The relation between the 2 - 10 keV , long term , excess variance and AGN black hole mass is considered in this work .
A significant anti-correlation is found between these two quantities in the sense that the excess variance decreases with increasing black hole mass .
This anti-correlation is consistent with the hypothesis that the 2 - 10 keV power spectrum in AGN follows a power law of slope -2 at high frequencies .
It then flattens to a slope of -1 below a break frequency , \nu _ { hfb } , until a second break frequency , \nu _ { lfb } , below which it flattens to a slope of zero .
The ratio \nu _ { hfb } / \nu _ { lfb } is equal to 10 - 30 , similar to the ratio of the respective frequencies in Cyg X-1 .
The power spectrum amplitude in the ( frequency \times power ) space does not depend on black hole mass .
Instead it is roughly equal to 0.02 in all objects .
The high frequency break decreases with increasing black hole mass according to the relation \nu _ { hfb } = 1.5 \times 10 ^ { -6 } / ( M/ 10 ^ { 7 } M _ { \odot } ) Hz , in the case of “ classical ” Seyfert 1 galaxies .
The excess variance of NGC 4051 , a Narrow Line Seyfert 1 object , is larger than what is expected for its black hole mass and X–ray luminosity .
This can be explained if its \nu _ { hfb } is 20 times larger than the value expected in the case of a “ classical ” Seyfert 1 with the same black hole mass .
Finally , the excess variance vs X–ray luminosity correlation is a byproduct of the excess variance vs black hole mass correlation , with AGN accreting at \sim 0.1 - 0.15 the Eddington limit .
These results are consistent with recent results from the power spectral analysis of AGN .
However , as they are based on data from a few objects only , further investigation is necessary to confirm that there is indeed a “ universal ” power spectrum shape in AGN ( in the sense that the value of the power spectrum parameters of most AGN will be distributed around the “ canonical ” slope , and amplitude values listed above ) .
One way to achieve this is to determine the excess variance vs black hole relation more accurately , using data from many more objects .
This will be possible in the near future , since it is easier to measure the excess variance of archival light curves than to estimate their power spectrum .
The excess variance vs black hole relation can therefore play an important role in the study of the X–ray variability scaling with black hole mass in AGN .