Synchrotron and Compton Spectra from a Steady-State Electron Distribution

TL;DR

This paper models steady-state electron and proton spectra in galactic regions, revealing that energy losses significantly lower energy density estimates compared to traditional power-law assumptions, impacting magnetic field and proton energy density calculations.

Contribution

It introduces a detailed steady-state spectral model accounting for various energy losses, refining estimates of particle energy densities and magnetic fields in galactic environments.

Findings

Energy losses flatten electron spectra, reducing energy density estimates.

Calculated spectra differ from simple power-law models, especially in starburst regions.

Implications for more accurate magnetic field and proton energy density estimates.

Abstract

Energy densities of relativistic electrons and protons in extended galactic and intracluster regions are commonly determined from spectral radio and (rarely) $\gamma$-ray measurements. The time-independent particle spectral density distributions are commonly assumed to have a power-law (PL) form over the relevant energy range. A theoretical relation between energy densities of electrons and protons is usually adopted, and energy equipartition is invoked to determine the mean magnetic field strength in the emitting region. We show that for typical conditions, in both star-forming and starburst galaxies, these estimates need to be scaled down substantially due to significant energy losses that (effectively) flatten the electron spectral density distribution, resulting in a much lower energy density than deduced when the distribution is assumed to have a PL form. The steady-state electron distribution in the nuclear regions of starburst galaxies is calculated by accounting for Coulomb, bremsstrahlung, Compton, and synchrotron losses; the corresponding emission spectra of the latter two processes are calculated and compared to the respective PL spectra. We also determine the proton steady-state distribution by taking into account Coulomb and pion production losses, and briefly discuss implications of our steady-state particle spectra for estimates of proton energy densities and magnetic fields.