Relativistic reflection features are commonly observed in the X-ray spectra of stellar-mass and supermassive black holes and originate from illumination of the inner part of the accretion disk by a hot corona. All the available relativistic reflection models assume that the disk is infinitesimally thin and the inner edge is at the innermost stable circular orbit or at a larger radius. However, we know that several sources, especially among supermassive black holes, have quite high mass accretion rates. In such a case, the accretion disk becomes geometrically thick and the inner edge of the disk is expected to be inside the innermost stable circular orbit. In this work, we employ the Polish donut model to describe geometrically thick disks and we study the iron line shapes from similar systems. We also simulate full reflection spectra and we analyze the simulated observations with a thin disk relativistic reflection model to determine the impact of the disk structure on the estimation of the model parameters, in particular in the case of tests of the Kerr hypothesis.
The main goal of this paper is to investigate one of the important astrophysical systems, namely Thick accretion disks, in the background of the spherically symmetric solution in Born-Infeld teleparallel gravity to examine observable predictions of the theory in the vicinity of black holes. Thus, the properties of the non-self-gravitating equilibrium surfaces characterising the Thick accretion disks model are studied. In addition, we find an observational bound on the parameter of the model as $λ\gtrsim 140$. We show this analytical accretion disk model for different values of $λ$ and compare …
X-ray reflection spectroscopy is a powerful tool for probing the strong gravity region of black holes and can be used for testing general relativity in the strong field regime. Simplifications of the available relativistic reflection models limit the capability of performing accurate measurements of the properties of black holes. In this paper, we present an extension of the model RELXILL_NK in which the accretion disk has a finite thickness rather than being infinitesimally thin. We employ the accretion disk geometry proposed by Taylor & Reynolds (2018) and we construct relativistic reflectio…
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…
General relativistic, axisymmetric flow of low angular momentum accretion around a Kerr black hole can have certain geometric configuration where the flow is maintained in hydrostatic equilibrium along the vertical direction (direction orthogonal to the equatorial plane of the flow). The flow thickness for such accretion models becomes a function of the local radial distance measured from the black hole horizon. There are three types of functions defined in the literature which resemble the thickness of the flow for such a configuration. We formulate the equations governing the steady state as…
The analysis of the thermal spectrum of geometrically thin and optically thick accretion disks of black holes, the so-called continuum-fitting method, is one of the leading techniques for measuring black hole spins. Current models normally approximate the disk as infinitesimally thin, while in reality the disk thickness is finite and increases as the black hole mass accretion rate increases. Here we present an XSPEC model to calculate the multi-temperature blackbody spectrum of a thin accretion disk of finite thickness around a Kerr black hole. We test our new model with an RXTE observation of…
Rotating black holes without equatorial reflection symmetry can naturally arise in effective low-energy theories of fundamental quantum gravity, in particular, when parity-violating interactions are introduced. Adopting a theory-agnostic approach and considering a recently proposed Kerr-like black hole model, we investigate the structure and properties of accretion disk around a rotating black hole without reflection symmetry. In the absence of reflection symmetry, the accretion disk is in general a curved surface in shape, rather than a flat disk lying on the equatorial plane. Furthermore, th…
In this paper we extend our previous works on spherically symmetric accretion onto black holes and super-spinars to the case in which the fluid has a finite angular momentum initially. We run 2.5D and 3D general relativistic hydrodynamic simulations of the accretion of a fat disk. We study how the accretion process changes by changing the values of the parameters of our model. We show that the value of the fluid angular momentum critically determines turn-on and off the production of powerful equatorial outflows around super-spinars. For corotating disks, equatorial outflows are efficiently ge…
