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Some time variations of cosmic rays
Journal of Atmospheric and Terrestrial Physics, 1950, Vol. 1, pp. 114 to 120. Butterworth-Springcr, London
Some time variations of cosmic rays A. R. HOGG C o m m o n w e a l t h Observatory, Mount Stromlo, Canberra
(Received 2 August 1950) ABSTRACT Cosmic r a y observations m a d e at Canberra have been e x a m i n e d for variations according to sidereal time a n d c o m p a r e d w i t h an analysis of results from other localities. The analysis w a s m a d e b y noting a n n u a l changes in the phase and amplitude of the first hmTnonic of the a p p a r e n t solar diurnal variation. A regular change of phase w i t h a period of one year m a y be caused b y a true sidereal diurnal variation. Such regular changes have been found in the results for several stations. :However these changes do n o t occur simultaneously over the globe. The changes differ in phase b y a b o u t 180 ° in the n o r t h e r n and s o u t h e r n hemispheres w i t h a tropical s t a t i o n h a v i n g an intermediate position. This suggests t h a t the variations arc not sidereal b u t are of a solar-seasonal n a t u r e . Changes in the amplitude of the solar diurnal variation display no obvious world-wide regularity in the results examined.
INTRODUCTION This paper aims at examining cosmic ray observations made at the Commonwealth Observatory, Canberra, for the presence of any sidereal variations and comparing the results with observations at other places. The question of a sidereal variation of cosmic rays has been of interest from quite early in the history of the subject as giving a possible clue to the plaee of origin of the rays [1]. Early observers claimed to have shown the existence of sidereal diurnal variations of the order of several per cent (see, for example, the summary by MIEHLNICKEL [2]). More recently, sidereal diurnal variations, if existent at all, have been found not to exceed 0.1 ~/o. FORBUS~ [3] has published the results of an examination of 595 days of observation at Cheltenham and 395 days of Huancayo results. He concluded t h a t they were insufficient to establish the existence of a sidereal variation of this smaller order. Theories of the sidereal variation of cosmic rays have developed along several lines. The earliest, based on an assumed galactic origin and a linear propagation of the rays, qualitatively suggested that a maximum intensity of the rays was to be expected when the galaxy was overhead. The failure to confirm the pronounced sidereal variation to be expected on these grounds was succeeded by a suggestion [4] t h a t small sidereal variations could be expected if the radiation was of extra-galactic origin, for its intensity would be affected with a sidereal period by that portion of the earth's motion due to galactic rotation. The rotation of the galaxy is such t h a t the earth, as part of the solar system, may be considered to be moving with respect to the remote galaxies at a velocity of 0.001c to a point, the solar apex, at c~=20 hrs 40 mins, and 3 = + 4 7 °. I f cosmic rays come uniformly from all the remote parts of the universe, then, because of the galactic motion of the earth and a type of DOPPLER effect, the intensity of the rays at that surface of the earth turned to the solar apex will be fractionally greater than on the opposite side. On an unmagnetized earth this would result in a 24 hour sidereal period with an amplitude of _+0.60/0 . Taking account of the earth's magnetism and assuming equal numbers of protons and electrons in the incident primary rays led COMPTO~ and GETTING l.
114
Some time variations of cosmic rays to give a figure of + 0.1% for the amplitude of the sidereal diurnal variation at a latitude of 45 °, the sidereal time of m a x i m u m being 20 hrs 40 mins. A later treatm e n t of the problem, given by VALLARTA,GRAEF,a n d KUSAKA [5] takes a c c o u n t more rigorously of the e a r t h ' s magnetic field, and traces the effect of various assumed compositions of the p r i m a r y radiation on the expected variations. Their results, referring to the magnetic equator, m a y be summarized t h u s : - Table 1 P r i m a r y Radiation (a) Composition
(b) Energy Spectrum
Positive 1O0°:~) ,,
E
,,
a
e -kE
Positive 50°(/j Negative 50%
E -a e-kE
Sidereal Time of Maximum
i Amplitude ' °o I
13h 20min 18h 00rain
i I
08h 40min 20h 40rain
0'17 0.24 0.06 0.19
W i t h this t h e o r y an accurate knowledge of the sidereal variation can be an i m p o r t a n t clue to the composition of the p r i m a r y radiation. 2. OBSERVATIONS The Canberra observations were made with an ionization vessel screened by l0 em of lead blocks and using a compensation method to measure the ionization current. The equipment, methods of observations and reduction are described in detail in other places [6], [7]. The observations, which were carried out over a period of five years commencing 1935, Sept. 1, were closely controlled and were corrected for variations of outdoor pressure and temperature using factors derived from a mei~hod of multiple correlation analysis. Physical reasons substantiating the validity of these corrections are given in another paper [6]. 3. APPARENT SIDEREAL VARIATIONS A direct m e t h o d of displaying sidereal variations consists in arranging the results according to sidereal time a n d averaging for the various hours. This m e t h o d is satisfactory p r o v i d e d a n y other periodic variations which m a y be present, cancel out effectively. This would not be so if a n y of the additional periodicities varied systematically in phase or amplitude. More specifically, a set of observations exhibiting only a solar diurnal variation, the amplitude or phase of which systematically varied t h r o u g h o u t the year, would, if t r e a t e d b y this m e t h o d show an a p p a r e n t sidereal variation. The a p p a r e n t sidereal variations q u o t e d in Table 2 Table 2 - - A p p a r e n t Sidereal Variations J
A
*Hafelekar (8) *Hafelekar (9) ?Capetown (10) *Canberra (6) tCheltenham (Md.) (3) CHuancayo (3)
~0.04°/o -~0.02 =t=0.05 ~0.08 =t=0-03 :~0.06
~
T
~ I I Ii
16h 12 24 20 22 5
Obs.
