Time-Dependent Stochastic Acceleration Model for the Fermi Bubbles

TL;DR

This paper develops a time-dependent stochastic acceleration model for the Fermi bubbles, explaining their photon spectra and surface brightness by considering turbulence decay and electron escape effects.

Contribution

It introduces a time-dependent model for stochastic acceleration in the Fermi bubbles, accounting for turbulence decay and electron escape, which improves understanding of their emission features.

Findings

Spatial distribution of high-energy particles differs from steady models.

Electron escape significantly softens the photon spectrum.

Hadronic models are unlikely due to energy budget constraints.

Abstract

We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin--Helmholtz, Rayleigh--Taylor, or Richtmyer--Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.