Relativistic reflection features in the X-ray spectra of black hole binaries and AGNs are thought to be produced through illumination of a cold accretion disk by a hot corona. In this work, we assume that the corona has the shape of an infinitesimally thin disk with its central axis the same as the rotational axis of the black hole. The corona can either be static or corotate with the accretion disk. We calculate the disk's emissivity profiles and iron line shapes for a set of coronal radii and heights. We incorporate these emissivity profiles into RELXILL_NK and we simulate some observations …
A Dark Matter Masquerade: Degeneracies in Black Hole and Accretion Inference from X-ray Reflection Measurements and Prospects for Compact Dark Matter Halo Constraints
Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；The University of Hong Kong（香港大学）；The Hong Kong Institute for Astronomy and Astrophysics, The University of Hong Kong（香港大学香港天文及天体物理研究所）
We study energy flows in geometrically thick accretion discs, both optically thick and thin, using general relativistic, three-dimensional simulations of black hole accretion flows. We find that for non-rotating black holes the efficiency of the total feedback from thick accretion discs is $3\%$ - roughly half of the thin disc efficiency. This amount of energy is ultimately distributed between outflow and radiation, the latter scaling weakly with the accretion rate for super-critical accretion rates, and returned to the interstellar medium. Accretion on to rotating black holes is more efficien…
We explore thick accretion disks around rotating attractors. We detail the configurations analysing the fluid angular momentum and finally providing a characterization of the disk morphology and different possible topologies. Investigating the properties of orbiting disks, a classification of attractors, possibly identifiable in terms of their spin-mass ratio, is introduced; then an attempt to characterize dynamically a series of different disk topologies is discussed, showing that some of the toroidal configuration features are determined by the ratio of the angular momentum of the orbiting m…
We revisit the vertical structure of black hole accretion disks in spherical coordinates. By comparing the advective cooling with the viscous heating, we show that advection-dominated disks are geometrically thick, i.e., with the half-opening angle > 2π/5, rather than slim as supposed previously in the literature.
We investigate clusters of misaligned (inclined) tori orbiting a central static Schwarzschild black hole. To this purpose we considered a set of geometrically thick, pressure supported, perfect fluid tori analyzing purely hydrodynamic models. We study the tori collision emergence and, consequently, the stability properties of the aggregates composed by tori with different inclination angles relative to a fixed distant observer. The aggregate of tilted tori is modeled as a single orbiting configuration, by introducing a leading function governing the distribution of toroids around the black hol…
We propose a geometrically thick, super-Eddington accretion disk model, where an optically thick wind is not necessary, to understand ultraluminous supersoft sources (ULSs). For high mass accretion rates $\dot M \ga 30\dot M_{\rm Edd}$ and not small inclination angles $θ\ga 25^{\circ}$, where $\dot M_{\rm Edd}$ is the Eddington accretion rate, the hard photons from the hot inner region may be shaded by the geometrically thick inner disk, and therefore only the soft photons from the outer thin disk and the outer photosphere of the thick disk can reach the observer. Our model can naturally expla…
Irradiation of the accretion disc causes reflection signatures in the observed X-ray spectrum, encoding important information about the disc structure and density. A Type I X-ray burst will strongly irradiate the accretion disc and alter its properties. Previous numerical simulations predicted the evolution of the accretion disc due to an X-ray burst. Here, we process time-averaged simulation data of six time intervals to track changes in the reflection spectrum from the burst onset to just past its peak. We divide the reflecting region of the disc within $r\lesssim50$ km into 6-7 radial zones…
When a thermonuclear X-ray burst ignites on an accreting neutron star, the accretion disk undergoes sudden strong X-ray illumination, which can drive a range of processes in the disk. Observations of superbursts, with durations of several hours, provide the best opportunity to study these processes and to probe accretion physics. Using detailed models of ionized reflection, we perform time resolved spectroscopy of the superburst observed from 4U 1636-536 in 2001 with RXTE. The spectra are consistent with a blackbody reflecting off a photoionized accretion disk, with the ionization state droppi…
