A light bending model for the X–ray temporal and spectral properties of accreting black holes

Some of the X–ray temporal and spectral properties of accreting black holes represent a challenge for current theoretical models. In particular, uncorrelated variability between direct continuum and reflection components (including the iron line, if present) has been reported in many cases. Here, we explore a light bending model in which we assume a primary source of X–rays located close to a central, maximally rotating Kerr black hole and illuminating both the observer at infinity and the accretion disc. We show that, due to strong light bending, the observed flux can vary by more than one order of magnitude as the height of the primary source above the accretion disc varies, even if its intrinsic luminosity is constant. We identify three different regimes in which the reflection–dominated component (and the iron line) is correlated, anti–correlated or almost independent with respect to the direct continuum. These regimes correspond to low, high and intermediate flux states of the X–ray source. As a general rule, the reflection component varies with much smaller amplitude than the continuum. X–ray observations of the Seyfert galaxy MCG–6-30-15 and of the Galactic black hole candidate XTE J1650–500 reveal that a series of predictions of our model are actually observed: the consistent behaviour of the iron line flux and equivalent width (EW) with respect to the direct continuum, as well as the increase of the relative strength of disc reflection as the flux drops, all match very well our predictions. The iron line profile is predicted to be narrower in high flux states and broader in (reflection–dominated) low flux states, in fairly good agreement with observations of the best–studied case of MCG–6-30-15. Observations of some other Narrow Line Seyfert 1 galaxies (e.g. NGC 4051) also seem to support our model, which may explain what are otherwise puzzling characteristics of some sources. We also show that beaming along the equatorial plane can enhance the re–emission of narrow reflection features from distant material during low flux states providing a possible contribution to the observed X–ray Baldwin effect.