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Context. The near-infrared (NIR) counterpart of Sagittarius A* (SgrA*) at the position of the 4 x 10(6) M(circle dot) supermassive black hole at the center of the Milky Way has strongly varying flux densities. The broad-band near-infrared spectral index is an essential parameter to determine the underlying emission mechanism for the observed flare emission. Aims. We present a method to derive the NIR spectral index of SgrA* between the H- and Ks-band from the statistics of the observed flare emission. Our spectral index derivation is therefore based on an unprecedentedly large timebase of about seven years of monitoring the infrared counterpart of SgrA*. Methods. We examined NIR light curves of SgrA* in the H- and Ks-band and established flare number distributions as a function of peak flare flux. We assume that in both bands the same optically thin dominant emission mechanism is at work and produces similar number distributions of flares. We cross-correlated these histograms and determined a statistical expectation value of the H-Ks-band spectral index during the bright phases of SgrA*. Results. With this new method, we can independently confirm that the expectation value of the spectral index for brighter flares is consistent with alpha = -0.7 (with the flux density (F(nu) proportional to nu(+alpha))) which is expected for pure synchrotron radiation. We find a tendency for weaker flares to exhibit a steeper spectrum. Conclusions. We conclude that the distribution of spectral indices as a function of Ks-band flux density can successfully be described by an exponential cutoff proportional to expleft perpendicular-(nu/nu(0))(0.5)right perpendicular because of synchrotron losses, with nu(0) being a characteristic cutoff frequency. Varying nu(0) between the NIR and sub-mm domain and assuming a sub-mm flux density variation of about one Jansky and optically thin spectral indices of alpha = -0.7 +/- 0.3 explains the observed spectral properties of SgrA* in the NIR.

The near-infrared spectral index of Sagittarius A* derived fromKs- andH-band flare statistics