Innermost Stable Circular Orbit Research Articles

Joule-Thomson expansion, motion of particles and QPOs around Bardeen-AdS black hole immersed in a fluid of strings

In this work, we investigate the dynamics of particles around a Bardeen AdS black hole immersed in a fluid of strings, focusing on how the black hole parameters affect particle motion. We observe the black hole's Joule-Thomson expansion and the impact of physical parameters on the cooling and heating zones. Using Joule-Thomson coefficients, we also discuss the stable and unstable configuration of the considered black hole for both cases. The stability of circular equatorial orbits is analyzed using the effective potential approach. We derive analytical expressions for the energy and angular momentum of these circular orbits as functions of the black hole parameters. We also explore the impact of these parameters on the innermost stable circular orbits and discuss the effective forces acting on the particles. In addition, we examine the epicyclic oscillations of particles near a stable equatorial orbits and calculate the corresponding oscillation frequencies as function of black hole parameters. The periastron frequency is also analyzed. Furthermore, we study particle collisions and the resulting center of mass-energy in the vicinity of the black hole. We show that the parameters of the model significantly influence particle motion. Lastly, we compare the particle dynamics around the Bardeen AdS black hole immersed in a fluid of strings with those around the Bardeen black hole and the Bardeen Reissner-Nordström black hole.

Self-consistent Disk-reflection Analysis of the Black Hole Candidate X-Ray Binary MAXI J1813−095 with NICER, Swift, Chandra, and NuSTAR

We present our analysis of MAXI J1813−095 during its hard state “stalled” outburst in 2018. This self-consistent analysis has been carried out using the Neutron Star Interior Composition Explorer, Swift, Chandra, and NuSTAR throughout seven observations of MAXI J1813−095. We find a relativistic iron line at ∼6.5 keV from the inner region of the accretion disk. Our results are consistent with a slightly truncated disk or nontruncated disk for an inner radius of ∼2R g and minimum spin of >0.7 with the best value of ∼0.9, assuming R in reaches the innermost stable circular orbit at L x ∼ 1% L Edd. We analyzed MAXI J1813−095 over its outburst, employing a spectral model that self-consistently couples the seed disk photons to the Comptonization and reflection components, also inclusive of reflection Comptonization. The unique aspect of this work is a reflection fraction of order unity, which is significantly higher than previous studies of this source and is a consequence of applying the self-consistent disk-Comptonization-reflection spectral model. Other key parameters, such as inclination and inner radius, are found to be consistent with other works.

2017 Outburst of H 1743–322: AstroSat and Swift View

We perform a comprehensive timing and broadband spectral analysis using an AstroSat observation of the low-mass black hole X-ray binary H 1743–322 during its 2017 outburst. Additionally, we use two Swift/XRT observations, one of which is simultaneous with AstroSat and the other taken three days earlier, for timing analysis. The hardness–intensity diagram indicates that the 2017 outburst was a failed one, unlike the previous successful outburst in 2016. We detect type C quasi-periodic oscillation (QPO) in the simultaneous AstroSat and Swift/XRT observations at ∼0.4 Hz, whereas an upper harmonic is noticed at ∼0.9 Hz in the AstroSat data only. Although these features are found to be energy-independent, we notice a shift of ∼0.08 Hz in the QPO frequency over the interval of three days. We also investigate the nature of variability in the two consecutive failed outbursts in 2017 and 2018. We detect soft time lags of 23.2 ± 12.2 ms and 140 ± 80 ms at the type C QPO frequencies in 2017 AstroSat and 2018 XMM-Newton data, respectively. The lag–energy spectra from both the outbursts suggest that the soft lags may be associated with reflection features. The broadband spectral analysis indicates that the source was in the low/hard state during the AstroSat observation. Modeling of the disk and reflection continuum suggests the presence of an accretion disk that is significantly truncated by at least 27.4r g from the innermost stable circular orbit when the source luminosity is ∼1.6% of the Eddington luminosity.

Massive scalar clouds and black hole spacetimes in Gauss-Bonnet gravity

We study static black holes in scalar-Gauss-Bonnet (sGB) gravity with a massive scalar field as an example of higher curvature gravity. The scalar mass introduces an additional scale and leads to a strong suppression of the scalar field beyond its Compton wavelength. We numerically compute sGB black hole spacetimes and scalar configurations and also compare with perturbative results for small couplings, where we focus on a dilatonic coupling function. We analyze the constraints on the parameters from requiring the curvature singularity to be located inside the black hole horizon r_hrh and the relation to the regularity condition for the scalar field. For scalar field masses m r_h \gtrsim 10^{-1}mrh≳10−1, this leads to a new and currently most stringent bound on sGB coupling constant \alphaα of \alpha/r_h^2\sim 10^{-1}α/rh2∼10−1 in the context of stellar mass black holes. Lastly, we look at several properties of the black hole configurations relevant for further work on observational consequences, including the scalar monopole charge, Arnowitt–Deser–Misner mass, curvature invariants and the frequencies of the innermost stable circular orbit and light ring.