3 years 1 year 3 years 5 years 595 days 395 days
* Corrected for atmospheric pressure and temperature. ? Corrected for atmospheric pressure alone. 115
A. R. HOGG have been obtained b y this direct m e t h o d and accordingly, although in some: instances t h e y might be fitted in with the foregoing theoretical considerations, shoul~t: be regarded with some reservation. The table indicates only results of substantial series of observations with some form of compensation a p p a r a t u s (ionization vessel). The times of maxima, T, are given in local sidereal time (L.S.T.) appropriate to the place of observation and the amplitudes of the first harmonic are denoted b y A. The results do not fit in with the more detailed t h e o r y taking account of the earth's magnetism and t h e y disagree amongst themselves to an e x t e n t greater t h a n would be e x p e c t e d if a true sidereal variation existed. 4. ANALYSIS OF APPARENT DIURNAL VARIATIONS OF IBT Methods for examining combined periodicities have been discussed b y J. BARTELS [11] and a modification specially applicable to combined solar and sidereal variations has been used b y J. L. THOMPSON" [12]. THOMPSON discusses a ease in which two simple diurnal periodicities are combined. The first periodicity (of period T I = I solar day) is assumed to have a constant phase (~) but to have an amplitude which varies according to the expression c÷2/c cos 2rrt/T s with a period T 3 of 1 year. The second diurnal periodicity (of period T 2 - 1 sidereal day) is t a k e n as having a constant phase fl and a constant amplitude h. These periodicities are combined to give
f(t) = ( c ÷ 2 k cos
~2
.2nt
2rrt
) sin (-T~ + ~ ) ÷ h sin ( - ~ ÷ f l )
in which the time t is expressed in solar days starting with Jan. 1 = 0 . THOMPSON shows t h a t if, in such a case, the results of a series of successive days of observation over a period of one y e a r be subjected to harmonic analysis and the first harmonic for each d a y be plotted on a conventional harmonic dial t h e n the points obtained will delineate an ellipse; f u r t h e r the points on the ellipse will follow a chronological sequence in either a clockwise or an anti-clockwise direction d e p e n d e n t on the values of the amplitudes and phases. The above results m a y be s u m m e d up in the diagram fR ~ j/?l~ ~ x
a ~ - - A 8
Fig. 1--Systems of co-ordinates and vectors used in analysis of diurnal variations. OA, OB=axes for cosine and sine components of the first harmonic of the apparent solar diurnal variation, AA, AB=axes for plotting deviations of the sine and cosine components from the mean solar vector. ox, oy=axes used for.determining ellipse of annual variation. c=mean solar vector (i.e., mean of the 12 monthly vectors). lrl, ]%=vectors determining amplitude change of the solar vector of phase co. h:si(tereal vector or vector determining phase change of the solar vector of phase ft. 8 OR=the resultant vector for any time t (not drawn in).
