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X-ray reverberation around accreting black holes

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Abstract

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.

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Notes

  1. In Blandford and McKee, and some subsequent optical and X-ray reverberation mapping work (including by the authors of this review), the impulse response is also called the transfer function. However, impulse response is the formally correct signal processing term to describe the time domain response of the system to a delta-function ‘impulse’, which is what we intend here (in signal processing terminology, the transfer function is in fact the Fourier transform of the impulse response).

  2. Even quasi-periodic oscillations seen in XRBs follow the same statistics as noise (van der Klis 1997).

  3. It is important to bear in mind that due to the highly skewed nature of the \(\chi ^{2}_{2}\) distribution, errors on the PSD only approach Gaussian after binning a large number of samples (\(KM>50\)). An alternative approach, which converges more quickly to Gaussian-distributed errors, is to bin \(\log (P_{n,m})\), which also necessitates adding a constant bias to the binned log-power, see Papadakis and Lawrence (1993), Vaughan (2005) for details.

  4. \(n^{2}=[({\bar{P}}_{X} (\nu _{j})-P_{X,\mathrm{noise}})P_{Y,\mathrm{noise}}+({\bar{P}}_{Y}(\nu _{j})-P_{Y,\mathrm{noise}})P_{X,\mathrm{noise}}+P_{X,\mathrm{noise}}P_{Y,\mathrm{noise}}]/KM\), where we assume that the binned PSDs are not already noise-subtracted. See Vaughan and Nowak (1997) for further details.

  5. Since the measured Fourier frequencies depend on segment length, binning is best done by making a frequency-ordered list of frequencies and power or cross-spectral value from all segments and then binning the power/cross-spectra according to frequency.

  6. Strictly speaking, the ‘covariance’ spectrum measures the square root of the covariance of each channel with the reference band.

  7. Note that the description of the calculation of the covariance spectrum and its errors given here should be used instead of that given in Cassatella et al. (2012a), which contains several typos. We would like to thank Simon Vaughan for bringing these errors to our attention.

  8. The covariance spectrum can also be calculated directly from the coherence, using \(Cv(\nu _{j})=\langle x \rangle \sqrt{\gamma ^{2}(\nu _{j})({\bar{P}}_{X}(\nu _{j}) - P_{X,\mathrm{noise}})\varDelta \nu _{j}}\).

  9. I.e. corresponding to half the separation in lag between the 15.87 and 84.13 percentile values of the distribution, which is equivalent to the standard deviation for a Gaussian distribution.

  10. The distributions in the low count rate regime are generated using only 300 realisations instead of \(10^{4}\), due to computational speed limitations.

  11. Black hole masses used by De Marco et al. (2013), Kara et al. (2013c) and in Fig. 12 were obtained from the literature, and estimated primarily using optical broad line reverberation. In a few cases, masses were estimated using the scaling relation between optical continuum luminosity and broad line region radius, which can be used to estimate black hole mass when combined with optical line width (e.g. Kaspi et al. 2000; Grier et al. 2012), or the correlation between black hole mass and host galaxy bulge stellar velocity dispersion (e.g. Gebhardt et al. 2000).

  12. The observed scaling is flatter than expected from a linear relationship, but this can be explained as a bias due to the fact that we only sample the higher frequency end of the soft lag range in the highest mass objects, which leads to systematically shorter lags than would be seen if we could sample the maximum amplitude of soft lags seen at lower frequencies (De Marco et al. 2013).

  13. Formally, a time shift multiplies the Fourier transform by \(\exp (-i\omega \tau _0)\), but here and throughout we use the convention that a positive phase lag corresponds to a delay, so we correct this convention by multiplying the imaginary part of the Fourier transform (and hence the resulting phase lags) by \(-1\).

  14. See also http://stronggravity.eu/public-outreach/animations/reverberation/ for further examples and explanatory animations by M. Dovčiak.

  15. For ATHENA we use the Wide Field Imager (WFI) effective area curve for both cases, since this instrument is able to observe sources with flux up to 1 Crab with minimal signal degradation due to pile-up. However, the high-resolution spectrometer (X-ray Integral Field Unit, X-IFU) will be able to observe fainter sources such as AGN, with only slightly reduced sensitivity compared to the WFI.

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Acknowledgments

We would like to thank Simon Vaughan for valuable discussions and comments and Zaven Arzoumanian and the NICER team for providing the latest NICER instrument response. ACF acknowledges support from the European Union Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 312789 (STRONGGRAVITY), the UK Science and Technology Facilities Council, and the ERC Advanced Grant FEEDBACK. EK thanks the Gates Cambridge Scholarship. DRW is supported by a CITA National Fellowship.

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Authors and Affiliations

  1. Anton Pannekoek Institute, University of Amsterdam, Postbus 94249, 1090 GE, Amsterdam, The Netherlands

    P. Uttley

  2. Department of Physics and Astronomy, Wayne State University, 666 W. Hancock, Detroit, MI, 48201, USA

    E. M. Cackett

  3. Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, UK

    A. C. Fabian & E. Kara

  4. Department of Astronomy and Physics, Saint Mary’s University, Halifax, NS, B3H 3C3, Canada

    D. R. Wilkins

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  1. P. Uttley
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  2. E. M. Cackett
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  3. A. C. Fabian
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  4. E. Kara
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  5. D. R. Wilkins
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Correspondence to P. Uttley.

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Uttley, P., Cackett, E.M., Fabian, A.C. et al. X-ray reverberation around accreting black holes. Astron Astrophys Rev 22, 72 (2014). https://doi.org/10.1007/s00159-014-0072-0

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