEYEARLYMEANSOFTHE~~~~-DAYPERIODFORTHEHORIZONTAL INTENSITY OF THE TERRESTRIAL MAGNETISM. CLASSIFICATION ACCORDING TO BARTELS' ROTATIONS. MEASUREMEW OFTHEADOLF-SCHMIDT-OBSERVATORY AT NIEMEGK(G. D.R.). AVERAGE FIELD STRENGTH H= 18530~. THE CALCULATED DASHED LINE CORRESPONDS TO A PERIOD LENGTH OF 27.2 DAYS.
Halle
IC-Kl
Rot. 1785
1786
1787
1789
1796
1790
1797
1791 1
9
I q&fI 18 Qys
1798 27
FIG. 3. HARMONIC ANALYSIS OF THE INDIVIDUAL ~~+DAY PERIODS OF THE ION CHAMBERS Kl ATHALLEFORTHETIMEOFTHEQUIETSUN(~~~~). THEDOUBLEARROWSINDICATETHEPOSITION ANDTHESIZEOFTHE~STHARMONICS. THEFT-YEARPERIODANDTHESEASONALVARIATIONHAVE BEEN ELIMINATED.
PERIODIC VARIATIONS OF THE COSMIC RADIATION
1145
4. FREQUENCY ANALYSIS In
order to determine the exact period length, a frequency analysis was carried out by the data of the ion chambers Kl. First, the daily means were corrected by the 1l-yr and the yearly variation. They were then tabulated according to Bartels’ rotations with 27.0 days. The frequency analysis was carried out in a way so that e.g. every 271st day was omitted for a period of 27.1 days, every 136th day for 27.2 days, every 91st for 27.3 days, etc. Since the maximum amplitude of 1*2x,, occurred at a period length of 272 days, the values of 27.17 and 27.25 days were included in the analysis. As Fig. 4 shows, the period Halle
1
K-K1
9
18 days
27
FIG. 4. FREQUENCY ANALYSISOFTHE~~-DAY PERIOD 0~ THE COSMIC RADIATION AT HALLEION CHAMBERS Kl. 1957-1968. THE Il-YR PERIOD AND THE SEASONAL VARIATION HAVE BEEN ELATED. ~HEOOLJBLE ARROWS~DICATE~E SiZEOFTHE 1ST HARMONIC.
length of2717 days yielded the maximum amplitude of 1*25x,. For comparison, the yearly means were again treated by a harmonic analysis with the periodicity of 27.17 days (Fig. 5). Most of the values are near the average (dashed line). The statistical fluctuation amounts to only S = &I25 days. 5. THE 27-DAY
PERIOD
UNDERGROUND
The ion chambers K4 at Halle measure the cosmic radiation underground (14m w.e.). In order to check the presence of a 27-day period at this high energy radiation (maximum energy 75 GeV), the data of the years from 1957 to 1967 were analyzed in the way described. A systematic course of the phase position of the 1st harmonic could not be observed. The correlation between the yearly means of the 27-day period at K4 and the ion chambers Kl was determined to be Y= +O-74 at maximum. On an average, however, the correlation coefficients amount to only P = +0*25 so that there does not really exist a connection over a longer time interval. Under 40m w.e., Kdta et al. (1970) did not identify a 27-day variation, either. The authors suppose Zwanzig (1965) to have mentioned a 27-day period underground. But for his investigations, Zwanzig only used the ion chambers Kl at sea level. Accordingly, a 27-day variation could not be proved underground. 5
1146
W. MESSERSCHMIDT Halle
IC-Kl
1967 1968 1
9
18 days
27
FIG. 5. THE IST HARMONICS FOR THE SINGLE YEARS AT A PERIOD LENGTH OF 27.17 DAYS AT HALLE ION CHAMBERS Kl. 1957-1968. CORRECTIONS ARE MADE AS IN FIG. 4. THE DASHED LINE SHOWS THE MEAN OF THE 1ST HARMONICS. 6. THE
27-DAY
VARIATION
OF THE DAILY PERIOD
By means of a few years data, the author (Messerschmidt, 1960,1963) proposed the idea that the daily period can show a 27-day variation, too (for a review, see Zwanzig, 1966). Zwanzig et al. (1966) analyzed the data of Huancayo from 1936 to 1955 with a period length of 27.3 days and found a real period with two maxima. The present paper is based on the material of all instruments at Halle from 1957 to 1967. These are the three ion chamber couples (Messerschmidt, 1958, 1960), and additionally, an IGY neutron monitor since 1961. The data of each instrument were treated in the following way: the statistical fluctuations of the b&hourly data were reduced by a progressing smoothing procedure over five values at a time. The values so obtained were plotted in diagrams. A daily period was attributed to the individual days if at least two of the three, or, since 1961, three of the four instruments showed sizes of the daily periods greater than 2x,,. Thus the following classification of days was carried out: (1) days with a daily period, (2) days where only one instrument showed a daily period and (3) days without any daily period. Only classes 1 and 3 were used. Selected days were again classified according to Bartels’ rotations and subjected to the frequency analysis. Here the 1st harmonic most clearly emerges with a periodicity of 27.3 days. The results of Fig. 6 have been smoothed over three days, except in the case of line 4 where they have been smoothed over five days. The curve of the zero days in line 5 (i.e. days without any daily period) is also best fitted to the 27*3-day period with opposite sign. According to Zwanzig (1966), the 2nd harmonic is relatively
PERIODIC VARIATIONS OF THE COSMIC RADIATION
I
In
1147
1
62 56 5L 60
._ 1
9
16
FIG. 6. THE27-DAYVARlATIONOFTHEDAILYPERIOD MRNTSAT
HALLE,l957-1967.
