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JETP LETTERS VOLUME 69, NUMBER 4 25 FEB. 1999

Azimuthal modulation of the event rate of cosmic-rayextensive air showers by the geomagnetic field

A. A. Ivanov,1) V. P. Egorova, V. A. Kolosov, A. D. Krasil’nikov,M. I. Pravdin, and I. E. SleptsovInstitute of Cosmophysical Research and Aeronomy, Siberian Branch of the RussianAcademy of Sciences, 677891 Yakutsk, Russia

~Submitted 29 December 1998!Pis’ma Zh. Eksp. Teor. Fiz.69, No. 4, 263–267~25 February 1999!

The effect of the Earth’s magnetic field on the azimuthal distribution ofthe number of extensive air showers is measured using data obtainedfrom many years of observations at the Yakutsk array. A uniform azi-muthal distribution of the event rates of these showers is rejected at a10214 significance level. The amplitude of the harmonic of the distri-bution depends on the zenith angle asA1'0.2 sin2u and is virtuallyindependent of the primary-particle energy, while the phase coincideswith the magnetic meridian. From the magnitude of the measured effecta correction factor for the particle density is determined which dependson the geomagnetic parameter of the shower. ©1999 American In-stitute of Physics.@S0021-3640~99!00204-2#

PACS numbers: 96.40.Pq

The trajectories of charged particles of an extensive air shower~EAS! developing inthe atmosphere from primary cosmic-ray particles are curved in the Earth’s magfield. As a result, the spatial distribution of the particles is broadened in a plane pedicular to the shower axis, in the direction of the Lorentz force. The observation ofeffect1 at the Yakutsk EAS array in strongly inclined showers with zenith angu.60° showed the presence of a pronounced asymmetry of the spatial distributiontion ~SDF! of the particles due to the deflection of the muons; this asymmetry is protional to the geomagnetic parameter of the shower, which is determined by thebetween the shower axis and the field vector:g5sinx/cos2u, wherex5cos21(cosu cosuH1sinu sinuH cos(a120)), whereuH514°, anda is the azimuthalangle. The influence of the geomagnetic field on the spatial distribution of the parhas been confirmed by observations2 for showers with zenith angles 20°,u,60°. Theresults of calculations of the expected effect in the GZK model was used to analyzshower with the highest energy detected at the Yakutsk EAS array,E0.1020 eV ~Ref. 3!,and in Ref. 4 it was shown that showers from ultrahigh energyg rays should exhibitnorth–south asymmetry. But for the latter effect there is a threshold with respect tenergy of the primaryg rays,Eg.331019 eV.

In the present letter we call attention to the fact that since the asymmetry of thedepends on the relative arrangement of the field vector and the particle velocitselecting showers with the same energy and zenith angles we should obtain mod

2880021-3640/99/69(4)/6/$15.00 © 1999 American Institute of Physics

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.

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289JETP Lett., Vol. 69, No. 4, 25 Feb. 1999 Ivanov et al.

of the EAS event rate with respect to the azimuthal angle because of the different bening of the SDF, which changes the observed energy of the primary particles anassociated primary cosmic-ray flux intensity.

Figure 1 shows the distribution of the number of EAS events with energy excee531016 eV measured at the Yakutsk array in the period 1974–1995 in the zenith-aintervals 20–30°, 40–50°, and 60–70°. The numbers of EAS events in theu intervalsthat were used in the analysis are presented in Table I.

The dependence of the amplitude and phase of the first three harmonicsdistribution on the zenith angle and energy of the primary EAS particle is shown in2 and 3. The amplitudes of the second and third harmonics correspond to the exvalue for a uniform distribution of azimuthal angles, shown by the dashed line, fomeasured number of showers in each interval. The short-dash lines show the erroridor for the expected amplitudes. The amplitude of the first harmonic is substandifferent from zero in the zenith-angle intervals Nos. 3–7 from Table I. In these inte

FIG. 1. Normalized numbers of EAS events in the zenith-angle intervals~shown on the right side! as a functionof the azimuthal angle for showers withE0.531016 eV. The dashed line shows the function 11A1cos(a2a1). The amplitude and phase of the first harmonic as functions ofu andE0 are presented in Figs. 2 and 3

TABLE I. Numbern of EAS events inu intervals.

