We consider a temporal response of relativistically broadened line spectrum of iron from black hole accretion irradiated by an X-ray echo under strong gravity. The physical condition of accreting gas is numerically calculated in the context of general relativistic hydrodynamics under steady-state, axisymmetry in Kerr geometry. With the onset of a point-like X-ray flare of a short finite duration just above the accretion surface, the gas is assumed to be ionized to produce a neutral iron fluorescent line. Using a fully relativistic ray-tracing approach, the response of line photons due to the X-ray illumination is traced as a function of time and energy for different source configurations around \sw and Kerr black holes. Our calculations show that the X-ray echo on the accretion surface clearly imprints a characteristic time-variability in the line spectral features depending on those parameters. Simulated line profiles, aimed for the future microcalorimeter missions of large collecting area such as {\it Athena}/X-IFU for typical radio-quiet Seyfert galaxies, are presented to demonstrate that state-of-the-art new observations could differentiate various source parameters by such an X-ray tomographic line reverberation.
The iron K$α$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates originates from X-ray fluorescence of the inner accretion disk. Accordingly, it can be used to map the spacetime geometry around these objects. In this paper, we extend previous work using the iron K$α$ line to test the Kerr black hole hypothesis. We adopt the Cardoso-Pani-Rico parametrization and we test the possibility of constraining possible deviations from the Kerr solution that can be obtained from observations across the range of black hole spins and inclination angles.…
The iron K$α$ line commonly observed in the X-ray spectrum of both stellar-mass and supermassive black hole candidates is produced by the illumination of a cold accretion disk by a hot corona. In this framework, the activation of a new flaring region in the hot corona imprints a time variation on the iron line spectrum. Future X-ray facilities with high time resolution and large effective areas may be able to measure the so-called 2-dimensional transfer function; that is, the iron line profile detected by a distant observer as a function of time in response to an instantaneous flare from the X…
The continuum-fitting and the iron line methods are currently the two leading techniques for probing the strong gravity region around accreting black holes. In the present work, we test the Kerr black hole hypothesis with the stellar-mass black hole in GRS 1915+105 by analyzing five disk-dominated RXTE spectra and one reflection-dominated Suzaku spectrum. The combination of the constraints from the continuum-fitting and the iron line methods has the potential to provide more stringent tests of the Kerr metric. Our constraint on the Johannsen deformation parameter $α_{13}$ is $-0.15 < α_{13} < …
Under the assumption that astrophysical black hole candidates are the Kerr black holes of general relativity, the continuum-fitting method and the analysis of the K$α$ iron line are today the only available techniques capable of providing a relatively reliable estimate of the spin parameter of these objects. If we relax the Kerr black hole hypothesis and we try to test the nature of black hole candidates, we find that there is a strong correlation between the measurement of the spin and possible deviations from the Kerr solution. The properties of the radiation emitted in a Kerr spacetime with…
QPOs are a common feature in the X-ray power density spectrum of black hole binaries and a potentially powerful tool to probe the spacetime geometry around these objects. Here we discuss their constraining power to test the Kerr black hole hypothesis within the relativistic precession model. We compare our results with the constraints that can be obtained from gravitational waves and iron line. We find that QPOs may provide very precise measurements, but they are strongly affected by parameter degeneracy, and it is difficult to test the Kerr metric with this approach in the absence of independ…
The iron K$α$ line commonly observed in the X-ray spectrum of black hole candidates is produced by X-ray fluorescence of the inner accretion disk. This line can potentially be quite a powerful tool to probe the spacetime geometry around these objects and test the Kerr black hole hypothesis. In a previous paper, we studied the ability to constrain possible deviations from the Kerr solution from the standard time-integrated iron line spectrum within the Cardoso-Pani-Rico framework. In the present work, we expand on that study and consider iron line reverberation mapping in the CPR framework. Tha…
Recently, two of us have studied iron line reverberation mapping to test black hole candidates, showing that the time information in reverberation mapping can better constrain the Kerr metric than the time-integrated approach. Motivated by this finding, here we explore the constraining power of another time-dependent measurement: an AGN iron line eclipse. An obscuring cloud passes between the AGN and the distant observer, covering different parts of the accretion disk at different times. Similar to the reverberation measurement, an eclipse might help to better identify the relativistic effects…