LlNt?S1-3:
HARMONIC
ONTHEDETERMIN
Y
days 27
OFTTiECOSMICRADIATION. ATIONOFTHEDAYSWITHADAILY
ANALYSIS WlTH A :zD
&LINSTRUPERIODSEE
LENGTH OF 27.0, 27.17 AND 27.3 DAYS.
3 DAYS. LmB 4: PERIOD LENGTH OF 27.3 DAYS. SMOOTHING OVER 5 DAYS. LINE 5: ZERODAYS(WITHOUT ADAILYPERIOD)W~THAPERIOD LENGTHOF~~.~ DAYS.SMCHYIHSMOOTHING OVER
nISTHENUMRER
OF
ING OVER 3 DAYS. A DAILY PERIOD (LINES 1-4)AND WITHOUT A DAILY PERIOD (LINE 5). DEMONSTRATE THE 1ST HARMONIC, THE THIN ONES THE 2ND.
DAYSWlTH
THE THICK DOUBLE ARROWS
prominent. The results do not contradict the 27*2-day period, established above, since the years before 1960, with a period of 27.3 days (Fig. l), occur with a slightly enhanced weight because of the procedure used. 7. DISCUSSION
The existence of a persistent wave of the 27-day variation of the cosmic radiation, observed by Zwanzig (1965) for the years from 1936 to 1956, could be proved up to 1968. It is most likely that the 27-day period is caused by the Sun activity modulating the cosmic radiation. In the evaluation of the data, periods with large Forbush decreases were not excluded. As has been proved, their exclusion altered the amplitude and phase of the yearly means of the 27-day period only alittle. Zwanzig et al. (1972) showed that the Forbush decreases essentially contribute to the 27-day period. The Forbush decreases, too, exhibit a persistent variation of 27.3 days during the investigated time interval from 1936 to 1956, with the number of the Forbush decreases having an opposite phase with respect to the cosmic ray intensity. Zwanzig et al. (1972) assume that active zones in the range of 530”
W. MESSERSCHMIDT
1148
of latitude away from the Sun equator cause the 27-day variation. In this connection they determined persistent active longitudes on the Sun. It is difficult to specify a source of the 27-day variation of the cosmic radiation. The solar wind, however, cannot be considered to cause it. According to Gosling and Bame (1972), its structure is not steady. Observations of the solar wind speed suggest that a wide variety of solar latitudes contribute to the solar wind measured near the Earth. Recurrence periods ranging from about 27 to 29 days have been observed. Wilcox and Wilborn (1970, 1972) investigated the interplanetary magnetic field during the time from 1963 to 1968. They ascertained that the rotation period of the field varies between 27.0 and 28.0 days. In this connection, the relative sunspot numbers (Kiepenheuer) were examined with respect to a persistent 27-day variation from 1957 to 1968. By the method described above the yearly means of the 27-O-day period were formed according to Bartels’ rotations. The slope of the sunspot numbers resulting from the eleven year period was eliminated. Figure 7 shows the 1st harmonics after single years have been analysed. The average proceeding of the phase per year amounts to about five days, which corresponds to a period length of 27.4 days for the sum total of all sunspots (calculated straight line in Fig. 7). Freon (1960) also established a period length of 27.4 days for the sunspot rotation and for the soft nucleonic component of the cosmic radiation during the years from 1956 to 1959, where a persistent wave existed. Since the rotation speed of the Sun surface decreases from the Equator, the 27.4-day period is adequate to a mean heliographic latitude of less than 20 degrees (Wilcox, 1972). For the time from 1957 to 1968 the correlation between the 27-day variation of the sunspot numbers on the one hand and of the cosmic radiation and of the terrestrial 1957 1956 1959 1960 1961 aR=lOl
1963 1964 1965 1966 1967 1966 1
9
18
FIG. 7. THE 1s~ HARMONICS OF THE YEARLY MEANS OFTHE~~+DAYVARIATION EORTHERELATIVE SUNSPOT NUMBERS. 1957-1967. CLASSIFICATION ACCORDING TO BARTELS' ROTATIONS. THE CALCULATED DASHED LINE CORRESPONDS TO A PERIOD LENGTH OF 27.4 DAYS.
