Evidence of geomagnetic effect on the azimuthal distribution of EAS in the ARGO-YBJ experiment

Available online at www.sciencedirect.com

Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 274–278 www.elsevier.com/locate/npbps

Evidence of geomagnetic effect on the azimuthal distribution of EAS in the ARGO-YBJ experiment S.N. Sbano on behalf of the ARGO-YBJ Collaboration Dipartimento di Matematica e Fisica "E. De Giorgi", Università del Salento, Lecce, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Lecce, Lecce, Italy E-mail: [email protected]

Abstract The geomagnetic field affects the trajectories of the secondary charged particles of extensive air showers, causing their lateral distribution to be stretched. Thus both the density of the secondaries near the shower axis and the trigger efficiency of detector arrays decrease. The effect depends on the direction of the showers, thus involving the measured azimuthal distribution. This work concerns the non-uniformity of the azimuthal distribution studied by means of ARGO-YBJ data. The modulation is deeply investigated for different zenith angles. The influence of the geomagnetic field and detector effects are studied by means of a Monte Carlo simulation. Keywords: Geomagnetic Field, Cosmic Rays, Extensive Air Showers, Azimuthal Distribution

1. Introduction High energy cosmic rays (CRs) generate extensive air showers (EAS) in the atmosphere and the geomagnetic field (GMF) affects the propagation of the EAS charged particles bending their trajectories. The lateral distribution of the shower particles results stretched mainly along the direction perpendicular to the GMF and the EAS charged components are separated. This effect depends on the direction of the shower and thus introduces an azimuthal modulation. Indeed the asymmetries in the density and charge distribution of the particles modify the trigger efficiency of EAS detector. The azimuthal modulation was observed at the Yakutsk array for EAS with energy above 50 PeV [1]. ARGO-YBJ [2] is a full-coverage array located in Tibet (P.R. of China) at 4300 m above sea level (90◦ 31 50 E, 30◦ 06 38 N). The granularity of the detector allows a detailed threedimensional reconstruction of the shower front with high temporal and spatial resolution. The trigger threshold is ∼1 TeV for primary CR, well beyond the rigidity cutoff of the well known East-West effect. 0920-5632/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysbps.2013.05.044

The GMF effect on the ARGO-YBJ data was studied and simulated [3]. Here those studies are updated and compared with a large data sample. 2. Influence of the geomagnetic field on extensive air shower A simple model has been developed in order to parameterize the GMF effect. EAS charged particles are affected by the Lorentz force in the plane (bending plane)  Along the GMF perpendicular to the magnetic field B. direction the force is null and the velocity is constant. Therefore, the main result of the GMF action is a shift of the particles in the bending plane. On the shower front the East-West shift results: d=

qB 2p



h cosθ

2 sinξ

(1)

where q is the electric charge, p is the particle momentum, h the vertical height of the particle path,  and p. θ the zenith angle and ξ is the angle between B

275

sinξ =



A0 + A1 cos(φ − φB ) + A2 cos[2(φ − φB )] (2)

where φ is the EAS azimuth angle and φB = 71.89◦ the GMF azimuth in the ARGO-YBJ reference frame. The coefficients are:   3 A0 = sin2 θ + sin2 θB 1 − sin2 θ 2 1 (3) A1 = − sin2θB sin2θ 2 1 A2 = − sin2 θB sin2 θ 2 where θB = 46.4◦ is the GMF zenith angle.

99.4 μ T 8

6

49.7 μ T

4

2

0.0 μ T 0 0

0.2

0.4

0.6

0.8

1

sin ξ

Figure 1: Simulation. Positive-negative core distance versus

sinξ for different magnetic fields. A linear fit is superimposed.

The GMF effect has been studied looking at negative and positive EAS components. Eq. (1) is validated by the fact that the distance between positive-particles core and negative-particles one increases linearly with sinξ and B (Fig. 1). It has been also verified that the shower stretching does not affect the reconstruction of the direction, but acts on the trigger efficiency. Fig. 2 shows clearly that the percentage of surviving1 simulated events linearly decreases as magnetic field or sin2 ξ increase. The values of sin2 ξ as function of θ and φ are shown in Fig. 3. percentage (%)

This equation does not describe fully the GMF effect because the particle time of flight is modified by the shift in the bending plane, then also a shift in the GMF direction is foreseen. The model should take into account all the particles in the EAS, each one with its values of q, p, θ and h. In short a Monte Carlo simulation is necessary and it will be presented in the next section. Besides hereafter ξ is the angle between the magnetic field and the primary direction. Far from the core the shower density is enhanced by the GMF effect proportionally to d2 and then to sin2 ξ [1, 4]. Close to the core a decrease is expected and consequently a reduction of the ARGO-YBJ trigger efficiency depending in some way on B and ξ. The angle is given by the equation:

positive-negative core distance (m)

