Innermost Stable Circular Orbit Research Articles

Observational appearances of hairy black holes in the framework of Gravitational Decoupling

Abstract We investigate the observation appearance of the static and spherical symmetric hairy black holes in the framework of the gravitational decoupling with the weak energy condition. Two types of thin illumination conditions are studied, named spherical accretion and disk accretion. As the hairy parameter increases, the size of the photon sphere and photon rings in both models decreases, and the overall luminosity attenuation becomes more pronounced. In spherical accretion, the luminosity of infalling accretion is significantly lower than that of stationary accretion. In disk accretion the luminosity of the black hole is contributed by direct emission, lensing ring and photon ring. With four types of astrophysical disk luminosity model employed, we investigate the appearance of halos and note that the luminosity of them do not superimpose when the source is on and beyond the innermost stable circular orbit.

Infinitely degenerate slowly rotating solutions in f(R) gravity

Abstract This work tests the no-hair conjecture in f(R) gravity models. No-hair conjecture asserts that all black holes in General Relativity coupled to any matter must be Kerr–Newman type. However, the conjecture fails in some cases with non-linear matter sources. Here, we address this by explicitly constructing multiple slow-rotating black hole solutions, up to second order in rotational parameter, for a class of f(R) models ( f(R) =(\alpha_{0} + \alpha_{1}\,R)^{p}, p > 1). Such an f(R) includes all higher-powers of R. We analytically show that multiple vacuum solutions satisfy the field equations up to the second order in the rotational parameter. In other words, we show that the multiple vacuum solutions depend on arbitrary constants, which depend on the coupling parameters of the model. Hence, our results indicate that the no-hair theorem for modified gravity theories merits extending to include the coupling constants. The uniqueness of our result stems from the fact that these are obtained directly from metric formalism without conformal transformation. We discuss the kinematical properties of these black hole solutions and compare them with slow-rotating Kerr. Specifically, we show that the circular orbits for the black holes in f(R) are smaller than that of Kerr. This implies that the inner-most stable circular orbit for black holes in f(R) is smaller than Kerr's; hence, the shadow radius might also be smaller. Finally, we discuss the implications of our results for future observations.

Continuum emission from within the plunging region of black hole discs

ABSTRACT The thermal continuum emission observed from accreting black holes across X-ray bands has the potential to be leveraged as a powerful probe of the mass and spin of the central black hole. The vast majority of existing ‘continuum fitting’ models neglect emission sourced at and within the innermost stable circular orbit (ISCO) of the black hole. Numerical simulations, however, find non-zero emission sourced from these regions. In this work, we extend existing techniques by including the emission sourced from within the plunging region, utilizing new analytical models that reproduce the properties of numerical accretion simulations. We show that in general the neglected intra-ISCO emission produces a hot-and-small quasi-blackbody component, but can also produce a weak power-law tail for more extreme parameter regions. A similar hot-and-small blackbody component has been added in by hand in an ad hoc manner to previous analyses of X-ray binary spectra. We show that the X-ray spectrum of MAXI J1820+070 in a soft-state outburst is extremely well described by a full Kerr black hole disc, while conventional models that neglect intra-ISCO emission are unable to reproduce the data. We believe this represents the first robust detection of intra-ISCO emission in the literature, and allows additional constraints to be placed on the MAXI J1820 + 070 black hole spin which must be low a• < 0.5 to allow a detectable intra-ISCO region. Emission from within the ISCO is the dominant emission component in the MAXI J1820 + 070 spectrum between 6 and 10 keV, highlighting the necessity of including this region. Our continuum fitting model is made publicly available.