We continue our study on the capabilities of present and future X-ray missions to test the nature of astrophysical black hole candidates via X-ray reflection spectroscopy and distinguish Kerr black holes from other solutions of 4-dimensional Einstein's gravity in the presence of a matter field. Here we investigate the case of Kerr black holes with Proca hair [1]. The analysis of a sample of these configurations suggests that even extremely hairy black holes can mimic the iron line profile of the standard Kerr black holes, and, at least for the configurations of our study, we find that current …
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…
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…
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）
The recent announcement of the detection of gravitational waves by the LIGO/Virgo collaboration has opened a new window to test the nature of astrophysical black holes. Konoplya & Zhidenko have shown how the LIGO data of GW 150914 can constrain possible deviations from the Kerr metric. In this letter, we compare their constraints with those that can be obtained from accreting black holes by fitting their reflected X-ray spectrum, the so-called iron line method. We simulate observations with eXTP, a next generation X-ray mission, finding constraints much stronger than those obtained by Konoplya…
The present paper is a sequel to our previous work [Y. Ni et al., JCAP 1607, 049 (2016)] in which we studied the iron K$α$ line expected in the reflection spectrum of Kerr black holes with scalar hair. These metrics are solutions of Einstein's gravity minimally coupled to a massive, complex scalar field. They form a continuous bridge between a subset of Kerr black holes and a family of rotating boson stars depending on one extra parameter, the dimensionless scalar hair parameter $q$, ranging from 0 (Kerr black holes) to 1 (boson stars). Here we study the limiting case $q=1$, corresponding to r…
We study the effect caused by external magnetic fields on the observed thermal spectra and iron line profiles of thin accretion discs formed around Kerr black holes and naked singularities. We aim to provide a tool that can be used to estimate the presence of magnetic fields in the neighbourhood of a compact object and to probe the cosmic censorship conjecture in these particular astrophysical environments. We developed a numerical scheme able to calculate thermal spectra of magnetised Page-Thorne accretion discs formed around rotating black holes and naked singularities as seen by an arbitrar…
Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, but there is not yet clear evidence that the geometry of the space-time around these objects is really described by the Kerr metric. In order to confirm the Kerr black hole hypothesis, we have to observe strong gravity features and check that they are in agreement with the ones predicted by General Relativity. In this paper, I study the broad K$α$ iron line, which is often seen in the X-ray spectrum of both stellar-mass and super-massive black hole candidates and whose shape is supposed …
Recently, a family of hairy black holes in 4-dimensional Einstein gravity minimally coupled to a complex, massive scalar field was discovered~\cite{hbh}. Besides the mass $M$ and spin angular momentum $J$, these objects are characterized by a Noether charge $Q$, measuring the amount of scalar hair, which is not associated to a Gauss law and cannot be measured at spatial infinity. Introducing a dimensionless scalar hair parameter $q$, ranging from 0 to 1, we recover (a subset of) Kerr black holes for $q=0$ and a family of rotating boson stars for $q=1$. In the present paper, we explore the poss…
MCG-5-23-16 is one of the first AGN where relativistic reverberation in the iron K line originating in the vicinity of the supermassive black hole was found, based on a short XMM-Newton observation. In this work, we present the results from long X-ray observations using Suzaku, XMM-Newton and NuSTAR designed to map the emission region using X-ray reverberation. A relativistic iron line is detected in the lag spectra on three different time-scales, allowing the emission from different regions around the black hole to be separated. Using NuSTAR coverage of energies above 10 keV reveals a lag bet…
It has been proposed that the supermassive black hole candidates at the centers of galaxies might be wormholes formed in the early Universe and connecting our Universe with other sister Universes. The analysis of the profile of the relativistic K$α$ iron line is currently the only available approach to probe the spacetime geometry around these objects. In this paper, I compute the expected K$α$ iron line in some wormhole spacetimes and I compare the results with the line produced around Kerr black holes. The line produced in accretion disks around non-rotating or very slow-rotating wormholes i…