We present a high density disc reflection spectral analysis of a sample of 17 Seyfert 1 galaxies to study the inner disc densities at different black hole mass scales and accretion rates. All the available XMM-Newton observations in the archive are used. OM observations in the optical/UV band are used to estimate their accretion rates. We find that 65% of sources in our sample show a disc density significantly higher than 1e15 cm^{-3}, which was assumed in previous reflection-based spectral analyses. The best-fit disc densities show an anti-correlation with black hole mass and mass accretion r…
Understanding the dynamics behind black hole state transitions and the changes they reflect in outbursts has become long-standing problem. The X-ray reflection spectrum describes the interaction between the hard X-ray source (the power-law continuum) and the cool accretion disc it illuminates, and thus permits an indirect view of how the two evolve. We present a systematic analysis of the reflection spectrum throughout three outbursts (500+ observations) of the black hole binary GX 339-4, representing the largest study applying a self-consistent treatment of reflection to date. Particular atte…
In the general accretion disk model theory, the accretion disk surrounding an astronomical object comprises fluid rings obeying Keplerian motion. However, we should consider relativistic and rotational effects as we close in toward the center of accretion disk surrounding spinning compact massive objects such as a black hole or a neutron star. In this study, we explore the geometry of the inner portion of the accretion disk in the context of Mukhopadhyay's pseudo Newtonian potential approximation for the full general relativity theory. We found that the shape of the accretion disk "puffs up" o…
X-ray reflection models are used to constrain the properties of the accretion disk, such as the degree of ionization of the gas and the elemental abundances. In combination with general relativistic ray tracing codes, additional parameters like the spin of the black hole and the inclination to the system can be determined. However, current reflection models used for such studies only provide angle-averaged solutions for the flux reflected at the surface of the disk. Moreover, the emission angle of the photons changes over the disk due to relativistic light bending. To overcome this simplificat…
X-ray reflection signatures are observed around multiple classes of accreting compact objects. Modelling these features yield important constraints on the physics of accretion disks, motivating the development of X-ray reflection models appropriate for a variety of systems and illumination conditions. Here, constant density ionized X-ray reflection models are presented for a disk irradiated with a very hard power-law X-ray spectrum (Γ< 1) and a variable high-energy cutoff. These models are then applied to the Suzaku data of the accreting X-ray pulsar LMC X-4, where very good fits are obtained …
If astrophysical black hole candidates are the Kerr black holes predicted by General Relativity, the value of their spin parameter must be subject to the theoretical bound $|a_*| \le 1$. In this work, we consider the possibility that these objects are either non-Kerr black holes in an alternative theory of gravity or exotic compact objects in General Relativity. We study the accretion process when their accretion disk is geometrically thick with a simple version of the Polish doughnut model. The picture of the accretion process may be qualitatively different from the one around a Kerr black ho…
Accretion disks around very compact objects such as very massive Black hole can grow according to thick toroidal models. We face the problem of defining how does change the thickness of a toroidal accretion disk spinning around a Schwarzschild Black hole under the influence of a toroidal magnetic field and by varying the fluid angular momentum. We consider both an hydrodynamic and a magnetohydrodynamic disk based on the Polish doughnut thick model. We show that the torus thickness remains basically unaffected but tends to increase or decrease slightly depending on the balance of the magnetic, …
At super-Eddington rates accretion flows onto black holes have been described as slim (aspect ratio $H/R \lesssim 1$) or thick (H/R >1) discs, also known as tori or (Polish) doughnuts. The relation between the two descriptions has never been established, but it was commonly believed that at sufficiently high accretion rates slim discs inflate, becoming thick. We wish to establish under what conditions slim accretion flows become thick. We use analytical equations, numerical 1+1 schemes, and numerical radiative MHD codes to describe and compare various accretion flow models at very high accreti…
We present X-ray timing and spectral analyses of simultaneous 150 ks Nuclear Spectroscopic Telescope Array (NuSTAR) and Suzaku X-ray observations of the Seyfert 1.5 galaxy NGC 4151. We disentangle the continuum emission, absorption, and reflection properties of the active galactic nucleus (AGN) by applying inner accretion disk reflection and absorption-dominated models. With a time-averaged spectral analysis, we find strong evidence for relativistic reflection from the inner accretion disk. We find that relativistic emission arises from a highly ionized inner accretion disk with a steep emissi…
