X-ray irradiation of the accretion disc leads to strong reflection features, which are then broadened and distorted by relativistic effects. We present a detailed, general relativistic approach to model this irradiation for different geometries of the primary X-ray source. These geometries include the standard point source on the rotational axis as well as more jet-like sources, which are radially elongated and accelerating. Incorporating this code in the RELLINE model for relativistic line emission, the line shape for any configuration can be predicted. We study how different irradiation geometries affect the determination of the spin of the black hole. Broad emission lines are produced only for compact irradiating sources situated close to the black hole. This is the only case where the black hole spin can be unambiguously determined. In all other cases the line shape is narrower, which could either be explained by a low spin or an elongated source. We conclude that for those cases and independent of the quality of the data, no unique solution for the spin exists and therefore only a lower limit of the spin value can be given

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Irradiation of an accretion disc by a jet: general properties and implications for spin measurements of black holes

Astrophysical black hole candidates are thought to be the Kerr black holes of general relativity, but there is not yet direct observational evidence that the spacetime geometry around these objects is described by the Kerr solution. The study of the properties of the electromagnetic radiation emitted by gas or stars orbiting these objects can potentially test the Kerr black hole hypothesis. This paper reviews the state of the art of this research field, describing the possible approaches to test the Kerr metric with current and future observational facilities and discussing current constraints.

Testing black hole candidates with electromagnetic radiation

We present 3–50keV NuSTAR observations of the active galactic nuclei Mrk 335 in a very low flux state. The spectrum is dominated by very strong features at the energies of the iron line at 5–7keV and Compton hump from 10–30keV. The source is variable during the observation, withthevariabilityconcentratedatlowenergies,whichsuggestingeitherarelativisticreflection oravariableabsorptionscenario.Inthiswork,wefocusonthereflectioninterpretation,making use of new relativistic reflection models that self consistently calculate the reflection fraction, relativistic blurring and angle-dependent reflection spectrum for different coronal heights to model the spectra. We find that the spectra can be well fitted with relativistic reflection, and that the lowest flux state spectrum is described by reflection alone, suggesting the effects of extreme light-bending occurring within ∼2 gravitational radii (RG) of the event horizon. The reflection fraction decreases sharply with increasing flux, consistent with a point source moving up to above 10 RG as the source brightens. We constrain the spin parameter to greater than 0.9 at the 3σ confidence level. By adding a spin-dependent upper limit on the reflection fraction to our models, we demonstrate that this can be a powerful way of constraining the spin parameter, particularly in reflection dominated states. We also calculate a detailed emissivity profile for the iron line, and find that it closely matches theoretical predictions for a compact source within a few RG of the black hole.

The NuSTAR spectrum of Mrk 335: extreme relativistic effects within two gravitational radii of the event horizon?

We discuss the application of simple relativistically-blurred X-ray reflection models to the determination of the spin and the inner radius of the disc in accreting black holes. Observationally, the nature of the corona is uncertain a priori, but a robust determination of the inner disk radius can be made when the disc emissivity index is tightly constrained. When the inner disc is well illuminated, the black hole spin can also be determined. Using reflection modelling derived from ray tracing, we show that robust determination of disc truncation requires that the location of the coronal source is quasi-static and at a height and radius less than the truncation radius of the disc. Robust spin measurements require that at least part of the corona lies less than about 10 gravitational radii above the black hole in order that the innermost regions, including the innermost stable circular orbit, are well illuminated. The width of the blurring kernel (e.g., the iron line) has a strong dependence on coronal height. These limitations may be particularly applicable at low Eddington fractions (e.g. the low/hard state, and low-luminosity AGN) where the height of the corona may be relatively large, or outflowing, and tied to jet production.

