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Lateral distribution of electrons in EAS at superhigh energies: predictions and experimental data
SUPPLEMENTS
Nuclear Physics B (Proc. Suppl.) 97 (2001) 274-277
ELSEVIER
Lateral Distribution of Electrons in EAS at Superhigh Predictions and Experimental Data A. A. Lagutin,
R. I. Raikin”
“Department 66, Dimitrova
of Theoretical str., Barnaul,
Physics, Altai State 656099, Russia
www.elsevier.nl/locate/npe
Energies:
University,
In this paper we present a new approximation for the lateral distribution function of electrons in extensive air showers based on the scaling property established in our recent works. The detailed comparisons of theoretical predictions for the lateral distribution of charged particles in EAS at superhigh energies obtained with the use of new LDF of electrons with the experimental data of AGASA and Yakutsk array are carried out. The influence of the scintillation detector response and the atmospheric temperature effect on the shape of the lateral distribution of electrons is discussed in brief.
1. INTRODUCTION Knowledge of the correct lateral distribution function (LDF) of extensive air shower (EAS) electrons and muons is of great importance for EAS research. The problem of fast calculations of LDF, proper and at the same time adequate to the experimental at very large distances from the shower axis (r 2 1 km), is not solved yet. The reliable results for such big distances are necessary for the interpretation of experimental data on giant air showers and for new experiments designing. The prevalent approach to super-high energy EAS simulation provides the analytical description of electromagnetic subshowers based on the different well known modifications of NKG formula obtained for distances up to some hundreds of meters from core location. In this case the formal extrapolation to radial distances about 1 km and farther is a source of mistakes. In our recent works [1,2] we established the new scaling property of the lateral distribution of electrons in both the electromagnetic cascade and extensive air shower. These results allow to get reliable data on the electron LDF up to T - (25 + 30)Rm.s.,., where R,.,.,. is the mean square radius of the electron component of the shower. It was shown that if we use the mean square radius as a radial scale parameter instead of the Moliere unit RM, the electron LDF is invariant with respect to the primary energy and
Now we present the the age of the cascade. new formula for the lateral distribution function of extensive air shower electrons. We carried out detailed comparisons of our predictions for the charged particles LDF obtained with the use of the proposed formula for LDF of electrons with the latest experimental data of AGASA and Yakutsk array. The influence of the scintillation detector response and the temperature effect under the specific atmospheric conditions on the shape of the lateral distribution of electrons is discussed in brief.
2. NEW
ERAL TRONS
APPROXIMATION DISTRIBUTION
OF LATOF ELEC-
Our calculations [l-3] were carried out in the framework of quark-gluon string model for vertical showers initiated by primary protons with energies Es = (lo5 t 10’) GeV for observation depths t&s = (614 f 1030) g/cm2 in the model of standard atmosphere. According to our calculational results, the electron local density at the distance r from the EAS core can be presented in a form:
0920-5632/01/$ - see liont matter 0 2001 Elsevier Science 1s.V. All rights reserved PI1 SO(~20-5632(01)01282-8
A.A. Lag&in.
x
R.I. Raikin /Nuclear
Physics B (Proc. Suppl.)
(l+( 1oRT,8,r,)2)m6, mm2, (1)
in order to estimate the charged particles density measured by the scintillation detector ps we use the following relation:
where C, = 0.28 is a normalization factor, N, is the total number of electrons at the observation depth tabs, (Y= 1.2, p = 4.53, 6 = 0.6. The mean square radius can be found using the following approximations: &n.,.,.
(EO,
275
97 (2001) 274-277
tabs)
=
pO Pobs
. A(tobs)
A
=
6.69. 1O-2 t&s - 5.25,
B
=
13.37 [l - 581.3 x x eXp{ -1.44
. 1om2t&}]
X
.
