X-Ray Variability and the Inner Region in Active Galactic Nuclei

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 $F_{var}\propto M_{\bullet }^{-0.4}$. 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, $8.02 \times 10^7 M_\odot$inMRK766and$4.68 \times 10^7 M_\odot$ 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 $4.25 \times 10^6$,containingtheobserved$Q$\mathrm{.}Thederivedvalueof$Q \sim$ 32 for REJ 1034+396 therefore suggests that the AGN hosts a thin disk.