Shadows and properties of spin-induced scalarized black holes with and without a Ricci coupling

In this work, we explore the properties and shadows of spin-induced scalarized black holes, as well as investigate how a Ricci coupling influences them. Our findings reveal significant deviations from the Kerr metric in terms of the location and geodesic frequencies of the innermost stable circular orbit and light ring, with the former exhibiting more pronounced disparities. The shadows of scalarized black holes exhibit relatively minor deviations when compared to those of Kerr black holes with the same mass and spin. Overall, the presence of a Ricci coupling is observed to mitigate deviations from the Kerr metric. Published by the American Physical Society 2024

Resolving the vicinity of supermassive black holes with gravitational microlensing

Abstract Upcoming wide field surveys will discover thousands of new strongly lensed quasars which will be monitored with unprecedented cadence by the Legacy Survey of Space and Time (LSST). Many of these quasars will undergo caustic-crossing events over the 10-year LSST survey, during which the quasar’s inner accretion disc crosses a caustic feature produced by an ensemble of microlenses. Such caustic-crossing events offer the unique opportunity to probe the vicinity of the central supermassive black hole, especially when combined with high cadence, multi-instrument follow-up triggered by LSST monitoring. To simulate the high cadence optical monitoring of caustic-crossing events, we use relativistic accretion disc models which leads to strong asymmetric features. We develop analysis methods to measure the Innermost Stable Circular Orbit (ISCO) crossing time of isolated caustic-crossing events and benchmark their performance on our simulations. We also use our simulations to train a Convolutional Neural Network (CNN) to infer the black hole mass, inclination angle, and impact angle directly from these light curves. As a pilot application of our methods, we used archival caustic-crossings of QSO 2237+0305 to estimate the black hole mass and inclination angle. From these data, two of these methods called the second derivative and wavelet methods measure an ISCO crossing time of 48.5 and 49.5 days, corresponding to a Kerr black hole mass of MBH = (1.5 ± 1.2) × 109M⊙ and MBH = (1.5 ± 1.3) × 109M⊙ respectively. The CNN inferred log10(MBH/M⊙) = 8.35 ± 0.30 when trained on Schwarzschild black hole simulations, and a moderate inclination of i = 45 ± 23○. These measurements are found to be consistent with previous estimates.

Dynamical Properties of Magnetized Low-angular-momentum Accretion Flows around a Kerr Black Hole

An essential factor for determining the characteristics of an accretion flow is its angular momentum. According to the angular momentum of the flow, semi-analytical analysis suggests various types of accretion solutions. It is critical to test these with numerical simulations, using the most advanced framework available (general relativistic magnetohydrodynamics), to understand how the flow changes with different angular momentum. By changing the initial condition of the accretion torus minimally, we can simulate a steady, low-angular-momentum accretion flow around a Kerr black hole. We focus primarily on the lower limits of angular momentum and find that an accretion flow with an intermediate range of angular momentum differs significantly from high- or very-low-angular-momentum flows. The intermediate-angular-momentum accretion flow has the highest density, pressure, and temperature near the black hole, making it easier to observe. We find that the density and pressure have power-law scalings ρ ∝ r n−3/2 and p g ∝ r n−5/2, which only hold for very-low-angular-momentum cases. With the increase in flow angular momentum, it develops a nonaxisymmetric nature. In this case, simple self-similarity does not hold. We also find that the sonic surface moves away from the innermost stable circular orbit as the angular momentum decreases. Finally, we emphasize that an intermediate-angular-momentum flow could provide a possible solution to explaining the complex observation features of the supermassive black hole Sgr A* at our galactic center.

On Innermost Stable Spherical Orbits near a Rotating Black Hole: A Numerical Study of the Particle Motion near the Plunging Region

According to general relativity, astrophysical black holes are described by a small number of parameters. Apart from the mass of the black hole (M), among the most interesting characteristics is the spin (a), which determines the degree of rotation, i.e., the angular momentum of the black hole. The latter is observationally constrained by the spectral and timing properties of the radiation signal emerging from an accretion disk of matter orbiting near the event horizon. In the case of the planar (standard, equatorial) accretion disk, this is the location of the innermost stable circular orbit that determines the observable radiation characteristics and allows us to measure the spin. In this paper, we discuss a more general case of the innermost stable spherical orbits (ISSOs) extending above and below the equatorial plane. To this end, we study the nonequatorial geodesic motion of particles following inclined, spherical, relativistically precessing trajectories with the aim of exploring the boundary between the regions of stable (energetically bound) and escaping (energetically unbound) motion. The concept of the radius of the ISSO should play a role in determining the inner rim of a tilted or geometrically thick accretion flow. We demonstrate that the region of inclined bound orbits has a complicated structure due to enhanced precession near the inner rim. We also explore the fate of particles launched below the radius of the marginally bound spherical orbit: these may either plunge into the event horizon or escape to radial infinity.

