  We show that the radial profiles of the temperature and density of the
electrons as well as the magnetic field strength around the massive black hole
at the Galactic center, SgrA*, may be constrained directly from existing radio
data without any need to make prior assumptions about the dynamics of the
emitting gas. The observed spectrum and wavelength-dependent angular size of
SgrA* indicate that the synchrotron emission originates from an optically-thick
plasma of quasi-thermal electrons. We find that the electron temperature rises
above the virial temperature within tens of Schwarzschild radii from the black
hole, suggesting that the emitting plasma may be outflowing. Constraints on the
electron density profile are derived from polarization measurements. Our
best-fit results differ from expectations based on existing theoretical models.
However, these models cannot be ruled out as of yet due to uncertainties in the
source size measurements. Our constraints could tighten considerably with
future improvements in the size determination and simultaneous polarization
measurements at multiple wavelengths.
