An X-ray/SDSS sample (II): outflowing gas plasma properties
  Galaxy-scale outflows are nowadays observed in many active galactic nuclei
(AGNs); however, their characterisation in terms of (multi-) phase nature,
amount of flowing material, effects on the host galaxy, is still unsettled. In
particular, ionized gas mass outflow rate and related energetics are still
affected by many sources of uncertainties. In this respect, outflowing gas
plasma conditions, being largely unknown, play a crucial role.
  Taking advantage of the spectroscopic analysis results we obtained studying
the X-ray/SDSS sample of 563 AGNs at z $<0.8$ presented in our companion paper,
we analyse stacked spectra and sub-samples of sources with high signal-to-noise
temperature- and density-sensitive emission lines to derive the plasma
properties of the outflowing ionized gas component. For these sources, we also
study in detail various diagnostic diagrams to infer information about
outflowing gas ionization mechanisms. We derive, for the first time, median
values for electron temperature and density of outflowing gas from medium-size
samples ($\sim 30$ targets) and stacked spectra of AGNs. Evidences of shock
excitation are found for outflowing gas.
  We measure electron temperatures of the order of $\sim 1.7\times10^4$ K and
densities of $\sim 1200$ cm$^{-3}$ for faint and moderately luminous AGNs
(intrinsic X-ray luminosity $40.5<log(L_X)<44$ in the 2-10 keV band). We
caution that the usually assumed electron density ($N_e=100$ cm$^{-3}$) in
ejected material might result in relevant overestimates of flow mass rates and
energetics and, as a consequence, of the effects of AGN-driven outflows on the
host galaxy.
