  The quiet Sun, i.e. in its non-flaring state or non-flaring regions, emits
thermal radiation from radio to ultraviolet. The quiet Sun produces also
non-thermal radiation observed in gamma rays due to interactions of Galactic
Cosmic Rays (GCR) with the solar gas and photons. We report 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 also 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 NuSTAR 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 quite Sun and its environment.
