Stellar gas flows into a dark cluster potential at the Galactic center

The evidence for the presence of a concentration of dark matter at the Galactic center (GC) is now very compelling. There is no question that the stellar and gas kinematics within ≈0.01 pc is dominated by underluminous 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 about 6 × 10¹³ cm at λ7 mm) 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 pointlike. 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 GC. In this paper, 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 GC 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 GC 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 for this source. We conclude that the cluster potential is too shallow for the trapped GC 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.