Rethinking the 67 Hz QPO in GRS 1915+105: Type C quasi-periodic oscillations at the innermost stable circular orbit

Context. We study quasi-periodic oscillations (QPO) at low and high frequency in the variability of the high-energy emission from black hole binaries and their physical interpretation in terms of signatures of General Relativity in the strong-field regime. Aims. We wish to understand the nature of the 67 Hz QPOs observed in the X-ray emission of the peculiar black hole binary GRS 1915+105 within the general classification of QPOs, and to determine the spin of the black hole in the system by applying the relativistic precession model (RPM). Methods. Within the RPM, the only relativistic frequency that is stable in time over a wide range of accretion rates and can be as low as 67 Hz (for a dynamically measured black hole mass) is the nodal frequency at the innermost stable circular orbit (ISCO). In the application of the model, this corresponds to type C QPOs. Under this assumption, it is possible to measure the spin of the black hole by using the mass of the black hole previously obtained via dynamical measurements. We re-analysed a large number of Rossi-XTE observations to determine whether other timing features confirm this hypothesis. Results. The identification of the 67 Hz QPO as the nodal frequency at ISCO yields a value of 0.706 ± 0.034 for the black hole spin. With this spin, the only two QPO detections at higher frequencies available in the literature are consistent with being orbital frequencies at a radius outside ISCO. The high-frequency bumps often observed at frequencies between 10 and 200 Hz follow the correlation expected for orbital and periastron-precession frequencies at even larger radii.

The universal power spectrum of quasars in optical wavelengths

Context. The optical variability of quasars is one of the few windows through which we can explore the behaviour of accretion discs around supermassive black holes. Aims. We aim to establish the dependence of variability properties, such as characteristic timescales and the variability amplitude, on basic quasar parameters such as black hole mass and the accretion rate, controlling for the rest-frame wavelength of emission. Methods. Using large catalogues of quasars, we selected the g-band light curves for 4770 objects from the Zwicky Transient Facility archive. All the selected objects fall into a narrow redshift bin, 0.6 < z < 0.7, but cover a wide range of accretion rates in Eddington units (REdd) and black hole masses (M). We grouped these objects into 26 independent bins according to these parameters, calculated low-resolution g-band variability power spectra for each of these bins, and approximated the power spectra with a simple analytic model that features a break at a timescale, tb. Results. We find a clear dependence of the break timescale, tb, on REdd, on top of the known dependence of tb on the black hole mass, M. In our fits, tb ∝ M0.65 − 0.55REdd0.35−0.3, where the ranges in the exponents correspond to the best-fitting parameters of different power spectrum models. This mass dependence is slightly steeper than that found in other studies. Scaling tb to the orbital timescale of the innermost stable circular orbit (ISCO), tISCO, results approximately in tb/tISCO ∝ (REdd/M)0.35. In the standard thin disc model, (REdd/M) ∝ Tmax4, where Tmax is the maximum disc temperature, so that tb/tISCO appears to scale approximately with the maximum temperature of the disc to a small power. The observed values of tb are ∼10 longer than the orbital timescale at the light-weighted average radius of the disc region emitting in the (observer frame) g-band. The different scaling of the break frequency with M and REdd shows that the shape of the variability power spectrum cannot be solely a function of the quasar luminosity, even for a single rest-frame wavelength. Finally, the best-fitting models have slopes above the break in the range between −2.5 and −3. A slope of −2, as in the damped random walk models, fits the data significantly worse.

