Proposed scaling relations of a characteristic timescale in the X-ray power spectral density of galactic and supermassive black holes have been used to argue that the accretion process is the same for small and large black holes .
Here , we report on the discovery of this timescale in the near-infrared radiation of Sgr A* , the 4 \cdot 10 ^ { 6 } \mbox { M } _ { \sun } black hole at the center of our Galaxy , which is the most extreme sub-Eddington source accessible to observations .
Previous simultaneous monitoring campaigns established a correspondence between the X-ray and near-infrared regime and thus the variability timescales are likely identical for the two wavelengths .
We combined Keck and VLT data sets to achieve the necessary dense temporal coverage , and a time baseline of four years allows for a broad temporal frequency range .
Comparison with Monte Carlo simulations is used to account for the irregular sampling .
We find a timescale at 154 ^ { +124 } _ { -87 } min ( errors mark the 90 % confidence limits ) which is inconsistent with a recently proposed scaling relation that uses bolometric luminosity and black hole mass as parameters .
However , our result fits the expected value if only linear scaling with black hole mass is assumed .
We suggest that the luminosity-mass-timescale relation applies only to black hole systems in the soft state .
In the hard state , which is characterized by lower luminosities and accretion rates , there is just linear mass scaling , linking Sgr A* to hard state stellar mass black holes .