  The sub-mm bump observed in the spectrum of Sgr A* appears to indicate the
existence of a compact emitting component within several Schwarzschild radii,
$r_S$, of the nucleus at the Galactic Center. This is interesting in view of
the predicted circularized flow within $\sim 5-10 r_S$, based on detailed
multi-dimensional hydrodynamic simulations of Bondi-Hoyle accretion onto this
unusual object. In this paper, we examine the physics of magnetic field
generation by a Keplerian dynamo subject to the conditions pertaining to Sgr
A*, and show that the sub-mm bump can be produced by thermal synchrotron
emission in this inner region. This spectral feature may therefore be taken as
indirect evidence for the existence of this circularization. In addition, the
self-Comptonization of the sub-mm bump appears to produce an X-ray flux
exceeding that due to bremsstrahlung from this region, which may account for
the X-ray counterpart to Sgr A* discovered recently by {\it Chandra}. However,
the required accretion rate in the Keplerian flow is orders of magnitude
smaller than that predicted by the Bondi-Hoyle simulations. We speculate that
rapid evaporation, in the form of a wind, may ensue from the heating associated
with turbulent mixing of gas elements with large eccentricity as they settle
down into a more or less circular (i.e., low eccentricity) trajectory. The
spectrum of Sgr A* longward of $\sim 1-2$ mm may be generated outside of the
Keplerian flow, where the gas is making a transition from a quasi-spherical
infall into a circularized pattern.
