We present theoretical models of X-ray variability attributable to orbital signatures from an accretion disk including emission region size , quasi-periodic oscillations ( QPOs ) and its quality factor Q , and the emergence of a break frequency in the power spectral density shape .
We find a fractional variability amplitude of F _ { var } \propto M ^ { -0.4 } _ { \bullet } .
We conduct a time series analysis on X-ray light curves ( 0.3 - 10 keV ) of a sample of active galactic nuclei ( AGNs ) .
A statistically significant bend frequency is inferred in 9 of 58 light curves ( 16 % ) from 3 AGNs for which the break timescale is consistent with the reported BH spin but not with the reported BH mass .
Upper limits of 2.85 \times 10 ^ { 7 } M _ { \odot } in NGC 4051 , 8.02 \times 10 ^ { 7 } M _ { \odot } in MRK 766 and 4.68 \times 10 ^ { 7 } M _ { \odot } in MCG-6-30-15 are inferred for maximally spinning BHs .
For REJ 1034+396 , where a QPO at 3733 s was reported , we obtain an emission region size of ( 6 - 6.5 ) M and a BH spin a \lesssim 0.08 .
The relativistic inner region of a thin disk , dominated by radiation pressure and electron scattering is likely to host the orbital features as the simulated Q ranges from 6.3 \times 10 ^ { -2 } to 4.25 \times 10 ^ { 6 } , containing the observed Q .
The derived value of Q \sim 32 for REJ 1034+396 therefore suggests that the AGN hosts a thin disk .