(3)
Here p&s is the density of the atmosphere at the observation level t&, po = 1.225 . 10m3 g/cm3. Note that the dependence of the shape of the lateral distribution function on the energy, observation depth and primary particle (in superposition model for primary nuclei) is described by the variation of the single parameter R,,,.,.,.. This is the essential difference between the LDF (1) and modified Linsley functions which are traditionally used for the approximation of experimental data of the biggest shower arrays AGASA and Yakutsk (see [4,5]). 3. COMPARISONS RESULTS WITH DATA
OF
THEORETICAL EXPERIMENTAL
The problem of correct comparisons of theoretical results on electron LDF with experimental data is very complicated because it is necessary to take into account the lateral distribution of muons (including particles with energies less than the threshold of muon detectors), detector response and some other features of the considered experiment, for example, the atmospheric temperature conditions of Yakutsk array, which are essentially different from the standard atmosphere. Here we consider only near vertical showers with relatively small fraction of muons. Firstly,
Ps = Ic,,P, + k,P,,
(4)
where pe is the electron density, calculated from eq. (l)-(3) with extrapolation up to extremely high energies, pfi is the muon density, k,, = 1.1 [6] is the conversion factor to the scintillation detector response and kP = 1.9 [7] takes into account low energetic muons and electrons produced from the decay of muons. In order to clearly recognize the effects which are caused by the electron component, we use for p,, the experimental muon densities measured by muon detectors at the considered array. Note that the muon lateral distributions measured by AGASA and Yakutsk array are in good agreement at Es 5 (1 f 3) x 1018 eV [7]. 3.1. AGASA We obtained the following relation between ~~(600) calculated from eq. (4) and primary energy for the atmospheric depth of AGASA Ee = 2.29. 10’7p,(600)1.01 which agrees tion [8]
quite
eV,
well with
Es = 2.03 . 1017p,(600)‘.02
(5) the AGASA
eV.
rela-
(6)
In fig. 1 our results on ps are presented in comparison with AGASA experimental data. It is seen that our results are in good agreement with the experiment but somewhat steeper than the approximation function used at AGASA. 3.2. Yakutsk Array The energy conversion formula as calculated Yakutsk atmospheric level (1020 g/cm2) is
for
EO = 2.81. 1017p,(600)1.0’
(7)
eV.
In order to directly compare with our results obtained under the standard atmospheric conditions, the Yakutsk conversion formula Es = 4.80. 10’7p,(600)1.0eV [5] should be recalculated. The method traditionally used for such correction is to take into account the ratio of the Moliere units at the observation depth. The corresponding correction coefficient is ~~(600; RL)/ps(600; RM) =
A.A. Lagutin, R.I. Raikin/Nuclear
216
Physics B (Proc. Suppl.) 97 (2001) 274-277
a m”
pm2
10”
10s
10’
104
103
13
101
101
10’
10’
1
1
10-l
10-I
102
r, m
102
b)
4
Figure 1. Lateral distributions of charged particles in EAS with (sec8) 5 1.1 measured by AGASA [4]. a) Es = 101g.3 eV, b) Es = 10 1g.7 eV. Dashed lines - approximation function used at AGASA. Solid lines - our results 0.80, where RM = 81 m for standard atmosphere, R& = 68 m for typical Yakutsk conditions (we use here the Yakutsk approximation formula for LDF of charged particles [9]). So we derive the new relation Es = 3.85. 10’7p,(600)‘.o
eV.
(8)
It is seen from the comparison of eq. (7) and (8) that the discrepancy is still essential. Note that approximately the same difference (by a factor N 1.4) occurs in comparisons of Yakutsk data with a number of theoretical results, for example, with QGSJET data [5]. There is evidence [lo] that the correct simulations of energy deposition in the detectors (this result obtained using the SIBYLL-MOCCA program) leads to the additional correction of Yakutsk primary energy spectrum by a factor x0.7. After that, the relations turn out to be in satisfactory agreement to each other. Fig. 2 shows Yakutsk experimental data on the LDF of charged particles in comparison with our calculational results obtained for the same ~~(600). It is seen that our calculational function is steeper than the experimental data at
Es = 2.101* eV as well as at Ec = 2 e10lg eV. If we take into consideration the additional steepening of experimental data as a consequence of the specific atmospheric conditions for the Yakutsk array, the difference becomes essential. 4. DISCUSSION Let us mention some additional factors that could partially compensate the differences be tween our calculational results and experimental data. First of all it should be noted that all our calculations were carried out for primary protons. In the case of a heavier primary composition, we obtain a flatter distribution function. In [2] we presented the results on the transition effect of EAS electrons in scintillation detectors of different thickness. It was shown that the correction factor Ic,, depends on the radial distance and has a minimum around r = 50 m. So the correct description of the scintillators response leads to a slightly flatter distribution function at large distances than usual method does. In our latest paper [ll] we investigated the in-
A.A. Lagutin, R.I. Raikin /Nuclear Physics B (Proc. Suppl.) 97 (2001) 274-277
217
P. m2 10'
l@
lo’
r,m
lo2
10'
r,m
b)
Figure 2. Lateral distributions of charged particles in EAS with (case) > 0.98 measured by Yakutsk array 151. a) Ec = 2 . 101* eV, b) Es = 2 . 101’ eV. Dashed lines - approximation function used at Yakutsk: Solid line - our calculational results
fluence of the variation of the temperature profile of the atmosphere on the shape of the LDF of electrons (atmospheric temperature effect). It was shown that the temperature effect depends on primary energy due to the influence of inhomogeneity of the atmosphere on the mean square radius of electromagnetic subshowers. So in case of large variations of the temperature profile, the scale transformation of LDF using the Moliere unit at the observation level is not adequate to describe the change of the LDF slope. 5. CONCLUSIONS In this paper we propose a new scaling lateral distribution function of EAS electrons. The calculational predictions for LDF of charged particles are in a good agreement with the experimental data of AGASA. The comparisons of our results with the data of Yakutsk array demonstrate some inconsistency, which requires additional investigations. REFERENCES 1.
