The Comptonisation of accretion disc X-ray emission: Consequences for X-ray reflection and the geometry of AGN coronae

D.R. Wilkins and L.C. Gallo, 2015, MNRAS 448, 703-712

We consider the Comptonisation of the photons that make up the relativistically blurred reflection that is commonly detected from the accretion discs of AGN by the coronae of energetic particles believed to give rise to the powerful X-ray continua by the inverse-Compton scattering of thermal seed photons from the disc. Recent measurements of the emissivity profiles of accretion discs as well as reverberation time lags between the primary X-ray continuum and the reflection suggest that this corona is situated at a low height above the disc and extends radially, tens of gravitational radii over the disc surface, hence should also Compton scatter the reflected X-rays. We find that the detection of blurred reflection from as close in as the innermost stable circular orbits (ISCOs) of maximally rotating black holes is consistent with such coronae, but requires that the corona be patchy, consisting perhaps of a number of isolated flares throughout the region. Considering only the requirement that it be possible to detect reflection from the ISCO, we find that at any given moment, the covering fraction of the inner part of the accretion disc by the corona needs to be less than 85 per cent, though allowing for the detection of 'reflection-dominated' spectra in which the total reflected flux exceeds that seen in the continuum requires covering fractions as low as 50 or 25 per cent.

New Constraints on the Black Hole Low/Hard State Inner Accretion Flow with NuSTAR

J.M. Miller, J.A. Tomsick, M. Bachetti, D.R. Wilkins et al., 2014. ApJL 799, L6

We report on an observation of the Galactic black hole candidate GRS 1739-278 during its 2014 outburst, obtained with NuSTAR. The source was captured at the peak of a rising "low/hard" state, at a flux of ~0.3 Crab. A broad, skewed iron line and disk reflection spectrum are revealed. Fits to the sensitive NuSTAR spectra with a number of relativistically blurred disk reflection models yield strong geometrical constraints on the disk and hard X-ray "corona". Two models that explicitly assume a "lamppost" corona find its base to have a vertical height above the black hole of h = 5 (+7, -2) GM/c^2 and h = 18 +/-4 GM/c^2 (90% confidence errors); models that do not assume a "lamppost" return emissivity profiles that are broadly consistent with coronae of this size. Given that X-ray microlensing studies of quasars and reverberation lags in Seyferts find similarly compact coronae, observations may now signal that compact coronae are fundamental across the black hole mass scale. All of the models fit to GRS 1739-278 find that the accretion disk extends very close to the black hole - the least stringent constraint is r = 5 (+3,-4) GM/c^2. Only two of the models deliver meaningful spin constraints, but a = 0.8 +/-0.2 is consistent with all of the fits. Overall, the data provide especially compelling evidence of an association between compact hard X-ray coronae and the base of relativistic radio jets in black holes.

Suzaku observations of Mrk 335: Confronting partial covering and relativistic reflection

L. C. Gallo, D. R. Wilkins, K. Bonson, C-Y. Chiang, D. Grupe, M. L. Parker, A. Zoghbi, A. C. Fabian, S. Komossa, A. L. Longinotti, 2014. MNRAS 446, 633-650

We report on the deepest X-ray observation of the narrow-line Seyfert 1 galaxy Mrk 335 in the low-flux state obtained with Suzaku. The data are compared to a 2006 high-flux Suzaku observation when the source was ~10-times brighter. Describing the two flux levels self-consistently with partial covering models would require extreme circumstances, as the source would be subject to negligible absorption during the bright state and ninety-five per cent covering with near Compton-thick material when dim. Blurred reflection from an accretion disc around a nearly maximum spinning black hole (a>0.91, with preference for a spin parameter as high as ~ 0.995) appears more likely and is consistent with the long-term and rapid variability. Measurements of the emissivity profile and spectral modelling indicate the high-flux Suzaku observation of Mrk 335 is consistent with continuum-dominated, jet-like emission (i.e. beamed away from the disc). It can be argued that the ejecta must be confined to within ~25 rg if it does not escape the system. During the low-flux state the corona becomes compact and only extends to about 5 rg from the black hole, and the spectrum becomes reflection-dominated. The low-frequency lags measured at both epochs are comparable indicating that the accretion mechanism is not changing between the two flux levels. Various techniques to study the spectral variability (e.g. principal component analysis, fractional variability, difference spectra, and hardness ratio analysis) indicate that the low-state variability is dominated by changes in the power law flux and photon index, but that changes in the ionisation state of the reflector are also required. Most notably, the ionisation parameter becomes inversely correlated with the reflected flux after a long-duration flare-like event during the observation.

