Stochastic acceleration in arbitrary astrophysical environments

TL;DR

This paper presents a semi-analytical solution for the steady-state momentum distribution of particles undergoing stochastic acceleration in arbitrary astrophysical environments, accounting for various momentum change processes and boundary conditions.

Contribution

It introduces the first semi-analytical model including continuous and catastrophic momentum changes applicable to any astrophysical system.

Findings

Universal pile-up bump at equilibrium momentum $ch_{ m eq}$

Impact of momentum changes significantly alters distribution shape

Power-law approximations often inadequate for realistic scenarios

Abstract

Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter these turbulence get on average 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 effect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semi-analytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any arbitrary astrophysical system of interest. Here, we adopt that the assigned magnetic turbulence is constrained on a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump -- that has for some special cases long been established -- is a universal feature of stochastic acceleration that emerges around the momentum $\chi_{\rm eq}$ where acceleration and continuous loss are in equilibrium if the particle's residence time in the system is sufficient at $\chi_{\rm eq}$. 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.