Galactic Modulation of Extragalactic Cosmic Rays: -- A Possible Origin of the Knee in the Cosmic Ray Spectrumc --

Abstract

The existence of the spectral break around ∼ 3 × 10 15 eV in the cosmic ray spectrum (referred to as the 'knee') is one of the biggest questions in cosmic ray astrophysics. At the same time, the origin of cosmic rays above the knee energies (between 10 15 and 10 18 eV) is also still unsettled. In this paper, we investigate how the hypothetical extragalactic CRs after modulated by the galactic wind contribute to the knee in the CR spectrum. We numerically calculate the modulated energy spectrum of the hypothetical cosmic rays coming into the galaxy from just outside of the "galactic sphere" where the galactic wind terminates. We show that the observed knee structure is reproduced well by a superposition of the modulated component and the galactic cosmic rays originating in supernova remnants. * ) For SN1006, there is discrepancy between the results of CANGAROO-I and HESS; an upper limit reported by HESS is below the flux detected by CANGAROO-I. 10) typeset using PTPT E X.cls Ver.0.9

Galactic modulation of extragalactic cosmic rays -Alternative scenario of the origin of the knee-

“…The expected composite model all-particle spectrum is shown by the thick solid curve in Fig. 2 when we adopted the same value for the relevant parameters, η = 250, R = 100 kpc, V = 300 km sec −1 , and B = 1µG, as adopted in our previous paper [19]. Our model spectrum reproduces well again the observed all-particle spectrum.…”

“…where η =η/(100), B =B/(1µG), R =R/(100kpc), and V =V /(300 km s −1 ), respectively [19]. This result indicates clearly that we can reproduce the knee by choosing appropriate values for these parameters.…”

“…In previous work, we have shown the model spectrum F total (E) around the knee for a two example cases [19]; one is a single component model for F modul (E) (e.g. F modul (E) = f p modul (E) or f Fe modul (E)), and the other is a composite model for F modul (E) which consists of the same spectrum of f p modul (E), f He modul (E), f CNO modul (E), f NeMgSi modul (E), and f Fe modul (E) at the boundary.…”

“…Fig. 1 shows the calculated differential energy spectra of hypothetical nuclear components labeled in the figure at Earth (r 0 = 8.5 kpc) as a function of total energy E [19]. Here we assume V = 300 km sec −1 , R = 100 kpc, B = 1µG and η = 1000 as an example [26].…”

“…We have examined such a possibility by solving numerically a coupled stochastic differential equations (SDEs) equivalent to the Fokker-Planck equation for the spherical symmetric case [19]. We have shown that the hypothetical extragalactic CR spectrum which is proportional to E −3 , where E is the total energy of a particle, breaks around the knee energy at Earth.…”