A powerful flare from Sgr A* confirms the synchrotron nature of the X-ray emission

We present the first fully simultaneous fits to the near-infrared (NIR) and X-ray spectral slope (and its evolution) during a very bright flare from Sgr A*, the supermassive black hole at the MilkyWay's centre. Our study arises from ambitious multiwavelength monitoring campaigns with XMM-Newton, NuSTAR and SINFONI. The average multiwavelength spectrum is well reproduced by a broken power law with Gamma(NIR) = 1.7 +/- 0.1 and Gamma(X) = 2.27 +/- 0.12. The difference in spectral slopes (Delta Gamma = 0.57 +/- 0.09) strongly supports synchrotron emission with a cooling break. The flare starts first in the NIR with a flat and bright NIR spectrum, while X-ray radiation is detected only after about 103 s, when a very steep X-ray spectrum (Delta Gamma = 1.8 +/- 0.4) is observed. These measurements are consistent with synchrotron emission with a cooling break and they suggest that the high-energy cut-off in the electron distribution (gamma(max)) induces an initial cut-off in the optical-UV band that evolves slowly into the X-ray band. The temporal and spectral evolution observed in all bright X-ray flares are also in line with a slow evolution of gamma(max). We also observe hints for a variation of the cooling break that might be induced by an evolution of the magnetic field (from B similar to 30 +/- 8 G to B similar to 4.8 +/- 1.7 G at the X-ray peak). Such drop of the magnetic field at the flare peak would be expected if the acceleration mechanism is tapping energy from the magnetic field, such as in magnetic reconnection. We conclude that synchrotron emission with a cooling break is a viable process for Sgr A*' s flaring emission.