Dependence of the position of the knee in the Galactic cosmic ray spectrum on the explosion energy distribution of supernovae

The position of the knee in the Galactic cosmic ray (GCR) spectrum is shown to depend on the explosion energy distribution function of supernovae (SN). The position of the knee in the GCR spectrum can be quantitatively explained by the dominating contribution of hypernovae with explosion energies of (～30–50)×10⁵¹ erg, the fraction of which must be no less than 1% of all SN. The model reproduces the main features in the spectrum of all particles measured in extensive air shower (EAS) experiments: the knee in the spectrum of all particles at energy of about 3 PeV, the change in slope by δ_γ ～ 0.3–0.5 after the knee point, and the steepening of the spectrum near 10¹⁸ eV. The model predicts a smooth knee if the SN explosion energy distribution is universal and a sharp knee if the hypernovae represent a separate class of events. The suggested model of the GCR spectrum is essentially based on the assumption that a spread in explosion energies exists and that the assumptions of the standard model for the CR acceleration in supernova remnants are valid.