(Figure 1) where c is the m e a n solar vector, k I and k 2 are equal vectors r o t a t i n g in opposite directions and coming simultaneously into line with c, and h is the sidereal vector. T h u s / q a n d / Q serve to alter the amplitude of c whilst h the sidereal vector controls the phase of the a p p a r e n t variation. The resultant of the vectors is the first harmonic of the diurnal variation. The c o m p o n e n t vectors for the results discussed here were d e t e r m i n e d b y first making a harmonic analysis of the a p p a r e n t solar 116
Some time variations of cosmic rays
diurnal variation as averaged for each month of the year over periods ranging from three to ten years. The results were plotted on the usual harmonic dial to show the month to month change of the first harmonic; for graphical presentation, the value for each month was smoothed by averaging it with the preceding and succeeding values. As described elsewhere [7] an ellipse was fitted to the unsmoothed points by harmonic analysis of the deviations from the mean of all the months. The elements of this ellipse led to values for the vectors k~, k~ and h. In the sequel, the vectors k 1 and k 2, which differ only in the sense of their rotation, are denoted by k. 5. OBSERVATIONS
In addition to the Canberra results (five years), sets of observations which have been published in a fashion suited for this method of analysis have been used as follows : (a) the vertical coincidence counts made by A. DUPERIER [13] at London (3 years) ; (b) the results summarized by ISABELLE LAI~'GE and S. E. FORBUSH [14] for observations with COMPTO~ " meters at Huancayo, Christchurch, Cheltenham, and Godhavn. These are later referred to as the Carnegie results. In these observations the different authors have made corrections for fluctuations of cosmic rays due to atmospheric causes by different methods. Thus for London and Canberra the observations were corrected for pressure and temperature changes using multiple correlational analysis to obtain the correction factors. These corrected results are termed IBT. The Carnegie results have been published with corrections for pressure alone (IB) and the diurnal temperature corrections are not available. An examination has been made of the Canberra values for both cases of I~ and IBT. Whilst the IB figures give a mean vector smaller and earlier than do the IeT figures there is a similarity in the annual march of the deviations fronl the mean vector and accordingly the h and k vectors do not differ greatly. One is thus encouraged to pursue the analysis of the Ix and the lZT values without making distinctions on account of the different methods of correction. The first harmonic for the Canberra results was computed from 24 hourly values averaged for each month of the year over a period of five years. The required figures for London were taken directly from DUPERIER'S paper which covered throe years of results. From the Carnegie results, periods of from seven years (Christchurch), to ten years (Huancayo), were used for the analysis. The results were. expressed in standard times for the locality concerned. For all localities except Godhavn standard times differ by less than 7 mins from the local mean times. In the case of Godhavn the standard time is 36 mins fast on the local mean time. The preliminary stage of the analysis is graphically represented in Figure 2. This shows as an inset the annual mean vector of the first harmonic for each locality together with results available for Hafelekar (IBT, 3 years). There is no obvious regularity in these vectors apart from the fact that the two highest stations Huaneayo (3350 m) and Hafelekar (2000 m) have much the earliest 24 hour wave but this relation is not maintained, for the Canberra results (800 m) show a 24 hour wave later than other lower stations. The month to month deviations from the mean vector smoothed as described above are shown separately for each station. It is seen that with the exception of 117
A. R. HOGG
Godhavn the deviations show a fairly regular monthly progression of the points. In t h e case o f t h e C a r n e g i e r e s u l t s t h e p r o g r e s s i o n is in t h e a n t i - c l o c k w i s e d i r e c t i o n , w h i l s t f o r L o n d o n a n d C a n b e r r a i t is c l o c k w i s e . T h e G o d h a v n r e s u l t s , p o s s i b l y o w i n g to the unusual situation of the station from both a meteorological and a magnetic v i e w p o i n t d o n o t g i v e a s i m p l e figure a n d i t h a s b e e n t h o u g h t i n a p p r o p r i a t e t o a t t e m p t t o fit, a n e l l i p s e t o t h e c u r v e .
&o
Che#enham(M~
AA o.1% 0.2%
Dec / ~ _ . ~ 0 . 0 ~
%
Jan'/" #vancayo ~ AA
Chm;~tchurchi'NZJ3A
+
3~o.7% .
Ca#befraI a d4y & c ~
,dA a-
U'~nberra ZST
London
~ ~ J a f , 7 /'Dec
b- Co'nberra~r c- godhavn d- ConbecraZ8 e- Chr/klchurch(#Z) d~- Che/fenhom/M~ #- #~elekar h-/luuncaavo Fig. 2--Annual changes in the first harmonic of the apparent solar diurnal variation at various stations. The points represent smoothed average values for the individual months of the year. Points for successive months are joined by lines. The diagram for London (after DUPERIEn) is arranged in groups of two months. 6. THE h AND k VECTORS
T h e ' h a n d k v e c t o r s , o b t a i n e d as d e s c r i b e d a b o v e a r e s h o w n i n T a b l e 3. T h e T a b l e also" s h o w s t h e p r o b a b l e e r r o r s f o r t h e L o n d o n , C a n b e r r a , a n d H u a n c a y o r e s u l t s .
Table 3--Summary of h and k vectors h Locality London IBT Cheltenham I/~ Huancayo I• Canberra IBT Canberra IB Christchurch IB
k
P 4-p.e. %
tmax±p.e. (L.S.T.)
