  The evidence for the presence of a concentration of dark matter at the
Galactic center is now very compelling. There is no question that the stellar
and gas kinematics within 0.01 pc is dominated by under-luminous matter in the
form of either a massive black hole, a highly condensed distribution of stellar
remnants, or a more exotic source of gravity. The unique, compact radio source
Sgr A* appears to be coincident with the center of this region, but its size
(less than 3x10^14 cm at lambda=1.35cm) is still significantly smaller than the
current limiting volume enclosing this mass. Sgr A* may be the black hole, if
the dark matter distribution is point-like. If not, we are left with a puzzle
regarding its nature, and a question of why this source should be so unique and
lie only at the Galactic center. Here, we examine an alternative to the black
hole paradigm---that the gravitating matter is a condensed cluster of stellar
remnants---and study the properties of the Galactic center wind flowing through
this region. Some of this gas is trapped in the cluster potential, and we study
in detail whether this hot, magnetized gas is in the proper physical state to
produce Sgr A*'s spectrum. We find that at least for the Galactic center
environment, the temperature of the trapped gas never attains the value
required for significant GHz emission. In addition, continuum (mostly
bremsstrahlung) emission at higher frequencies is below the current
measurements and upper limits for this source. We conclude that the cluster
potential is too shallow for the trapped Galactic center wind to account for
Sgr A*'s spectrum, which instead appears to be produced only within an
environment that has a steep-gradient potential like that generated by a black
hole.
