AGN Coronal Emission models I. The Predicted Radio Emission
  Accretion discs in AGN may be associated with coronal gas, as suggested by
their X-ray emission. Stellar coronal emission includes radio emission, and AGN
corona may also be a significant source for radio emission in radio quiet (RQ)
AGN. We calculate the coronal properties required to produce the observed radio
emission in RQ AGN, either from synchrotron emission of power-law (PL)
electrons, or from cyclo-synchrotron emission of hot mildly-relativistic
thermal electrons. We find that a flat spectrum, as observed in about half of
RQ AGN, can be produced by corona with a disc or a spherical configuration,
which extends from the innermost regions out to a pc scale. A spectral break to
an optically thin power-law emission is expected around 300-1000 GHz, as the
innermost corona becomes optically thin. In case of thermal electrons, a sharp
spectral cutoff is expected above the break. The position of the break can be
measured with VLBI observations, which exclude the cold dust emission, and it
can be used to probe the properties of the innermost corona. Assuming
equipartition of the coronal thermal energy density, the PL electrons energy
density, and the magnetic field, we find that the energy density in a disc
corona should scale as $\sim R^{-1.3}$, to get a flat spectrum. In the
spherical case the energy density scales as $\sim R^{-2}$, and is $\sim 4\times
10^{-4}$ of the AGN radiation energy density. In paper II we derive additional
constraints on the coronal parameters from the Gudel-Benz relation, $L_{\rm
Radio}/L_{\rm X-ray}\sim 10^{-5}$, which RQ AGN follow.
