Powerlaw spectra from stochastic acceleration

TL;DR

This paper explains the emergence of powerlaw spectra in particle acceleration within magnetized turbulence by modeling stochastic acceleration as a continuous-time random walk, highlighting the importance of timescale effects.

Contribution

It introduces a novel interpretation of powerlaw spectra as resulting from particle segregation based on acceleration rates, modeled via continuous-time random walks.

Findings

Powerlaw spectra arise when the observation timescale is shorter than the full waiting time distribution.

Analytical solutions match numerical Monte Carlo simulations of the stochastic process.

The model can be applied to astrophysical phenomena involving particle acceleration.

Abstract

Numerical simulations of particle acceleration in magnetized turbulence have recently observed powerlaw spectra where pile-up distributions are rather expected. We interpret this as evidence for particle segregation based on acceleration rate, which is likely related to a non-trivial dependence of the efficacy of acceleration on phase space variables other than the momentum. We describe the corresponding transport in momentum space using continuous-time random walks, in which the time between two consecutive momentum jumps becomes a random variable. We show that powerlaws indeed emerge when the experimental (simulation) timescale does not encompass the full extent of the distribution of waiting times. We provide analytical solutions, which reproduce dedicated numerical Monte Carlo realizations of the stochastic process, as well as analytical approximations. Our results can be readily extrapolated for applications to astrophysical phenomenology.