Measuring Black Hole Spin using X-ray Reflection Spectroscopy

TL;DR

The paper addresses how to measure black hole spin across the full mass range using relativistic X-ray reflection spectroscopy. It details the core physical assumption that disks extend to the ISCO, with $r_{ m ISCO}$ a function of the spin parameter $a$, and outlines a practical modeling framework that combines a blurred, ionized reflection spectrum with a Kerr transfer function, plus distant reflection and absorption components. The author reports that many SMBHs exhibit high spins ($a>0.8$) and discusses case studies (e.g., NGC 3783 and Fairall 9) that illustrate both robust spin constraints and model degeneracies, as well as cross-method comparisons with continuum fitting in BH-XRBs. The review also highlights the emerging field of relativistic reverberation mapping, where time lags between continuum and reflection signatures confirm the reflection paradigm and promise new insights with future missions like LOFT, advancing tests of strong-field gravity and jet–spin connections.

Abstract

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.

Figures (7)

• Figure 1: Left panel : Rest-frame X-ray reflection spectrum for photospheric ionization parameters of $\log\xi=0,1,2,3$ (from bottom to top). In all cases, the irradiating source has a power-law spectrum with photon index $\Gamma=2$. Right panel : Demonstration of the effects of relativistic Doppler/gravitational blurring on the reflection spectrum. Curves show the $\log\xi=0$ rest-frame reflection spectrum (bottom), relativistic blurring with $r_{\rm in}=10r_g$ and emissivity index $\beta=3$ (middle curve), and extreme blurring with $r_{\rm in}=2r_g$ and $\beta=4$. In all cases, a disk inclination of $i=30$ degrees is assumed.
• Figure 2: Spin constraints on the SMBH in NGC3783 from the 2009 Suzaku observation. Left panel : Goodness of fit relative to the best fit, $\Delta\chi^2$, as a function of the spin parameter $a$. Different lines show the effects of different data analysis assumptions; a fiducial analysis (black), an analysis in which the warm absorber parameters are frozen at their best values (red), an analysis in which the XIS and PIN instrumental cross-normalizations are allowed to float (blue), and an analysis that ignores all data below 3 keV. From Brenneman et al. (2011). Right panel : Probability distribution for $a$ as derived from a Monte Carlo Markov Chain (MCMC) analysis using the fiducial spectral model. From Reynolds et al. (2012).
• Figure 3: Demonstration of the spectral signatures which, in practice, drive spin constraints using the Suzaku data for NGC 3783. Left panel : Unfolded XIS data overlaid with the best fitting model (top) and the associated data/model ratio (bottom). Right panel : Same, except that the spin parameter has been frozen at $a=0$ and (for physical consistency) the irradiation indices have been frozen at $\beta_1=\beta_2=3$. All other parameters (including those associated with the warm absorbers) have been allowed to fit freely. For both panels, the model components are colored as follows: absorbed power-law continuum (red), distant reflection (green), and relativistically smeared disk reflection (blue). Figure from Reynolds et al. (2012).
• Figure 4: Influence of iron abundance on the measured spin, illustrated using the 2009 Suzaku data for NGC 3783 . Left panel : Two-dimensional probability distribution for iron abundance $Z_{\rm Fe}$ and spin $a$ showing the existence of a statistical correlation between these two variables. Right panel : Probability distribution for spin $a$ assuming a free-fitting iron abundance (blue) and an iron abundance fixed to solar values. Figures from Reynolds et al. (2012).
• Figure 5: Left panel : Unfolded spectra for the two XMM-Newton (blue and magneta) and two Suzaku pointings (red and black) of Fairall 9. The 1.5-2.5 keV band have been excluded from the Suzaku spectra due to the presence of known calibration artifacts. Note the presence of the soft excess that appears to become more prominent as the source brightens. Right panel : Extrapolation of the two spectral models for Fairall 9 to higher energies; the red line shows the model with a thermal Comptonization soft excess, and the blue shows the case where the soft excess is described by an additional highly ionized relativistic reflection component. Figures from Lohfink et al. (2012b).