The Distribution of Cosmic Ray Electrons in Star-Forming Galaxies

TL;DR

This paper provides explicit algebraic solutions for the steady-state distribution of cosmic ray electrons in star-forming galaxies, aiding interpretation of radio observations and offering an alternative to energy equipartition assumptions.

Contribution

It derives accurate, versatile solutions for cosmic ray electron distributions considering arbitrary source distributions, improving modeling of galactic radio emissions.

Findings

Solutions are accurate within 10% across various parameters.

The method applies to arbitrary source distributions, not just Gaussian.

Results facilitate better interpretation of radio astronomical data.

Abstract

We derive explicit, algebraic expressions for the steady-state number density of cosmic ray electrons as a function of position and energy using Green's function of the diffusion equation with energy losses for an axisymmetric distributions of the particle sources in the galactocentric radius $r$ and distance to the mid-plane $z$. The solution is obtained for a Gaussian distribution of the particle sources in $r$ and $z$ but we show that it can be used for an arbitrary spatial distribution of the sources. The accuracy of our results is about 10\% or better in wide ranges of $r$, $z$ and particle energies. These solutions can be used in the interpretation of radio astronomical observations of galaxies, particularly in the studies of the radio luminosities for large galaxy samples, and represent a physically justifiable and efficient alternative to the assumption of the energy equipartition between cosmic rays and interstellar magnetic fields.