  Low-frequency radio observations of diffuse synchrotron radiation offer a
unique vantage point for investigating 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, which dictate the effective energy distribution of relativistic
electrons, primarily responsible for the observable synchrotron radiation.
Notably, cosmic-ray electrons (CRe) with energies 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 ($j_e$) remains elusive due to solar
modulation. We propose deriving observational constraints on this energy gap of
interstellar CRe through the brightness temperature spectral index of
low-frequency radio emission, here denoted as $\beta_{\rm obs}$. We introduce a
new parametric analytical model that fits available data of $j_e$ in accordance
with the $\beta_{\rm obs}$ values measured in the literature between 50 MHz to
1 GHz for diffuse emission in the Milky Way. Our model allows to account for
multiple observations considering magnetic-field strengths consistent with
existing measurements below 10 $\mu$G. 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 in preparation
for the imminent arrival of the Square Kilometre Array.