In a recent paper [Ghasemi-Nodehi & Bambi, EPJC 76 (2016) 290], we have proposed a new parametrization for testing the Kerr nature of astrophysical black hole candidates. In the present work, we study the possibility of constraining the "Kerr parameters" of our proposal using X-ray reflection spectroscopy, the so-called iron line method. We simulate observations with the LAD instrument on board of the future eXTP mission assuming an exposure time of 200~ks. We fit the simulated data to see if the Kerr parameters can be constrained. If we have the correct astrophysical model, 200~ks observation…
The nature of the super-massive black hole candidates in galactic nuclei can be tested by analyzing the profile of the K$α$ iron line observed in their X-ray spectrum. In this paper, we consider the possibility that the spacetime in the immediate vicinity of these objects may be described by some non vacuum exact solutions of Einstein's equations resulting as the end-state of gravitational collapse. The vacuum far away portion of the spacetime is described by the Schwarzschild metric, while the interior part may be either regular or have a naked singularity at the center. The iron line generat…
Astrophysical black hole candidates are thought to be the Kerr black holes of general relativity, but the actual nature of these objects has still to be confirmed. The continuum-fitting and the iron line methods are currently the only available techniques to probe the spacetime geometry around these bodies and test the Kerr black hole paradigm. The continuum-fitting method is a robust approach, but the shape of the disk's thermal spectrum is in general too simple to measure the spin and to constrain possible deviations from the Kerr solution at the same time. The iron line analysis is potentia…
We present results of the spectral and timing analysis of the X-ray pulsar LMC X-4 with the NuSTAR observatory in the broad energy range 3-79 keV. Along with the detailed analysis of the averaged source spectrum, the high-precision pulse phased-resolved spectra were obtained for the first time. It has been shown that the comptonization model gives the best approximation of the obtained spectra. The evolution of its parameters was traced depending on the pulse phase as well. The search for the possible cyclotron absorption line was performed for all energy spectra in the 5-55 keV energy range. …
Recently, a rotating black hole solution was found in Vector-Tensor Galileons modified gravity that has some significant differences from the Kerr black hole solution. We study the iron line shape that is part of the reflection spectrum of accretion disks around black holes in this new black hole solution. We simulate and compare the iron lines of this solution with those of the Kerr solution to see if the technique of iron line spectroscopy can be used as a tool to test Vector-Tensor Galileons modified gravity. Our analysis shows that current X-ray facilities can, in principle, be used to tes…
If an accretion disk around a black hole is illuminated by hard X-rays from non-thermal coronae, fluorescent iron lines will be emitted from the inner region of the accretion disk. The emission line profiles will show a variety of strong field effects, which may be used as a probe of the spin parameter of the black hole and the structure of the accretion disk. In this paper we generalize the previous relativistic line profile models by including both the black hole spinning effects and the non-axisymmetries of warped accretion disks. Our results show different features from the conventional ca…
We methodically model the broad-band Suzaku spectra of a small sample of six 'bare' Seyfert galaxies: Ark 120, Fairall 9, MCG-02-14-009, Mrk 335, NGC 7469 and SWIFT J2127.4+5654. The analysis of bare Seyferts allows a consistent and physical modelling of AGN due to a weak amount of any intrinsic warm absorption, removing the degeneracy between the spectral curvature due to warm absorption and the red-wing of the Fe K region. Through effective modelling of the broad-band spectrum and investigating the presence of narrow neutral or ionized emission lines and reflection from distant material, we …
According to the no-hair theorem, astrophysical black holes are fully characterized by their masses and spins and are described by the Kerr metric. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we calculate the profiles of fluorescent iron lines emitted from the accretion flows around black hole candidates within a framework that allows us to perform the calculation as a function of its mass and spin as well as of a free parameter that measures potential deviations from the Kerr metric. We s…
It is commonly thought that the final product of gravitational collapse is a black hole. Nevertheless, theoretical studies have not yet provided a final answer to the question whether black holes are the only possible outcome or whether naked singularities are also allowed. Observational tests may thus represent a complementary approach. In the present paper, we consider the Janis-Newman-Winicour metric, which describes a rotating source with a surface-like naked singularity. We calculate iron line shapes in the reflection spectrum of a putative disk around a Janis-Newman-Winicour singularity …