Modeling reflection spectra of super-Eddington X-ray sources
Fudan University（复旦大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Ulugh Beg Astronomical Institute（乌鲁格别克天文研究所）；Institut für Astronomie und Astrophysik, Eberhard-Karls Universität Tübingen（蒂宾根大学天文与天体物理研究所）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高等研究院）；University of Warwick（华威大学）；Institute of Astronomy, University of Cambridge（剑桥大学天文学研究所）
We consider the Comptonisation of the photons that make up the relativistically blurred reflection that is commonly detected from the accretion discs of AGN by the coronae of energetic particles believed to give rise to the powerful X-ray continua by the inverse-Compton scattering of thermal seed photons from the disc. Recent measurements of the emissivity profiles of accretion discs as well as reverberation time lags between the primary X-ray continuum and the reflection suggest that this corona is situated at a low height above the disc and extends radially, tens of gravitational radii over …
We study properties of an accretion ring in a steady mass flow from a companion star to a compact object in an X-ray binary. The accretion ring is a place where matter inflowing from a companion star sojourns for a while to bifurcate to accretion and excretion flows due to angular momentum transfer in it. The matter in the accretion ring rotates along the Keplerian circular orbit determined by the intrinsic specific angular momentum of the inflowing matter and forms a thick ring-envelope. Two internal flows are expected to appear in the thick envelope. One is a mass spreading flow bifurcating …
Continuum and reflection spectral models have each been widely employed in measuring the spins of accreting black holes. However, the two approaches have not been implemented together in a photon-conserving, self-consistent framework. We develop such a framework using the black-hole X-ray binary GX 339-4 as a touchstone source, and we demonstrate three important ramifications: (1) Compton scattering of reflection emission in the corona is routinely ignored, but is an essential consideration given that reflection is linked to the regimes with strongest Comptonization. Properly accounting for th…
We have calculated the relativistic reflection component of the X-ray spectra of accretion disks in active galactic nuclei (AGN). Our calculations have shown that the spectra can be significantly modified by the motion of the accretion flow and the gravity and rotation of the central black hole. The absorption edges in the spectra suffer severe energy shifts and smearing, and the degree of distortion depends on the system parameters, in particular, the inner radius of the accretion disk and the disk viewing inclination angles. The effects are significant. Fluorescent X-ray emission lines from …
We present spectroscopic X-ray data of two candidate ultra-compact X-ray binaries: 4U~0614+091 and 4U~1543$-$624. We confirm the presence of a broad O VIII Ly$α$ reflection line (at $\approx18\ Å$) using {\it XMM-Newton} and {\it Chandra} observations obtained in 2012 and 2013. The donor star in these sources is carbon-oxygen or oxygen-neon-magnesium white dwarf. Hence, the accretion disc is enriched with oxygen which makes the O VIII Ly$α$ line particularly strong. We also confirm the presence of a strong absorption edge at $\approx14$ Å so far interpreted in the literature as due to absorpti…
Type I X-ray bursts and superbursts from accreting neutron stars illuminate the accretion disk and produce a reflection signal that evolves as the burst fades. Examining the evolution of reflection features in the spectra will give insight into the burst-disk interaction, a potentially powerful probe of accretion disk physics. At present, reflection has been observed during only two bursts of exceptional duration. We investigate the detectability of reflection signatures with four of the latest well-studied X-ray observatory concepts: Hitomi, NICER, Athena, and LOFT. Burst spectra are modeled …
We construct a general relativistic radiative transfer (RT) formulation, applicable to particles with or without mass in astrophysical settings. Derived from first principles, the formulation is manifestly covariant. Absorption and emission, as well as relativistic, geometrical and optical depth effects are treated self-consistently. The RT formulation can handle 3D geometrical settings and structured objects with variations and gradients in the optical depths across the objects and along the line-of-sight. The presence of mass causes the intensity variation along the particle bundle ray to be…
Shadows and Polarization Images of a Four-dimensional Gauss-Bonnet Black Hole Irradiated by a Thick Accretion Disk
