  Bright AGN frequently show ultra-fast outflows (UFOs) with outflow velocities
vout ~0.1c. These outflows may be the source of AGN feedback on their host
galaxies sought by galaxy formation modellers. The exact effect of the outflows
on the ambient galaxy gas strongly depends on whether the shocked UFOs cool
rapidly or not. This in turn depends on whether the shocked electrons share the
same temperature as ions (one temperature regime; 1T) or decouple (2T), as has
been recently suggested. Here we calculate the Inverse Compton spectrum emitted
by such shocks, finding a broad feature potentially detectable either in
mid-to-high energy X-rays (1T case) or only in the soft X-rays (2T). We argue
that current observations of AGN do not seem to show evidence for the 1T
component. The limits on the 2T emission are far weaker, and in fact it is
possible that the observed soft X-ray excess of AGN is partially or fully due
to the 2T shock emission. This suggests that UFOs are in the energy-driven
regime outside the central few pc, and must pump considerable amounts of not
only momentum but also energy into the ambient gas. We encourage X-ray
observers to look for the Inverse Compton components calculated here in order
to constrain AGN feedback models further.