Modelling the Extreme X-ray Spectrum of IRAS 13224-3809

C.-Y. Chiang, D.J. Walton, A.C. Fabian, D.R. Wilkins and L.C. Gallo, 2015. MNRAS 446, 759-769

The extreme NLS1 galaxy IRAS 13224-3809 shows significant variability, frequency depended time lags, and strong Fe K line and Fe L features in the long 2011 XMM-Newton observation. In this work we study the spectral properties of IRAS 13224-3809 in detail, and carry out a series of analyses to probe the nature of the source, focusing in particular on the spectral variability exhibited. The RGS spectrum shows no obvious signatures of absorption by partially ionised material (warm absorbers). We fit the 0.3-10.0 keV spectra with a model that includes relativistic reflection from the inner accretion disc, a standard powerlaw AGN continuum, and a low-temperature (~0.1 keV) blackbody, which may originate in the accretion disc, either as direct or reprocessed thermal emission. We find that the reflection model explains the time-averaged spectrum well, and we also undertake flux-resolved and time-resolved spectral analyses, which provide evidence of gravitational light-bending effects. Additionally, the temperature and flux of the blackbody component are found to follow the L∝T^4 relation expected for simple thermal blackbody emission from a constant emitting area, indicating a physical origin for this component.

The NuSTAR spectrum of Mrk 335: Extreme relativistic effects within 2 gravitational radii of the event horizon?

M.L. Parker, D.R. Wilkins, A.C. Fabian, D. Grupe, T. Dauser, G. Matt, F.A. Harrison et al, 2014, MNRAS 443, 1723-1732

We present 3-50 keV 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 5-7 keV and Compton hump from 10-30 keV. The source is variable during the observation, with the variability concentrated at low energies, which suggesting either a relativistic reflection or a variable absorption scenario. In this work, we focus on the reflection interpretation, 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.

Caught in the act: Measuring the changes in the corona that cause the extreme variability of 1H0707-495

D.R. Wilkins, E. Kara, A.C. Fabian and L.C. Gallo, 2014, MNRAS 443, 2746-2756

The X-ray spectra of the narrow line Seyfert 1 galaxy, 1H0707-495, obtained with XMM-Newton, from time periods of varying X-ray luminosity are analysed in the context of understanding the changes to the X-ray emitting corona that lead to the extreme variability seen in the X-ray emission from active galactic nuclei (AGN). The emissivity profile of the accretion disc, illuminated by the X-ray emitting corona, along with previous measurements of reverberation time lags are used to infer the spatial extent of the X-ray source. By fitting a twice-broken power law emissivity profile to the relativistically-broadened iron K fluorescence line, it is inferred that the X-ray emitting corona expands radially, over the plane of the accretion disc, by 25 to 30 per cent as the luminosity increases, contracting again as the luminosity decreases, while increases in the measured reverberation lag as the luminosity increases would require also variation in the vertical extent of the source above the disc. The spectrum of the X-ray continuum is found to soften as the total X-ray luminosity increases and we explore the variation in reflected flux as a function of directly-observed continuum flux. These three observations combined with simple, first-principles models constructed from ray tracing simulations of extended coron self-consistently portray an expanding corona whose average energy density decreases, but with a greater number of scattering particles as the luminosity of this extreme object increases.

X-ray reverberation around accreting black holes

P. Uttley, E.M. Cackett, A.C. Fabian, E. Kara and D.R. Wilkins, 2014, A&ARv 22, 72 (Invited Review Article)

Luminous accreting stellar mass and supermassive black holes produce power-law continuum X-ray emission from a compact central corona. Reverberation time lags occur due to light travel time-delays between changes in the direct coronal emission and corresponding variations in its reflection from the accretion flow. Reverberation is detectable using light curves made in different X-ray energy bands, since the direct and reflected components have different spectral shapes. Larger, lower frequency, lags are also seen and are identified with propagation of fluctuations through the accretion flow and associated corona. We review the evidence for X-ray reverberation in active galactic nuclei and black hole X-ray binaries, showing how it can be best measured and how it may be modelled. The timescales and energy-dependence of the high frequency reverberation lags show that much of the signal is originating from very close to the black hole in some objects, within a few gravitational radii of the event horizon. We consider how these signals can be studied in the future to carry out X-ray reverberation mapping of the regions closest to black holes.

