Secondary Acceleration of Cosmic Rays by Supernova Shocks

In the common model supernova shock-acceleration of cosmic rays there are two open questions: 1. where does the high energy cosmic rays below the knee (10 − 10 Gev) come from, and 2. are cosmic ray accelerated only at their origin or contineuosly during their residence in the Galaxy. We show that 105 eV light nuclei are probably accelerted by associations of supernovae. The ratio of the spectra of secondary to primary cosmic rays would be affected by repeated (or secondary) acceleration in the ISM during their propagation in the galaxy. The observed secondary and primary CR spectra are used to constrain the amount of such secondary acceleration by supernova remnants (SNR). Two cases are considered: weak shocks (1 < M < 2) of old, dispersed remnants, and strong shocks (M > 3) of relatively young remnants. It is shown that weak shocks produce more secondary acceleration than what is permitted in the framework of the standard leaky box (SLB) model, making it inconsistent with dispersed acceleration that should be produced by SNR. If the SLB is modified to allow a moderate amount of RA by week shocks, the RA produced by old SNRs agrees with the rate reqired to fit the secondary-to primaray cosmic-ray data, making a self consistent picture. Significant secondary acceleration by strong shocks of young SNRs should lead to flattening of the secondary-to primaray ratio at high energies, near 1TeV/nucleon. WHAT IS SECONDARY ACCELERATION? The cosmic ray spectrum in the range 1-10 is probably produced by shock acceleration in the Galaxy (e.g. Axford 1981). Its power-law shape J(p) ∼ p is beleived to be produced by strong shocks, probably of young SNR (Blandford and Ostriker, 1980), combined with escape from the Galaxy. After the cosmic ray particle has left the SNR site and is propagating in the Galaxy, it may enconter another SNR, be trapped and be accelerated to a higher energy. However, the probability to encounter a SNR is proportional to its volume. It turns out to be significant only for old SNR, hens with weak shocks. Indeed, Observations of the ratio of primary to seconday cosmic rays suggest such a secondary acceleration process, but at the same time constrain its amount (Eichler 1980, Cowsick 1986). Wande et.al. (1987) have calculated the cosmic ray spectrum and the constraints on secondary acceleration set by the data under various secondary acceleration models, with the secondary acceleration amount and the shock-strength as parameters. Applying these models to RA by SNR (Wandel 1987;1988) shows that one cannot avoid secondary acceleration if one assumes that the primary cosmic rays are produced by supernovae: the young SNR producing the the cosmic rays will expand and occupy a large enough fraction of the Galaxy to contribute a considerable amount of secondary acceleration . The standard leaky-box model has therefore to be modified to include RA by SNR. BEYOND THE KNEE Acceleration by supernova shocks can produce cosmic rays with energy up to 10 eV. It is difficult to reach higher energies, because when the gyroradius of the accelerated particles becomes of the order of the shock size, the shock-acceleration mechanism cannot function, as the particle escapes. The gyroradius is given by R = p eZB ∼ (10pc) E15 ZB(μG) , (1) so that the maximal energy is E15 = 0.1R(pc)ZB(μG). (2) where E15 is the maximal energy in units of 10 15 eV. To reach energies beyond 10 eV, larger shocks are required, and those can be obtained by going to older SNR and to associations of supernovae. Older SNR have weaker shockes, which produce a steaper power law. Indeed, a significant steepening is observed in the cosmic ray spectrum beyond 10. This could indicate that old SNR associate to produce shocked volumes of sizes of 100pc and more. With galactic magnetic fields of 3μG 100pc shocks, if abundant enough, could produce the observed cosmic ray spectrum up to 3 10eV for protons and up to 10eV for iron. The formalism presented by Wandel (1988) is used to convolve the size of the SNR with teir age and shock strength, to determine the probability and rate of secondary acceleration , and the efffective slope of the produced cosmic ray spectrum. THE SECONDARY ACCELERATION MODEL The steady state distribution of a particle population subject to contineous acceleration during its propagation is described by the integral equation Jo(p)− (R + S)J(p) = B(q) [