A dynamic black hole corona in an active galaxy through X-ray reverberation mapping


X-ray reverberation echoes are assumed to be produced in the strongly distorted spacetime around accreting supermassive black holes. This signal allows us to spatially map the geometry of the inner accretion flow1,2—a region that cannot yet be spatially resolved by any telescope—and provides a direct measure of the black hole mass and spin. The reverberation timescale is set by the light travel path between the direct emission from a hot X-ray corona and the reprocessed emission from the inner edge of the accretion disk3,4,5,6. However, there is an inherent degeneracy in the reverberation signal between black hole mass, inner disk radius and height of the illuminating corona above the disk. Here we use a long X-ray observation of the highly variable active galaxy IRAS 13224−3809 to track the reverberation signal as the system evolves on timescales of a day7,8. With the inclusion of all the relativistic effects, modelling reveals that the height of the X-ray corona increases with increasing luminosity, providing a dynamic view of the inner accretion region. This simultaneous modelling allows us to break the inherent degeneracies and obtain an independent timing-based estimate for the mass and spin of the black hole. The uncertainty on black hole mass is comparable to the leading optical reverberation method9, making X-ray reverberation a powerful technique, particularly for sources with low optical variability10.

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Fig. 1: The relativistic transfer function model used to fit the time-lag spectra.
Fig. 2: The observed 2–10 keV luminosity of the intrinsic component versus the source height.
Fig. 3: The posterior distribution for black hole mass from the best-fitting model.

Data availability

The data that support the plots in Fig. 2 and Extended Data Figs. 1 and 4 are included as source data in the Supplementary Information. All other data used in figures within this paper and other findings of this study are available from the corresponding author upon request. All data used in this work is publicly available. The XMM-Newton observations can be accessed from the XMM-Newton science archive (http://nxsa.esac.esa.int/nxsa-web/).

Code availability

All the code used for the data reduction is available from their respective websites. XSPEC is freely available online. The transfer function model KYNREVERB is available at https://projects.asu.cas.cz/stronggravity/kynreverb. The MCMC sampler EMCEE is available at http://emcee.readthedocs.io/en/stable/index.html, with the XSPEC implementation available at https://github.com/jeremysanders/xspec_emcee.


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W.N.A. and A.C.F. acknowledge support from the European Research Council through Advanced Grant 340442, on Feedback. M.L.P. and C.P. acknowledge support from ESA Research Fellowships. M.D. and M.D.C.-G. acknowledge support provided by the GA CR grant 18-00533S. M.D.C.-G. acknowledges funding from ESA through a partnership with IAA-CSIC (Spain). D.J.W. and M.J.M. appreciate support from an Ernest Rutherford STFC fellowship. D.J.K.B. acknowledges a Science and Technology Facilities Council studentship. C.S.R. thanks the UK Science and Technology Facilities Council for support under Consolidated Grant ST/R000867/1. This research has been partially funded by the Spanish State Research Agency (AEI) project no. ESP2017-87676-C5-1-R and no. MDM-2017-0737 Unidad de Excelencia “María de Maeztu”—Centro de Astrobiología (CSIC-INTA). G.M. acknowledges funding by the Spanish State Research. Agency (AEI) project no. ESP2017-86582-C4-1-R. B.D.M. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement no. 798726. This paper is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA member states and the United States (NASA).

Author information




W.N.A. performed the data analysis and lag modelling, and wrote the manuscript. E.K. performed a complementary time-lag data analysis. C.P. and J.J. performed the time-averaged spectral modelling. M.L.P. performed the rms-spectrum modelling. The remaining authors contributed to the discussion and interpretation.

Corresponding author

Correspondence to William N. Alston.

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Extended data

Extended Data Fig. 1 Lag frequency spectra for the 16 XMM-Newton orbits.

The best-fitting transfer function model, where MBH, spin a, Rin and inclination i are tied, but free, is shown in black solid line. The reverberation component is shown in red and the intrinsic component is shown in dotted grey. The zero time-lag as a function of frequency is shown as a black horizontal line. The black circles are the data with their 1σ error bars. The time-lag estimate at 2x10-4 Hz in observation 3039 has τ = 307 ± 87 s, but is clipped from the plotting region. The lower panels show the standard residuals. Source data

Extended Data Fig. 2 Table of source properties and best-fitting model posteriors.

Column 1 shows the XMM-Newton orbit number. Column 2 shows the 2–10 keV luminosity in units of 1042 ergs-1. Column 3 shows the photon index Γ from the time-averaged spectral model fits. Column 4 shows the posterior values for source height h from best-fitting the transfer function model fit with parameters Rin, inclination i and spin free and tied across the lag spectra.

Extended Data Fig. 3 Posterior distributions for source height from the best fitting model.

The model has parameters MBH, Rin, inclination i and spin a, free and tied. The median and 68% credible regions (equivalent to 1σ of a Gaussian distribution) are shown in grey.

Extended Data Fig. 4 L2–10 keV luminosity vs source height h from the model fit with fixed spin.

Panel a shows the spin value a = 0.998, panel b shows a = 0.7, and panel c shows a = 0. The corresponding fixed inner disc radius Rin is stated. The solid line is the best-fitting linear regression model together with the 1σ confidence region on the model. The error bars on individual data points are 1σ (see Methods). Source data

Extended Data Fig. 5 MCMC posterior densities for the best fitting model with parameters free.

Panel a shows the spin a, panel b shows the inner disc radius Rin, and panel c shows the inclination i. The median and 68% credible regions (equivalent to 1-sigma of a Gaussian distribution) are shown in grey vertical lines.

Extended Data Fig. 6 Scatter plots for the MCMC posterior parameter distributions.

Shown are the posteriors for spin a, inclination i, Rin, MBH, as well as source height h for two representative observations, with a low (3049) and high (3052) source flux.

Extended Data Fig. 7 The posterior parameters MBH and source height h from the model fit to just one individual lag spectra.

Panel a shows the model fit to observation 3049 and panel b that for observation 3050. The degeneracy between the model parameters can be seen. The red contours are the MCMC posteriors for the joint fit.

Extended Data Fig. 8 Modelling the rms-spectrum with the disc reflection scenario.

The solid blue lines are the model with the inclusion of the ultrafast outflow (UFO) and the dashed blue lines are without the UFO (see Methods for details). Panel a shows the ‘Broad’ rms-spectrum calculated from [0.08,6.0] x 10-4 Hz. Panel b shows the rms-spectra for a low frequency band, LF = [1.0,5.0] x 10-5 Hz. Panel c shows that of the high frequency band, HF = [4.0,20.0] x 10-4 Hz. Panel d shows the power spectral density (PSD) for the data, with the frequency ranges used for the rms-spectra indicated by the vertical solid (Broad), dashed (LF), and dotted (HF) lines. The HF band is where the reverberation signal dominates. 1σ error bars are shown on all data points.

Source data

Source Data Fig. 2

Data values for Fig. 2, ASCII.

Source Data Extended Data Fig. 1

Time lags as a function of frequency for the individual XMM-Newton observations, ASCII.

Source Data Extended Data Fig. 4

Data values for the three plots in Extended Data Fig. 4, ASCII.

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Alston, W.N., Fabian, A.C., Kara, E. et al. A dynamic black hole corona in an active galaxy through X-ray reverberation mapping. Nat Astron 4, 597–602 (2020). https://doi.org/10.1038/s41550-019-1002-x

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