P 4-p.e. °/o
0.214-0.02 0.03 -0.044-0.008 0.05 4-0.02 0.044-0.02 0.04 --
21h --22h -03.0h 4-0"lh 09.6hi0.7h 08.0h 4-0"7h 08.1h - -
0.36±0.02 0.02 -0.07 ±0"008 0.224-0-02 0.17=[=0.02 0.01 --
118
tmax4-p.e. June
--
:Nov. 1 Jan. 8 4-3d Mar. 27 ± 10d Mar. 16 ± 10d Apl. 2 1 -
Some time variations of cosmic rays
The probable errors for London are as given by DUPERIER, the Canberra errors are ultimately based on the probable error of the estimate, b y the correlational analysis method, of a single hourly value. The Huancayo probable errors are based on an average probable error of a single bi-hourly value in the average monthly diurnal variation curves. This information was not available for the other Carnegie stations and the errors were not computed. The Huancayo errors may be taken as a guide to the magnitude of the errors to be expected in the other cases. The regular progression of the points from month to month also supports belief in the reality of the variation. The h vector, though small, is present in all the sets of observations, with of course the possible exception of Godhavn. The amplitudes are approximately the same for all of the localities except London, and are several times the probable errors sho~m. The London results, obtained as they were with vertical coincidence counters are not strictly comparable with the others. The phase of the vector is expressed as the local sidereal time (L.S.T.) of occurrence of the maximum. The maximum is in the sense that the vector has its greatest effect in advancing the phase of the apparent solar diurnal variation at the indicated time. This maximum exhibits certain regularities. Thus in the two stations in the northern temperate zone the " sidereal " maximum occurs near 21 hrs L.S.T., whilst at the two stations in the southern temperate zone it occurs about 12 hours earlier. At the single equatorial station the time of maximum differs by six hours from these figures. This variation in the time of maximum strongly suggests that the phenomenon is not a true sidereal effect but is in some way under solar control and t h a t the differences between the phase should be regarded not as twelve hours or six hours of sidereal time but as six months or three months. Tim ]c vector, which directly affects the amplitude of the apparent solar diurnal variation, is of very variable amplitude and does not display the same degree of regularity shown by the h vector. Thus the vector is probably negligible in the case of Christchurch and Cheltenham but is present at Huancayo, Canberra and London. The much larger values at Canberra and London require explanation. It is these large values of k which bring about the clockwise rotation of the points in the harmonic variation diagrams for Canberra and London. 7. CONCLUSION
The examination of a considerable amount of cosmic ray data has failed to disclose the existence of any true sidereal variation in the ordinary sense. It has been shown t h a t certain changes in the phase of the apparent solar diurnal variation exhibit seasonal regularities for stations in the temperate and equatorial zones. Any explanation of the cause of the h vector of these changes is likely to be complex an~t should take into account the recent results of ELLIOT and DOLBEA~ [16] at Manchester which demonstrate differences in the diurnal variation obtained from rays arriving at different angles from the zenith. The difference between the directional counts at London and the hemispherical incidence results at the other stations dealt with here might well be related to the Manchester results. Also the appearance of Figure 7, in ELLIOT and DOLBEAR'S paper suggests t h a t the h and ~" vectors could be mainly associated with rays arriving from a particular direction, for the figure shows t h a t the counts with the equipment pointing to the north exhibited mainly a seasonal change of phase with only a small change in amplitude (cf. h vector) whilst with rays arriving from the south the seasonal change is mainly in 119
A. R. HOGG : Some time variations of cosmic rays
the amplitude (cf. k vector). This statement is of course more by way of illustrating the multiple nature of the ionization vessel results rather than to imply at the present stage an actual identification of the h and k vectors with any N and S components. REFERENCES [1] KOllLHORSTER and v o ~ SALIS; Naturwiss. 1926 14 1936. [2] MIEHLNICKEL, ]~].; " Hohenstrahlung ".
Dresden: Steinkopff 1938. [3] FORBUSH, S. E.; Phys. Rev. 1937 52 1254. [4] COMPTOSr, A. H. and (lETTING, I.; Phys. Rev. 1935 47 817. [5] VALLARTA, 3I. S., GRAEF, C. and KUSA:KA,S.; Phys. Rex,. 1939 55 ]. [6] HOGG, A. F,.; Prec. Roy. See. Lend. A 1947 192 128. [7] He(m, A. 1%.; Mere. Commonwealth Observatory No. l0 1950. [8] ILLJNG, ~,V.; Terr. Magn. 1936 41 185, [9] DEMMELMAIR, A.; Sitz. Akad. ~Vien 1937 IIa 146 643. [10] SCHONLAND, B. F., DELATITZKY and GASKELL; Terr. Magn. 1937 42 137. [ l l ] BAltTELS, J.; Terr. Magn. 1936 41 185. [12] THOMPSON, J. L.; Phys. Rev. 1939 55 l l . [13] DUPERIEt/, A.; Nature 1946 158 196. [14] ISABELLE LANOE and FORBUSH, S. E.; Res. Dept. Terr. Mag. 1948 14 182. [15] HESS, V. F. and GRAZIADEI, H. T.; Terr. Mag. 1936 41 1. [16] ELLIOT, H. and DOLBEAR, D. %V. N.; Prec. Phys. See. 1950 63 137.
