Innermost Stable Circular Orbit Research Articles

Implications of the Spin-Induced Accretion Disk Truncation on the X-ray Binary Broadband Emission

Black hole X-ray binary systems consist of a black hole accreting mass from its binary companion, forming an accretion disk. As a result, twin relativistic plasma ejections (jets) are launched towards opposite and perpendicular directions. Moreover, multiple broadband emission observations from X-ray binary systems range from radio to high-energy gamma rays. The emission mechanisms exhibit thermal origins from the disk, stellar companion, and non-thermal jet-related components (i.e., synchrotron emission, inverse comptonization of less energetic photons, etc.). In many attempts at fitting the emitted spectra, a static black hole is often assumed regarding the accretion disk modeling, ignoring the Kerr metric properties that significantly impact the geometry around the usually rotating black hole. In this work, we study the possible implications of the spin inclusion in predictions of the X-ray binary spectrum. We mainly focus on the most significant aspect inserted by the Kerr geometry, the innermost stable circular orbit radius dictating the disk’s inner boundary. The outcome suggests a higher-peaked and hardened X-ray spectrum from the accretion disk and a substantial increase in the inverse Compton component of disk-originated photons. Jet-photon absorption is also heavily affected at higher energy regimes dominated by hadron-induced emission mechanisms. Nevertheless, a complete investigation requires the full examination of the spin contribution and the resulting relativistic effects beyond the disk truncation.

Orbital Precession in Janis–Newman–Winicour Spacetime

We have investigated the Janis–Newman–Winicour spacetime through three fundamental tests of theories of gravity, namely, gravitational lensing, perihelion shift, and redshift due to gravitational force. Focusing initially on the circular motion of a massive particle within the equatorial plane, the analysis disregards external scalar field interactions. The Janis–Newman–Winicour (JNW) spacetime’s unique parameters, mass (M) and the scalar parameter (n), are examined, revealing an intriguing relationship between the innermost stable circular orbit position of the test particle and the scalar field parameter. The study also explores photon motion around a gravitational object in JNW spacetime, revealing the expansion of the photon sphere alongside a diminishing shadow, influenced by the external scalar field. Despite these complexities, gravitational bending of light remains consistent with general relativity predictions. The investigation extends to perihelion precession, where the trajectory of a massive particle in JNW spacetime exhibits eccentricity-dependent shifts, distinguishing it from Schwarzschild spacetime. Finally, oscillatory motion of massive particles in JNW spacetime is explored, providing analytical expressions for epicyclic frequencies using perturbation methods. The study concludes with the application of MCMC analyses to constrain the JNW spacetime parameters based on observational data.

Circular motion and QPOs near black holes in Kalb–Ramond gravity

General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

Orbital motion, epicyclic oscillations, and collision of particles around conformally coupled charged black hole

The orbital and oscillatory motion of test particles around a non-rotating, conformally coupled charged black hole with scalar hair is studied in this work. The impact of the black hole parameters on particle motion is investigated. The stable circular orbits, specific angular momentum, and radial profiles with specific energy are computed using an analytical approach. We discuss the stability of circular orbits using the effective potential technique. We also compute the effective force and innermost stable circular orbits around a conformally connected charged black hole with scalar hair. In addition, we display the trajectories of particles around a conformally connected charged black hole with scalar hair and numerically integrate the equations of motion for the test particle. Additionally, we determine the formulae for the frequencies of latitudinal and radial harmonic oscillations about the mass of the black hole and the model’s parameters. The main characteristics of quasi-periodic oscillations close to stable circular orbits in the black hole’s equatorial plane are examined for test particles. Furthermore, the Periastron precession process is explored. We show particle motion around black holes strongly depends on the model parameters. It is important to note that the graphical behavior describing our findings is viable.

