Context : We report on a successful , simultaneous observation and modeling of the sub-millimeter to near-infrared flare emission of the Sgr A* counterpart associated with the super-massive ( 4 \times 10 ^ { 6 } M _ { \odot } ) black hole at the Galactic center .

Aims : We study and model the physical processes giving rise to the variable emission of Sgr A* .

Methods : Our non-relativistic modeling is based on simultaneous observations that have been carried out on 03 June , 2008 .
We used the NACO adaptive optics ( AO ) instrument at the European Southern Observatory ’ s Very Large Telescope and the LABOCA bolometer at the Atacama Pathfinder Experiment ( APEX ) .
We emphasize the importance of a multi-wavelength simultaneous fitting as a tool for imposing adequate constraints on the flare modeling .

Results : The observations reveal strong flare activity in the 0.87 mm ( 345 GHz ) sub-mm domain and in the 3.8 \mu /2.2 \mu m NIR .
Inspection and modeling of the light curves show that the sub-mm follows the NIR emission with a delay of 1.5 \pm 0.5 hours .
We explain the flare emission delay by an adiabatic expansion of the source components .
The derived physical quantities that describe the flare emission give a source component expansion speed of v _ { exp } \sim 0.005 c , source sizes around one Schwarzschild radius with flux densities of a few Janskys , and spectral indices of \alpha =0.8 to 1.8 , corresponding to particle spectral indices \sim 2.6 to 4.6 .
At the start of the flare the spectra of these components peak at frequencies of a few THz .

Conclusions : These parameters suggest that the adiabatically expanding source components either have a bulk motion greater than v _ { exp } or the expanding material contributes to a corona or disk , confined to the immediate surroundings of Sgr A* .