ALMA Observations of the Terahertz Spectrum of Sagittarius A*

We present ALMA observations at 233, 678, and 870 GHz of the Galactic Center black hole, Sagittarius A*. These observations reveal a flat spectrum over this frequency range with spectral index $\alpha \approx -0.3$, where the flux density $S \propto \nu^\alpha$. We model the submm and far infrared spectrum with a one zone synchrotron model of thermal electrons. We infer electron densities $n = (2-5) \times 10^6$ cm$^{-3}$, electron temperatures $T_e = (1-3) \times 10^{11}$ K, and magnetic field strength $B = 10-50$ G. The parameter range can be further constrained using the observed quiescent X-ray luminosity. The flat submm spectrum results in a high electron temperature and implies that the emitting electrons are efficiently heated. We also find that the emission is most likely optically thin at 233 GHz. These results indicate that millimeter and submillimeter wavelength very long baseline interferometry of Sgr A* including those of the Event Horizon Telescope should see a transparent emission region down to event horizon scales.