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 has 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 (≳10 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 ∼40 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 the 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.