Radiation pressure confinement -- V. The predicted free-free absorption
  and emission in active galactic nuclei
  The effect of radiation pressure compression (RPC) on ionized gas in Active
Galactic Nuclei (AGN) likely sets the photoionized gas density structure. The
photoionized gas free-free absorption and emission are therefore uniquely set
by the incident ionizing flux. We use the photoionization code Cloudy RPC model
results to derive the expected relations between the free-free emission and
absorption properties and the distance from the AGN centre, for a given AGN
luminosity. The free-free absorption frequency of RPC gas is predicted to
increases from $\sim$100 MHz on the kpc scale, to $\sim$100 GHz on the sub-pc
scale, consistent with observations of spatially resolved free-free absorption.
The free-free emission at 5 GHz is predicted to yield a radio loudness of
$R\sim 0.03$, below the typical observed values of $R\sim 0.1-1$ in radio-quiet
AGN. However, the flat free-free radio continuum may become dominant above 100
GHz. The suggested detection of optically thin free-free emission in NGC 1068,
on the sub pc torus scale, is excluded as the brightness temperature is too
high for optically thin free-free emission. However, excess emission observed
with ALMA above 150 GHz in NGC 1068, is consistent with the predicted free-free
emission from gas just outside the broad line region, a region which overlaps
the hot dust disc resolved with GRAVITY. Extended $\sim$100 pc scale free-free
emission is also likely present in NGC 1068. Future sub mm observation of radio
quiet AGN with ALMA may allow to image the free-free emission of warm
photoionized gas in AGN down to the 30 mas scale, including highly absorbed
AGN.
