Stochastic Particle Acceleration in Cosmic Objects

Abstract

A simple model for the evolution of energetic particle momentum spectra in cosmic objects is developed. Particles are accelerated by stochastic resonant scattering off hydromagnetic waves and by shock waves, but lose momentum in ionization, bremsstrahlung, radiation and spallation interactions with ambient matter, radiation and electromagnetic fields. A fundamental transport equation for the equilibrium momentum distribution function is derived which is a generalized heat-conduction equation with convection and diffusion terms both in momentum and position space. By introducing the age distribution of energetic particles it is possible to decouple the spatial from the momentum transport, and simple leaky-box type equations result. Exact analytical solutions of the latter equations in the steady-state and time-dependent case are given and compared with observations. The solutions indicate the coexistence of monoenergetic, power law, exponential and relativistic Maxwellian particle spectra. Since this variety of particle spectra is seen in cosmic sources, our results are very encouraging and definitely in favour of continuous acceleration models. Finally the secondary/primary ratio in galactic cosmic radiation is discussed, and the invalidity of arguments against continuous acceleration models, raised in the past, is demonstrated. Once the momentum dependence of the escape lifetimes and the different source distributions of primary and secondary nuclei are adequately taken into account, the measured decrease of this ratio can be successfully explained in the framework of continuous acceleration models.