Particle dynamics with trajectories and epicyclic oscillations around a piece-wise black hole immersed in dark matter

We investigate the dynamics of neutral test particles revolving around a non-rotating black hole immersed in dark matter DM. We derive exact solutions for the radial profiles of specific angular momentum and energy for equatorial stable circular orbits as a function of the parameters of the black hole. Using the effective potential approach, we explore the stability of these circular orbits and the effective force acting on particles in the presence of dark matter. Additionally, we examine the impact of dark matter on the innermost stable circular orbits. By numerically integrating the equations of motion, we plot the trajectories of particles around the black hole and analyze how dark matter affects these trajectories. We also calculate the analytical frequencies of radial and latitudinal harmonic oscillations as functions of the dark matter parameter for both local and distant observers. We compare these results with scenarios where dark matter is absent. Furthermore, we study the effects of dark matter on periastron precession. We present an analysis of the constraints on the dark matter and black hole mass parameters using Markov Chain Monte Carlo (MCMC) methods. Our study focuses on QPOs observed in X-ray binaries, in particular, the microquasars GRO J1655-40 and XTE J1550-564, and the centers of the galaxies M82 X-1 and Sgr A⁎. We also analyze the particle collisions, discussing the center-of-mass energy of the colliding particles. Our observations reveal that the motion of particles revolving around the black hole is significantly affected by varying the model parameters.

Observational signature of QPOs with particle motion around non-commutative Schwarzschild black hole surrounded by perfect fluid dark matter

We analyze the orbital and oscillatory motion of test particles in the vicinity of a non-commutative black hole submerged in perfect fluid dark matter and derive analytical solutions for the specific angular momentum and radial profiles of energy. Using the effective potential approach, we discuss the stability of circular orbits. Furthermore, we calculate the innermost stable circular orbits. The effective force acting on particles has also been discussed. We find the expressions for frequencies of radial and latitudinal harmonic oscillations as a function of the black hole mass and the model’s parameters. The key features of quasi-periodic oscillations of test particles near the stable circular orbits in an equatorial plane of the black hole are discussed. Furthermore, Periastron precession has been discussed. We demonstrate that the parameters of the model have a strong influence on particle motion around black holes. By using the observational data of four different X-ray binary systems GRO J1655-40, XTE J1550-564, XTE J1859+226, and GRS 1915+105, within the scope of Monte Carlo Markov Chain, we constrain the involved parameters α and β. It is necessary to mention that our presented investigations through graphical behavior are viable with required physical behavior.

QPOs and circular orbits around black holes in Chaplygin-like cold dark matter

Understanding the nature of dark energy in the universe is an actual issue in theoretical astrophysics and cosmology. One way to do it is by probing dark fluids with different equations of states (EoS). In the present work, we consider a Schwarzschild black hole (BH) surrounded by a dark fluid with a Chaplygin-like EoS as a generalized version of the Chaplygin EoS. We first investigate the effects of the dark fluid parameters on the horizon properties of the BH. The effective mass of the spacetime is calculated and analyzed under the dark fluid parameters. The scalar invariants of the BH spacetime are also calculated, and it is shown that the spacetime curvature increases as the dark fluid parameter increases. Next, we studied the circular motion of the test particle around the BH. As standard particle motion investigations, we analyze the effective potential of the particles for circular motion, specific energy, and angular corresponding to circular orbits with zero and nonvanishing values of the dark fluid intensity. In addition, we study the innermost stable circular orbits (ISCO). It is observed that there is an outermost stable circular orbit (OSCO) due to the presence of the dark fluid. It also shows that at a critical value of the dark fluid intensity parameter, ISCO and OSCO take the same radius. We calculate the frequency of Keplerian orbits and radial and vertical oscillations of the particles along stable circular orbits. We also applied orbital data from hotspots observed near Sgr A* to obtain upper and lower values for the EoS parameter. Finally, we investigate quasiperiodic oscillations and obtain the mass-to-EoS parameter relations for GRS J1915-105 and XTE 1550-564.

Insight-HXMT, NICER, and NuSTAR Views to the Newly Discovered Black Hole X-Ray Binary Swift J151857.0–572147

The systematic properties are largely unknown for the black hole X-ray binary Swift J151857.0–572147 newly discovered in the 2024 outburst. The nature of a black hole can be completely defined by specifying the mass and dimensionless spin parameter. Therefore, accurate measurement of the two fundamental parameters is important for understanding the nature of black holes. The joint spectral fitting of a reflection component with simultaneous observations from Insight-HXMT, NICER, and NuSTAR reveals for the first time a black hole dimensionless spin of 0.84−0.26+0.17 and an inclination angle of 21.1−3.6+4.5 degrees for this system. Monitoring of the soft state by NICER results in disk flux and temperature following Fdisk∝Tin3.83±0.17 . For the standard thin disk, Ldisk≈4πRin2σTin4 , so the relationship between the flux and temperature of the disk we measured indicates that the inner radius of the disk is stable and the disk is in the innermost stable circular orbit. With an empirical relation built previously between the black hole outburst profile and the intrinsic power output, the source distance is estimated as 5.8 ± 2.5 kpc according to the outburst profile and peak flux observed by Insight-HXMT and NICER. Finally, a black hole mass of 3.67 ± 1.79–8.07 ± 4.20M ⊙ can be inferred from a joint diagnostic of the aforementioned parameters measured for this system. This system is also consistent with most black hole X-ray binaries with high spin and a mass in the range of 5–20 M ⊙.

