We continue exploring the constraining capabilities of X-ray reflection spectroscopy to test the Kerr-nature of astrophysical black holes and we present the results of our analysis of two NuSTAR observations of Cygnus X-1 in the soft state. We find that the final measurement can strongly depend on the assumption of the intensity profile. We conclude that Cygnus X-1 is not suitable for tests of general relativity using X-ray reflection spectroscopy and we discuss the desired properties of a source to be a good candidate for our studies.
Astrophysical black holes are ideal laboratories for testing Einstein's theory of general relativity in the strong field regime. In this manuscript, we present an analysis of Suzaku and NuSTAR spectra of the black hole binary Cygnus X-1 using RELXILL_NK. Unlike our previous study on Cygnus X-1 with NuSTAR data, here we are able to constrain the Johannsen deformation parameter $α_{13}$. However, despite the high energy resolution near the iron line provided by Suzaku, our constraints on the Kerr metric from Cygnus X-1 are not very stringent in comparison with those that have been obtained from …
In general, it is very difficult to test the Kerr-nature of an astrophysical black hole candidate, because it is not possible to have independent measurements of both the spin parameter $a_*$ and possible deviations from the Kerr solution. Non-Kerr objects may indeed look like Kerr black holes with different spin. However, it is much more difficult to mimic an extremal Kerr black hole. The black hole candidate in Cygnus X-1 has the features of a near extremal Kerr black hole, and it is therefore a good object to test the Kerr black hole paradigm. The 3$σ$-bounds $a_* > 0.95$ and $a_* > 0.983$ …
Einstein's theory of General Relativity predicts that the spacetime metric around astrophysical black holes is described by the Kerr solution. In this work, we employ state-of-the-art in relativistic reflection modeling to analyze a selected set of NuSTAR spectra of Galactic black holes to obtain the most robust and precise constraints on the Kerr black hole hypothesis possible today. Our constraints are much more stringent than those from other electromagnetic techniques, and with some sources we get stronger constraints than those currently available from gravitational waves.
We present a new analysis of NuSTAR and Suzaku observations of the black hole Cygnus X-1 in the intermediate state. The analysis uses kerrC, a new model for analyzing spectral and spectropolarimetric X-ray observations of black holes. kerrC builds on a large library of simulated black holes in X-ray binaries. The model accounts for the X-ray emission from a geometrically thin, optically thick accretion disk, the propagation of the X-rays through the curved black hole spacetime, the reflection off the accretion disk, and the Comptonization of photons in coronae of different 3-D shapes and physi…
The spacetime geometry around astrophysical black holes is supposed to be well approximated by the Kerr metric, but deviations from the Kerr solution are predicted in a number of scenarios involving new physics. Broad iron K$α$ lines are commonly observed in the X-ray spectrum of black holes and originate by X-ray fluorescence of the inner accretion disk. The profile of the iron line is sensitively affected by the spacetime geometry in the strong gravity region and can be used to test the Kerr black hole hypothesis. In this paper, we extend previous work in the literature. In particular: i) as…
Signature of iron line profile from a Kerr-like wormhole
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（李政道研究所，上海交通大学）；School of Physics and Astronomy, Shanghai Jiao Tong University（物理与天文学院，上海交通大学）；Key Laboratory for Particle Astrophysics and Cosmology (MOE) and Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University（粒子天体物理与宇宙学教育部重点实验室和上海市粒子物理与宇宙学重点实验室，上海交通大学）；Institute for Theoretical Physics & Cosmology, Zhejiang University of Technology（理论物理与宇宙学研究所，浙江工业大学）
We extend our previous work on tests of the Kerr black hole hypothesis using X-ray reflection spectroscopy and we infer observational constraints on the Johannsen deformation parameter $ε_3$. We analyze a NuSTAR observation of the stellar-mass black hole in GS 1354-645, Suzaku data of the supermassive black holes in Ark 564, 1H0419-577, and PKS 0558-504, and some simultaneous XMM-Newton and NuSTAR observations of the supermassive black hole in MCG-6-30-15. All our measurements of $ε_3$ are consistent with the Kerr metric and we find quite strong constraints from Ark 564 and MCG-6-30-15. We dis…
Astrophysical black holes are thought to be the Kerr black holes predicted by general relativity, but macroscopic deviations from the Kerr solution can be expected from a number of scenarios involving new physics. In Paper I, we studied the reflection features in NuSTAR and XMM-Newton spectra of the supermassive black hole at the center of the galaxy MCG-06-30-15 and we constrained a set of deformation parameters proposed by Konoplya, Rezzolla & Zhidenko (Phys. Rev. D93, 064015, 2016). In the present work, we analyze the X-ray data of a stellar-mass black hole within the same theoretical frame…
