Synchrotron and inverse-Compton emission from radio galaxies with non-uniform magnetic field and electron distributions

TL;DR

This paper examines how non-uniform, isotropic magnetic fields in radio galaxies influence synchrotron and inverse-Compton emissions, providing a numerical method to estimate these effects and implications for magnetic field measurements.

Contribution

It derives a simple integral for synchrotron emissivity in non-uniform fields and analyzes the impact on spectral aging and magnetic field estimates in radio galaxies.

Findings

Difference in synchrotron emissivity is small but increases with electron energy density scaling.

Aged electron spectra produce curved synchrotron spectra differing from classical models.

Inverse-Compton emission is moderately affected by magnetic field structure.

Abstract

I investigate the effect of non-uniform magnetic fields in the extended structures of radio galaxies on the observed synchrotron and inverse-Compton emission. On the assumption of an isotropic field, with a given power spectrum and a Gaussian distribution of the Cartesian components of the magnetic field strength, I derive a simple integral that can be used numerically to calculate the synchrotron emissivity from any electron population. In the case of power-law spectra, I show that it is possible to estimate the difference between the synchrotron emissivity from a region with such a field and that from the commonly assumed arrangement where $B$ is constant everywhere, though fully tangled, and that this difference is small, though it increases if the electron energy density scales with the field. An aged electron spectrum in such a field produces a characteristic curved synchrotron spectrum which differs significantly from the classical Jaffe-Perola spectrum, and I discuss some effects that this might have on standard spectral age fitting. Finally, I show that inverse-Compton scattering of the cosmic microwave background is only moderately affected by such a field structure, with the effects becoming more important if the electrons follow the field. Magnetic-field estimates in the literature from combined synchrotron and inverse-Compton modelling will give reasonable estimates of the mean magnetic field energy density if the field is non-uniform but isotropic.