Skip to main content
Log in

Towards Precision Measurements of Accreting Black Holes Using X-Ray Reflection Spectroscopy

  • Published:
Space Science Reviews Aims and scope Submit manuscript


Relativistic reflection features are commonly observed in the X-ray spectra of accreting black holes. In the presence of high quality data and with the correct astrophysical model, X-ray reflection spectroscopy can be quite a powerful tool to probe the strong gravity region, study the morphology of the accreting matter, measure black hole spins, and possibly test Einstein’s theory of general relativity in the strong field regime. In the last decade, there has been significant progress in the development of the analysis of these features, thanks to more sophisticated astrophysical models and new observational facilities. Here we review the state-of-the-art in relativistic reflection modeling, listing assumptions and simplifications that may affect, at some level, the final measurements and may be investigated better in the future. We review black hole spin measurements and the most recent efforts to use X-ray reflection spectroscopy for testing fundamental physics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others


  1. The origine of the soft excess is still matter of debate and two scenarios have been proposed and tested, namely blurred ionized reflection and warm Comptonization. In the first case, the soft excess would be due the relativistic reflection and it has been successfully tested on a number of different sources (see, e.g., Walton et al. 2013b). On the other hand, the warm Comptonization scenario has proved to be a viable explanation from the ultraviolet to soft X-rays of a number of nearby Seyfert galaxies for which simultaneous broadband data were used (see, e.g., Porquet et al. 2018; Ursini et al. 2019; Middei et al. 2020; Matzeu et al. 2020a).

  2. We note that since we include no zero-stress inner boundary condition, we do not have the factor of 3 enhancement of the dissipation at large radii, which would be present with that condition due to the resulting redistribution of the gravitationally released power. Moreover, the expression is valid for a pure hydrogen plasma. In the general case, \(L_{\mathrm{E}}\) is \(2/(1+X)\) times larger, where \(X\) is the hydrogen abundance.





  7. For the comparison of the line shape among relline, kyn, and reflkerr, see Fig. 11 in Niedźwiecki et al. (2019). The agreement between the reflection spectra of relxill and reltrans is shown in Fig. 5 in Ingram et al. (2019).

  8. Note that the arctan function must properly resolve the phase ambiguity associated with the tan function (e.g. typically the function atan2(y,x) in many programming languages).

  9. At lower luminosities, the disk can still be described by the Novikov-Thorne model, but it may be truncated (\(R_{\mathrm{in}} > R_{\mathrm{ISCO}}\)).

  10. In the case of a power-law spectrum with an exponential cut-off, different definitions of \(E_{\mathrm{cut}}\) (i.e. in either the observer’s or the source frame) give essentially the same physical results (if all redshift corrections are self-consistently taken into account) because \(E_{\mathrm{cut}}\) may be simply rescaled by the redshift factor. On the other hand, in the case of a thermal Comptonization continuum, using the temperature defined in the observer’s frame may lead to invalid results because the redshifted Comptonized spectrum is not, in general, correctly reproduced by a simple scaling of electron temperature.

  11. On the other hand, the high reflection fraction observed in some AGN suggests that the reflection scattering is weak for those sources and, in turn, that the corona is not very extended and does not cover well the inner part of the accretion disk (like in the lamppost model).


  13. Details on the Weak Equivalence Principle, the Local Lorentz Invariance, and the Local Position Invariance, as well as the classification of gravity theories in which these principles are preserved or violated, can be found in Will (2014).



Download references


We wish to thank Barbara De Marco and Erin Kara for useful comments and suggestions. All authors are members of the International Team 458 at the International Space Science Institute (ISSI), Bern, Switzerland. J.G. and A.A.Z. are also members of the International Team 486 at the International Space Science Institute (ISSI), Bern, Switzerland. The work of C.B., H.L., and A.T. is supported by the Innovation Program of the Shanghai Municipal Education Commission, Grant No. 2019-01-07-00-07-E00035, the National Natural Science Foundation of China (NSFC), Grant No. 11973019, and Fudan University, Grant No. JIH1512604. V.G. is supported through the Margarete von Wrangell fellowship by the ESF and the Ministry of Science, Research and the Arts Baden-Württemberg. J.J. is supported by the Tsinghua Shui’Mu Scholar Program and the Tsinghua Astrophysics Outstanding Fellowship. R.M. acknowledges the financial support of INAF (Istituto Nazionale di Astrofisica), Osservatorio Astronomico di Roma, ASI (Agenzia Spaziale Italiana) under contract to INAF: ASI 2014-049-R.0 dedicated to SSDC. A.N. is supported by the Polish National Science Centre under the grants 2015/18/A/ST9/00746 and 2016/21/B/ST9/02388. A.A.Z. is supported by the Polish National Science Centre under the grants 2015/18/A/ST9/00746 and 2019/35/B/ST9/03944.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Cosimo Bambi.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bambi, C., Brenneman, L.W., Dauser, T. et al. Towards Precision Measurements of Accreting Black Holes Using X-Ray Reflection Spectroscopy. Space Sci Rev 217, 65 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: