Innermost Stable Circular Orbit Research Articles

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.

Motion of spinning particles around dynamic phantom AdS black holes

This work is devoted to discussing spinning particles’ motion in the surrounding dynamic phantom AdS Black hole (BH) with phantom scalar field k. The primary goal of this research is to differentiate between the effects of electric and magnetic charges on dynamic phantom AdS BH. The study analyzes the dependence of the innermost stable circular orbit (ISCO), responsible for interactions between charged particles and the external magnetic field, and observes the circular orbits of particles revolving around the compact object. It is also observed that as electric and magnetic charges increase, the ISCO radius decreases. Additionally, stability of orbit, Keplerian frequency, and harmonic oscillations of charged particles are also discussed. We also find the condition, electric and magnetic charges of the dynamic phantom AdS BH effect the energy of the center of mass with magnetized, electrically charged, and neutral particles due to the collision. Lastly, we discuss the accretion process and obtain generalized equations for the speed of sound cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c^2_{s}$$\\end{document} sec, 4-velocity u(r), energy density ρ(r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho (r)$$\\end{document} and mass (M˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\dot{M}}$$\\end{document}). We also plot these physical parameters against constant values of mass, electric and magnetic charges, and distinct values of state parameter ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} to study the accretion process. We observe that radial velocity and energy density of the fluid remain positive and negative, and the rate of change of mass is increased and decreased for stiff, dust, quintessence, and phantom-like fluid, respectively.

Gravitational analogue of radiation reaction in STVG

We have studied influence of STVG in circular motion of massive particle around the Schwarzschild-MOG black hole and discussed the Innermost Stable Circular Orbit (ISCO) and Marginally Bound Orbit (MBO) position of massive test particle. This research explores dynamics of massive particles within the framework of Scalar–Tensor–Vector Gravity (STVG) when navigating the vicinity of Schwarzschild-MOG black holes. The study extends its investigation to the angular velocity of massive particles orbiting Schwarzschild-MOG black holes, comparing it to predictions from general relativity. Finally, we have investigated gravitational analogue of radiation reaction by considering Landau–Abraham–Dirac equation in STVG. We have shown that because of radiation reaction massive test particle falls down to the black hole.

Charged spinning and magnetized test particles orbiting quantum improved charged black holes

In the present work, we aimed to investigate the dynamics of spinning charged and magnetized test particles around both electrically and magnetically charged quantum-improved black holes. We derive the equations of motion for charged spinning test particles using the Mathisson-Papapetrou-Dixon ***equations with the Lorentz coupling term. The radius of innermost stable circular orbits (ISCOs), specific angular momentum, and energy for charged spinless, uncharged spinning, and charged spinning test particles around the charged and non-charged quantum-improved black holes are analyzed separately. We found that the quantum parameter increases the maximum spin value, smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document}, which leads to the nonphysical motion (superluminal motion) of the charged spinning test particle. In contrast, the black hole charge decreases its value. We also found that, in contrast to the Reissner Nordström black hole, spinning charged test particles in the quantum-improved charged black hole have higher smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document}; moreover, positively charged spinning particles can have higher values of smax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_\ extrm{max}$$\\end{document} near the extreme black hole cases when compared with uncharged spinning particles. Finally, we investigate the magnetized test particle’s dynamics in the spacetime of a quantum-improved magnetically charged black hole in Quantum Einstein Gravity using the Hamilton–Jacobi equation. We show that the presence of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} increases the maximum value of the effective potential and decreases the minimum energy and angular momentum of magnetized particles at their circular orbits. We found an upper constraint in the black hole charge at the ISCO.

