The quiet Sun, i.e. in its non-flaring state or non-flaring regions, produces non-thermal radiation
observed in gamma rays due to interactions of Galactic Cosmic Rays (GCR) with the solar gas
and photons.Here, we report our very recent study (Orlando et al. 2023, ApJ 943, 173) on a new
component: the synchrotron emission by GCR electrons in the solar magnetic field. To the best
of our knowledge this is the first time this emission has been theoretically claimed and modeled.
We find that the measured GCR electrons with energies from tens of GeV to a few TeV produce
synchrotron emission in X-rays, which is a few orders of magnitude lower than current upper
limits of the quiet Sun set by RHESSI and FOXSI. For a radially decreasing solar magnetic field
we find the expected synchrotron intensity to be almost constant in the solar disk, to peak in the
close proximity of the Sun, and to quickly drop away from the Sun. We estimate the synchrotron
emission from radio to gamma rays and we compare it with current observations, especially
with LOFAR. While it is negligible from radio to UV compared to the solar thermal radiation,
this emission can potentially be observed at high energies with X-ray instruments and more
promising future FOXSI observations. This could potentially allow for constraining CR densities
and magnetic-field intensities at the Sun. This study provides a more complete description and a
possible new way for understanding the quiet Sun and its environment.