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

G. Miniutti 0 A. C. Fabian 0 0 Institute of Astronomy, University of Cambridge , Madingley Road, Cambridge CB3 0HA A B S T R A C T 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, anticorrelated 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 is actually observed; the consistent behaviour of the iron line flux and equivalent width 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. - The X-ray temporal and spectral properties of a class of active galactic nuclei (AGNs) show interesting behaviour that is difficult to understand within the current theoretical view. This is most true for those systems in which reflection spectral components and fluorescent iron lines have been detected. Reflection in AGNs is generally believed to be associated with the reprocessing of the primary continuum by cold material in the accretion disc close to the central black hole (George & Fabian 1991; Matt, Perola & Piro 1991) and/or by more distant material, such as the putative torus of unified models (Antonucci 1993). The presence of broad and redshifted iron lines in some sources indicates that special and general relativistic effects play an important role in producing the line shape, supporting the idea that reflection from the inner regions of an accretion disc is present (Fabian et al. 1989; Laor 1991; Martocchia & Matt 1996; Reynolds & Begelman 1997). However, the variability of the reflection component, and most remarkably of the iron line, is not correlated in a trivial manner to that of the observed continuum. The iron line does not always respond to variations in the continuum as simple reflection models predict. In some cases, an anticorrelation between the iron line and the continuum has been reported; sometimes, the iron line can appear to be constant while the continuum varies with large amplitude (see, for example, Markowitz, Edelson & Vaughan 2003a). Furthermore, the profile of the broad iron line (most remarkably in the Seyfert 1 galaxy MCG6-30-15) exhibits a singular behaviour: qualitatively, the line tends to be very broad in low flux states, while a narrower core is detected in high flux states (Iwasawa et al. 1996; Wilms et al. 2001; Lee et al. 2002). Moreover, in many sources, the line equivalent width (EW) and the reflection fraction tend to anticorrelate (or, in some cases, to remain constant) with the continuum (Lamer, Uttley & McHardy 2000; Papadakis et al. 2002). If the continuum that we observe is the same that illuminates the disc, these behaviours are difficult to understand. The uncorrelated variability between the iron line and the continuum may be explained by requiring that it originates from a distant reflector so that the variability of the illuminating continuum is averaged out. However, this interpretation conflicts with the observation of broad and redshifted iron lines in some sources that strongly suggests an origin close to the central black hole (see, for example, Fabian et al. 2000 and Reynolds & Nowak 2003 for a review on iron lines). Alternative explanations for the observed spectra which do not require emission from the inner regions of the accretion disc have been proposed (see, for example, Inoue & Matsumoto 2003). Here we consider a model based on the gravitational light bending suffered by the radiation emitted in the near vicinity of a rotating black hole with the aim of reconciling the observed puzzling properties of some X-ray sources with the theory of reflection models from accretion discs. We investigate the variability induced by light bending by assuming that the primary source of hard X-rays is centrally concentrated near the axis of a Kerr black hole. Variations in the height of the primary source above the accretion disc produce the bulk of the variability of both the observed continuum and the reflection component (Martocchia, Matt & Karas 2002a; Fabian & Vaughan 2003). This idea was presented in Miniutti et al. (2003) and successfully explained the puzzling uncorrelated variability of the broad iron line and continuum seen in a 325-ks XMMNewton observation of the Seyfert 1 galaxy MCG6-30-15 (Fabian et al. 2002a; Fabian & Vaughan 2003; Vaughan & Fabian 2004). After presenting the main properties and predictions of the light bending model, we review the phenomenology of some X-ray sources, and compare our predictions with the available data. 2 L I G H T B E N D I N G M O D E L In this section, we describe the most relevant assumptions and the basic idea of our model for the spectral variability of accreting black hole sources that exhibit a spectral disc reflection component (see also Miniutti et al. 2003). 2.1 Assumptions and computational set-up We assume the presence of a central maximally rotating Kerr black hole with specific angular momentum a = 0.998. A geometrically thin accretion disc lies in the hole equatorial plane and matter in the disc is accreted along stable circular geodesics of the Kerr space time. The disc extends down to the marginal stable orbit (with radial coordinate rin = rms 1.24 rg) and has an outer radius of rout = 100rg. Relativistic effe (...truncated)