PERIODIC
VARIATIONS
OF THE COSMIC
RADIATION
1149
horizontal magnetic field on the other hand has been investigated (Table 2). As the period length of the cosmic rays amounts to 27.2 days and that of all sunspot numbers to 27.4 days, a sliding phase shift arises, which will be expressed in the behaviour of the correlation coefficients with a periodic change of the signs. Thus it is difficult to decide the signs of the correlation coefficients to be either positive or negative. TABLE 2. 27*0-DAY PERIOD. BEHAVIOUROF THE RELATIVESUNSPOTNUMBERS AND THE CORRELATION COEFFICIENTSBETWEENTHESUNSPOTNUMBERS,THECOSMICRADIATION,ANDTHETERRESTRU\LHORlZONTALMAGNE~C INTENSITY
Correlation Year
R
2a
Rel. fluctuation
1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
181 185 160 106 51 34 23 10 15 42 89 96
20 45 50 35 25 16 13 9 12 20 27 30
0.11 0.24 0.31 0.33 0.49 0.47 0.59 o-90 0.80 0.48 0.30 0.31
coefficients r of the 27.0&y
period
R-IC
R-NM
R-CR
R-H
-0.50 $0.35 $0.03 -0.59 -0.10 -0.51 -0.62 -0.45 $0.65 $0.55 i-0.51 -0.66
f0.20 +0*24 -0.85 -0.12 -0.24 -0.79 -0.77 + 0.40 to.46 to.37 -0.86
-0.50 -to*27 $0.14 -0.72 -0.11 -0.37 -0.70 -0.61 $0.52 + 0.50 +0*44 -0.76
-0.16 +0.21 +0*26 -0.38 -0.35 -0.28 -0.75 -0-53 -0.47 +0*76 +@55 -0.51
R = daily mean of the relative sunspot numbers. 2u = variation of the 27-day period of the relative sunspot numbers. IC = the summed ion chambers. NM = the summed neutron monitors. CR = cosmic radiation, the mean of IC and NM. H = terrestrial horizontal magnetic field.
Since the 27-day periods of the cosmic radiation and of the terrestrial horizontal magnetic field are correlated positively (Table 1) and since, besides, their correlations with the relative sunspot numbers (Table 2) have the same signs, the 27-day period of the cosmic radiation and the relative sunspot numbers must be correlated positively. As a persistent variation of the cosmic rays could be proved from 1936 to 1968 with a period length between 27.2 and 27.3 days, the source of this modulation effect is supposed on the Sun to be in a relatively small area between about f15 degrees of heliographic latitude which is turned towards the Earth. REPERENCES Adolf-Schmidt-Obs. Terr. Magn. Niemegk. Jahrbuch 1957-1968. Akademie, Berlin. BEACH,L. and FOWJSH, S. E. (1961). Researches Dep. terr. Magn. Carnegie Inst. Wash. 21, Pub]. 175. BEACH, L. and FORBUSH, S. E. (1969). Researches Dep. terr. Magn. Carnegie Inst. Wash. 22, Pub]. 175. DORMAN, L. I. (1963). Progress in Elementary Particle and Cosmic Ray Physics, Vol. VII, pp. 98-107. North-Holland, Amsterdam. DYRINO, E., HAUSRA, H. and KANDEGAL, B. (1970). Actaphys. hung. 29, Suppl. 2,209-214. FORBUSH,S. E. (1966). Encyclopaedia ofPhysics (Ed. S. Fltigge), Vol. 49/l, Chapter D, IV, pp. 198-204. Springer, Berlin. GCWNG, J. T. and BAME, S. J. (1972). J. geophys. Res. 77, 12-26. KDZPENHEUER, K. 0. Map ofthe Sun. Freiburg Br. F.G.R. K~TA, J., SOMOOYI,A., VA~AS, G. and VARGA, A. (1970). Actaphys. hung. 29, Suppl. 2,215-217. LANGE, I. and FORBUSH, S. E. (1948). Researches Dep. terr. Magn. Carnegie Inst. Wash. 14, Publ. 175.
1150
W. MESSERSCHMIDT
LANGE, I. and FORBUSH,S. E. (1957). Researches Dep. terr. Magn. Carnegie Inst. Wash. 20, Publ. 175. MESSERSCHMIDT, W. (1958). Exp. Tech. Phys. 6,145-156. MESSERSCHMIDT, W. (1960). Z. Naturf. lSA, 470-484. MESSERSCHMIDT, W. (1963). Z. Naturf. 18A, 66-78. MESSERSCHMIDT, W. (1970). Planet. Space Sci. l&509-524. MESSERSCHMIDT, W. (1971). Planet. Space Sci. 19,1025-1040. W-x, J. M. (1972). Cosmic Plasma Physics (Ed. K. Schiudler), pp. 157-164. Plenum, New York. WILCOX, J. M. and W-RN, D. S. (1970). J. geophys. Res. 75,6366-6370. WILCOX, J. M. and W-RN, D. S. (1972). J. geophys. Res. 77,751-756. ZWANZIO, W. (1961). 2. Nat@ 16A, 1237-1239. ZWANZIG, W. (1965). Nuovo Cim. 4OA, 65-75. ZWANZIC+, W., FIEBER,W. and FLOHR, B. (1966). Ann. Phys. 17,127-131. ZWANZIG, W. and L&ER, G. (1973). To be published in Wiss. Z. Univ. Halle 22. ZWANZIQ,W., FRANK, A. and KUMMERT,S. (1973). Wiss. Z. Univ. Haile 22, 99-104.