College of Physics and Electronic Engineering, Chongqing Normal University（重庆师范大学物理与电子工程学院）；School of Material Science and Engineering, Chongqing Jiaotong University（重庆交通大学材料科学与工程学院）；Department of Mathematics, School of Science, University of Management and Technology（管理技术大学理学院数学系）；Department of Mathematics, COMSATS University Islamabad, Lahore Campus（科摩特斯伊斯兰堡大学拉合尔校区数学系）
Measuring black hole spins with x-ray reflection spectroscopy: A GRMHD outlook
Fudan University（复旦大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Ulugh Beg Astronomical Institute（乌鲁伯格天文学研究所）；Eberhard-Karls Universität Tübingen（蒂宾根大学）；Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交通大学李政道研究所）；Shanghai Jiao-Tong University（上海交通大学）；Goethe Universität（法兰克福歌德大学）
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…
X-ray reflection spectroscopy (or iron line method) is a powerful tool to probe the strong gravity region of black holes, and currently is the only technique for measuring the spin of the supermassive ones. While all the available relativistic reflection models assume thin accretion disks, we know that several sources accrete near or above the Eddington limit and therefore must have thick accretion disks. In this work, we employ the Polish donut model for the description of thick disks. We thus estimate the systematic error on the spin measurement when a source with a thick accretion disk is f…
The relativistically-broadened reflection spectrum, observed in both AGN and X-ray binaries, has proven to be a powerful probe of the properties of black holes and the environments in which they reside. Being emitted from the inner-most regions of the accretion disk, this X-ray spectral component carries with it information not only about the plasma that resides in these extreme conditions, but also the black hole spin, a marker of the formation and accretion history of these objects. The models currently used to interpret the reflection spectrum are often simplistic, however, approximating th…
Accretion disks play an important role in the evolution of their relativistic inner compact objects. The emergence of a new generation of interferometers will allow to resolve these accretion disks and provide more information about the properties of the central gravitating object. Due to this instrumental leap forward it is crucial to investigate the accretion disk physics near various types of inner compact objects now to deduce later constraints on the central objects from observations. A possible candidate for the inner object is the boson star. Here, we will try to analyze the differences…
X-ray reverberation in AGN, believed to be the result of the reprocessing of corona photons by the underlying accretion disk, has allowed us to probe the properties of the inner-most regions of the accretion flow and the central black hole. This process is modeled via raytracing in the Kerr metric, with the disk thickness almost ubiquitously assumed to be negligible (razor-thin) and the corona commonly approximated as a point source located along the polar axis (a lamppost). In this work, we use the new raytracing suite, Fenrir, to explore the effect that accretion disk geometry has on reverbe…
An interesting feature in active galactic nuclei (AGN) accreting at low rate is the weakness of the reflection features in their X-ray spectra, which can result from the gradual disappearance of the torus with decreasing accretion rates. It has been suggested that low luminosity AGN (LLAGN) would have a different reflector configuration compared with high luminosity AGN, either covering a smaller fraction of the sky or simply having less material. Additionally, we note that the determination of the spectral index ($Γ$) and the cut-off energy of the primary power-law emission is affected by the…
We analyze 15,000 spectra of 29 stellar-mass black hole candidates collected over the 16-year mission lifetime of RXTE using a simple phenomenological model. As these black holes vary widely in luminosity and progress through a sequence of spectral states, which we broadly refer to as hard and soft, we focus on two spectral components: The Compton power law and the reflection spectrum it generates by illuminating the accretion disk. Our proxy for the strength of reflection is the equivalent width of the Fe-K line as measured with respect to the power law. A key distinction of our work is that …
When a black hole is accreting well below the Eddington rate, a geometrically thick, radiatively inefficient state of the accretion disk is established. There is a limited number of closed-form physical solutions for geometrically thick (non-selfgravitating) toroidal equilibria of perfect fluids orbiting a spinning black hole, and these are predominantly used as initial conditions for simulations of accretion in the aforementioned mode. However, different initial configurations might lead to different results and thus observational predictions drawn from such simulations. We expand the known e…