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

A.C. Fabian, M.L. Parker, D.R. Wilkins, J.M. Miller, E. Kara, C.S. Reynolds and T. Dauser, 2014, MNRAS 439, 2307-2313

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.

Modelling the broad Fe Kα reverberation in the AGN NGC 4151

E.M. Cackett, A. Zoghbi, C.S. Reynolds, A.C. Fabian, E. Kara, P. Uttley and D.R. Wilkins, 2014, MNRAS 438, 2980-2994

The recent detection of X-ray reverberation lags, especially in the Fe Kα line region, around active galactic nuclei (AGN) has opened up the possibility of studying the time-resolved response (reflection) of hard X-rays from the accretion disc around supermassive black holes. Here, we use general relativistic transfer functions for reflection of X-rays from a point source located at some height above the black hole to study the time lags expected as a function of frequency and energy in the Fe Kα line region. We explore the models and the dependence of the lags on key parameters such as the height of the X-ray source, accretion disc inclination, black hole spin and black hole mass. We then compare these models with the observed frequency- and energy-dependence of the Fe Kα line lag in NGC 4151. Assuming the optical reverberation mapping mass of 4.6 × 107 Msun, we get a best fit to the lag profile across the Fe Kα line in the frequency range (1-2) × 10-5 Hz for an X-ray source located at a height h = 7(+2.9,-2.6) rg with a maximally spinning black hole and an inclination i < 30°.

Discovery of high frequency iron K lags in Ark 564 and Mrk 335

E. Kara, A.C. Fabian, E.M. Cackett, P. Uttley, D.R. Wilkins and A. Zoghbi, 2013, MNRAS 434, 1129-1137

We use archival XMM-Newton observations of Ark 564 and Mrk 335 to calculate the frequency-dependent time lags for these two well-studied sources. We discover high-frequency Fe K lags in both sources, indicating that the red wing of the line precedes the rest-frame energy by roughly 100 and 150 s for Ark 564 and Mrk 335, respectively. Including these two new sources, Fe K reverberation lags have been observed in seven Seyfert galaxies. We examine the low-frequency lag-energy spectrum, which is smooth, and shows no feature of reverberation, as would be expected if the low-frequency lags were produced by distant reflection off circumnuclear material. The clear differences in the low- and high-frequency lag-energy spectra indicate that the lags are produced by two distinct physical processes. Finally, we find that the amplitude of the Fe K lag scales with black hole mass for these seven sources, consistent with a relativistic reflection model where the lag is the light travel delay associated with reflection of continuum photons off the inner disc.

The origin of the lag spectra observed in AGN: Reverberation and the propagation of X-ray source fluctuations

D.R. Wilkins and A.C. Fabian, 2013, MNRAS 430, 247-258

The X-ray emission from active galactic nuclei (AGN) is highly variable. Measurements of time lags (characterised by lag spectra) between variability in the light curves in energy bands corresponding to directly observed continuum emission from the corona around the black hole and to X-rays reflected from the accretion disc adds a further dimension to studies of the structure and energetics of these systems. We seek to understand these measurements in terms of the physical parameters of the X-ray source (its location, extent, etc.) through the calculation of theoretical lag spectra for a range of source parameters in general relativistic ray tracing simulations, combined with knowledge of the observed variability of the X-ray emission from AGN. Due to the proximity of the emission to the central black hole, Shapiro delays are important and the effects of general relativity should be considered when interpreting the lags as the light travel time between the source and reflector. We show that it is important to consider dilution of the lag by the contribution of both the primary and reflected spectral components to the observed energy bands rather than observing pure continuum and reflected emission, reducing the measured lag by up to 75 per cent compared to the 'intrinsic' time lag due to light travel times. We find that the observed lag spectrum of the narrow line Seyfert 1 galaxy 1H 0707-495 implies an X-ray source extending radially outwards to around 35rg and at a height of around 2rg above the plane of the accretion disc, consistent with the constraints obtained independently by considering the emissivity profile of the accretion disc. By investigating the influence of the propagation of X-ray luminosity fluctuations through the source region we find it is possible to reproduce the shape of the low frequency part of the lag spectrum (where the hard 'primary' band lags behind the soft 'reflected' band) as the effect of luminosity fluctuations originating in the centre of the X-ray source, close to the black hole, and propagating outwards.