PERIODIC
VARIATIONS OF THE COSMIC THE 27-DAY VARIATION
RADIATION-III.
W. MESSERSCHMIDT Sektion Physik der Martin-Luther-Universitlt in Halle &ale), G.D.R.
(Received inear
form 14 l)ece&er 1972)
Abstract-The relation between the 27-day variation of the cosmic radiation and of the terrestrial horizontal magnetic intensity has been investigated by means of the data recorded from 1957 to 1968. The periods have a correiation of about t0.5. The cosmic radiation is undoubtedly modulated by the Sun. A persistent wave with a periodicity of approximately 27.2 days could be proved from the data of several ion chamber and neutron monitor stations, but not underground (14m w.e.). The frequency of the daily period of the cosmic radiation shows a 27.3 day variation, too. The sum total of the relative sunspot numbers has a period length of 27.4 days. Their ~onn~ion with the cosmic radiation is discussed. 1. INTRODUCTION
The 27-day variation of the cosmic radiation is directly related to the solar activity. It influences the cosmic radiation as well as the terrestrial magnetic field. According to the report by Forbush (1966), the cosmic rays have opposite phase with respect to the magnetic character figures, and correspondingly, equal phase with the horizontal intensity. Dyring et al. (1970) investigated the k, values from 1932 to 1968 and the cosmic radiation data of the neutron monitor Deep River from 1962 to 1968. They proved a well defined repetitive effect of the 27-day period with its phase and size varying every year. The k, values showed marked overtones, in contrast to the cosmic radiation. Forbush (1966) takes the view that a statistically real persistent 27-day wave does not exist at a period length of 27-O days. Zwanzig (1961, 1965) found that from 1936 to 1956 a real persistent wave with a periodicity of 27.3 days occurred at the ion chamber stations of Huancayo, Cheltenham and Christchurch (data of Beach, Lange and Forbush, 1948,1957,1961). It is the aim of the present paper to investigate the existence of a persistent 27-day wave for the following time and the relation between the cosmic radiation, the terrestrial magnetism and the solar activity. Dorman (1963) gives a summarizing report on the 27-day period of the cosmic radiation. 2. COSMIC RAYS AND TERRRSTRIAL MAGNETISM
The data available for the time from 1957 to 1968 were the measurements of the ion chambers at Huancayo and Frederiksburg (Beach and Forbush, I969), the two ion chambers Kl at Halle at sea level, the two underground ion chambers K4 at Halle (14m w.e.) and the neutron monitors at Lindau and Halle. A list of the positions of the stations is contained in Messerschmidt (1970, 1971). First, the data were classified according to Bartels’ rotation numbers (rot. no. 1961 . . . 1852). In order to eliminate the yearly course of the ion chamber measurements, yearly means of the 27”day variation were formed with each year containing 13 or 14 Bartels’ rotations, respectively. The values of the horizontal intensity of the terrestrial magnetic field (data of the Adolf-Schmidt-Obse~ato~, Niemegk, G.D.R.) were treated the same way with regard to Bartels rotations. Since among the different cosmic ray stations, the variations obtained of the yearly means of the 27-day period agreed well, the measurements of the ion chambers as well as those of the neutron monitors were summarized, The correlation coefficients among the different cosmic ray stations are about +0+8. The correlation coefficients of the yearly means of the 27-day variation between the 1141
1142
W. MESSERSCHMIDT
cosmic radiation and the horizontal magnetic intensity are shown in Table 1. The values of the single years show a great scattering. With a mean correlation of r = +05, the ratio between the variation of the cosmic ray intensity and of the horizontal intensity of the terrestrial magnetism amounts to approximately 2*2%,/1Oy in the case of the ion chambers, and to about S%,,/lOy in the case of the neutron monitors. The extent of the effects corresponds to the ratio of the variations of both the instrument types. This ratio amounts to NM/IC = 3. The question arises whether there exists a causal relationship between the 27-day period of the cosmic radiation and the geomagnetic data, or not. The positive correlation contradicts the terrestrial latitude dependence of the cosmic rays. This dependence is a genuine TABLE 1. CORRELATION COEFFICIENTS BETWEEN THEYEARLYMEANS OF THE 27-DAY