The exterior geometry of a neutron star can be approximated by relativistic multipole moments of a parametrized metric using Ernst potential formalism. This spacetime can be tested with electromagnetic wave observation of astrophysical black holes. In the present paper, I simulate X-ray reflection spectra of a thin accretion disk with future X-ray missions. The purpose of this work is to understand whether X-ray reflection spectroscopy can distinguish the neutron star from the Kerr solution of General Relativity. I found that for the higher value of spin and multipole moment parameters, there …
We study the iron line shape expected in the reflection spectrum of accretion disks around black holes in asymptotically safe gravity. We compare the results of our simulations with the iron line shapes expected in the reflection spectrum of accretion disks around Kerr black holes to see if the technique of iron line spectroscopy can be used as a tool to test asymptotically safe gravity. Our analysis shows that current X-ray facilities are surely unable to distinguish black holes in asymptotically safe gravity from black holes in Einstein's gravity. In the case of the next generation of X-ray …
We describe a new numerical algorithm for ray tracing in the external spacetimes of spinning compact objects characterized by arbitrary quadrupole moments. Such spacetimes describe non-Kerr vacuum solutions that can be used to test the no-hair theorem in conjunction with observations of accreting black holes. They are also appropriate for neutron stars with spin frequencies in the 300-600 Hz range, which are typical of the bursting sources in low-mass X-ray binaries. We use our algorithm to show that allowing for the quadrupole moment of the spacetime to take arbitrary values leads to observab…
The reverberation associated with the iron line is the time lag between direct photons from the corona and the photons reflected from the disk. The resulting line spectrum is called the 2D transfer function. The shape of the 2D transfer function is determined by the geometry of spacetime and the properties of BH. In a paper (Ghasemi-Nodehi and Bambi in EPJC 76:290, 2016), the authors have proposed a parametrization. This parametrization is aimed to test the Kerr nature of astrophysical black hole candidates. In this paper, I provide a reverberation mapping of the Ghasemi-Nodehi-Bambi metric in…
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…
Context. Quasi-periodic variability has been observed in a number of X-ray binaries harboring black hole candidates. In general relativity, black holes are uniquely described by the Kerr metric and, according to the cosmic censorship conjecture, curvature singularities always have to be clothed by an event horizon. Aims. In this paper, we study the effect of an external magnetic field on the observed light curves of orbiting hot spots in thin accretion discs around Kerr black holes and naked singularities. Methods. We employ a ray-tracing algorithm to calculate the light curves and power spect…
It is thought that the spacetime geometry around black hole candidates is described by the Kerr solution, but an observational confirmation is still missing. Today, the continuum-fitting method and the analysis of the iron K$α$ line cannot unambiguously test the Kerr paradigm because of the degeneracy among the parameters of the system, in the sense that it is impossible with current X-ray data to distinguish a Kerr black hole from a non-Kerr object with different values of the model parameters. In this paper, we study the possibility of testing the Kerr nature of black hole candidates with X-…
X-ray reflection spectroscopy can be a powerful tool to test the nature of astrophysical black holes. Extending previous work on Kerr black holes with scalar hair [1] and on boson stars [2], here we study whether astrophysical black hole candidates may be horizonless, self-gravitating, vector Bose-Einstein condensates, known as Proca stars [3]. We find that observations with current X-ray missions can only provide weak constraints and rule out solely Proca stars with low compactness. There are two reasons. First, at the moment we do not know the geometry of the corona, and therefore the uncert…
In a previous paper, one of us has showed that, at least in some cases, the Kerr-nature of astrophysical black hole candidates is extremely difficult to test and current techniques, even in presence of excellent data not available today, cannot distinguish a Kerr black hole from a Bardeen one, despite the substantial difference of the two backgrounds. In this paper, we investigate if the detection of the "shadow" of nearby super-massive black hole candidates by near future mm/sub-mm very long baseline interferometry experiments can do the job. More specifically, we consider the measurement of …
According to the no-hair theorem, an astrophysical black hole is uniquely described by only two quantities, the mass and the spin. In this series of papers, we investigate a framework for testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. We formulate our approach in terms of a parametric spacetime which contains a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation of the black-hole quadrupole moment from its Kerr value has to be zero. We analyze in detail the properties of this quasi-Ker…