Exploring dark forces with multimessenger studies of extreme mass ratio inspirals

The exploration of dark sector interactions via gravitational waves (GWs) from binary inspirals has been a subject of recent interest. We study dark forces using extreme mass ratio inspirals (EMRIs), pointing out two issues of interest. Firstly, the innermost stable circular orbit (ISCO) of the EMRI, which sets the characteristic length scale of the system and hence the dark force range to which it exhibits enhanced sensitivity, probes force mediator masses that complement those studied with supermassive black hole (SMBH) or neutron star binaries. The LISA mission (the proposed μAres detector) will probe mediators with masses m V ∼ 10-16 eV (m V ∼ 10-18 eV), corresponding to ISCOs of 106 M ⊙ (108 M ⊙) central SMBHs. Secondly, while the sensitivity to dark couplings is typically limited by the uncertainty in the binary component masses, independent mass measurements of the central SMBH through reverberation mapping campaigns or the motion of dynamical tracers enable one to break this degeneracy. Our results therefore highlight the necessity for coordinated studies, loosely referred to as “multimessenger”, between future μHz- mHz GW observatories and ongoing and forthcoming SMBH mass measurement campaigns, including OzDES-RM, SDSS-RM, and SDSS-V Black Hole Mapper.

Exploring a novel feature of ellis spacetime: Insights into scalar field dynamics

We have studied neutral and charged massive particles dynamics in Ellis spacetime in the presence of the external scalar field. Focusing on the circular motion of massive particles, the impact of an external scalar field on the Innermost Stable Circular Orbit (ISCO) position is analyzed, revealing a non-linear relationship with the scalar field parameter. Perturbation techniques are employed to investigate oscillatory motion near stable orbits in the Ellis spacetime, yielding analytical expressions for radial and angular oscillations. The throat of the wormhole has been constrained by comparing theoretical and observational results for fundamental frequencies of particles from quasars. Finally, scalar and gravitational perturbations in the Ellis spacetime have been studied. It is shown that the equation for the scalar profile function is fully independent from the tensor functions and the solution can be represented in terms of the confluent Heun function. However, it has been shown that equations for the tensor profile functions strongly depend on the scalar profile functions in the Ellis spacetime and they are reduced to the Regge–Wheeler–Zerilli equation. Finally, numerical solutions to the Regge–Wheeler–Zerilli equation for the radial functions in the Ellis have been presented.

Accreting black holes in dark matter halos

We examine the thin accretion disk behaviors surrounding black holes embedded in cold dark matter halos and scalar field dark matter halos. We first calculate the event horizons and derive the equations of motion and effective potential in black hole geometries with different dark matter halos. We then compute the specific energy, specific angular momentum, and angular velocity of particles moving along circular orbits. We also derive the effective potentials to find the locations of the innermost stable circular orbit (ISCO) and compare them to the Schwarzschild and Kerr black holes without the dark matter halos. We also use the observed ISCO of the supermassive black hole at the Galactic Center of the Milky Way, Sagittarius A*, to constrain the dark matter halos. Published by the American Physical Society 2024

Dynamics and collision of particles in modified black-bounce geometry

In the present work, we first regularize a black hole spacetime in modified gravity (MOG) in the presence of the scalar-tensor-vector (STV) field, called the Schwarzschild MOG black hole, under the transformation r2→r2+a2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^2 \\rightarrow r^2 + a^2$$\\end{document}, known as the Simpson–Visser (SV) spacetime (where a is regularization or black-bounce parameter). The spacetime can represent a black hole and a wormhole. We analyze horizon properties and calculate the effective mass of the spacetime. Also, we find black hole-wormhole regions in black-bounce and MOG parameter spacetime. We also analyze scalar invariants of spacetime, such as the Ricci scalar, the square of the Ricci tensor, and the Kretchmann scalar. We study test particle motion in the SV-MOG spacetime by considering the interaction between the particle and the STV field. We investigate how the STV fields change the innermost stable circular orbits (ISCOs), energy, and angular momentum of the test particle’s ISCO. It is shown that the ISCO decreases in the presence of the black bounce parameter and increases in the STV field. We also study the collisions of test particles and analyze how the MOG and black-bounce parameters influence the critical angular momentum of colliding particles and their center of mass energy.

