Can the relativistic light bending model explain X-ray spectral variations of Seyfert galaxies?

Many Seyfert galaxies are known to exhibit Fe-K broad emission line features in their X-ray energy spectra. The observed lines have three distinct features; (1) the line profiles are skewed and show significant low-energy tails, (2) the Fe-K band have low variability, which produces a broad and deep dip in the root-mean-square (rms) spectra, and (3) photons in this band have time lags behind those in the adjacent energy bands with amplitudes of several $R_g/c$, where $R_g$ is the gravitational radius. The "relativistic light bending model" is proposed to explain these observed features, where a compact X-ray source (lamp post) above an extreme Kerr black hole illuminates the innermost area of the accretion disc. In this paper, we critically examine the relativistic light bending model by computing the rms spectra and the lag features using a ray-tracing technique, when a lamp post moves vertically on the black hole spin axis. As a result, we found that the observed deep rms dip requires that the iron is extremely overabundant ($\gtrsim10$ solar), whereas the observed lag amplitude is consistent with the normal iron abundance. Furthermore, disappearance of the lag in the high-flux state requires a source height as high as $\sim40\,R_g$, which contradicts the relativistically broad emission line feature. Our simulations agree with the data that the reverberation feature moves to lower frequencies with larger source height, however, if this scenario is correct, the simulations predict detection of a clear Fe-K lag at low frequencies, which is not constrained in the data. Therefore, we conclude that the relativistic light bending model may not explain the characteristic Fe-K spectral variations in Seyfert galaxies.