The lifetime of cosmic rays in the Milky Way

Abstract

The most reliable method to estimate the residence time of cosmic rays in the Galaxy is based on the study of the suppression, due to decay, of the flux of unstable nuclei such as beryllium-10, that have lifetime of appropriate duration. The Cosmic Ray Isotope Spectrometer (CRIS) collaboration has measured the ratio between the fluxes of beryllium-10 and beryllium-9 in the energy range E_0 \simeq 70-145 MeV/nucleon, and has used the data to estimate an escape time tau_{ esc} = 15.0 +- 1.6 Myr. This widely quoted result has been obtained in the framework of a simple leaky-box model where the distributions of escape time and age for stable particles in the Galaxy are identical and have exponential form. In general, the escape time and age distributions do not coincide, they are not unique (because they depend on the injection or observation point), and do not have a simple exponential shape. It is therefore necessary to discuss the measurement of the beryllium ratio in a framework that is more general and more realistic than the leaky-box model. In this work we compute the escape time and age distributions of cosmic rays in the Galaxy in a model based on diffusion that is much more realistic than the simple leaky-box, but that remains sufficiently simple to have exact analytic solutions. Using the age distributions of the model to interpret the measurements of the beryllium-10 suppression, one obtains a cosmic ray residence time that is significantly longer (a factor 2 to 4 depending on the extension of the cosmic ray halo) than the leaky-box estimate. This revised residence time implies a proportional reduction of the power needed to generate the galactic cosmic rays.Comment: Latex, 21 pages, 14 figure