Cosmic-rays and diffuse γ-rays: Spatial gradients of Galactic parameters

Spatial gradients of the Galactic parameters in both the longitudinal and the latitudinal directions are estimated from cosmic-ray (CR) and diffuse γ-ray (Dγ) data. We apply our three-dimensional CR propagation model for the derivation of the CR density, Np(r;E), at a position r in the Galaxy (E: kinetic energy of CR per nucleon), and also apply our semi-empirical production cross-section for γ's in p-p collisions, σpp→γ(E,Eγ), to determine the emissivity of γ's (Eγ: γ-ray energy), obtained by combining σpp→γ with Np. Based on the most recent data for the CR energy spectra, particularly those for protons and helium nuclei from AMS and BESS with excellent accuracy over the 1-100 GeV per nucleon range, and from JACEE and RUNJOB covering the very high energy region up to 500 TeV per particle, we estimate the emissivity of γ's at various locations, and compare it with those given by other works. We also present the intensity of the Dγ's originating near the Galactic plane, expected mainly due to the collisions between CRs and the ISM gas, while we use the results from previous simulations for the contributions from electron bremsstrahlung (EB) and inverse Compton (IC) scattering, and compare them with those obtained by the space-based EGRET detector and the current generation of ground-based telescopes. We find that the EGRET data are well reproduced in the energy region Eγ≲2 GeV, in both the spectral shape and the absolute value, with use of the Galactic parameters determined from the CR data, while the intensity of the Dγ's gives a significant enhancement, by approximately the factor 2-3, at ≳2 GeV as compared to those expected from the CR spectrum. We present the scale heights of the diffusion coefficient, corresponding to the halo size, with (rD,zD)=(≳100kpc,2-3kpc), and those of the gas density with (rn,zn)=(20kpc,200-300pc), indicating a much larger radial halo size than commonly assumed, while the latitudinal size is in line with current expectations.