120
Some time variations of cosmic rays A. R. HOGG C o m m o n w e a l t h Observatory, Mount Stromlo, Canberra
(Received 2 August 1950) ABSTRACT Cosmic r a y observations m a d e at Canberra have been e x a m i n e d for variations according to sidereal time a n d c o m p a r e d w i t h an analysis of results from other localities. The analysis w a s m a d e b y noting a n n u a l changes in the phase and amplitude of the first hmTnonic of the a p p a r e n t solar diurnal variation. A regular change of phase w i t h a period of one year m a y be caused b y a true sidereal diurnal variation. Such regular changes have been found in the results for several stations. :However these changes do n o t occur simultaneously over the globe. The changes differ in phase b y a b o u t 180 ° in the n o r t h e r n and s o u t h e r n hemispheres w i t h a tropical s t a t i o n h a v i n g an intermediate position. This suggests t h a t the variations arc not sidereal b u t are of a solar-seasonal n a t u r e . Changes in the amplitude of the solar diurnal variation display no obvious world-wide regularity in the results examined.
INTRODUCTION This paper aims at examining cosmic ray observations made at the Commonwealth Observatory, Canberra, for the presence of any sidereal variations and comparing the results with observations at other places. The question of a sidereal variation of cosmic rays has been of interest from quite early in the history of the subject as giving a possible clue to the plaee of origin of the rays [1]. Early observers claimed to have shown the existence of sidereal diurnal variations of the order of several per cent (see, for example, the summary by MIEHLNICKEL [2]). More recently, sidereal diurnal variations, if existent at all, have been found not to exceed 0.1 ~/o. FORBUS~ [3] has published the results of an examination of 595 days of observation at Cheltenham and 395 days of Huancayo results. He concluded t h a t they were insufficient to establish the existence of a sidereal variation of this smaller order. Theories of the sidereal variation of cosmic rays have developed along several lines. The earliest, based on an assumed galactic origin and a linear propagation of the rays, qualitatively suggested that a maximum intensity of the rays was to be expected when the galaxy was overhead. The failure to confirm the pronounced sidereal variation to be expected on these grounds was succeeded by a suggestion [4] t h a t small sidereal variations could be expected if the radiation was of extra-galactic origin, for its intensity would be affected with a sidereal period by that portion of the earth's motion due to galactic rotation. The rotation of the galaxy is such t h a t the earth, as part of the solar system, may be considered to be moving with respect to the remote galaxies at a velocity of 0.001c to a point, the solar apex, at c~=20 hrs 40 mins, and 3 = + 4 7 °. I f cosmic rays come uniformly from all the remote parts of the universe, then, because of the galactic motion of the earth and a type of DOPPLER effect, the intensity of the rays at that surface of the earth turned to the solar apex will be fractionally greater than on the opposite side. On an unmagnetized earth this would result in a 24 hour sidereal period with an amplitude of _+0.60/0 . Taking account of the earth's magnetism and assuming equal numbers of protons and electrons in the incident primary rays led COMPTO~ and GETTING l.
114
Some time variations of cosmic rays to give a figure of + 0.1% for the amplitude of the sidereal diurnal variation at a latitude of 45 °, the sidereal time of m a x i m u m being 20 hrs 40 mins. A later treatm e n t of the problem, given by VALLARTA,GRAEF,a n d KUSAKA [5] takes a c c o u n t more rigorously of the e a r t h ' s magnetic field, and traces the effect of various assumed compositions of the p r i m a r y radiation on the expected variations. Their results, referring to the magnetic equator, m a y be summarized t h u s : - Table 1 P r i m a r y Radiation (a) Composition
(b) Energy Spectrum
Positive 1O0°:~) ,,
E
,,
a
e -kE
Positive 50°(/j Negative 50%
E -a e-kE
Sidereal Time of Maximum
i Amplitude ' °o I
13h 20min 18h 00rain
i I
08h 40min 20h 40rain
0'17 0.24 0.06 0.19
W i t h this t h e o r y an accurate knowledge of the sidereal variation can be an i m p o r t a n t clue to the composition of the p r i m a r y radiation. 2. OBSERVATIONS The Canberra observations were made with an ionization vessel screened by l0 em of lead blocks and using a compensation method to measure the ionization current. The equipment, methods of observations and reduction are described in detail in other places [6], [7]. The observations, which were carried out over a period of five years commencing 1935, Sept. 1, were closely controlled and were corrected for variations of outdoor pressure and temperature using factors derived from a mei~hod of multiple correlation analysis. Physical reasons substantiating the validity of these corrections are given in another paper [6]. 3. APPARENT SIDEREAL VARIATIONS A direct m e t h o d of displaying sidereal variations consists in arranging the results according to sidereal time a n d averaging for the various hours. This m e t h o d is satisfactory p r o v i d e d a n y other periodic variations which m a y be present, cancel out effectively. This would not be so if a n y of the additional periodicities varied systematically in phase or amplitude. More specifically, a set of observations exhibiting only a solar diurnal variation, the amplitude or phase of which systematically varied t h r o u g h o u t the year, would, if t r e a t e d b y this m e t h o d show an a p p a r e n t sidereal variation. The a p p a r e n t sidereal variations q u o t e d in Table 2 Table 2 - - A p p a r e n t Sidereal Variations J
A
*Hafelekar (8) *Hafelekar (9) ?Capetown (10) *Canberra (6) tCheltenham (Md.) (3) CHuancayo (3)
~0.04°/o -~0.02 =t=0.05 ~0.08 =t=0-03 :~0.06
~
T
~ I I Ii
16h 12 24 20 22 5
Obs.
