On the spectrum of relativistic electrons accelerated in cosmic-ray sources

Abstract

The data on the spectrum of the cosmic-ray electron component near the earth, on the radio-spectra of radio-galaxies, quasars and the Crab Nebula, as well as the data pertaining to the X-ray spectrum of the cosmic background, all agree that the sources of cosmic-ray electrons (such as supernovae and galactic nuclei) inject particles characterized by a power spectrumN(E)=KE^−γ0, with γ0≃1.5–2.5. A mechanism is known in which the source emits a proton-nuclear component of cosmic rays with a spectrumN_n(E)=K_nE^−γ_n, γ_n = δ + 2, δ=wcr/(w−wcr), wherewcr is the cosmic-ray energy density in the source, andw=wcr+wn+w_turb, the total energy density. We obtain γ=2.5 in agreement with observations on the natural assumption that δ=0.5. Within the framework of the same model with some additional assumptions, the electrons in the source, as well as those ejected by the source, are shown to have a power-spectrum characterized with γ₀ ≤ γ_n = δ + 2. Thus the model discussed gives an adequate spectrum for both the proton-nuclear and the electron components of cosmic rays.