Strong evidence is emerging that winds can be driven from the central regions of accretion disks in both active galactic nuclei (AGN) and Galactic black hole binaries (GBHBs). Direct evidence for highly-ionized, Compton-thin inner-disk winds comes from observations of blueshifted (v~0.05-0.1c) iron-K X-ray absorption lines. However, it has been suggested that the inner regions of black hole accretion disks can also drive Compton-thick winds --- such winds would enshroud the inner disk, preventing us from seeing direct signatures of the accretion disk (i.e. the photospheric thermal emission, or…
The primary X-ray emission from AGN, described by a power law, irradiates the accretion disc producing reflection features in the spectrum. The reflection features arising from the inner regions of the disc can be significantly modified by the relativistic effects near the black hole. We investigate the relationship between the relativistic reflection fraction $R_f$, defined as the ratio of the coronal intensity that illuminates the accretion disc to the coronal intensity observed directly, and the hard X-ray photon index $Γ$ of a NuSTAR sample of Seyfert 1 galaxies. The X-ray spectra are mode…
We confirm that the spectra are best fit by a model containing two Compton reflection components, one from distant material, and the other displaying relativistic broadening, most likely from the inner accretion disk. The degree of relativistic broadening indicates a preference for high black hole spin, but the reflection is weaker than that expected for a flat disk illuminated by a point source. We investigate the Compton reflection signatures as a function of luminosity, redshift and obscuration, confirming an X-ray Baldwin effect for both the narrow and broad components of the iron line. An…
Supercritical accretion onto compact objects may drive massive winds that are nearly spherical, optically thick, and Eddington limited. Blackbody emission from the photosphere is the direct observational signature of the wind. Here we investigate whether or not it can explain the soft emission component seen in the energy spectra of ultraluminous X-ray sources (ULXs). Based on high-quality XMM-Newton spectra of 15 ULXs, we find that the soft component can be modeled as blackbody emission with a nearly constant luminosity, and the 5 known pulsating ULXs (PULXs) in the sample display a blackbody…
We study accretion environments of active galactic nuclei when a super-massive black hole wanders in a circum-nuclear region and passes through an interstellar medium there. It is expected that a Bondi-Hoyle-Lyttleton type accretion of the interstellar matter takes place and an accretion stream of matter trapped by the black hole gravitational field appears from a tail shock region. Since the trapped matter is likely to have a certain amount of specific angular momentum, the accretion stream eventually forms an accretion ring around the black hole. According to the recent study, the accretion …
Existence of relatively cool ($k_B T \lesssim 10~{\rm keV}$) and optically thick ($τ\gtrsim 3$) coronae are inferred above super-Eddington accretion flow such as ultraluminous X-ray sources (ULXs), GRS 1915+105, and narrow-line Seyfert 1 galaxies (NLS1), which contrasts the cases in sub-Eddington accretion flows, which are associated with coronae with $k_B T \sim 100~{\rm keV}$ and $τ\sim 1$. To understand their physical origin, we investigate the emission properties of the corona which is formed by the gas blown off the super-Eddington inner disk by radiation pressure. We assume that the coro…
The co-evolution of a supermassive black hole with its host galaxy through cosmic time is encoded in its spin. At $z>2$, supermassive black holes are thought to grow mostly by merger-driven accretion leading to high spin. However, it is unknown whether below $z\sim1$ these black holes continue to grow via coherent accretion or in a chaotic manner, though clear differences are predicted in their spin evolution. An established method to measure the spin of black holes is via the study of relativistic reflection features from the inner accretion disk. Owing to their greater distances, there has h…
We study the force balance and resulting acceleration of gas in general relativity basing on simulations of accretion on a stellar-mass, non-rotating black hole. We compare properties of acceleration in an optically thin, radiatively inefficient disk, and in an optically thick, super-critical disk accreting at 10 times the Eddington rate. We study both the average forces acting at given location and forces acting on a gas parcel along its trajectory. We show that the acceleration is not a continuous process - in most cases gas is accelerated only in short-lasting episodes. We find that in the …
