Stochastic Acceleration in Weakly Turbulent Astrophysical Environments

Abstract Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter this turbulence are typically accelerated according to the so-called second-order Fermi process. However, in most astrophysical environments there are additional competing processes, such as different kinds of first-order energy changes and particle escape, that affect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semianalytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any astrophysical system of interest that is under the influence of weak magnetic turbulence. Here, we adopt that the assigned magnetic turbulence is constrained to a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump—which has long been established for some special cases—is a universal feature of stochastic acceleration that emerges around the momentum χ eq where acceleration and continuous loss are in equilibrium if the particle’s residence time in the system is sufficient at χ eq . In general, the impact of continuous and catastrophic momentum changes plays a crucial role in the shape of the steady-state momentum distribution of the accelerated particles, where simplified unbroken power-law approximations are often not adequate.