New constraints on Galactic cosmic - ray propagation

An extensive program for the calculation of galactic cosmic-ray propagation has been developed. Primary and secondary nucleons, primary and secondary electrons, secondary positrons and antiprotons are included. Fragmentation and energy losses are computed using realistic distributions for the interstellar gas and radiation fields. Models with diffusion and convection only do not account naturally for the observed energy dependence of B/C, while models with reacceleration reproduce this easily. The height of the halo propagation region is determined, using recent Be/ Be measurements, as greater than 4 kpc. The radial distribution of cosmic-ray sources required is broader than current estimates of the SNR distribution for all halo sizes. Our results include an estimate of cosmic-ray antiproton and positron spectra, and the Galactic diffuse γ-ray emission (see accompanying paper: Moskalenko 1998b). Introduction. We are constructing a model which aims to reproduce self-consistently observational data of many kinds related to cosmic-ray (CR) origin and propagation: direct measurements of nuclei, electrons, positrons, antiprotons, gamma rays, and synchrotron radiation. These data provide many independent constraints on any model and our approach is able to take advantage of this since it must be consistent with all types of observation. Here we present our results on the evaluation of diffusion/convection and reacceleration models based on the B/C and Be/ Be ratios, and set limits on the halo size. A re-evaluation of the halo size is desirable since new Be/ Be data are now available from Ulysses (Connell 1998) with better statistics than previously. Our preliminary results were presented in Strong (1997a,b) and full results for protons, Helium, positrons, and electrons in Moskalenko (1998a). Some illustrative results for gamma-rays and synchrotron radiation are given in Strong (1997a) and Moskalenko (1998b) and all details are given in Strong (1998)1. The model description. The models are three dimensional with cylindrical symmetry in the Galaxy, and the basic coordinates are (R, z, p), where R is Galactocentric radius, z is the distance from the Galactic plane, and p is the particle momentum. The propagation equations are solved numerically on a grid by the method described in Strong (1998). R⊙ is taken as 8.5 kpc. The propagation region is bounded by R = Rh, z = zh beyond which free escape is assumed. We take Rh = 30 kpc. The range zh = 1−20 kpc is considered. For a given zh the diffusion coefficient as a function of momentum is determined by B/C for the case of no reacceleration; if reacceleration is assumed then the reacceleration strength (re1For more details see http://www.gamma.mpe–garching.mpg.de/∼aws/aws.html Proc. 16th European Cosmic-Ray Symp., 1998 (Alcala), OG-2.5 2 Fig. 1. Left panel: B/C ratio for diffusion/convection models without break in diffusion coefficient (Strong 1998 and references therein), for zh = 3 kpc, dV/dz = 0 (solid line), 5 (dotted line), and 10 km s kpc (dashed line); solid line: interstellar ratio, shaded area: modulated to 300 – 500 MV; data: HEAO-3, Voyager, Ulysses. Right panel: B/C ratio for diffusive reacceleration models (Strong 1998) with zh = 5 kpc, vA = 0 (dotted), 15 (dashed), 20 (thin solid), 30 km s (thick solid). In each case the interstellar ratio and the ratio modulated to 500