3 years 1 year 3 years 5 years 595 days 395 days
* Corrected for atmospheric pressure and temperature. ? Corrected for atmospheric pressure alone. 115
A. R. HOGG have been obtained b y this direct m e t h o d and accordingly, although in some: instances t h e y might be fitted in with the foregoing theoretical considerations, shoul~t: be regarded with some reservation. The table indicates only results of substantial series of observations with some form of compensation a p p a r a t u s (ionization vessel). The times of maxima, T, are given in local sidereal time (L.S.T.) appropriate to the place of observation and the amplitudes of the first harmonic are denoted b y A. The results do not fit in with the more detailed t h e o r y taking account of the earth's magnetism and t h e y disagree amongst themselves to an e x t e n t greater t h a n would be e x p e c t e d if a true sidereal variation existed. 4. ANALYSIS OF APPARENT DIURNAL VARIATIONS OF IBT Methods for examining combined periodicities have been discussed b y J. BARTELS [11] and a modification specially applicable to combined solar and sidereal variations has been used b y J. L. THOMPSON" [12]. THOMPSON discusses a ease in which two simple diurnal periodicities are combined. The first periodicity (of period T I = I solar day) is assumed to have a constant phase (~) but to have an amplitude which varies according to the expression c÷2/c cos 2rrt/T s with a period T 3 of 1 year. The second diurnal periodicity (of period T 2 - 1 sidereal day) is t a k e n as having a constant phase fl and a constant amplitude h. These periodicities are combined to give
f(t) = ( c ÷ 2 k cos
~2
.2nt
2rrt
) sin (-T~ + ~ ) ÷ h sin ( - ~ ÷ f l )
in which the time t is expressed in solar days starting with Jan. 1 = 0 . THOMPSON shows t h a t if, in such a case, the results of a series of successive days of observation over a period of one y e a r be subjected to harmonic analysis and the first harmonic for each d a y be plotted on a conventional harmonic dial t h e n the points obtained will delineate an ellipse; f u r t h e r the points on the ellipse will follow a chronological sequence in either a clockwise or an anti-clockwise direction d e p e n d e n t on the values of the amplitudes and phases. The above results m a y be s u m m e d up in the diagram fR ~ j/?l~ ~ x
a ~ - - A 8
Fig. 1--Systems of co-ordinates and vectors used in analysis of diurnal variations. OA, OB=axes for cosine and sine components of the first harmonic of the apparent solar diurnal variation, AA, AB=axes for plotting deviations of the sine and cosine components from the mean solar vector. ox, oy=axes used for.determining ellipse of annual variation. c=mean solar vector (i.e., mean of the 12 monthly vectors). lrl, ]%=vectors determining amplitude change of the solar vector of phase co. h:si(tereal vector or vector determining phase change of the solar vector of phase ft. 8 OR=the resultant vector for any time t (not drawn in).
