2 A quantitative proposal for the origin of galactic cosmic rays

Cosmic rays arrive at Earth with energies from several hundred MeV/particle to 3 10²⁰ eV; their spectrum for protons is at GeV energies close to E^-2.75, and for He and higher elements close to E^-2.65 below a knee at $\approx 5~10^{15}$ eV, where the spectrum turns down to about E^-3.1, to flatten out again near 3 10¹⁸ eV, called the ankle (e.g. Lawrence et al.${\,}$1991; Nagano et al.${\,}$1992; Zatsepin 1995). The chemical composition is roughly similar to that of the interstellar medium, with reduced hydrogen and helium relative to silicon.

A proposal (see, e.g., Biermann 1993a, 1997a) is that three sites of origin account for the cosmic rays observed, i) supernova explosions into the interstellar medium, ISM-SN, ii) supernova explosions into the stellar wind of the predecessor star, wind-SN, and iii) radio galaxy hot spots. Here, in this concept, the cosmic rays attributed to supernova-shocks in stellar winds, wind-SN, produce an important contribution at all energies up to 3 10⁹ GeV.

We note that the nucleosynthesis in Wolf-Rayet stars (e.g., Prantzos et al. 1987), and their contribution to cosmic rays has been discussed previously (Yanagita et al. 1990). It appears that they do make a substantial contribution, even as seen in the context of the standard leaky box model approach.

Particle energies go up to 100 Z TeV for ISM-SN, and to 100 Z PeV with a bend at 600 Z TeV for wind-SN, the knee (Stanev et al.${\,}$ 1993), where Z is the charge of the nucleus considered. Radiogalaxy hot spots contribute up to about 100 EeV at the source, with some sources up to 4 10²¹ eV (Biermann 1997b). These numerical values are estimates with uncertainties of surely larger than a factor of 2, since they derive from an estimated strength of the magnetic field, and estimated values of the effective shock velocity.

The spectra are predicted to be $E^{-2.75 \pm 0.04}$ for ISM-SN, and E^{-2.67+0.00_-0.04} for wind-SN below the knee, and E^{-3.07+0.00_-0.14} for wind-SM above the knee, and about E^-2.0 at injection for radiogalaxy hot spots.

These predictions can be compared at some detail with data, and we have given comparisons in previous work (e.g. Biermann 1993a; Biermann 1993b; Wiebel-Sooth et al.${\,}$1998; Biermann 1996; Biermann 1997a, 1997b). Newer data confirm some of the general trends near the knee (Glasmacher et al.${\,}$1999a; Glasmacher et al.${\,}$1999b).