No. 1 2 3 4 5 6 7 8

u, deg 0–10 10–20 20–30 30–40 40–50 50–60 60–70 70n 25924 69114 83226 66649 37575 16384 6609 17

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angle.:

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290 JETP Lett., Vol. 69, No. 4, 25 Feb. 1999 Ivanov et al.

a uniform distribution over the azimuthal angle can be rejected with a probability of eof less than 10214, based on the probability that for the uniform distribution the amplituof the first harmonic is greater thanA1 : P(.A1)5exp(2n•A1

2/4). The phase of the firsharmonic coincides with the magnetic meridian at Yakutsk. As a result of the smallof the magnetic field vector in the region of the array (uH514°), the first harmonic of thedistribution of azimuthal angles predominates for 20,u,70°. The picture could bedifferent for other arrays. For example, for the Tibet array, where the direction of theis inclined by 45° relative to the vertical, the first and second harmonics shoulpronounced for anglesu.50°, while for the Chakalta� array (uH588°) the secondharmonic will predominate.

To determine the effect of the array geometry on the magnitude of the modulawe constructed the azimuthal-angle distribution of the event rate in the sample of shdetected using detectors arranged in a circle 1.5 km in radius around the centerarray~azimuthally symmetric part of the setup!. We found that the amplitude and phaof the first harmonic in the sample are different from the corresponding values foinitial distribution by amounts that are certainly smaller than the statistical errors.therefore assumed the azimuthal modulation to be independent of the array geom

FIG. 2. Amplitudes of the first three harmonics and phase of the first harmonic as functions of the zenithThe vertical bars show the statistical error and the horizontal bars show the angular intervals. Notationsm —first, s — second,h — third harmonics. The dot-and-dash line shows the function 0.2 sin2u. The dashed curveshows the expected amplitudes of the harmonics for a uniform azimuthal distribution; the dotted curvethe variance of the expected amplitudes (1s).

of anpar-

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higher

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291JETP Lett., Vol. 69, No. 4, 25 Feb. 1999 Ivanov et al.

The showers at the Yakutsk array are analyzed by adjusting the parametersaxisymmetric function used to fit the charged-particle density in the detectors. Theticle densityr300 found 300 m from the shower axis according to this function is cverted to the energy of the primary particle of the EAS. Let us see howr300 varies as aresult of the geomagnetic scattering of the particles for an SDF of the formr r5cr2h,wherer is the distance from the shower axis in a plane perpendicular to the EASThe positive- and negative-particle density functions shift relative to the shower axa certain distance

r rg5c@~~r cosw1d!21r 2 sin2w!2h/21~~r cosw2d!21r 2 sin2w!2h/2#/2,

whered is the displacement of the charges andw,(0° –360°).

For d!r we obtain, averaging over a circle of radiusr 5300 m, r300g 'r300

g50(11(h•d300/2)2). Hereh'3,1 andd3005d/300 m. On average the particle densities in tdetectors are higher than the density expected with no geomagnetic field~i.e., g50). Forshowers arriving from the north the observed particle densities in the detectors arethan in the ‘‘southern’’ showers of equal energy and the same zenith angle.

When we select showers with the same densitiesr300, the primary-particle energy islower for showers arriving from the north. This decreases the corresponding EASrate, as is evident from Fig. 1, since in the range 1016,E0,1018 eV the number of

FIG. 3. Amplitudes of the first three harmonics and phase of the first harmonic versus the energy of the pparticle of an EAS. The notation is the same as in Fig. 2.