Electrically charged black holes in gravity with a background Kalb–Ramond field

We derive the exact solutions for electrically charged black holes both in the absence and presence of a cosmological constant in the gravitational theory with Lorentz violation induced by a background Kalb–Ramond (KR) field. The corresponding thermodynamic properties are investigated. It is found that the standard first law of thermodynamics and the Smarr formula remain valid for the charged KR black holes. Nevertheless, the Lorentz-violating effect influences their ranges of local thermodynamic stability and the first- and second-order phase transition points. Furthermore, to examine the impact of Lorentz violation on the motion of test particles in the spacetime, we analyze the shadow and the innermost stable circular orbit (ISCO) of these black holes. Our results reveal that both the shadow and ISCO radii exhibit a high sensitivity to the Lorentz-violating parameter ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}, with a decrease observed as ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document} increases.

Constraints on Schwarzschild-like black hole from QPOs data

The search for compact astrophysical objects, such as black holes and wormholes, along with the testing of gravity theories, are crucial topics in relativistic astrophysics. In this context, theoretical and observational studies of quasi periodic oscillations (QPOs) detected in (micro)quasars prove useful for investigating their central object. We explore the massive particle motion around black hole in Schwarzschild-like spacetime and using the equation of motion, the dependence of innermost stable circular orbits (ISCO) on the parameter l was obtained. The frequencies of radial and vertical oscillations of particles around stable circular orbits have been studied and used to explain the mechanism of quasi periodic oscillations in the relativistic precession (RP) model. Using observational data from GRO J1655-40 and XTE J1550-564, we have determined a constraint on the parameter l in Schwarzschild-like spacetime through Monte-Carlo-Markovian-Chain (MCMC) analyses.

Spinning particle motion around charged black hole from T-duality

This study examines a spinning particle motion around a charged black hole from T-duality. Initially, our investigation focuses on the lapse function of the metric, revealing that the presence of the black hole’s charge solely induces a shift in the location of the black hole’s horizon. However, with the introduction of l0, we observe the emergence of the second Cauchy horizon (r−). Additionally, we determine the maximum values of black hole parameters within the T-duality framework, guided by the criterion for the existence of the black hole horizon. We employ the Mathisson-Papapetrous-Dixon (MPD) equation to analyze the dynamics of the spinning test particles. Our exploration delves into the influence of the particle’s spin and associated parameters Q and l0 on the effective potential. Subsequently, we investigate the innermost stable circular orbit (ISCO) to establish relationships between the particle’s energy, angular momentum at ISCO, ISCO radius, and the particle’s spin, along with black hole parameters from T-duality. We also focus on superluminal motion, a crucial characteristic distinguishing time-like particles from space-like ones. Numerical values for the particle’s critical spin (smax) necessary to maintain time-like behavior are determined. Finally, we address the collision of spinning particles in the proximity of a compact object. Within this context, we endeavor to identify critical values of the particle’s angular momentum, permitting particles to approach the compact object closely.

Shadows, rings and optical appearance of a magnetically charged regular black hole illuminated by various accretion disks

Abstract The Event Horizon Telescope (EHT) imaging of the supermassive black holes at the centers of Messier 87 galaxy (M87) and the Milky Way galaxy (Sgr A) marks a significant step in observing the photon rings and central brightness depression that define the optical appearance of black holes with an accretion disk scenario. Inspired by this, we take into account a static and spherically symmetric magnetically charged regular black hole (MCRBH) metric characterized by its mass and an additional parameter q, which arises from the coupling of Einstein gravity and nonlinear electrodynamics (NLED) in the weak field approximation. This parameterized model offers a robust foundation for testing the coupling of Einstein gravity and NLED in the weak-field approximation, using the EHT observational results. In this study, we investigate the geodesic motion of particles around the solution, followed by a discussion of its fundamental geometrical characteristics such as scalar invariants. Using null geodesics, we examine how the model parameter influences the behavior of the photon sphere radius and the associated shadow silhouette. We seek constraints on q by applying the EHT results for supermassive black holes M87* and Sgr A*. Furthermore, it is observed that the geodesics of time-like particles are susceptible to variations in q, which can have an impact on the traits of the innermost stable circular orbit and the marginally bounded orbit. Our primary objective is to probe how the free parameter q affects various aspects of the accretion disk surrounding the MCRBH using the thin-disk approximation. Next, we discuss the physical characteristics of the thin accretion disk as well as the observed shadows and rings of the MCRBH, along with its luminosity, across various accretion models. Ultimately, variations in accretion models and the parameter q yield distinct shadow images and optical appearances of the MCRBH.

