  (abridged) The connection between black hole, accretion disk, and radio jet
can be best constrained by fitting models to observations of nearby low
luminosity galactic nuclei, in particular the well studied sources Sgr~A* and
M87. There has been considerable progress in modeling the central engine of
active galactic nuclei by an accreting supermassive black hole coupled to a
relativistic plasma jet. However, can a single model be applied to a range of
black hole masses and accretion rates? Here we want to compare the latest
three-dimensional numerical model, originally developed for Sgr A* in the
center of the Milky Way, to radio observations of the much more powerful and
more massive black hole in M87. We postprocess three-dimensional GRMHD models
of a jet-producing radiatively inefficient accretion flow around a spinning
black hole using relativistic radiative transfer and ray-tracing to produce
model spectra and images. As a key new ingredient to these models, we allow the
proton-electron coupling in these simulations depend on the magnetic properties
of the plasma. We find that the radio emission in M87 is well described by a
combination of a two-temperature accretion flow and a hot single-temperature
jet. The model fits the basic observed characteristics of the M87 radio core.
The best fit model has a mass-accretion rate of Mdot approx 9x10^{-3} MSUN/YR
and a total jet power of P_j \sim 10^{43} erg/s. Emission at 1.3mm is produced
by the counter jet close to the event horizon. Its characteristic crescent
shape surrounding the black hole shadow could be resolved by future
millimeter-wave VLBI experiments. The model was successfully derived from one
for the supermassive black hole in center of the Milky Way by appropriately
scaling mass and accretion rate. This suggests the possibility that this model
could also apply to a larger range of low-luminosity black holes.