We employ the accretion disk reflection model RELXILL_NK to test the spacetime geometry around the stellar-mass black hole in GRS 1915+105. We adopt the Johannsen metric with the deformation parameters $α_{13}$ and $α_{22}$, for which the Kerr solution is recovered when $α_{13} = α_{22} = 0$. We analyze a NuSTAR observation of 2012, obtaining vanishing and non-vanishing values of the deformation parameters depending on the astrophysical model adopted. Similar difficulties were not found in our previous tests with other sources. The results of this work can shed light on the choice of sources s…
We analyze simultaneous observations with NuSTAR and Swift of the black hole binary GX 339-4 in which we clearly detect both a strong thermal component and prominent relativistic reflection features. We employ NKBB and RELXILL_NK, which are the state of the art of, respectively, the thermal and reflection models to test the Kerr black hole hypothesis. We obtain unprecedented precise measurements of the Johannsen deformation parameter $α_{13}$: $α_{13} = -0.012_{-0.039}^{+0.011}$ (lamppost coronal geometry) and $α_{13} = -0.010_{-0.018}^{+0.024}$ (broken power-law emissivity profile) at a 90% c…
The continuum-fitting and the iron-line methods are currently the two leading techniques for measuring the spins of accreting black holes. In the past few years, these two methods have been developed for testing fundamental physics. In the present work, we employ state-of-the-art models to test black holes through the continuum-fitting and the iron-line methods and we analyze three NuSTAR observations of the black hole binary GRS 1716-249 during its outburst in 2016-2017. In these three observations, the source was in a hard-intermediate state and the spectra show both a strong thermal compone…
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 ligh…
Recently, we have extended the X-ray reflection model relxill to test the spacetime metric in the strong gravitational field of astrophysical black holes. In the present Letter, we employ this extended model to analyze XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495 and test deviations from a Kerr metric parametrized by the Johannsen deformation parameter $α_{13}$. Our results are consistent with the hypothesis that the spacetime metric around the black hole in 1H0707-495 is described by the Kerr solution.
Astrophysical black hole candidates are thought to be the Kerr black holes of general relativity. However, macroscopic deviations from the Kerr background are predicted by a number of scenarios beyond Einstein's gravity. X-ray reflection spectroscopy can be a powerful tool to probe the strong gravity region of these objects and test the Kerr black hole hypothesis. Here I briefly review the state of the art of this line of research and I present some constraints on possible deviations from the Kerr metric obtained with the new X-ray reflection model relxill_nk and XMM-Newton, NuSTAR, and Swift …
In a previous paper, we tried to test the Kerr nature of the stellar-mass black hole in GRS 1915+105 by analyzing NuSTAR data of 2012 with our reflection model RELXILL_NK. We found that the choice of the intensity profile of the reflection component is crucial and eventually we were not able to get any constraint on the spacetime metric around the black hole in GRS 1915+105. In the present paper, we study the same source with Suzaku data of 2007. We confirm that the intensity profile plays an important role, but now we find quite stringent constraints consistent with the Kerr hypothesis. The k…
X-ray reflection spectroscopy is a powerful technique for probing the nature of gravity around black holes in the so-called strong field regime. One of the most popular of such probes is to look at theory-agnostic deviations away from the Kerr solution, which is the only astrophysically relevant black hole solution within classical general relativity, in order to verify whether astrophysical black holes are described by the Kerr metric. We have recently extended our X-ray reflection spectroscopy framework to a class of very general axisymmetric non-Kerr black holes proposed by Konoplya, Rezzol…
Astrophysical black hole systems are the ideal laboratories for testing Einstein's theory of gravity in the strong field regime. We have recently developed a framework which uses the reflection spectrum of black hole systems to perform precision tests of general relativity by testing the Kerr black hole hypothesis. In this paper, we analyze XMM-Newton and NuSTAR observations of the supermassive black hole in the Seyfert 1 galaxy MCG-06-30-15 with our disk reflection model. We consider the Johannsen metric with the deformation parameters $α_{13}$ and $α_{22}$, which quantify deviations from the…
