A new analytical model of the cosmic-ray energy flux for Galactic diffuse radio emission

Abstract

Low-frequency radio observations of diffuse synchrotron radiation offer a unique vantage point from which to investigate the intricate relationship between gas and magnetic fields in the formation of structures within the Galaxy, spanning from the diffuse interstellar medium (ISM) to star-forming regions. Achieving this pivotal objective hinges on a comprehensive understanding of cosmic-ray properties; these dictate the effective energy distribution of relativistic electrons, which are primarily responsible for the observable synchrotron radiation. Notably, cosmic-ray electrons (CRe) with energies of between 100 MeV and 10 GeV play a crucial role in determining the majority of the sky brightness below the GHz range. However, their energy flux (je) remains elusive because of solar modulation. We propose a way to derive observational constraints on this energy gap of interstellar CRe through the brightness temperature spectral index of low-frequency radio emission, here denoted βobs. We introduce a new parametric analytical model that fits available data for je in accordance with the βobs values measured in the literature between 50 MHz and 1 GHz for diffuse emission in the Milky Way. Our model accounts for multiple observations considering magnetic-field strengths consistent with existing measurements below 10 μG. We present a first all-sky map of the average component of the magnetic field perpendicular to the line of sight and validate our methodology against state-of-the art numerical simulations of the diffuse ISM. This research makes headway in modeling Galactic diffuse emission with a practical, parametric form. It provides essential insights that will help preparations for the imminent arrival of the Square Kilometre Array.