Circular motion and collisions of spinning test particles around Kerr–Kiselev black holes

Exploring the effect of exotic fields around black holes on particle dynamics may help to understand the nature of dark matter and energy. The quintessential field can be treated as one of such fields. In this work, we investigate the motion of spinning particles in the vicinity of rotating black holes immersed in quintessential dark energy, characterized by the equation of state (EoS) parameter ω∈(−1;−1/3) governing the equation of state of the dark energy and dimensionless quintessential field parameter C. Using the Mathisson–Papapetrou–Dixon (MPD) equations, we derive the effective potential and study superluminal bound values for the particle spin. Also, we investigate the behaviors of the innermost and outermost stable circular orbit (ISCO & OSCO) of spinning test particles and their energy and angular momentum at the orbits. Note that the OSCO exists due to the third cosmological-like horizon caused by the quintessential field and shows that the ISCO and OSCO coincide at critical values of the quintessential field and EoS parameters, which also depend on the particle and black hole spin. Finally, we explore collisions of spinning particles and analyze the center-of-mass energies and critical angular momentum, which allows the collisions of the particles near the black hole.

Circular motion and collisions of charged spinning particles near Kerr Newman black holes

We investigate the dynamics of spinning particles with an electric charge orbiting electrically charged Kerr–Newman black holes. First, we derive the equations of motion for the test particles using the Mathisson-Papapetrou-Dixon (MPD) equations, taking into account electromagnetic interaction and the interaction between the particle spin and the spacetime curvature known as the Lorentz coupling term in the MPD equation. We analyze the related effective potential in various scenarios of particle spin, angular momentum, and black hole spin orientation. In addition, we provide graphical analyses of the radius of innermost stable circular orbits (ISCOs) of the particles, their angular momentum, and energy at ISCOs and superluminal bounds. The ISCOs for positive and negatively charged particles are almost the same. The combined effects of the black hole and particle spins enhance the Coulomb interaction effect on the ISCO radius. The ISCO energy and angular momentum decrease with the increase in particle spin. In the Reissner–Nordström (RN) black hole limit, the decreasing rate is faster at positive values of the particle spin, and the spin limit changes in the Kerr–Newman black hole case. Finally, we study collisions between spinning charged particles near Kerr–Newman black holes. The critical values of the angular momentum of spinning charged particles are explored, and the particles can collide in various cases of particle and black hole spin, as well as the particle angular momentum. We also analyze electromagnetic and spin effects on the center-of-mass energy of the colliding particles.

Electric Penrose, circular orbits and collisions of charged particles near charged black holes in Kalb–Ramond gravity

General relativity (GR) is a well-tested theory of gravity in strong and weak field regimes. Many modifications to this theory were obtained, including different scalar, vector, and tensor fields to the GR with non-minimal coupling to gravity. Kalb–Ramond (KR) gravity is also a modified theory formulated in the presence of a bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BH). In this work, we study the circular motion of charged particles and explore energetic processes around charged BHs in KR theory. First, we investigated the event horizon radius and analyzed horizon-no horizon regions in the BH charge and KR parameter space. Considering the Coulomb interaction, we derive and analyze the effective potential for charged particles around a charged KR BH. We investigate charged particles’ angular momentum and energy corresponding to circular orbits. We also investigate how the KR non-minimal coupling parameter affects the radius of the innermost stable circular orbits, the corresponding energy, and the angular momentum. We also investigated the electric Penrose process and charged-particle collisions near the KR BH. The presence of the nonzero KR parameter results in a decrease in the energy efficiency of the Penrose process. Also obtained is that the KR parameter’s positive (negative) values cause a decrease (increase) in the center of mass energy of colliding particles near the BH horizon.

Innermost stable circular orbits around a spinning black hole binary

Innermost stable circular orbits around a spinning black hole binary