VARIATION
OF THE COSMIC
HORIZONTAL
Year 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
MAONFTIC
RADIATION
ILH +0*33 +0.47 +0.90 +0.48 t-O.63 +0.22 +0.72 +0*10 -0.41 $0.70 to.66 +0*41 i = t-o.44
AND
OF THE
INTENSITY
N&H
f f f f f f & & f f f *
o-11 0.10 0.02 0.10 0.08 0.13 0.06 0.12 0.11 0.06 0.07 0.11
+0.02 $0.91 $0.54 +0.71 $0.20 +0.76 $0.48 -0.13 +0.52 +0.82 +0*62
f
0.1
+0*50 * 0.1
f f * f f f f f * f f
0.13 0.02 0.09 0.06 0.13 0.05 0.10 0.13 0.09 0.04 0.08
magnetic effect with the maximum of the horizontal magnetic intensity coinciding with the minimum of the cosmic radiation. On the other hand the variations of both quantities of the 27-day period are most certainly caused by the solar activity by a modulation in the interplanetary space between the Sun and the Earth. On account of the scattering of the correlation coefficients in Table 1, for comparison the correlation of the single daily means has been investigated for the years with extreme correlation coefficients of the 27-day period by means of the corrected data of the IC Kl (1959 with r = +0*9 and 1965 with r = -0.4, respectively). In both cases r amounted to the small value with equal sign r = +0*31 f 0.03 with the average slope being about 1*5%,/1Oy. 3. PERSISTENCE
ANALYSIS
According to Zwanzig (1961,1965) the 27-day variation showed a persistent wave of 27.3 days with an amplitude of O-S%,during the years from 1936 to 1965. At this, the values of the three ion chamber stations investigated-Huancayo, Christchurch and Cheltenhamagreed well with each other. The statistical foundation of such results has also been discussed by Zwanzig (1965). It is the aim of the present paper to follow the existence of the persistent wave also in the following years. Zwanzig showed the continuation in the ion chamber measurements at Halle till 1961. As mentioned above the summed daily means
PERIODIC VARIATIONS
OF THE! COSMIC RADIATION
1143
of the ion chamber stations of Huancayo, Frederiksburg and Halle, and of the neutron monitors at Lindau and Halle were classified according to Bartels’ rotation numbers, and then summarized to yearly means. Those were subjected to a harmonic analysis up to the 4th harmonic. The amplitudes of the 3rd and 4th harmonics are small, whereas those of the 2nd sometimes exceed those of the 1st one. But since the phase of the 2nd harmonic is not stable, a persistent wave of 13.5 days cannot be proved. At a period of 27.0 days, the first harmonics of the different instruments show a progressing phase shift (Fig. la). This is more clearly expressed in the summary of Fig. l(b). The slope of the calculated straight line corresponds to a period length of 27.2 days. The phase obviously varies so that a period of 27.3 days might also be attributed to the time interval from 1957 to 1963. There is a regression, however, in 1964 and 1965. The whole time is best represented by a period length of 27.2 days (exactly 27.17 days). The variations of the horizontal intensity of the terrestrial magnetism have been investigated in the same way (Fig. 2). The calculated straight line points to a periodicity of 27.2 days, too. Additionally, the phase stability of the 27-day variation of the cosmic radiation was investigated for single rotations of several years. Figure 3 shows an example of the time of the quiet Sun (ion chambers Kl during 1964) with the yearly variation, caused by the temperature effect, being eliminated. The individual amplitudes are essentially greater than those of the yearly means. Most maxima are situated near the mean (dashed line), thus pointing to the fact that the individual periods show a certain phase stability.
FIG. l(a).PLOT OF THE MEANS OF THEIONCIIAMBERSTATIONSOFHUANCAYO,FREDERIKSBURG ANDHALLE(FULLL~NE),THEMEANSOFTHEIGYNECITRONMON~TORSAT LMDAUANDHALLE (DASHEDLINE)ANDTHEIONCHAMBERSK~ ATHALLE,CORRECTED BYTHEII-YEARPERIOD AND THE SEASONAL VARIATION (DOTTED LINE). FIG. l(b). MEANS OF ALL STATIONS,THE CALCULATEDDASHEDLINECORRESWNDSTOAPERIOD LENGTH OF 27.2 DAYS.
W. MESSERSCHMIDT
1144
1957
\ \
1958
‘\
1 \
1959
\\ \\ \
I
1980
1961
‘.
hv 1 1
1963 1964
1.965 1966 1967 1969 1
18
9
27days
FIG. 2. THE~STHARMONICSOPTHEYEARLYMEANSOFTHE~~~~-DAYPERIODFORTHEHORIZONTAL INTENSITY OF THE TERRESTRIAL MAGNETISM. CLASSIFICATION ACCORDING TO BARTELS' ROTATIONS. MEASUREMEW OFTHEADOLF-SCHMIDT-OBSERVATORY AT NIEMEGK(G. D.R.). AVERAGE FIELD STRENGTH H= 18530~. THE CALCULATED DASHED LINE CORRESPONDS TO A PERIOD LENGTH OF 27.2 DAYS.