Collisions and dynamics of particles with magnetic dipole moment and electric charge near magnetized rotating Kerr black holes

Analysis of test magnetized and charged particles around black holes immersed in external magnetic fields may help to explain the observed astrophysical phenomena related to black holes, such as the acceleration of particles up to high energies. In this sense, we studied the circular motion of test-charged particles with magnetic dipole orbiting around magnetized rotating Kerr black holes. First, we derive the effective potential for the circular motion of such particles, including interactions between the external magnetic field and the electric charge, and the magnetic interaction between the magnetic dipole. In addition, we analyze the angular momentum and energy of particles corresponding to circular orbits. The effects of magnetic interaction and coupling parameters on the position of innermost stable circular orbits (ISCOs), the energy and angular momentum of the particles at ISCO, and the energy efficiency from the Novikov-Thorne accretion disc have been investigated. We also find cases of degeneracy between magnetic dipole interaction and magnetic coupling parameters, giving the same ISCO radius. Finally, we studied various cases of collisions of neutral, magnetized, and electrically charged particles near rotating Kerr black holes in the presence of external magnetic fields. The critical angular momentum of spinning charged particles is found in which the particles can collide. We also analyze the effects of both magnetic interactions on the center-of-mass energy of the colliding particles.

The dynamics of accretion flows near to the innermost stable circular orbit

ABSTRACT Accretion flows are fundamentally turbulent systems, yet are classically modelled with viscous theories only valid on length scales significantly greater than the typical size of turbulent eddies in the flow. We demonstrate that, while this will be a reasonable bulk description of the flow at large radii, this must break down as the flow approaches absorbing boundaries, such as the innermost stable circular orbit (ISCO) of a black hole disc. This is because in a turbulent flow large velocity fluctuations can carry a fluid element over the ISCO from a finite distance away, from which it will not return, a process without analogy in conventional models. This introduces a non-zero directional bias into the velocity fluctuations in the near-ISCO disc. By studying reduced random walk problems, we derive a number of implications of the presence of an absorbing boundary in an accretion context. In particular, we show that the average velocity with which a typical fluid element crosses the ISCO is much larger than is assumed in traditional theories. This enhanced velocity modifies the thermodynamic properties of black hole accretion flows on both sides of the ISCO. In particular, thermodynamic quantities for larger ISCO stresses no longer display pronounced cusps at the ISCO in this new formalism, a result with relevance for a number of observational probes of the intra-ISCO region. Finally, we demonstrate that these extended models reproduce the trans-ISCO behaviour observed in GRMHD simulations of thin discs.

Circular orbits and collisions of particles with magnetic dipole moment near magnetized Kerr black holes in modified gravity

Throughout this work, we explored the dynamics of test particles with magnetic dipole moment around magnetized rotating Kerr black holes in scalar–vector–tensor gravity theory (STVG), known as modified gravity theory (MOG). We assume that the black hole is immersed in external asymptotically uniform magnetic fields. We derive effective potential for circular orbits of the magnetized particles, taking into account both the magnetic and STVG interactions. We study profiles of the position of the innermost stable circular orbits (ISCOs) of the magnetized particles. We show that the MOG interaction is essentially, and the magnetic interaction enhances its effects on the ISCO radius and the angular momentum at ISCO. Also, we consider collisional cases of magnetized particles and the maximum and minimum limits of angular momentum that ensure the particle colliding near the horizon. Finally, we analyze the center-of-mass energy of colliding magnetized particles near the black hole horizon.

Investigating the hard state of MAXI J1820 + 070: a comprehensive Bayesian approach to black hole spin and accretion properties

