A Possible Approach to Three‐dimensional Cosmic‐Ray Propagation in the Galaxy. II. Stable Nuclei with Energy Change

Abstract

We extend our model of three-dimensional cosmic-ray propagation without energy change to that including energy change due to reacceleration and ionization energy loss. We assume that there is no boundary in both the radial spread of the disk and the latitudinal spread of the halo, and that the three critical parameters, the diffusion coefficient D, the gas density n, and the cosmic-ray source density Q, depend on both the space position r and the rigidity R of the cosmic-ray particle. It is possible to apply the weighted slab technique to the transport equation, even including the energy change process, if the diffusion coefficient is separable in r and R, i.e., D(r; R) ¼ (v/c)R D(r), and combining it with the first-pole approximation in the path length distribution, we can obtain the analytical solution rather easily. We show that the rigidity dependence of the secondary-to-primary ratio behaves as R À in the high-energy region and as vR in the low-energy region. We compare our numerical results with experimental data in both the low-and the high-energy regions and find that our model reproduces all components over the wide energy range 1 GeV nucleon À1 to 100 TeV nucleon À1 , with the adoption of appropriate scale heights in D, n, and Q. We also confirm that the reacceleration process actually occurs during the propagation in the Galaxy and that its magnitude is comparable with that expected from reasonable numerical choices for three parameters, D, n, and the velocity of the hydromagnetic turbulence v M .

A POSSIBLE APPROACH TO THREE-DIMENSIONAL COSMIC-RAY PROPAGATION IN THE GALAXY. IV. ELECTRONS AND ELECTRON-INDUCED Γ-Rays

“…Under these situations, we have studied the three-dimensional CR propagation model analytically, and found excellent agreement with the experimental data for various hadronic components, stable primaries, secondaries such as boron and sub-iron elements (Z =21-23), isotopes such as 10 Be, and antiprotons as well, in four papers, (Shibata et al 2004(Shibata et al , 2006(Shibata et al , 2007a(Shibata et al , 2008, hereafter referred to as Papers I, II, III and IV, respectively.…”

Production cross-section of antiprotons for the study of cosmic-ray propagation in the Galaxy

“…p ðr; E p Þ will be presented separately, taking the position dependency into account, where one should note that the CR-proton density at the solar system, N p ðr ; E p Þ, is of approximately 35% lower than that at the Galactic center, N p ð0; E p Þ [28]. We will present the CR-p flux in the near future, based on the present result by combining with the CR density as summarized in our previous papers [25,26], and compare it with those obtained by recent experimental data, particularly the BESS data.…”

“…has developed a model of the three-dimensional CR propagation in the Galaxy, which reproduces very well both the stable [25,26], and unstable [27] CR nuclear components, and also the diffuse c-ray 0927-6505/$ -see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.astropartphys.2007.…”

Ionization in Atmospheres of Brown Dwarfs and Extrasolar Planets. Iv. The Effect of Cosmic Rays

“…The broken power-law spectrum changes sharply in flux at < 2 × 10 8 eV. This change results from "leaky-box" models (Lerche & Schlickeiser 1982;Shibata et al 2006), and is argued to be caused by low-energy shocks from either supernova remnants or possibly OB stellar atmospheres interacting with the ambient medium (Bykov & Fleishman 1992). The initial flux density used in this paper is given as (based on Indriolo et al 2009, their Eq.…”