  Odd radio circles (ORCs) are mysterious rings of faint, diffuse emission
recently discovered in radio surveys, some of which may be associated with
galaxies in relatively dense environments. We propose such ORCs to be
synchrotron emission from remnants of explosive galactic outflows, calling them
OGREs, and discuss their broadband non-thermal emission and evolution. We posit
that a large amount of energy was ejected from the central galaxy in the past,
creating an outgoing shock that accelerates cosmic rays. Assuming plausible
values for the density, temperature and magnetic field of the ambient medium,
consistency with the observed spectral index, size and power of the ORCs
requires the energy to be as high as ~10^60 erg, suggesting that their sources
could be active galactic nuclei. We calculate the spectral energy distributions
(SEDs) of the OGREs and their evolution, including synchrotron, inverse Compton
(IC) and bremsstrahlung emission from electrons, and pion-decay emission from
protons. We find that the SEDs of the younger OGREs are not greatly different
from those of older ones currently observable as ORCs if radiative cooling of
electrons is effective. As such younger OGREs are expected to be rarer and
smaller, they may not be readily observable. However, if radiative cooling of
electrons is ineffective, younger OGREs may be detectable in X-rays.