Halle
IC-Kl
Rot. 1785
1786
1787
1789
1796
1790
1797
1791 1
9
I q&fI 18 Qys
1798 27
FIG. 3. HARMONIC ANALYSIS OF THE INDIVIDUAL ~~+DAY PERIODS OF THE ION CHAMBERS Kl ATHALLEFORTHETIMEOFTHEQUIETSUN(~~~~). THEDOUBLEARROWSINDICATETHEPOSITION ANDTHESIZEOFTHE~STHARMONICS. THEFT-YEARPERIODANDTHESEASONALVARIATIONHAVE BEEN ELIMINATED.
PERIODIC VARIATIONS OF THE COSMIC RADIATION
1145
4. FREQUENCY ANALYSIS In
order to determine the exact period length, a frequency analysis was carried out by the data of the ion chambers Kl. First, the daily means were corrected by the 1l-yr and the yearly variation. They were then tabulated according to Bartels’ rotations with 27.0 days. The frequency analysis was carried out in a way so that e.g. every 271st day was omitted for a period of 27.1 days, every 136th day for 27.2 days, every 91st for 27.3 days, etc. Since the maximum amplitude of 1*2x,, occurred at a period length of 272 days, the values of 27.17 and 27.25 days were included in the analysis. As Fig. 4 shows, the period Halle
1
K-K1
9
18 days
27
FIG. 4. FREQUENCY ANALYSISOFTHE~~-DAY PERIOD 0~ THE COSMIC RADIATION AT HALLEION CHAMBERS Kl. 1957-1968. THE Il-YR PERIOD AND THE SEASONAL VARIATION HAVE BEEN ELATED. ~HEOOLJBLE ARROWS~DICATE~E SiZEOFTHE 1ST HARMONIC.
length of2717 days yielded the maximum amplitude of 1*25x,. For comparison, the yearly means were again treated by a harmonic analysis with the periodicity of 27.17 days (Fig. 5). Most of the values are near the average (dashed line). The statistical fluctuation amounts to only S = &I25 days. 5. THE 27-DAY
PERIOD
UNDERGROUND
The ion chambers K4 at Halle measure the cosmic radiation underground (14m w.e.). In order to check the presence of a 27-day period at this high energy radiation (maximum energy 75 GeV), the data of the years from 1957 to 1967 were analyzed in the way described. A systematic course of the phase position of the 1st harmonic could not be observed. The correlation between the yearly means of the 27-day period at K4 and the ion chambers Kl was determined to be Y= +O-74 at maximum. On an average, however, the correlation coefficients amount to only P = +0*25 so that there does not really exist a connection over a longer time interval. Under 40m w.e., Kdta et al. (1970) did not identify a 27-day variation, either. The authors suppose Zwanzig (1965) to have mentioned a 27-day period underground. But for his investigations, Zwanzig only used the ion chambers Kl at sea level. Accordingly, a 27-day variation could not be proved underground. 5
1146
W. MESSERSCHMIDT Halle
IC-Kl
1967 1968 1
9
18 days
27
FIG. 5. THE IST HARMONICS FOR THE SINGLE YEARS AT A PERIOD LENGTH OF 27.17 DAYS AT HALLE ION CHAMBERS Kl. 1957-1968. CORRECTIONS ARE MADE AS IN FIG. 4. THE DASHED LINE SHOWS THE MEAN OF THE 1ST HARMONICS. 6. THE
27-DAY
VARIATION
OF THE DAILY PERIOD
By means of a few years data, the author (Messerschmidt, 1960,1963) proposed the idea that the daily period can show a 27-day variation, too (for a review, see Zwanzig, 1966). Zwanzig et al. (1966) analyzed the data of Huancayo from 1936 to 1955 with a period length of 27.3 days and found a real period with two maxima. The present paper is based on the material of all instruments at Halle from 1957 to 1967. These are the three ion chamber couples (Messerschmidt, 1958, 1960), and additionally, an IGY neutron monitor since 1961. The data of each instrument were treated in the following way: the statistical fluctuations of the b&hourly data were reduced by a progressing smoothing procedure over five values at a time. The values so obtained were plotted in diagrams. A daily period was attributed to the individual days if at least two of the three, or, since 1961, three of the four instruments showed sizes of the daily periods greater than 2x,,. Thus the following classification of days was carried out: (1) days with a daily period, (2) days where only one instrument showed a daily period and (3) days without any daily period. Only classes 1 and 3 were used. Selected days were again classified according to Bartels’ rotations and subjected to the frequency analysis. Here the 1st harmonic most clearly emerges with a periodicity of 27.3 days. The results of Fig. 6 have been smoothed over three days, except in the case of line 4 where they have been smoothed over five days. The curve of the zero days in line 5 (i.e. days without any daily period) is also best fitted to the 27*3-day period with opposite sign. According to Zwanzig (1966), the 2nd harmonic is relatively
PERIODIC VARIATIONS OF THE COSMIC RADIATION
I
In
1147
1
62 56 5L 60
._ 1
9
16
FIG. 6. THE27-DAYVARlATIONOFTHEDAILYPERIOD MRNTSAT
HALLE,l957-1967.