Lagutin A.A. (1997) 285.
et al. Proc.
25th ICRC,
V. 6,
Lagutin A.A. et al. Nucl. Phys. B (Proc. Suppl.) 75A, (1999) 290. Univer3. Lagutin A.A. et al. Preprint/Saitama sity, Urawa, Japan; No 1 (1997). 4. Hayashida N. et al. Proc. 26th ICRC, V. 1, (1999) 353. 5. Glushkov A.V. et al. Proc. 26th ICRC, V. 1, (1999) 399. 6. Teshima M. et al. J. Phys. G: Nucl. Phys., 12 (1986) 1097. 7. Glushkov A.V. et al. Yad. Fiz., 58, (1995) 1265. 8. Dai H.Y. et al. J. Phys. G: Nucl. Phys., 14 (1988) 793. M.N. et al. Cosmic radiation of 9. Diakonov extremely high energy. Novosibirsk, Nauka, (1991) (in Russian) 10. Hillas A.M. Nucl. Phys. B (Proc. Suppl.), 75 A, (1999) 109. 11. Lagutin A.A. et al. Preprint/ASU; No 2000/2, (2000). 2.
Nuclear Physics B (Proc. Suppl.) 97 (2001) 274-277
ELSEVIER
Lateral Distribution of Electrons in EAS at Superhigh Predictions and Experimental Data A. A. Lagutin,
R. I. Raikin”
“Department 66, Dimitrova
of Theoretical str., Barnaul,
Physics, Altai State 656099, Russia
www.elsevier.nl/locate/npe
Energies:
University,
In this paper we present a new approximation for the lateral distribution function of electrons in extensive air showers based on the scaling property established in our recent works. The detailed comparisons of theoretical predictions for the lateral distribution of charged particles in EAS at superhigh energies obtained with the use of new LDF of electrons with the experimental data of AGASA and Yakutsk array are carried out. The influence of the scintillation detector response and the atmospheric temperature effect on the shape of the lateral distribution of electrons is discussed in brief.
1. INTRODUCTION Knowledge of the correct lateral distribution function (LDF) of extensive air shower (EAS) electrons and muons is of great importance for EAS research. The problem of fast calculations of LDF, proper and at the same time adequate to the experimental at very large distances from the shower axis (r 2 1 km), is not solved yet. The reliable results for such big distances are necessary for the interpretation of experimental data on giant air showers and for new experiments designing. The prevalent approach to super-high energy EAS simulation provides the analytical description of electromagnetic subshowers based on the different well known modifications of NKG formula obtained for distances up to some hundreds of meters from core location. In this case the formal extrapolation to radial distances about 1 km and farther is a source of mistakes. In our recent works [1,2] we established the new scaling property of the lateral distribution of electrons in both the electromagnetic cascade and extensive air shower. These results allow to get reliable data on the electron LDF up to T - (25 + 30)Rm.s.,., where R,.,.,. is the mean square radius of the electron component of the shower. It was shown that if we use the mean square radius as a radial scale parameter instead of the Moliere unit RM, the electron LDF is invariant with respect to the primary energy and
Now we present the the age of the cascade. new formula for the lateral distribution function of extensive air shower electrons. We carried out detailed comparisons of our predictions for the charged particles LDF obtained with the use of the proposed formula for LDF of electrons with the latest experimental data of AGASA and Yakutsk array. The influence of the scintillation detector response and the temperature effect under the specific atmospheric conditions on the shape of the lateral distribution of electrons is discussed in brief.