(Figure 1) where c is the m e a n solar vector, k I and k 2 are equal vectors r o t a t i n g in opposite directions and coming simultaneously into line with c, and h is the sidereal vector. T h u s / q a n d / Q serve to alter the amplitude of c whilst h the sidereal vector controls the phase of the a p p a r e n t variation. The resultant of the vectors is the first harmonic of the diurnal variation. The c o m p o n e n t vectors for the results discussed here were d e t e r m i n e d b y first making a harmonic analysis of the a p p a r e n t solar 116
Some time variations of cosmic rays
diurnal variation as averaged for each month of the year over periods ranging from three to ten years. The results were plotted on the usual harmonic dial to show the month to month change of the first harmonic; for graphical presentation, the value for each month was smoothed by averaging it with the preceding and succeeding values. As described elsewhere [7] an ellipse was fitted to the unsmoothed points by harmonic analysis of the deviations from the mean of all the months. The elements of this ellipse led to values for the vectors k~, k~ and h. In the sequel, the vectors k 1 and k 2, which differ only in the sense of their rotation, are denoted by k. 5. OBSERVATIONS
In addition to the Canberra results (five years), sets of observations which have been published in a fashion suited for this method of analysis have been used as follows : (a) the vertical coincidence counts made by A. DUPERIER [13] at London (3 years) ; (b) the results summarized by ISABELLE LAI~'GE and S. E. FORBUSH [14] for observations with COMPTO~ " meters at Huancayo, Christchurch, Cheltenham, and Godhavn. These are later referred to as the Carnegie results. In these observations the different authors have made corrections for fluctuations of cosmic rays due to atmospheric causes by different methods. Thus for London and Canberra the observations were corrected for pressure and temperature changes using multiple correlational analysis to obtain the correction factors. These corrected results are termed IBT. The Carnegie results have been published with corrections for pressure alone (IB) and the diurnal temperature corrections are not available. An examination has been made of the Canberra values for both cases of I~ and IBT. Whilst the IB figures give a mean vector smaller and earlier than do the IeT figures there is a similarity in the annual march of the deviations fronl the mean vector and accordingly the h and k vectors do not differ greatly. One is thus encouraged to pursue the analysis of the Ix and the lZT values without making distinctions on account of the different methods of correction. The first harmonic for the Canberra results was computed from 24 hourly values averaged for each month of the year over a period of five years. The required figures for London were taken directly from DUPERIER'S paper which covered throe years of results. From the Carnegie results, periods of from seven years (Christchurch), to ten years (Huancayo), were used for the analysis. The results were. expressed in standard times for the locality concerned. For all localities except Godhavn standard times differ by less than 7 mins from the local mean times. In the case of Godhavn the standard time is 36 mins fast on the local mean time. The preliminary stage of the analysis is graphically represented in Figure 2. This shows as an inset the annual mean vector of the first harmonic for each locality together with results available for Hafelekar (IBT, 3 years). There is no obvious regularity in these vectors apart from the fact that the two highest stations Huaneayo (3350 m) and Hafelekar (2000 m) have much the earliest 24 hour wave but this relation is not maintained, for the Canberra results (800 m) show a 24 hour wave later than other lower stations. The month to month deviations from the mean vector smoothed as described above are shown separately for each station. It is seen that with the exception of 117
A. R. HOGG
Godhavn the deviations show a fairly regular monthly progression of the points. In t h e case o f t h e C a r n e g i e r e s u l t s t h e p r o g r e s s i o n is in t h e a n t i - c l o c k w i s e d i r e c t i o n , w h i l s t f o r L o n d o n a n d C a n b e r r a i t is c l o c k w i s e . T h e G o d h a v n r e s u l t s , p o s s i b l y o w i n g to the unusual situation of the station from both a meteorological and a magnetic v i e w p o i n t d o n o t g i v e a s i m p l e figure a n d i t h a s b e e n t h o u g h t i n a p p r o p r i a t e t o a t t e m p t t o fit, a n e l l i p s e t o t h e c u r v e .
&o
Che#enham(M~
AA o.1% 0.2%
Dec / ~ _ . ~ 0 . 0 ~
%
Jan'/" #vancayo ~ AA
Chm;~tchurchi'NZJ3A
+
3~o.7% .
Ca#befraI a d4y & c ~
,dA a-
U'~nberra ZST
London
~ ~ J a f , 7 /'Dec
b- Co'nberra~r c- godhavn d- ConbecraZ8 e- Chr/klchurch(#Z) d~- Che/fenhom/M~ #- #~elekar h-/luuncaavo Fig. 2--Annual changes in the first harmonic of the apparent solar diurnal variation at various stations. The points represent smoothed average values for the individual months of the year. Points for successive months are joined by lines. The diagram for London (after DUPERIEn) is arranged in groups of two months. 6. THE h AND k VECTORS
T h e ' h a n d k v e c t o r s , o b t a i n e d as d e s c r i b e d a b o v e a r e s h o w n i n T a b l e 3. T h e T a b l e also" s h o w s t h e p r o b a b l e e r r o r s f o r t h e L o n d o n , C a n b e r r a , a n d H u a n c a y o r e s u l t s .
Table 3--Summary of h and k vectors h Locality London IBT Cheltenham I/~ Huancayo I• Canberra IBT Canberra IB Christchurch IB
k
P 4-p.e. %
tmax±p.e. (L.S.T.)