LlNt?S1-3:
HARMONIC
ONTHEDETERMIN
Y
days 27
OFTTiECOSMICRADIATION. ATIONOFTHEDAYSWITHADAILY
ANALYSIS WlTH A :zD
&LINSTRUPERIODSEE
LENGTH OF 27.0, 27.17 AND 27.3 DAYS.
3 DAYS. LmB 4: PERIOD LENGTH OF 27.3 DAYS. SMOOTHING OVER 5 DAYS. LINE 5: ZERODAYS(WITHOUT ADAILYPERIOD)W~THAPERIOD LENGTHOF~~.~ DAYS.SMCHYIHSMOOTHING OVER
nISTHENUMRER
OF
ING OVER 3 DAYS. A DAILY PERIOD (LINES 1-4)AND WITHOUT A DAILY PERIOD (LINE 5). DEMONSTRATE THE 1ST HARMONIC, THE THIN ONES THE 2ND.
DAYSWlTH
THE THICK DOUBLE ARROWS
prominent. The results do not contradict the 27*2-day period, established above, since the years before 1960, with a period of 27.3 days (Fig. l), occur with a slightly enhanced weight because of the procedure used. 7. DISCUSSION
The existence of a persistent wave of the 27-day variation of the cosmic radiation, observed by Zwanzig (1965) for the years from 1936 to 1956, could be proved up to 1968. It is most likely that the 27-day period is caused by the Sun activity modulating the cosmic radiation. In the evaluation of the data, periods with large Forbush decreases were not excluded. As has been proved, their exclusion altered the amplitude and phase of the yearly means of the 27-day period only alittle. Zwanzig et al. (1972) showed that the Forbush decreases essentially contribute to the 27-day period. The Forbush decreases, too, exhibit a persistent variation of 27.3 days during the investigated time interval from 1936 to 1956, with the number of the Forbush decreases having an opposite phase with respect to the cosmic ray intensity. Zwanzig et al. (1972) assume that active zones in the range of 530”
W. MESSERSCHMIDT
1148
of latitude away from the Sun equator cause the 27-day variation. In this connection they determined persistent active longitudes on the Sun. It is difficult to specify a source of the 27-day variation of the cosmic radiation. The solar wind, however, cannot be considered to cause it. According to Gosling and Bame (1972), its structure is not steady. Observations of the solar wind speed suggest that a wide variety of solar latitudes contribute to the solar wind measured near the Earth. Recurrence periods ranging from about 27 to 29 days have been observed. Wilcox and Wilborn (1970, 1972) investigated the interplanetary magnetic field during the time from 1963 to 1968. They ascertained that the rotation period of the field varies between 27.0 and 28.0 days. In this connection, the relative sunspot numbers (Kiepenheuer) were examined with respect to a persistent 27-day variation from 1957 to 1968. By the method described above the yearly means of the 27-O-day period were formed according to Bartels’ rotations. The slope of the sunspot numbers resulting from the eleven year period was eliminated. Figure 7 shows the 1st harmonics after single years have been analysed. The average proceeding of the phase per year amounts to about five days, which corresponds to a period length of 27.4 days for the sum total of all sunspots (calculated straight line in Fig. 7). Freon (1960) also established a period length of 27.4 days for the sunspot rotation and for the soft nucleonic component of the cosmic radiation during the years from 1956 to 1959, where a persistent wave existed. Since the rotation speed of the Sun surface decreases from the Equator, the 27.4-day period is adequate to a mean heliographic latitude of less than 20 degrees (Wilcox, 1972). For the time from 1957 to 1968 the correlation between the 27-day variation of the sunspot numbers on the one hand and of the cosmic radiation and of the terrestrial 1957 1956 1959 1960 1961 aR=lOl
1963 1964 1965 1966 1967 1966 1
9
18
FIG. 7. THE 1s~ HARMONICS OF THE YEARLY MEANS OFTHE~~+DAYVARIATION EORTHERELATIVE SUNSPOT NUMBERS. 1957-1967. CLASSIFICATION ACCORDING TO BARTELS' ROTATIONS. THE CALCULATED DASHED LINE CORRESPONDS TO A PERIOD LENGTH OF 27.4 DAYS.