2. NEW
ERAL TRONS
APPROXIMATION DISTRIBUTION
OF LATOF ELEC-
Our calculations [l-3] were carried out in the framework of quark-gluon string model for vertical showers initiated by primary protons with energies Es = (lo5 t 10’) GeV for observation depths t&s = (614 f 1030) g/cm2 in the model of standard atmosphere. According to our calculational results, the electron local density at the distance r from the EAS core can be presented in a form:
0920-5632/01/$ - see liont matter 0 2001 Elsevier Science 1s.V. All rights reserved PI1 SO(~20-5632(01)01282-8
A.A. Lag&in.
x
R.I. Raikin /Nuclear
Physics B (Proc. Suppl.)
(l+( 1oRT,8,r,)2)m6, mm2, (1)
in order to estimate the charged particles density measured by the scintillation detector ps we use the following relation:
where C, = 0.28 is a normalization factor, N, is the total number of electrons at the observation depth tabs, (Y= 1.2, p = 4.53, 6 = 0.6. The mean square radius can be found using the following approximations: &n.,.,.
(EO,
275
97 (2001) 274-277
tabs)
=
pO Pobs
. A(tobs)
A
=
6.69. 1O-2 t&s - 5.25,
B
=
13.37 [l - 581.3 x x eXp{ -1.44
. 1om2t&}]
X
.
(3)
Here p&s is the density of the atmosphere at the observation level t&, po = 1.225 . 10m3 g/cm3. Note that the dependence of the shape of the lateral distribution function on the energy, observation depth and primary particle (in superposition model for primary nuclei) is described by the variation of the single parameter R,,,.,.,.. This is the essential difference between the LDF (1) and modified Linsley functions which are traditionally used for the approximation of experimental data of the biggest shower arrays AGASA and Yakutsk (see [4,5]). 3. COMPARISONS RESULTS WITH DATA
OF
THEORETICAL EXPERIMENTAL
The problem of correct comparisons of theoretical results on electron LDF with experimental data is very complicated because it is necessary to take into account the lateral distribution of muons (including particles with energies less than the threshold of muon detectors), detector response and some other features of the considered experiment, for example, the atmospheric temperature conditions of Yakutsk array, which are essentially different from the standard atmosphere. Here we consider only near vertical showers with relatively small fraction of muons. Firstly,
Ps = Ic,,P, + k,P,,
(4)
where pe is the electron density, calculated from eq. (l)-(3) with extrapolation up to extremely high energies, pfi is the muon density, k,, = 1.1 [6] is the conversion factor to the scintillation detector response and kP = 1.9 [7] takes into account low energetic muons and electrons produced from the decay of muons. In order to clearly recognize the effects which are caused by the electron component, we use for p,, the experimental muon densities measured by muon detectors at the considered array. Note that the muon lateral distributions measured by AGASA and Yakutsk array are in good agreement at Es 5 (1 f 3) x 1018 eV [7]. 3.1. AGASA We obtained the following relation between ~~(600) calculated from eq. (4) and primary energy for the atmospheric depth of AGASA Ee = 2.29. 10’7p,(600)1.01 which agrees tion [8]
quite
eV,
well with
Es = 2.03 . 1017p,(600)‘.02
(5) the AGASA
eV.
rela-
(6)
In fig. 1 our results on ps are presented in comparison with AGASA experimental data. It is seen that our results are in good agreement with the experiment but somewhat steeper than the approximation function used at AGASA. 3.2. Yakutsk Array The energy conversion formula as calculated Yakutsk atmospheric level (1020 g/cm2) is
for
EO = 2.81. 1017p,(600)1.0’
(7)
eV.