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he

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thece

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2

78

292 JETP Lett., Vol. 69, No. 4, 25 Feb. 1999 Ivanov et al.

showers detected at the Yakutsk array decreases with energy. The amplitude of thharmonic is determined by the relative change in the densityr300 measured for southernand northern showers:

2A15DJ/J5g~Dr300/r300!,

whereJ is the EAS event rate andg5 ln J/ln r300. The zenith-angle dependence of tamplitudeA1 is described well by the function 0.2sin2u ~Fig. 2!, but the variation ofgwith increasing zenith angle has the effect thatDr300/r300 cannot be described by suchsimple function. It is known5 that the maximum zenith angle separating showers in whthe electron–photon and muon components of the shower predominate at sea ler 5300 m is about 50°. Figure 2 shows that the geomagnetic effect in an EAS is obsin both of these regions.

The asymmetry of the SDF due to the geomagnetic field is determined bydisplacement of the charges. Letj be the ratio of the longest to the shortest distancorresponding to a fixed particle densityr300

g50 . Then

j'11h12

2d300

2 '11Dr300/r300

for h53. Therefore the measurements of the ‘‘ovalness’’ of the SDF can be useestimate the variation ofr300 due to the geomagnetic field. In Ref. 1 it is shown thatcoefficient of linear proportionality between the degree of asymmetry of the SDF angeomagnetic parameter of strongly inclined showers isdj/dg50.160.04. Using thisvalue in the entire region of zenith angles, we obtain the correction factors to the der300 that depend on the zenith angleu ~see Table II!.

As one can see from Fig. 3, the amplitude of the first harmonic is virtually indedent ofE0 in the energy range containing an adequate number of events. Therefoenergy dependence of the factors can be neglected.

At the Yakutsk arrayr300 is converted toE0 using a method that relatesr300 ininclined and vertical showers via a line of equal intensity in spectra at different zeangles. Since these intensities correspond to the same primary-particle energy of aand since geomagnetic corrections can be neglected in vertical showers, in estimatE0

its zenith-angle dependence is taken into account correctly but the variation of the ewith the azimuth is averaged. This produces a small systematic error, proportionalA1,in the estimate of the primary-particle energy. The absorption range ofr300 determinedaccording to the lines of equal intensity is overestimated by'10% relative to the valuefor g50.

The exponent of the EAS spectrum forr300 (r600 for showers recorded by th‘‘Grandmaster,’’ with 1 km between the detectors! increases when geomagnetic corre

TABLE II. Correction factors for the measured densityr300.

u, deg 20 30 40 50 60

r300g50/r300

g northern showers 0.94 0.92 0.88 0.82 0.7

southern showers 0.99 0.96 0.93 0.87 0.

y thegiesof

n

erva-

293JETP Lett., Vol. 69, No. 4, 25 Feb. 1999 Ivanov et al.

tions are introduced. This is because the fraction of inclined showers detected barray increases withr300. Thus for showers with zenith angles less than 60° and enerof 1018, 331018, and 1019 eV the change in the exponent in the power-law spectrumthe EAS is 0.01, 0.07, and 0.24 and the relative intensity changeDJ/J is 0.16, 0.19, and0.28, respectively.

This work was supported by the Russian Ministry of Science~Program for Supportof Unique Devices! and the Russian Fund for Fundamental Research~Grant No. 98-07-90315!.

1!e-mail: a.a.ivanov@sci.yakutia.ru

1M. N. D’yakonov, T. A. Egorov, N. N. Efimovet al., Extremely High-Energy Cosmic Rays@in Russian#,Nauka, Novosibirsk, 1991.

2T. A. Egorov, B. N. Afanasiev, M. N. Dyakonovet al., in Proceedings of the International Workshop oTechniques for the Study of EHECR, Tokyo, 1993, p. 35.

3E. E. Antonov, A. V. Glushkov, L. G. Dedenkoet al., JETP Lett.68, 185 ~1998!.4S. Karakula and W. Bednarek, in24th International Conference on Cosmic Rays, Rome, 1995, Vol. 1, p. 266;K. Kasahar, inProceedings of the International Symposium on EHECR: Astrophysics and Future Obstories,Tokyo, 1996, p. 221.

5A. A. Ivanov, Yad. Fiz.51, 1820~1990! @Sov. J. Nucl. Phys.51, 1147~1990!#.

Translated by M. E. Alferieff