# On the Radio Emitting Particles of the Crab Nebula: Stochastic Acceleration Model

## TL;DR

This paper proposes that radio-emitting particles in the Crab Nebula are stochastically accelerated by turbulence inside the nebula, providing a new explanation for their energy distribution and spectral properties.

## Contribution

It introduces a stochastic acceleration model for radio-emitting particles in PWNe, extending previous models to better explain observed spectra and flux decay.

## Key findings

- Reproduces the broadband spectrum of the Crab Nebula.
- Suggests acceleration timescale of a few decades.
- Indicates acceleration duration of a few hundred years.

## Abstract

The broadband emission of Pulsar Wind Nebulae (PWNe) is well described by non-thermal emissions from accelerated electrons and positrons. However, the standard shock acceleration model of PWNe does not account for the hard spectrum in radio wavelengths. The origin of the radio-emitting particles is also important to determine the pair production efficiency in the pulsar magnetosphere. Here, we propose a possible resolution for the particle energy distribution in PWNe; the radio-emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside PWNe. We upgrade our past one-zone spectral evolution model including the energy diffusion, i.e., the stochastic acceleration, and apply to the Crab Nebula. A fairly simple form of the energy diffusion coefficient is assumed for this demonstrative study. For a particle injection to the stochastic acceleration process, we consider the continuous injection from the supernova ejecta or the impulsive injection associated with supernova explosion. The observed broadband spectrum and the decay of the radio flux are reproduced by tuning the amount of the particle injected to the stochastic acceleration process. The acceleration time-scale and the duration of the acceleration are required to be a few decades and a few hundred years, respectively. Our results imply that some unveiled mechanisms, such as back reaction to the turbulence, are required to make the energies of stochastically and shock accelerated particles comparable.