The closest look at 1H 0707-495: X-ray reverberation lags with 1.3 Ms of data

E. Kara, A.C. Fabian, E.M. Cackett, J. Steiner, P. Uttley, D.R. Wilkins and A. Zoghbi, 2012, MNRAS 428, 2795-2804

Reverberation lags in AGN were first discovered in the NLS1 galaxy, 1H0707-495. We present a follow-up analysis using 1.3 Ms of data, which allows for the closest ever look at the reverberation signature of this remarkable source. We confirm previous findings of a hard lag of ~100 seconds at frequencies v ~ [0.5 - 4] e-4 Hz, and a soft lag of ~30 seconds at higher frequencies, v ~ [0.6 - 3] e-3 Hz. These two frequency domains clearly show different energy dependences in their lag spectra. We also find evidence for a signature from the broad Fe K line in the high frequency lag spectrum. We use Monte Carlo simulations to show how the lag and coherence measurements respond to the addition of Poisson noise and to dilution by other components. With our better understanding of these effects on the lag, we show that the lag-energy spectra can be modelled with a scenario in which low frequency hard lags are produced by a compact corona responding to accretion rate fluctuations propagating through an optically thick accretion disc, and the high frequency soft lags are produced by short light-travel delay associated with reflection of coronal power-law photons off the disc.

Long XMM observation of the narrow line Seyfert 1 galaxy IRAS 13224-3809: Rapid variability, high spin and a soft lag

A.C. Fabian, E. Kara, D. Walton, D.R. Wilkins, R.R. Ross, K. Lozanov, P. Uttley, L. Gallo, A. Zoghb et al , 2013, MNRAS 429, 2917-2923

Results are presented from a 500ks long XMM-Newton observation of the Narrow-Line Seyfert 1 galaxy IRAS13224-3809. The source is rapidly variable on timescales down to a few 100s. The spectrum shows strong broad Fe-K and L emission features which are interpreted as arising from reflection from the inner parts of an accretion disc around a rapidly spinning black hole. Assuming a power-law emissivity for the reflected flux and that the innermost radius corresponds to the innermost stable circular orbit, the black hole spin is measured to be 0.988 with a statistical precision better than one per cent. Systematic uncertainties are discussed. A soft X-ray lag of 100s confirms this scenario. The bulk of the power-law continuum source is located at a radius of 2-3 gravitational radii.

Understanding X-ray reflection emissivity profiles in AGN: Locating the X-ray source

D.R. Wilkins and A.C. Fabian, 2012, MNRAS 424, 1284-1296

The illumination pattern (or emissivity profile) of the accretion disc due to the reflection of X-rays in AGN can be understood in terms of relativistic effects on the rays propagating from a source in a corona surrounding the central black hole, both on their trajectories and on the accretion disc itself. Theoretical emissivity profiles due to isotropic point sources as well as simple extended geometries are computed in general relativistic ray tracing simulations performed on graphics processing units (GPUs). Such simulations assuming only general relativity naturally explain the accretion disc emissivity profiles determined from relativistically broadened emission lines which fall off steeply (with power law indices of between 6 and 8) over the inner regions of the disc, then flattening off to almost a constant before tending to a constant power law of index 3 over the outer disc. Simulations for a variety of source locations, extents and geometries show how the emissivity profiles depend on these properties, and when combined with reverberation time lags allow the location and extent of the primary X-ray source to be constrained. Comparing the emissivity profile determined from the broadened iron K emission line in spectra of 1H 0707-495 obtained in January 2008 to theoretical emissivity profiles and applying constraints from reverberation lags suggest that there exists an extended region of primary X-ray emission located as low as 2rg above the accretion disc, extending outwards to a radius of around 30rg.

On the determination of the spin of the black hole in Cyg X-1 from X-ray reflection spectra

A.C. Fabian, D.R. Wilkins, J.M. Miller, R.C. Reis, C.S. Reynolds, E.M. Cackett, M.A. Nowak, G.G. Pooley, K. Pottschmidt, J.S. Sanders, R.R. Ross, J. Wilms, 2012, MNRAS 424, 217-223

The spin of Cygnus X-1 is measured by fitting reflection models to Suzaku data covering the energy band 0.9-400 keV. The inner radius of the accretion disc is found to lie within 2 gravitational radii (rg=GM/c^2) and a value for the dimensionless black hole spin is obtained of 0.97. This agrees with recent measurements using the continuum fitting method by Gou et al. and of the broad iron line by Duro et al. The disc inclination is measured at 23.7 deg, which is consistent with the recent optical measurement of the binary system inclination by Orosz et al of 27+/-0.8 deg. We pay special attention to the emissivity profile caused by irradiation of the inner disc by the hard power-law source. The X-ray observations and simulations show that the index q of that profile deviates from the commonly used, Newtonian, value of 3 within 3rg, steepening considerably within 2rg, as expected in the strong gravity regime.