PERIODIC
VARIATIONS
OF THE COSMIC
RADIATION
1149
horizontal magnetic field on the other hand has been investigated (Table 2). As the period length of the cosmic rays amounts to 27.2 days and that of all sunspot numbers to 27.4 days, a sliding phase shift arises, which will be expressed in the behaviour of the correlation coefficients with a periodic change of the signs. Thus it is difficult to decide the signs of the correlation coefficients to be either positive or negative. TABLE 2. 27*0-DAY PERIOD. BEHAVIOUROF THE RELATIVESUNSPOTNUMBERS AND THE CORRELATION COEFFICIENTSBETWEENTHESUNSPOTNUMBERS,THECOSMICRADIATION,ANDTHETERRESTRU\LHORlZONTALMAGNE~C INTENSITY
Correlation Year
R
2a
Rel. fluctuation
1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
181 185 160 106 51 34 23 10 15 42 89 96
20 45 50 35 25 16 13 9 12 20 27 30
0.11 0.24 0.31 0.33 0.49 0.47 0.59 o-90 0.80 0.48 0.30 0.31
coefficients r of the 27.0&y
period
R-IC
R-NM
R-CR
R-H
-0.50 $0.35 $0.03 -0.59 -0.10 -0.51 -0.62 -0.45 $0.65 $0.55 i-0.51 -0.66
f0.20 +0*24 -0.85 -0.12 -0.24 -0.79 -0.77 + 0.40 to.46 to.37 -0.86
-0.50 -to*27 $0.14 -0.72 -0.11 -0.37 -0.70 -0.61 $0.52 + 0.50 +0*44 -0.76
-0.16 +0.21 +0*26 -0.38 -0.35 -0.28 -0.75 -0-53 -0.47 +0*76 +@55 -0.51
R = daily mean of the relative sunspot numbers. 2u = variation of the 27-day period of the relative sunspot numbers. IC = the summed ion chambers. NM = the summed neutron monitors. CR = cosmic radiation, the mean of IC and NM. H = terrestrial horizontal magnetic field.
Since the 27-day periods of the cosmic radiation and of the terrestrial horizontal magnetic field are correlated positively (Table 1) and since, besides, their correlations with the relative sunspot numbers (Table 2) have the same signs, the 27-day period of the cosmic radiation and the relative sunspot numbers must be correlated positively. As a persistent variation of the cosmic rays could be proved from 1936 to 1968 with a period length between 27.2 and 27.3 days, the source of this modulation effect is supposed on the Sun to be in a relatively small area between about f15 degrees of heliographic latitude which is turned towards the Earth. REPERENCES Adolf-Schmidt-Obs. Terr. Magn. Niemegk. Jahrbuch 1957-1968. Akademie, Berlin. BEACH,L. and FOWJSH, S. E. (1961). Researches Dep. terr. Magn. Carnegie Inst. Wash. 21, Pub]. 175. BEACH, L. and FORBUSH, S. E. (1969). Researches Dep. terr. Magn. Carnegie Inst. Wash. 22, Pub]. 175. DORMAN, L. I. (1963). Progress in Elementary Particle and Cosmic Ray Physics, Vol. VII, pp. 98-107. North-Holland, Amsterdam. DYRINO, E., HAUSRA, H. and KANDEGAL, B. (1970). Actaphys. hung. 29, Suppl. 2,209-214. FORBUSH,S. E. (1966). Encyclopaedia ofPhysics (Ed. S. Fltigge), Vol. 49/l, Chapter D, IV, pp. 198-204. Springer, Berlin. GCWNG, J. T. and BAME, S. J. (1972). J. geophys. Res. 77, 12-26. KDZPENHEUER, K. 0. Map ofthe Sun. Freiburg Br. F.G.R. K~TA, J., SOMOOYI,A., VA~AS, G. and VARGA, A. (1970). Actaphys. hung. 29, Suppl. 2,215-217. LANGE, I. and FORBUSH, S. E. (1948). Researches Dep. terr. Magn. Carnegie Inst. Wash. 14, Publ. 175.
1150
W. MESSERSCHMIDT
LANGE, I. and FORBUSH,S. E. (1957). Researches Dep. terr. Magn. Carnegie Inst. Wash. 20, Publ. 175. MESSERSCHMIDT, W. (1958). Exp. Tech. Phys. 6,145-156. MESSERSCHMIDT, W. (1960). Z. Naturf. lSA, 470-484. MESSERSCHMIDT, W. (1963). Z. Naturf. 18A, 66-78. MESSERSCHMIDT, W. (1970). Planet. Space Sci. l&509-524. MESSERSCHMIDT, W. (1971). Planet. Space Sci. 19,1025-1040. W-x, J. M. (1972). Cosmic Plasma Physics (Ed. K. Schiudler), pp. 157-164. Plenum, New York. WILCOX, J. M. and W-RN, D. S. (1970). J. geophys. Res. 75,6366-6370. WILCOX, J. M. and W-RN, D. S. (1972). J. geophys. Res. 77,751-756. ZWANZIO, W. (1961). 2. Nat@ 16A, 1237-1239. ZWANZIG, W. (1965). Nuovo Cim. 4OA, 65-75. ZWANZIC+, W., FIEBER,W. and FLOHR, B. (1966). Ann. Phys. 17,127-131. ZWANZIG, W. and L&ER, G. (1973). To be published in Wiss. Z. Univ. Halle 22. ZWANZIQ,W., FRANK, A. and KUMMERT,S. (1973). Wiss. Z. Univ. Haile 22, 99-104.