Context : We report on a successful , simultaneous observation and modelling of the millimeter ( mm ) to near-infrared ( NIR ) flare emission of the Sgr A* counterpart associated with the supermassive ( 4 \times 10 ^ { 6 } M _ { \odot } ) black hole at the Galactic centre ( GC ) .
We present a mm/sub-mm light curve of Sgr A* with one of the highest quality continuous time coverages .

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

Methods : Our non-relativistic modelling is based on simultaneous observations carried out in May 2007 and 2008 , using the NACO adaptive optics ( AO ) instrument at the ESO ’ s VLT and the mm telescope arrays CARMA in California , ATCA in Australia , and the 30 m IRAM telescope in Spain .
We emphasize the importance of multi-wavelength simultaneous fitting as a tool for imposing adequate constraints on the flare modelling .
We present a new method for obtaining concatenated light curves of the compact mm-source Sgr A* from single dish telescopes and interferometers in the presence of significant flux density contributions from an extended and only partially resolved source .

Results : The observations detect flaring activity in both the mm domain and the NIR .
Inspection and modelling of the light curves show that in the case of the flare event on 17 May 2007 , the mm emission follows the NIR flare emission with a delay of 1.5 \pm 0.5 hours .
On 15 May 2007 , the NIR flare emission is also followed by elevated mm-emission .
We explain the flare emission delay by an adiabatic expansion of source components .
For two other NIR flares , we can only provide an upper limit to any accompanying mm-emission of about 0.2 Jy .
The derived physical quantities that describe the flare emission give a source component expansion speed of v _ { \mathrm { exp } } \sim 0.005 c - 0.017 c , source sizes of about one Schwarzschild radius , flux densities of a few Janskys , and spectral indices of \alpha =0.6 to 1.3 .
These source components peak in the THz regime .

Conclusions : These parameters suggest that either the adiabatically expanding source components have a bulk motion greater than v _ { \mathrm { exp } } or the expanding material contributes to a corona or disk , confined to the immediate surroundings of Sgr A* .
Applying the flux density values or limits in the mm- and X-ray domain to the observed flare events constrains the turnover frequency of the synchrotron components that are on average not lower than about 1 THz , such that the optically thick peak flux densities at or below these turnover frequencies do not exceed , on average , about \sim 1 Jy .