  Feedback from outflows driven by active galactic nuclei (AGN) can affect the
distribution and properties of the gaseous halos of galaxies. We study the
hydrodynamics and non-thermal emission from the forward outflow shock produced
by an AGN-driven outflow. We consider a few possible profiles for the halo gas
density, self-consistently constrained by the halo mass, redshift and the disk
baryonic concentration of the galaxy. We show that the outflow velocity levels
off at $\sim 10^3\,\rm km\, s^{-1}$ within the scale of the galaxy disk.
Typically, the outflow can reach the virial radius around the time when the AGN
shuts off. We show that the outflows are energy-driven, consistently with
observations and recent theoretical findings. The outflow shock lights up the
halos of massive galaxies across a broad wavelength range. For Milky Way (MW)
mass halos, radio observations by The Jansky Very Large Array (JVLA) and The
Square Kilometer Array (SKA) and infrared/optical observations by The James
Webb Space Telescope (JWST) and Hubble Space Telescope (HST) can detect the
emission signal of angular size $\sim 8"$ from galaxies out to redshift
$z\sim5$. Millimeter observations by The Atacama Large Millimeter/submillimeter
Array (ALMA) are sensitive to non-thermal emission of angular size $\sim 18"$
from galaxies at redshift $z\lesssim1$, while X-ray observations by Chandra,
XMM-Newton and The Advanced Telescope for High Energy Astrophysics (ATHENA) is
limited to local galaxies ($z\lesssim 0.1$) with an emission angular size of
$\sim2'$. Overall, the extended non-thermal emission provides a new way of
probing the gaseous halos of galaxies at high redshifts.