In order to directly compare with our results obtained under the standard atmospheric conditions, the Yakutsk conversion formula Es = 4.80. 10’7p,(600)1.0eV [5] should be recalculated. The method traditionally used for such correction is to take into account the ratio of the Moliere units at the observation depth. The corresponding correction coefficient is ~~(600; RL)/ps(600; RM) =
A.A. Lagutin, R.I. Raikin/Nuclear
216
Physics B (Proc. Suppl.) 97 (2001) 274-277
a m”
pm2
10”
10s
10’
104
103
13
101
101
10’
10’
1
1
10-l
10-I
102
r, m
102
b)
4
Figure 1. Lateral distributions of charged particles in EAS with (sec8) 5 1.1 measured by AGASA [4]. a) Es = 101g.3 eV, b) Es = 10 1g.7 eV. Dashed lines - approximation function used at AGASA. Solid lines - our results 0.80, where RM = 81 m for standard atmosphere, R& = 68 m for typical Yakutsk conditions (we use here the Yakutsk approximation formula for LDF of charged particles [9]). So we derive the new relation Es = 3.85. 10’7p,(600)‘.o
eV.
(8)
It is seen from the comparison of eq. (7) and (8) that the discrepancy is still essential. Note that approximately the same difference (by a factor N 1.4) occurs in comparisons of Yakutsk data with a number of theoretical results, for example, with QGSJET data [5]. There is evidence [lo] that the correct simulations of energy deposition in the detectors (this result obtained using the SIBYLL-MOCCA program) leads to the additional correction of Yakutsk primary energy spectrum by a factor x0.7. After that, the relations turn out to be in satisfactory agreement to each other. Fig. 2 shows Yakutsk experimental data on the LDF of charged particles in comparison with our calculational results obtained for the same ~~(600). It is seen that our calculational function is steeper than the experimental data at
Es = 2.101* eV as well as at Ec = 2 e10lg eV. If we take into consideration the additional steepening of experimental data as a consequence of the specific atmospheric conditions for the Yakutsk array, the difference becomes essential. 4. DISCUSSION Let us mention some additional factors that could partially compensate the differences be tween our calculational results and experimental data. First of all it should be noted that all our calculations were carried out for primary protons. In the case of a heavier primary composition, we obtain a flatter distribution function. In [2] we presented the results on the transition effect of EAS electrons in scintillation detectors of different thickness. It was shown that the correction factor Ic,, depends on the radial distance and has a minimum around r = 50 m. So the correct description of the scintillators response leads to a slightly flatter distribution function at large distances than usual method does. In our latest paper [ll] we investigated the in-
A.A. Lagutin, R.I. Raikin /Nuclear Physics B (Proc. Suppl.) 97 (2001) 274-277
217
P. m2 10'
l@
lo’
r,m
lo2
10'
r,m
b)
Figure 2. Lateral distributions of charged particles in EAS with (case) > 0.98 measured by Yakutsk array 151. a) Ec = 2 . 101* eV, b) Es = 2 . 101’ eV. Dashed lines - approximation function used at Yakutsk: Solid line - our calculational results
fluence of the variation of the temperature profile of the atmosphere on the shape of the LDF of electrons (atmospheric temperature effect). It was shown that the temperature effect depends on primary energy due to the influence of inhomogeneity of the atmosphere on the mean square radius of electromagnetic subshowers. So in case of large variations of the temperature profile, the scale transformation of LDF using the Moliere unit at the observation level is not adequate to describe the change of the LDF slope. 5. CONCLUSIONS In this paper we propose a new scaling lateral distribution function of EAS electrons. The calculational predictions for LDF of charged particles are in a good agreement with the experimental data of AGASA. The comparisons of our results with the data of Yakutsk array demonstrate some inconsistency, which requires additional investigations. REFERENCES 1.
Lagutin A.A. (1997) 285.
et al. Proc.
25th ICRC,
V. 6,
Lagutin A.A. et al. Nucl. Phys. B (Proc. Suppl.) 75A, (1999) 290. Univer3. Lagutin A.A. et al. Preprint/Saitama sity, Urawa, Japan; No 1 (1997). 4. Hayashida N. et al. Proc. 26th ICRC, V. 1, (1999) 353. 5. Glushkov A.V. et al. Proc. 26th ICRC, V. 1, (1999) 399. 6. Teshima M. et al. J. Phys. G: Nucl. Phys., 12 (1986) 1097. 7. Glushkov A.V. et al. Yad. Fiz., 58, (1995) 1265. 8. Dai H.Y. et al. J. Phys. G: Nucl. Phys., 14 (1988) 793. M.N. et al. Cosmic radiation of 9. Diakonov extremely high energy. Novosibirsk, Nauka, (1991) (in Russian) 10. Hillas A.M. Nucl. Phys. B (Proc. Suppl.), 75 A, (1999) 109. 11. Lagutin A.A. et al. Preprint/ASU; No 2000/2, (2000). 2.