Testing the accuracy of radiative cooling approximations in SPH simulations

Daniel R. Wilkins and Cathie J. Clarke, 2011, MNRAS 419, 3368-3377

Hydrodynamical simulations of star formation have stimulated a need to develop fast and robust algorithms for evaluating radiative cooling. Here we undertake a critical evaluation of what is currently a popular method for prescribing cooling in SPH simulations, i.e. the polytropic cooling due originally to Stamatellos et al. This method uses the local density and potential to estimate the column density and optical depth to each particle and then uses these quantities to evaluate an approximate expression for the net radiative cooling. We evaluate the algorithm by considering both spherical and disc-like systems with analytic density and temperature structures. In spherical systems, the total cooling rate computed by the method is within around 20 for the astrophysically relevant case of opacity dominated by ice grains and is correct to within a factor of order unity for a range of opacity laws. In disc geometry, however, the method systematically under-estimates the cooling by a large factor at all heights in the disc. For the self-gravitating disc studied, we find that the method under-estimates the total cooling rate by a factor of 200. This discrepancy may be readily traced to the method's systematic over-estimate of the disc column density and optical depth, since (being based only on the local density and potential) it does not take into account the low column density route for photon escape normal to the disc plane. We note that the discrepancy quoted above applies in the case that the star's potential is not included in the column density estimate and that even worse agreement is obtained if the full (star plus disc) potential is employed. These results raise an obvious caution about the method's use in disc geometry whenever an accurate cooling rate is required, although we note that there are situations where the discrepancies highlighted above may not significantly affect the global outcome of simulations. Finally, we draw attention to our introduction of an analytic self-gravitating disc structure that may be of use in the calibration of future cooling algorithms.

1H 0707-495 in 2011: An X-ray source within a gravitational radius of the event horizon

A.C. Fabian, A. Zoghbi, D. Wilkins, T. Dwelly, P. Uttley, N. Schartel, G.Miniutti, L. Gallo, D. Grupe, S. Komossa, M. Santos-Lleo, 2011, MNRAS 419, 116-123

The Narrow Line Seyfert 1 Galaxy 1H 0707-495 went in to a low state from 2010 December to 2011 February, discovered by a monitoring campaign using the X-Ray Telescope on the Swift satellite. We triggered a 100 ks XMM-Newton observation of the source in 2011 January, revealing the source to have dropped by a factor of ten in the soft band, below 1 keV, and a factor of 2 at 5 keV, compared with a long observation in 2008. The sharp spectral drop in the source usually seen around 7 keV now extends to lower energies, below 6 keV in our frame. The 2011 spectrum is well fit by a relativistically-blurred reflection spectrum similar to that which fits the 2008 data, except that the emission is now concentrated solely to the central part of the accretion disc. The irradiating source must lie within 1 gravitational radius of the event horizon of the black hole, which spins rapidly. Alternative models are briefly considered but none has any simple physical interpretation.

Determination of the X-ray reflection emissivity profile of 1H0707-495

D.R. Wilkins and A.C. Fabian, 2011, MNRAS 414, 1269-1277

When considering the X-ray spectrum resulting from the reflection off the surface of accretion discs of AGN, it is necessary to account for the variation in reflected flux over the disc, i.e. the emissivity profile. This will depend on factors including the location and geometry of the X-ray source and the disc characteristics. We directly obtain the emissivity profile of the disc from the observed spectrum by considering the reflection component as the sum of contributions from successive radii in the disc and fitting to find the relative weightings of these components in a relativistically-broadened emission line. This method has successfully recovered known emissivity profiles from synthetic spectra and is applied to XMM-Newton spectra of the Narrow Line Seyfert 1 galaxy 1H 0707-495. The data imply a twice-broken power law form of the emissivity law with a steep profile in the inner regions of the disc (index 7.8) and then a flat region between 5.6rg and 34.8rg before tending to a constant index of 3.3 over the outer regions of the disc. The form of the observed emissivity profile is consistent with theoretical predictions, thus reinforcing the reflection interpretation.