According to the no-hair theorem, astrophysical black holes are uniquely described by the Kerr metric. In order to test this theorem with observations in either the electromagnetic or gravitational-wave spectra, several Kerr-like spacetimes have been constructed which describe potential deviations from the Kerr spacetime in parametric form. For electromagnetic tests of the no-hair theorem, such metrics allow for the proper modeling of the accretion flows around candidate black holes and the radiation emitted from them. In many of these models, the location of the inner edge of the accretion di…
According to the no-hair theorem, astrophysical black holes are uniquely described by their mass and spin. In this paper, we review a new framework for testing the no-hair hypothesis with observations in the electromagnetic spectrum. The approach is formulated in terms of a Kerr-like spacetime containing a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation from the Kerr metric quadrupole has to be zero. We show how upcoming VLBI imaging observations of Sgr A* as well as spectroscopic observations of iron lines from accreting black…
According to the general-relativistic no-hair theorem, astrophysical black holes depend only on their masses and spins and are uniquely described by the Kerr metric. Mass and spin are the first two multipole moments of the Kerr spacetime and completely determine all other moments. The no-hair theorem can be tested by measuring potential deviations from the Kerr metric which alter such higher-order moments. In this review, I discuss tests of the no-hair theorem with current and future observations of such black holes across the electromagnetic spectrum, focusing on near-infrared observations of…
Relativistic Thermal Emission from Accretion Disks in Kerr-MOG Spacetimes
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大汤川研究所）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；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）；Institut für Theoretische Physik, Goethe-Universität Frankfurt（法兰克福歌德大学理论物理研究所）；Institute for Theoretical Physics & Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）
General relativity has been tested by many experiments, which, however, almost exclusively probe weak spacetime curvatures. In this thesis, I create two frameworks for testing general relativity in the strong-field regime with observations of black holes in the electromagnetic spectrum using current or near-future instruments. In the first part of this thesis, I design tests of the no-hair theorem, which uniquely characterizes the nature of black holes in general relativity in terms of their masses and spins and which states that these compact objects are described by the Kerr metric. I invest…
Iron K$α$ signatures from accretion disks around fermionic dark matter cores
Fac. de Ciencias Astronómicas y Geofísicas, UNLP（拉普拉塔国立大学天文与地球物理学院）；Instituto Argentino de Radioastronomía, CONICET-CICPBA-UNLP（阿根廷射电天文研究所，阿根廷国家科学研究委员会、布宜诺斯艾利斯省研究促进委员会及拉普拉塔国立大学）；ICRANet（国际相对论天体物理中心网络）；ICRA, Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系国际相对论天体物理中心）；ICRANet-Ferrara, Dipartimento di Fisica e Scienze della Terra, UNIFE（费拉拉大学地球与物理科学系国际相对论天体物理中心费拉拉分部）
A series of optical and one near-infrared nebular spectra covering the first year of the Type Ia supernova SN 2011fe are presented and modelled. The density profile that proved best for the early optical/ultraviolet spectra, "rho-11fe", was extended to lower velocities to include the regions that emit at nebular epochs. Model rho-11fe is intermediate between the fast deflagration model W7 and a low-energy delayed-detonation. Good fits to the nebular spectra are obtained if the innermost ejecta are dominated by neutron-rich, stable Fe-group species, which contribute to cooling but not to heatin…
In general relativity without a cosmological constant, a classical theorem due to Hawking states that stationary black holes must be topologically spherical. This result is one of the several ingredients that collectively imply the uniqueness of the Kerr metric. If, however, general relativity describes gravity inexactly at high energies or over cosmological scales, Hawking's result may not apply, and black holes with non-trivial topology may be, at least mathematically, permissible. While tests involving electromagnetic and gravitational-wave data have been used to place tight constraints on …
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 …
Recently, two of us have found numerically rotating Ellis wormholes as solutions of 4-dimensional Einstein gravity coupled to a phantom field. In this paper, we investigate possible observational signatures to identify similar objects in the Universe. These symmetric wormholes have a mass and are compact, so they may look like black holes. We study the iron line profile in the X-ray reflection spectrum of a thin accretion disk around rotating Ellis wormholes and we find some specific observational signatures that can be used to distinguish these objects from Kerr black holes. We simulate some …
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.…
