Rigidity-dependent cosmic ray energy spectra in the knee region obtained with the GAMMA experiment

Abstract

On the basis of the extensive air shower (EAS) data obtained by the GAMMA experiment, the energy spectra and elemental composition of the primary cosmic rays are derived in the 10 3 −10 5 TeV energy range. The reconstruction of the primary energy spectra is carried out using an EAS inverse approach in the framework of the SIBYLL2.1 and QGSJET01 interaction models and the hypothesis of powerlaw primary energy spectra with rigidity-dependent knees. The energy spectra of primary H, He, O-like and F e-like nuclei obtained with the SIBYLL interaction model agree with corresponding extrapolations of the balloon and satellite data to ∼ 10 3 TeV energies. The energy spectra obtained from the QGSJET model show a predominantly proton composition in the knee region. The rigidity-dependent knee feature of the primary energy spectra for each interaction model is displayed at the following rigidities: E R ≃ 2500 ± 200 TV (SIBYLL) and E R ≃ 3100 − 4200 TV (QGSJET).All the results presented are derived taking into account the detector response, the reconstruction uncertainties of the EAS parameters, and fluctuations in the EAS development.

Mutually compensative pseudo solutions of primary energy spectra in the knee region

“…This fact directly follows from eq. (2) for pseudo solutions and is well confirmed by the identity of the GAMMA [11,12] and KASCADE [6] all-particle energy spectra in spite of disagreements of the elemental (p, He, F e) primary energy spectra (see [11,12]). …”

“…The results show that the reconstruction of primary energy spectra using unfolding algorithms [6,15] can not be effective and the disagreement between the KASCADE [6] and GAMMA [11,12] data is insignificant in comparison with the large domains of the mutually compensative pseudo solutions (Fig 4) of the unfolded spectra [6].…”

“…To decrease the contributions of the mutually compensative pseudo solutions one may apply a parameterization of the integral equations (1) [1,2,4,11,12] using a priori (expected from theories [17,18,19]) known primary energy spectra with a set of free spectral parameters. This transforms the EAS inverse problem into a set of equations with unknown spectral parameters, and thereby the EAS inverse problem is transmuted into a test of the given primary energy spectra using detected EAS data [4].…”

“…knees) in the primary energy spectra at 10 15 − 10 16 eV may erroneously be smoothed by regularization algorithms and vice versa, be imitated by the unavoidable oscillations [15] of the solutions. Furthermore, the EAS inverse problem implies evaluations of at least two or more unknown primary energy spectra from the integral equation set of Fredholm kind [6,11,12]. These peculiarities have not been studied in detail and the problem of the uniqueness of solutions can limit the number of evaluated spectra.…”

“…Basically, it follows from the high accuracies of recent experiments [8,9,10,11,12] and the availability of the EAS simulation code [13], which was developed in the framework of contemporary interaction models in order to compute the kernel functions of a corresponding integral equation set [6,11]. At the same time, the energy spectra of primary (H, He and F e) nuclei obtained from the KASCADE experiment [6] using the EAS inverse approach disagree with the same data from the ongoing GAMMA experiment [11,12], where parameterization of the EAS inverse problem is used.…”