Discovery of a relation between black hole mass and soft X-ray time lags in active galactic nuclei

We carried out a systematic analysis of time lags between X-ray energy bands in a large sample (32 sources) of unabsorbed, radio quiet active galactic nuclei (AGN), observed by XMM-Newton. The analysis of X-ray lags (up to the highest/shortest frequencies/time-scales), is performed in the Fourier-frequency domain, between energy bands where the soft excess (soft band) and the primary power law (hard band) dominate the emission. We report a total of 15 out of 32 sources displaying a high frequency soft lag in their light curves. All 15 are at a significance level exceeding 97 per cent and 11 are at a level exceeding 99 per cent. Of these soft lags, 7 have not been previously reported in the literature, thus this work significantly increases the number of known sources with a soft/negative lag. The characteristic time-scales of the soft/negative lag are relatively short (with typical frequencies and amplitudes of \nu\sim 0.07-4 \times 10^{-3} Hz and \tau\sim 10-600 s, respectively), and show a highly significant (\gsim 4\sigma) correlation with the black hole mass. The measured correlations indicate that soft lags are systematically shifted to lower frequencies and higher absolute amplitudes as the mass of the source increases. To first approximation, all the sources in the sample are consistent with having similar mass-scaled lag properties. These results strongly suggest the existence of a mass-scaling law for the soft/negative lag, that holds for AGN spanning a large range of masses (about 2.5 orders of magnitude), thus supporting the idea that soft lags originate in the innermost regions of AGN and are powerful tools for testing their physics and geometry.