The spins of a number of supermassive and stellar-mass black holes have been measured based on detections of thermal continuum emission and relativistically broadened iron lines in their x-ray spectra. Likewise, quasiperiodic variability has been observed in several sources. Such measurements commonly make the assumption that black holes are described by the Kerr metric, which according to the no-hair theorem characterizes black holes uniquely in terms of their masses and spins. This fundamental property of black holes can be tested observationally by measuring potential deviations from the Ke…
In a previous paper, we presented an extension of our reflection model RELXILL_NK to include the finite thickness of the accretion disk following the prescription in Taylor & Reynolds (2018). In this paper, we apply our model to fit the 2013 simultaneous observations by NuSTAR and XMM-Newton of the supermassive black hole in MCG-06-30-15 and the 2019 NuSTAR observation of the Galactic black hole in EXO 1846-031. The high-quality data of these spectra had previously led to precise black hole spin measurements and very stringent constraints on possible deviations from the Kerr metric. We find th…
In this paper we present RELXILLDGRAD_NK, a relativistic reflection model in which the electron density of the accretion disk is allowed to have a radial power-law profile. The ionization parameter has also a non-constant radial profile and is calculated self-consistently from the electron density and the emissivity. We show the impact of the implementation of the electron density gradient in our model by analyzing a NuSTAR spectrum of the Galactic black hole in EXO 1846-031 during its last outburst in 2019 and a putative future observation of the same source with Athena and eXTP. For the NuST…
In a previous paper, one of us calculated iron K$α$ line profiles emitted from possible accretion disks around traversable wormholes as a first step to use X-ray reflection spectroscopy to search for astrophysical wormholes in active galactic nuclei. In the present paper, we extend that work and construct an XSPEC model for the whole relativistic reflection spectrum. We apply our model to XMM-Newton and NuSTAR observations of the supermassive object in MCG-6-30-15 and we check whether these observations prefer the hypothesis that the central body is a Kerr black hole or a traversable wormhole.…
In this paper, we review our current efforts to test General Relativity in the strong field regime by studying the reflection spectrum of supermassive black holes. So far we have analyzed 11 sources with observations of NuSTAR, Suzaku, Swift, and XMM-Newton. Our results are consistent with general relativity, according to which the spacetime metric around astrophysical black holes should be well approximated by the Kerr solution. We discuss the systematic uncertainties in our model and we present a preliminary study on the impact of some of them on the measurement of the spacetime metric.
X-ray reflection spectroscopy is currently one of the leading techniques for studying the inner part of accretion disks around black holes, measuring black hole spins, and even testing fundamental physics in strong gravitational fields. However, the accuracy of these measurements depends on the reflection models employed for the spectral analysis, which are sometimes questioned. In this work, we use a general relativistic magnetohydrodynamic (GRMHD) code to generate a thin accretion disk in Kerr spacetime and ray-tracing techniques to calculate its relativistically broadened reflection spectru…
Recently, two of us have found a family of singularity-free rotating black hole solutions in Einstein's conformal gravity. These spacetimes are characterized by three parameters: the black hole mass $M$, the black hole spin angular momentum $J$, and a parameter $L$ that is not specified by the theory but can be expected to be proportional to the black hole mass $M$. The Kerr black hole solution of Einstein's gravity is recovered for $L = 0$. In a previous paper, we showed that X-ray data of astrophysical black holes require $L/M < 1.2$. In the present paper, we report the results of a more sop…
The presence of spacetime singularities in physically relevant solutions of the Einstein Equations is normally interpreted as a symptom of the breakdown of classical general relativity at very high densities/curvatures. However, despite significant efforts in the past decades, we do not have yet any robust theoretical framework to solve the problem of spacetime singularities. In this context, the past few years have seen an increasing interest in the study of phenomenological scenarios to describe singularity-free black holes, gravitational collapses, and cosmological models. In the present wo…