S.N. Sbano / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 274–278

18

0.0 μT

17.5 17 16.5

3. Simulation

49.7 μT

16

Beams of primary protons have been simulated with the same primary energy (3 TeV), zenith angle (45◦ ) and interaction height (19 km), but with different azimuth angles (φ = 71.5◦ , 115.5◦ , 161.5◦ and 251.5◦ ) in order to get different values of sinξ (0.02, 0.51, 0.87 and 1 respectively). Three intensities of the magnetic field have been used: 0.0, 49.7 (actual GMF at the ARGO-YBJ site) and 99.4 nT (twice the actual GMF). The CORSIKA code [5] has been used to reproduce the shower development and a GEANT3-based code [6] to simulate the detector response. The primary trajectory has been projected at the center of the carpet. At first the detector acceptance has been studied by simulating the showers in absence of the GMF. The result is an azimuthal modulation of ∼ 0.3% with phase 90◦ and periodicity 180◦ due to analysis cuts (see section 4) and trigger condition (Nhit  20 in a time window of 420 ns).

15.5 15 14.5 14

99.4 μT 0

0.2

0.4

0.6

0.8

1 sin2 ξ

Figure 2: Simulation. Percentage of surviving events versus

sin2 ξ for different magnetic fields. A linear fit is superimposed.

4. Data analysis The following analysis refers to events collected in 8 days (October 7th-14th, 2010). The array has been 1 Events

fulfilling trigger and analysis requirements.

276

S.N. Sbano / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 274–278

3

×10

sin2 ξ

0.9 0.8

1

0.7

0.8

events

1

250

0.6 0.6

0.4

0.2

0.3

0 90 θ ( 80 70 °)

15°

0.5

0.4

0.1 50

40

30

20

10

0 0

50

300 350) φ (° 200 250 150 100

30°

200

θ=35°

θ=10°

0.2

60

25°

20°

150

0

40° 45°

100

50

5° 50°

Figure 3: Value of sin2 ξ versus local angular coordinates (θ and

φ) of the arrival direction of a charged particle in the ARGOYBJ reference frame. ξ is the angle between the magnetic field at YangBaJing and the primary direction.

55° 0 0

0.2

0.4

0.6

0.8

1 sin2 ξ

Figure 4: Profiles of the number of events versus sin2 ξ for dif-

carefully time-calibrated [7] because also small errors in the angle reconstruction introduce large systematic errors in the azimuthal distribution, especially for small zenith angles. In order to get a reliable reconstruction of the shower direction, the following cuts have been applied: shower core reconstructed inside a square of 40 × 40 m2 at the center of the carpet, EAS zenith angle lower than 60◦ . These selections lead to a data set of ∼ 347 millions of events. Taking into account the results on trigger efficiency given by Monte Carlo simulation (Fig. 2), it can be expected that the number of collected EAS in a fixed θrange depends on φ by: Nθ = Nθ,MAX (1 − ηsin ξ) 2

ferent values of θ. The number of events is calculated in angular windows of 5◦ × 5◦ in θ and φ. The value of sin2 ξ is calculated for θ and φ window central values. The ranges of sin2 ξ vary for different values of θ (see Fig. 3).

bution can be fitted by a double harmonic function:    dN = N0 1 + g1 cos (φ − φ1 ) + g2 cos 2 (φ − φ2 ) (5) dφ The fit results are (only statistical errors): g1 = (1.5071 ± 0.0076)% φ1 = 72.75◦ ± 0.29◦ g2 = (0.5458 ± 0.0076)% φ2 = 87.00◦ ± 0.40◦ χ2 /nd f = 641.9/67

(4)

where Nθ,MAX is the number of events (depending on the zenith angle θ) if the GMF effect is null and η is a coefficient depending only on B value. Eq. (4) has been verified and confirmed by data. Indeed Fig. 4 shows the profiles of the number of collected EAS versus sin2 ξ for different value of θ. It is clear the linear decrease of collected events with respect to the increase of sin2 ξ, i.e. with respect to the increase of the GMF effect. By means of this analysis it is possible to estimate the maximum event loss (η) due to GMF. For ARGO-YBJ detector η is ∼ 4% and, as expected, does not show a dependence on θ. Integrating on the zenith angle the azimuthal distri-

The high value of χ2 /nd f (9.6) is mainly due to some inefficiencies at φ ∼ n90◦ (n = 0, 1, 2, 3) which do not invalidate this analysis and are not discussed here. The fit improves adding negative terms to take into account these inefficiencies (χ2 /nd f becomes 1.7). According to the model it is expected: φ1 = φ2 = φB g1 ∝ −A1 ∝ sin2θ