P 4-p.e. °/o
0.214-0.02 0.03 -0.044-0.008 0.05 4-0.02 0.044-0.02 0.04 --
21h --22h -03.0h 4-0"lh 09.6hi0.7h 08.0h 4-0"7h 08.1h - -
0.36±0.02 0.02 -0.07 ±0"008 0.224-0-02 0.17=[=0.02 0.01 --
118
tmax4-p.e. June
--
:Nov. 1 Jan. 8 4-3d Mar. 27 ± 10d Mar. 16 ± 10d Apl. 2 1 -
Some time variations of cosmic rays
The probable errors for London are as given by DUPERIER, the Canberra errors are ultimately based on the probable error of the estimate, b y the correlational analysis method, of a single hourly value. The Huancayo probable errors are based on an average probable error of a single bi-hourly value in the average monthly diurnal variation curves. This information was not available for the other Carnegie stations and the errors were not computed. The Huancayo errors may be taken as a guide to the magnitude of the errors to be expected in the other cases. The regular progression of the points from month to month also supports belief in the reality of the variation. The h vector, though small, is present in all the sets of observations, with of course the possible exception of Godhavn. The amplitudes are approximately the same for all of the localities except London, and are several times the probable errors sho~m. The London results, obtained as they were with vertical coincidence counters are not strictly comparable with the others. The phase of the vector is expressed as the local sidereal time (L.S.T.) of occurrence of the maximum. The maximum is in the sense that the vector has its greatest effect in advancing the phase of the apparent solar diurnal variation at the indicated time. This maximum exhibits certain regularities. Thus in the two stations in the northern temperate zone the " sidereal " maximum occurs near 21 hrs L.S.T., whilst at the two stations in the southern temperate zone it occurs about 12 hours earlier. At the single equatorial station the time of maximum differs by six hours from these figures. This variation in the time of maximum strongly suggests that the phenomenon is not a true sidereal effect but is in some way under solar control and t h a t the differences between the phase should be regarded not as twelve hours or six hours of sidereal time but as six months or three months. Tim ]c vector, which directly affects the amplitude of the apparent solar diurnal variation, is of very variable amplitude and does not display the same degree of regularity shown by the h vector. Thus the vector is probably negligible in the case of Christchurch and Cheltenham but is present at Huancayo, Canberra and London. The much larger values at Canberra and London require explanation. It is these large values of k which bring about the clockwise rotation of the points in the harmonic variation diagrams for Canberra and London. 7. CONCLUSION
The examination of a considerable amount of cosmic ray data has failed to disclose the existence of any true sidereal variation in the ordinary sense. It has been shown t h a t certain changes in the phase of the apparent solar diurnal variation exhibit seasonal regularities for stations in the temperate and equatorial zones. Any explanation of the cause of the h vector of these changes is likely to be complex an~t should take into account the recent results of ELLIOT and DOLBEA~ [16] at Manchester which demonstrate differences in the diurnal variation obtained from rays arriving at different angles from the zenith. The difference between the directional counts at London and the hemispherical incidence results at the other stations dealt with here might well be related to the Manchester results. Also the appearance of Figure 7, in ELLIOT and DOLBEAR'S paper suggests t h a t the h and ~" vectors could be mainly associated with rays arriving from a particular direction, for the figure shows t h a t the counts with the equipment pointing to the north exhibited mainly a seasonal change of phase with only a small change in amplitude (cf. h vector) whilst with rays arriving from the south the seasonal change is mainly in 119
A. R. HOGG : Some time variations of cosmic rays
the amplitude (cf. k vector). This statement is of course more by way of illustrating the multiple nature of the ionization vessel results rather than to imply at the present stage an actual identification of the h and k vectors with any N and S components. REFERENCES [1] KOllLHORSTER and v o ~ SALIS; Naturwiss. 1926 14 1936. [2] MIEHLNICKEL, ]~].; " Hohenstrahlung ".
Dresden: Steinkopff 1938. [3] FORBUSH, S. E.; Phys. Rev. 1937 52 1254. [4] COMPTOSr, A. H. and (lETTING, I.; Phys. Rev. 1935 47 817. [5] VALLARTA, 3I. S., GRAEF, C. and KUSA:KA,S.; Phys. Rex,. 1939 55 ]. [6] HOGG, A. F,.; Prec. Roy. See. Lend. A 1947 192 128. [7] He(m, A. 1%.; Mere. Commonwealth Observatory No. l0 1950. [8] ILLJNG, ~,V.; Terr. Magn. 1936 41 185, [9] DEMMELMAIR, A.; Sitz. Akad. ~Vien 1937 IIa 146 643. [10] SCHONLAND, B. F., DELATITZKY and GASKELL; Terr. Magn. 1937 42 137. [ l l ] BAltTELS, J.; Terr. Magn. 1936 41 185. [12] THOMPSON, J. L.; Phys. Rev. 1939 55 l l . [13] DUPERIEt/, A.; Nature 1946 158 196. [14] ISABELLE LANOE and FORBUSH, S. E.; Res. Dept. Terr. Mag. 1948 14 182. [15] HESS, V. F. and GRAZIADEI, H. T.; Terr. Mag. 1936 41 1. [16] ELLIOT, H. and DOLBEAR, D. %V. N.; Prec. Phys. See. 1950 63 137.
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