Average value of the cosmic ray injection exponent at Galactic sources

Abstract

The energy spectrum of high energy cosmic rays emitted by sources change during propagation in the Galaxy. Using the spectrum observed at the Earth and two different transport models, based on anomalous and normal diffusion equations, we have retrieved an average value of the cosmic ray injection exponent at Galactic sources taking into account the inhomogeneity of the interstellar medium. We have shown that the average value of the injection index p, obtained in the framework of both transport models, equals to p ∼ (2.8 − 3.0).

Origin of hardening and universality of cosmic rays spectra in GV–PV rigidity region

“…It is not taken into account in this work. (iii) The highly inhomogeneous distribution of matter and magnetic fields in the Galaxy leads to the anomalous diffusion of CRs [20]. Anomalous diffusion is manifested, in particular, by abnormally large free paths of particles (so-called "Lévy flights") with a power-law distribution p(r, R)…”

“…It should be noted that the spectrum (2) has the "knee" [19,20,22,23]. The spectral index for observed particles η at the knee rigidity R = R k is equal to spectral exponent for particles generated by the source: η| R=R k = γ.…”