Black holes with Abelian and Non-Abelian charges and their impact on matter accretion flows

In this paper, we study the black hole spacetime structure of a model consisting of the standard Maxwell theory and a p-power-Yang–Mills term. This non-linear contribution introduces a non-Abelian charge into the global solution, resulting in a modified structure of the standard Reissner–Nordström black hole. Specifically, we focus on the model with p=1/2, which gives rise to a new type of modified Reissner–Nordström black hole. For this class of black holes, we compute the event horizon, the innermost stable circular orbit, and the conditions to preserve the weak cosmic censorship conjecture. The latter condition sets a well-established relation between the electric and the Yang–Mills charges. As a first astrophysical implication, the accretion properties of spherical steady flows around this new modified Reissner–Nordström black hole are investigated in detail. Concretely, we compute the critical radius that establishes the condition for having stable transonic flow in terms of the local sound speed and the involved charges. Extensive numerical examples of how the Yang–Mills charge affects the accretion process of an isothermal fluid in comparison to the standard Reissner–Nordström and Schwarzschild black holes are displayed. Finally, analytical solutions in the fully relativistic regime, along with numerical computations, of the mass accretion rate for a polytropic fluid in terms of the electric and Yang–Mills charges are obtained. As a main result, the mass accretion rate efficiency is considerably improved, with respect to the standard Reissner–Nordström and Schwarzschild solutions, for negative values of the Yang–Mills charge.

Accretion flows in the hard state of black hole X-ray binaries: the effect of hot gas condensation

ABSTRACT It is commonly believed that accretion discs are truncated and their inner regions are described by advection dominated accretion flows (ADAFs) in the hard spectral state of black hole X-ray binaries. However, the increasing occurrence of a relativistically blurred Fe K α line together with a hard continuum points to the existence of a thin disc located near the innermost stable circular orbit (ISCO). Assuming the accretion in the hard state is via an ADAF extending to near 100 Schwarzschild radii, which is supplied by either a stellar wind from a companion star or resulting from an evaporated disc, we study the possible condensation of the hot gas during its accretion towards the black hole. It is found that a small fraction of the ADAF condenses into a cold disc as a consequence of efficient radiative cooling at small distances, forming a disc-corona configuration near the ISCO. This takes place for low accretion rates corresponding to luminosities ranging from ∼10−3 to a few per cent of the Eddington luminosity. The coexistence of the weak inner disc and the dominant hot accretion flow provides a natural explanation of the broad K α line in the hard state. Detailed computations demonstrate that such accretion flows produce a hard X-ray spectrum accompanied by a weak disc component with a negative correlation between the 2 and 10 keV photon index and the Eddington ratio. The predicted spectrum of Cygnus X-1 and the correlation between the photon index and the Eddington ratio are in good agreement with observations.

Charged particles motion and quasiperiodic oscillation in Simpson–Visser spacetime in the presence of external magnetic fields

The present work is devoted to the study of the dynamics of charged particles around Simpson–Visser black holes (with the length parameter lle 2) and wormholes (l>2) immersed in an external asymptotically uniform magnetic field. To do this, first, we solve the Maxwell equation for 4-potentials of the electromagnetic field and show that the difference between the numerical solution and Wald’s solution is small enough to neglect it, which may allow us to use the solution obtained by Wald. We also study fundamental frequencies of in the vertical and radial oscillations of charged particles around circular stable orbits around the magnetized black hole. The effects of the magnetic interaction and length parameters on the fundamental frequencies. We investigate the quasiperiodic oscillations (QPOs) around the black hole in relativistic precession and epicyclic resonance models. It is also shown that the combined effects of magnetic interaction for negatively charged particles and length parameters can mimic the spacetime effects of the Schwarzschild black hole compensating for their effects, as well as the spin of rotating Kerr black holes. The distance between an orbit where a QPO is generated with the ratio of upper and lower frequencies 3: 2 and innermost stable circular orbits is also studied. It is found that the QPO orbits are very close to ISCO in the RP model at l<2. This implies that the obtained result helps to determine the ISCO around black holes. We also study the applications of observed QPOs around stellar-mass black holes in microquasars and supermassive black holes.

Back to Business: SLX 1746–331 after 13 Years of Silence

The black hole candidate system SLX 1746–331 was back to business in 2023, after a long silence of roughly 13 years. An outburst was observed thoroughly by Insight-HXMT and NICER. The outburst is characterized by spectral dominance of the soft state, where the joint Insight-HXMT and NICER spectral analysis shows the temperature dependence of the disk flux follows , and thus suggests that the inner disk reaches its innermost stable circular orbit during almost the entire outburst. By assuming 0.3 L Edd for the peak flux and an inclination angle of zero degrees, the lower limit of the compact object hosted in this system is estimated as 3.28 ± 2.14 M ⊙. We also look into the relation between the disk temperature and disk flux for a sample of black hole systems, and by taking the disk temperature derived in the outburst of SLX 1746–331, such a relation results in a mass estimation of 5.2 ± 4.5 M ⊙. Finally, the spin of the compact object is constrained to be larger than 0.8 with the spectral model KERRBB.