ABSTRACT We analyse the X-ray spectrum of the black hole (BH) X-ray binary MAXI J1820 + 070 using observations from XMM-Newton and NuSTAR during ‘hard’ states of its 2018–2019 outburst. We take a fully Bayesian approach, and this is one of the first papers to present a fully Bayesian workflow for the analysis of an X-ray binary X-ray spectrum. This allows us to leverage the relatively well-understood distance and binary system properties (like inclination and BH mass), as well as information from the XMM-Newton RGS data to assess the foreground X-ray absorption. We employ a spectral model for a ‘vanilla’ disc-corona system: the disc is flat and in the plane perpendicular to the axis of the jet and the BH spin, the disc extends inwards to the innermost stable circular orbit around the BH, and the (non-thermal) hard X-ray photons are up-scattered soft X-ray photons originating from the disc thermal emission. Together, these provide tight constraints on the spectral model and, in combination with the strong prior information about the system, mean we can then constrain other parameters that are poorly understood such as the disc colour correction factor. By marginalizing over all the parameters, we calculate a posterior density for the BH spin parameter, a. Our modelling suggests a preference for low or negative spin values, although this could plausibly be reproduced by higher spins and a modest degree of disc truncation. This approach demonstrates the efficacy and some of the complexities of Bayesian methods for X-ray spectral analysis.

Test particles and quasiperiodic oscillations around Kiselev black hole with cloud of strings* *Supported by the F-FA-2021-510 Grant of the Ministry of Innovative Development of Uzbekistan

In the present study, we investigate the dynamics of test particles around a Schwarzschild black hole surrounded by quintessence and immersed in a scalar string cloud field. We start our study by defining the possible values of the quintessence and cloud of string parameters corresponding to the existence of the black hole horizon for fixed values of the parameters of the equation of state for dark energy. We also study the effects of the effective potential on the circular motion, energy, and angular momentum of the test particles together with the innermost stable circular orbits (ISCOs). We investigate the fundamental frequencies in the particle oscillations along stable circular orbits. We relate the stability of the orbits to the Lyapunov exponent, and the chaotic behavior is studied graphically. Finally, we apply the fundamental frequencies to describe quasiperiodic oscillations (QPOs) and find that, in the presence of both fields, low-frequency twin-peak QPOs are not observed. In addition, we obtain the constraint values for the string cloud parameter and mass of the black hole candidates located in the center of the microquasars GRO J1655-40 and GRS 1915+105 as well as the Milky Way galaxy.

Rastall gravity: accretion disk image in the context of radiation fields and visual transformations compared to Reissner-Nordström black hole* *Supported by the National Natural Science Foundation of China (42230207), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (G1323523064), and the Sichuan Youth Science and Technology Innovation Research Team (21CXTD0038)

In this study, we investigated the astronomical implications of Rastall gravity, particularly its behavior amidst a radiation field compared to Reissner-Nordström (RN) black holes. We found a crucial correlation between the dynamics of the accretion disk and the parameters Q and , which properly reflect the influence of spacetime metrics on the disk’s appearance. Elevated electric charge Q causes contraction in the disk’s orbit due to enhanced gravitational effects, while higher values lead to outward expansion, influenced by the attributes of the radiation field. Interestingly, the charged black holes surrounded by radiation fields exhibit distinct visual disparities from RN black holes. Brightness decreases and expansion occurs within the innermost stable circular orbit of the accretion disk with rising values. Our study also reveals the process by which the accretion disk transitions from a conventional disk-like structure to a hat-like form at different observation angles, with the redshift effect gradually intensifying. Moreover, the results of the considered Rastall gravity radiation field are consistent with the constraints of the gravitational lensing of the host galaxy on Rastall gravity parameters, thereby enhancing the consistency between theoretical predictions and actual observations.

Charged Particles Orbiting Charged Black-Bounce Black Holes

The detailed and comprehensive analysis of radiation processes in accretion disks consisting of electrically charged particles around black holes may provide powerful information about the spacetime geometry of the central black hole. We investigate the circular orbits of electrically charged particles around an electrically charged black-bounce Reissner–Nordström (RN) black hole, known as an RN Simpson–Visser (SV) black hole. We also study the profiles of the innermost stable circular orbits (ISCOs), energy, and angular momentum of the particles in their ISCOs, as well as the efficiency of energy release processes in the accretion disk in the Novikov–Thorne model. Finally, we calculate and study the effects of the black-bounce parameter as well as the black-hole charge on the intensity of the radiation of ultrarelativistic charged particles orbiting the charged RN SV black hole along circular orbits and falling into the black hole. It is observed that the black-bounce parameter essentially decreases the ISCO radius, and consequently the energy extraction and intensity of electromagnetic radiation.