On the determination of the spin and disc truncation of accreting black holes using X-ray reflection

Accreting stellar mass black holes (BHs) routinely exhibit Type-C quasi-periodic oscillations (QPOs). These are often interpreted as Lense–Thirring precession of the inner accretion flow, a relativistic effect whereby the spin of the BH distorts the surrounding space–time, inducing nodal precession. The best evidence for the precession model is the recent discovery, using a long joint XMM–Newton and NuSTAR observation of H 1743−322, that the centroid energy of the iron florescence line changes systematically with QPO phase. This was interpreted as the inner flow illuminating different azimuths of the accretion disc as it precesses, giving rise to a blueshifted/redshifted iron line when the approaching/receding disc material is illuminated. Here, we develop a physical model for this interpretation, including a self-consistent reflection continuum, and fit this to the same H 1743−322 data. We use an analytic function to parametrize the asymmetric illumination pattern on the disc surface that would result from inner flow precession, and find that the data are well described if two bright patches rotate about the disc surface. This model is preferred to alternatives considering an oscillating disc ionization parameter, disc inner radius and radial emissivity profile. We find that the reflection fraction varies with QPO phase (3.5σ), adding to the now formidable body of evidence that Type-C QPOs are a geometric effect. This is the first example of tomographic QPO modelling, initiating a powerful new technique that utilizes QPOs in order to map the dynamics of accreting material close to the BH.

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Tomographic reflection modelling of quasi-periodic oscillations in the black hole binary H 1743-322

Context. X-ray reflection off the accretion disc surrounding a black hole, together with the associated broad iron Kα line, has been widely used to constrain the innermost accretion-flow geometry and black hole spin. Some recent measurements have revealed steep reflection emissivity profiles in a number of active galactic nuclei and X-ray binaries. Aims. We explore the physically motivated conditions that give rise to the observed steep disc-reflection emissivity profiles. Methods. We perform aset of simulations based on the configuration of a possible future high-resolution X-raymission. Computations are carried out for typical X-ray bright Seyfert-1 galaxies. Results. We find that steep emissivity profiles with q ∼ 4−5 (where the emissivity is � (r) ∝ r −q ) are produced considering either i) a lamp-post scenario where a primary compact X-ray source is located close to the black hole, or ii) the radial dependence of the disc ionisation state. If both effects are taken into account, emissivity profiles as steep as q ∼ 7 can be obtained from X-ray spectra modelled via conventional reflection models. We also highlight the role of the reflection angular emissivity: the radial emissivity index q is overestimated when the standard limb-darkening law is used to describe the data. Conclusions. Very steep emissivity profiles with q ≥ 7 are naturally obtained by applying reflection models that take into account the radial profile ξ(r) of the disc ionisation induced by a compact X-ray source located close to the central black hole.

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Origin of the X-ray disc-reflection steep radial emissivity

X-ray reflection off the accretion disc surrounding a black hole, together with the associated broad iron K$\alpha$ line, has been widely used to constrain the innermost accretion-flow geometry and black hole spin. Some recent measurements have revealed steep reflection emissivity profiles in a number of active galactic nuclei and X-ray binaries. We explore the physically motivated conditions that give rise to the observed steep disc-reflection emissivity profiles. We perform a set of simulations based on the configuration of a possible future high-resolution X-ray mission. Computations are carried out for typical X-ray bright Seyfert-1 galaxies. We find that steep emissivity profiles with $q\sim 4-5$ (where the emissivity is $\epsilon (r) \propto r^{-q}$) are produced considering either i) a lamp-post scenario where a primary compact X-ray source is located close to the black hole, or ii) the radial dependence of the disc ionisation state. We also highlight the role of the reflection angular emissivity: the radial emissivity index $q$ is overestimated when the standard limb-darkening law is used to describe the data. Very steep emissivity profiles with $q \geq 7$ are naturally obtained by applying reflection models that take into account radial profile $\xi (r)$ of the disc ionisation induced by a compact X-ray source located close to the central black hole.

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Prashin Jethwa

Papers

Origin of the X-ray disc-reflection steep radial emissivity

Origin of the X-ray disc-reflection steep radial emissivity