QPOs from charged particles around magnetized black holes in braneworlds

Quasiperiodic oscillations (QPOs) are a powerful tool for testing gravity theories, probing gravitational and electromagnetic field properties, and obtaining constraints on the black hole and field parameters. This work considers charged particle dynamics near uniformly magnetized black holes in braneworlds. First, we obtain the solution of the Maxwell equation for magnetic fields and calculate the radial and angular magnetic field components. We derive and analyze the effective potential of charged particles for circular orbits and investigate the energy and angular momentum for the circular orbits. We also analyze the combined effects of magnetic interaction and braneworlds on the charged particles’ innermost stable circular orbits (ISCOs). We calculate the angular momentum of charged particles in Keplerian orbits in the presence of an external magnetic field and braneworlds. Also, we investigate frequencies of the particle oscillations along vertical and angular directions. We applied our studies on particle oscillations to the QPO studies in the relativistic precession model. Finally, we obtain constraints on magnetic interaction and braneworld parameters together with the black hole mass and QPO orbits using Monte Carlo Markov Chain (MCMC) simulation in the four-dimensional parameter space for the QPOs observed in the microquasars XTE J1550-564, GRO J1655-40 & GRS 1915-105, and at the center of galaxies M82 and Milky Way.

Particle dynamics and quasi-periodic oscillations in the GUP-modified Schwarzschild spacetime: Constraint using micro-quasars data

In this work, we have worked out dynamical aspects for the particles moving around the GUP-corrected-Schwarzschild (S-GUP) black hole. We have calculated the innermost stable circular orbit (ISCO) around black hole and explored its implications for different microquasars. Additionally, we have shown that the Kerr black hole mimics S-GUP black hole after some tuning of parameters. Finally, considering the S-GUP black hole as a microquasar source, we have studied quasi-periodic oscillation (QPO). Further utilizing the available observational data of few microquasars, we have obtained constrains on the GUP parameter ϵ as well.

Influence of scalar field in massive particle motion in JNW spacetime

In this paper, we investigated the motion of massive particles in the presence of scalar and gravitational fields, particularly focusing on the Janis-Newman-Winicour (JNW) naked singularity solution. It is shown that the innermost stable circular orbit radius strongly depends on scalar coupling parameter. Additionally, we explored the radiation reaction effects on particle dynamics, incorporating a reaction term into the motion equations. Numerical simulations indicated minimal impact on particle trajectories from radiation reaction. We also examined the oscillatory motion of particles around compact objects in the JNW spacetime, focusing on radial and vertical oscillations. Our analysis indicated that the scalar field’s coupling parameter and the spacetime deformation parameter n significantly alter the fundamental frequencies of these oscillations. Furthermore, we studied quasiperiodic oscillations (QPOs) in x-ray binaries, using the relativistic precession model to analyze upper- and lower-frequency relationships. Our results indicated that increasing parameters (n and gs) shifts the frequency ratio of 3∶2 QPOs closer to the naked singularity, with n decreasing and gs increasing both frequencies. Finally, we analyzed QPO data from four selected x-ray binary systems using Markov chain Monte Carlo analysis to constrain JNW parameters. Our findings provided insights into the mass, coupling, and deformation parameter for each system, enhancing our understanding of compact object dynamics in strong gravitational fields. Published by the American Physical Society 2024

A new class of traversable wormhole metrics

In this work, we have formulated a new class of traversable wormhole metrics. Initially, we have considered a wormhole metric in which the temporal component is an exponential function of r but the spatial components of the metrics are fixed. Following that, we have again constructed a generalized wormhole metric in which the spatial component is an exponential function of r, but the temporal component is fixed. Finally, we have considered the generalized wormhole metric in which both the temporal and spatial components are generalized exponential functions of r. We have also studied some of their properties including throat radius, stability, and energy conditions, examined singularity, the metric in curvature coordinates, effective refractive index, innermost stable circular orbit (ISCO) and photon sphere, Regge–Wheeler potential and their quasinormal modes, gravitational entropy, and determined the curvature tensor. The radius of the throat is found to be consistent with the properties of wormholes and does not contain any types of singularities. Most interestingly, we find that their throat radius is the same for the same spatial component and the same range of values of m. In addition to these, they also violate the Null Energy Condition (NEC) near the throat. These newly constructed metrics form a new class of traversable wormholes.

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.