We present the first fully simultaneous fits to the NIR and X-ray spectral slope ( and its evolution ) during a very bright flare from Sgr A ^ { \star } , the supermassive black hole at the Milky Way ’ s center .
Our study arises from ambitious multi-wavelength monitoring campaigns with XMM-Newton , NuSTAR and SINFONI .
The average multi-wavelength spectrum is well reproduced by a broken power-law with \Gamma _ { NIR } = 1.7 \pm 0.1 and \Gamma _ { X } = 2.27 \pm 0.12 .
The difference in spectral slopes ( \Delta \Gamma = 0.57 \pm 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 10 ^ { 3 } s , when a very steep X-ray spectrum ( \Delta \Gamma = 1.8 \pm 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 \sim 30 \pm 8 G to B \sim 4.8 \pm 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 ^ { \star } ’ s flaring emission .