We present the first systematic physical modelling of the time-lag spectra between the soft ( 0.3–1 keV ) and the hard ( 1.5–4 keV ) X-ray energy bands , as a function of Fourier frequency , in a sample of 12 active galactic nuclei which have been observed by XMM - Newton .
We concentrate particularly on the negative X-ray time-lags ( typically seen above 10 ^ { -4 } Hz ) i.e .
soft band variations lag the hard band variations , and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry .
We also assume that the response of the accretion disc , in the soft X-ray bands , is adequately described by the response in the neutral Fe K \alpha line at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution .
These response functions , and thus the corresponding time-lag spectra , yield much more realistic results than the commonly-used , but erroneous , top-hat models .
Additionally we parametrize the positive part of the time-lag spectra ( typically seen below 10 ^ { -4 } Hz ) by a power-law .
We find that the best-fitting BH masses , M , agree quite well with those derived by other methods , thus providing us with a new tool for BH mass determination .
We find no evidence for any correlation between M and the BH spin parameter , \alpha , the viewing angle , \theta , or the height of the X-ray source above the disc , h .
Also on average , the X-ray source lies only around 3.7 gravitational radii above the accretion disc and \theta is distributed uniformly between 20 and 60° .
Finally , there is a tentative indication that the distribution of \alpha may be bimodal above and below 0.62 .