Reflecting on naked singularities: iron line fitting as a probe of the cosmic censorship conjecture

ABSTRACT We demonstrate that the X-ray iron line fitting technique can be leveraged as a powerful probe of the cosmic censorship conjecture. We do this by extending existing emission line models to arbitrary spin parameters of the Kerr metric, no longer restricted to black hole metrics with |a•| < 1. We show that the emission lines from naked singularity metrics (|a•| > 1) show significant differences to their black hole counterparts, even for those metrics with identical locations of the innermost stable circular orbit, i.e. emission line fitting does not suffer from the degeneracy which affects continuum fitting approaches. These differences are entirely attributable to the disappearance of the event horizon for |a•| > 1. We highlight some novel emission line features of naked singularity metrics, such as ‘inverted’ emission lines (with sharp red wings and extended blue wings) and ‘triple lines’. The lack of detection of any of these novel features provides support of the cosmic censorship conjecture. We publicly release xspec packages skline and skconv which can now be used to probe the cosmic censorship conjecture in Galactic X-ray binaries and active galactic nuclei. The inclusion of super-extremal space–times can be alternatively posed as a way of stress testing conventional models of accretion.

Circular geodesics in the field of double-charged dilatonic black holes

A non-extreme dilatonic charged (by two “color electric” charges) black hole solution is examined within a four-dimensional gravity model that incorporates two scalar (dilaton) fields and two Abelian vector fields. The scalar and vector fields interact through exponential terms containing two dilatonic coupling vectors. The solution is characterized by a dimensionless parameter a(0<a<2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(0< a < 2)$$\\end{document}, which is a specific function of dilatonic coupling vectors. The paper presents solutions for timelike and null circular geodesics that may play a crucial role in different astrophysical scenarios, including quasinormal modes of various test fields in the eikonal approximation. For a=1/2,1,3/2,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a = 1/2,1, 3/2,2 $$\\end{document}, the radii of the innermost stable circular orbit are presented and analyzed.

Particle dynamics, black hole shadow and weak gravitational lensing in the f (Q) theory of gravity

We study the particle dynamics around a black hole (BH) in f(Q) gravity. First, we investigate the influence of the parameters of f(Q) gravity on the horizon structure of the BH, photon orbits and the radius of the innermost stable circular orbit (ISCO) of massive particles. We further study the effects of the parameters of f(Q) gravity on the shadow cast by the BH. Moreover, we consider weak gravitational lensing using the general method, where we also explore the deflection angle of light rays around the BH in f(Q) gravity in uniform and nonuniform plasma mediums.

Dynamics of Particles with Electric Charge and Magnetic Dipole Moment near Schwarzschild-MOG Black Hole

The study of electromagnetic interactions among test particles with electric charges and magnetic dipole moments is of great significance when examining the dynamics of particles within strong gravitational fields surrounding black holes. In this work, we focus on investigating the dynamics of particles possessing both electric charges and magnetic dipole moments in the spacetime of a Schwarzschild black hole within the framework of modified gravity (MOG), denoted as a Schwarzschild-MOG black hole. Our approach begins by offering a solution to Maxwell’s equations for the angular component of the electromagnetic four potentials within Schwarzschild-MOG spacetime. Subsequently, we derive the equations of motion and establish the effective potential for particles engaged in circular motion. This is achieved using a hybrid formulation of the Hamilton–Jacobi equation, encompassing interactions between electric charges and magnetic dipole moments, the external magnetic field (assumed to be asymptotically uniform), and interactions between the particles and the MOG field. Furthermore, we investigate the impacts of these three types of interactions on critical parameters, including the radius of innermost stable circular orbits (ISCOs), as well as the energy and angular momentum of particles when situated at their respective ISCOs. Finally, a detailed analysis concerning the effects of these interactions on the center-of-mass energy is presented in collisions involving neutral, electrically charged, and magnetized particles.