(6)

g2 ∝ −A2 ∝ sin2 θ if the origin of the modulation is only geomagnetic. Indeed the measured phase φ1 is compatible with the GMF azimuth. Also the dependence of g1 on sin2θ is verified (Fig. 5). This is not the case for coefficient and phase

277

S.N. Sbano / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 274–278

3

1635

3

× 10

events

events

events

3

× 10 1640

2480

× 10 810

2460

800

2440

790

1630 1625 1620

780

2420

1615

γ

770

β

2400

α

1610

760

1605 0

50

100

150

200

250

300

2380 0

350

azimuth angle (°)

50

100

150

200

250

300

350

azimuth angle (°)

0

50

100

150

200

250

300

350

azimuth angle (°)

1

g coefficient (%)

Figure 6: Azimuthal distribution in different θ-ranges (0◦ - 20◦ , 20◦ - 40◦ and 40◦ - 60◦ ). Fit with function (7) is superimposed.

k1 (%) k2B (%) φ1 (◦ ) gα2A (%) gβ2A (%) gγ2A (%) φ2A (◦ ) χ2 /nd f

2.2 2 1.8 1.6 1.4 1.2 1 0.8

χ2 / ndf

0.6

k1

35.19 / 14 2.057 ± 0.01242

0.4 0.2 0 0

10

20

30

40

50

2.078 ± 0.010 0.68 ± 0.20 72.18 ± 0.28 0.139 ± 0.015 0.341 ± 0.038 1.236 ± 0.083 92.1 ± 1.8 1043/209

60

zenith angle (°)

Figure 5: Coefficient g1 versus θ. The fit g1 = k1 sin2θ is super-

Table 1: Results of the fit with function (7) of the distributions in Fig. 6 (only statistical errors).

imposed (only statistical errors).

of the second harmonic. The anomaly can be solved taking into account the detector effect observed in the simulation without magnetic field. Therefore the second harmonic can be split in two components: one (2B) is due to the GMF, the other one (2A) to the detector acceptance. Three different data sets have been selected on the basis of the zenith angle in order to disentangle these two effects. The φ-distributions of the subsamples (see Fig. 6) have been fitted all together with a single function: dN = Ni {1 + k1 sin2θi cos (φ − φ1 ) dφ   + k2B sin2 θi cos 2 (φ − φ1 )   + gi2A cos 2 (φ − φ2A )

(7)

where the coefficients of the magnetic component are deduced from eq.s (6), the phase φ1 is used for first and magnetic second harmonic and the index i = α, β, γ indicates the subsamples. Then the fit parameters are k1 , k2B , φ1 , gα2A , gβ2A , gγ2A and φ2A . The new fit is quite good (χ2 /nd f = 1043/209 and it decreases taking into account the inefficiencies at n 90◦ ). The parameter values

(see Tab. 1) confirm that the azimuthal distribution depends on magnetic and detector effects. Again the phase φ1 is almost equal to φB , the coefficients gi2A increase with θ and φ2A is compatible with 90◦ as expected for the detector effect. 5. Conclusion The azimuthal distribution of a large EAS sample recorded by the ARGO-YBJ detector has been analyzed. A modulation is present and it is well described by means of two harmonics. The first one is of the order of 1.5% and is due to the geomagnetic force on the shower charged particles. The second one is of the order of 0.5% and is the sum of magnetic and detector effects. It has been estimated also the maximum loss (∼ 4%) in EAS detection by ARGO-YBJ detector due to geomagnetic field. References [1] A.A. Ivanov et al., JETP Letters 69 (1999) 288-293 [2] G. Aielli et al. (ARGO-YBJ Coll.), Nuclear Instrum. Methods A 661 (2012) S50

278

S.N. Sbano / Nuclear Physics B (Proc. Suppl.) 239–240 (2013) 274–278

[3] H.H. He et al., Proc. of 29th Int. Cosmic Ray Conf. (Pune) 6 (2005) 5-8. P. Bernardini et al., Proc. of 32nd Int. Cosmic Ray Conf. (Beijing) (2011) HE1.1 0755, (preprint arXiv:1110.0670) [4] P. Abreu et al. (Pierre Auger Coll.), J. Cosmol. Astropart. Phys. JCAP11 (2011) 022 [5] www-ik.fzk.de/corsika/ [6] wwwasd.web.cern.ch/wwwasd/geant/ [7] H.H. He et al., Astropart. Physics 27 (2007) 528-532. G. Aielli et al. (ARGO-YBJ Coll.), Astropart. Physics 30 (2009) 287-292