Testing the Kerr Black Hole Hypothesis Using X-Ray Reflection Spectroscopy

Abstract

We present the first X-ray reflection model for testing the assumption that the metric of astrophysical black holes is described by the Kerr solution. We employ the formalism of the transfer function proposed by Cunningham. The calculations of the reflection spectrum of a thin accretion disk are split into two parts: the calculation of the transfer function and the calculation of the local spectrum at any emission point in the disk. The transfer function only depends on the background metric and takes into account all the relativistic effects (gravitational redshift, Doppler boosting, and light bending). Our code computes the transfer function for a spacetime described by the Johannsen metric and can easily be extended to any stationary, axisymmetric, and asymptotically flat spacetime. Transfer functions and single line shapes in the Kerr metric are compared with those calculated from existing codes to check that we reach the necessary accuracy. We also simulate some observations with NuSTAR and LAD/eXTP and fit the data with our new model to show the potential capabilities of current and future observations to constrain possible deviations from the Kerr metric.

Testing Einstein-dilaton-Gauss-Bonnet gravity with the reflection spectrum of accreting black holes

“…In the presence of high-quality data and with the correct astrophysical model, the analysis of the iron line can be a powerful tool to probe the near horizon region. This technique was proposed and developed to estimate the black hole spin under the assumption of the Kerr background [46,47], and only more recently has it been extended to test alternative theories of gravity [11][12][13][14]. The technique is often called the iron line method, because the iron Kα line is the most prominent feature, but any measurement of the spacetime metric around black holes should be done by fitting the whole reflection spectrum, not only the iron line.…”

“…Tests with electromagnetic radiation include, but are not limited to, the study of the thermal spectrum of thin accretion disks [7][8][9][10], the analysis of the reflection spectrum of thin disks [11][12][13][14], the measurements of the frequencies of quasiperiodic oscillations [15][16][17][18], and the possible future detection of black hole shadows [19][20][21][22][23][24][25]. Among these techniques, x-ray reflection spectroscopy is the only one that can be already used to test astrophysical black holes and promise to be able to provide stringent constraints with the next generation of x-ray facilities [26][27][28].…”

Testing General Relativity with the Reflection Spectrum of the Supermassive Black Hole in 1H0707-495

“…In Ref. [8], we have described RELXILL_NK, an extension of RELXILL to non-Kerr spacetimes (here NK stands for non-Kerr), and we have shown with some simulations how this new model can test the nature of astrophysical black holes. In this Letter, we employ RELXILL_NK for the first time to analyze real data and constrain possible deviations from the Kerr solution.…”

“…In Ref. [8], generic simulations were performed to test the capabilities of RELXILL_NK in analyzing observations from present and future instruments. We found that LAD/eXTP [20] can provide significantly stronger constraints on α 13 than NuSTAR.…”

Iron Kα line of Proca stars

“…Assuming the Kerr metric, the analysis of the iron Kα line can be used to measure the BH spin parameter [21,22]. Relaxing the Kerr BH hypothesis, the technique can probe the metric around the compact object [23,24]. Actually one has to analyze the whole reflection spectrum, not only the iron line, but most of the information about the spacetime metric in the strong gravity region is in the iron line and for this reason the technique is often referred to as the iron line method.…”