Investigation on the stability and quantum phase transition of the charged rotating Kiselev Black Hole embedded in Quintessence field with quantum fluctuation of entropy

Immediate local impacts of cosmic acceleration upon a rapidly rotating black hole are very interesting in recent studies. In this paper, the stability of a rapidly rotating black hole and the minimum value of the ratio between the black hole’s angular momentum to it’s mass which ensures the stability, are investigated simultaneously. Also, two modern forms of uncertainty relations are proposed by enhancing the usual Heisenberg algebra with superior terms, in order to supervise on thermodynamic properties of the rotating black hole. An asymptotically flat Kiselev black hole solution, cultivated by quintessence field is chosen for this purpose. The local shifts in spacetime geometry next to the rotating black hole can be resolved from a modified metric, occupying the surrounding spacetime of the black hole. The angular momentum of a rotating black hole depends on the rate of change in acquiring mass by it. On the other hand, at the same time, due to the effect of the quintessence field, there exists repulsive gravitational force inside the black hole. So, there is an uncertainty in the position of innermost stable circular orbit as well as radius of the rotating black hole. This uncertainty is also investigated in our work. Relying on two new forms of uncertainty principle, the modified thermodynamic variables like black hole’s Hawking temperature, heat-capacity, entropy at the black hole’s event horizon, etc. are computed under rotation. Quantum corrections of black hole’s Hawking temperature, entropy, free-energy, etc. are also explored. Further, quantum corrected heat capacity of the rotating black hole is studied and also thermal stability is inquired. The existence of transitions of phase in case of a rapidly rotating black hole are also found out. Again, quantum corrected entropy of black hole contains logarithmic terms and their effects on thermal stability of the rotating black hole are also discussed. Modifications in the mass-temperature, specific heat, etc. of a rotating black hole are also presented according to the modified extension parameters.

Analysis of Accretion Disk Around the Euler‐Heisenberg Anti‐de Sitter Black Hole

AbstractThe investigation of thin accretion disc surrounding the Einstein‐ Euler‐ Heisenberg‐ Anti‐ de Sitter black hole is demonstrated. Additionally, the black hole event horizons and compute their effective potential and equations of motion is analyzed. The specific energy, specific angular momentum, and specific angular velocity of the particles that move in circular orbits above the thin accretion disk are obtained. Also, the effects of parameters of the Einstein‐ Euler‐ Heisenberg‐ Anti De sitter black hole on specific angular velocity, specific heat energy, and specific angular momentum, have been discussed in detail. The positions of the innermost stable circular orbits and illustrate the effective potential are displayed. Furthermore, the circular orbits of black hole are obtained numerically and locates the position of the innermost stable circular orbit and event horizon. Also, the Gamma ray burst emitted from the Einstein Euler Heisenberg Anti de sitter black hole is studied.

Impact of neutron star spin on Poynting–Robertson drag during a type I X-ray burst

ABSTRACT External irradiation of a neutron star (NS) accretion disc induces Poynting–Robertson (PR) drag, removing angular momentum and increasing the mass accretion rate. Recent simulations show PR drag significantly enhancing the mass accretion rate during Type I X-ray bursts, which could explain X-ray spectral features such as an increase in the persistent emission and a soft excess. However, prograde spin of the NS is expected to weaken PR drag, challenging its importance during bursts. Here, we study the effect of spin on PR drag during X-ray bursts. We run four simulations, with two assuming a non-spinning NS and two using a spin parameter of a* = 0.2, corresponding to a rotation frequency of 500 Hz. For each scenario, we simulate the disc evolution subject to an X-ray burst and compare it to the evolution found with no burst. PR drag drains the inner disc region during a burst, moving the inner disc radius outwards by ≈1.6 km in the a* = 0 and by ≈2.2 km in the a* = 0.2 simulation. The burst enhances the mass accretion rate across the innermost stable circular orbit ≈7.9 times when the NS is not spinning and ≈11.2 times when it is spinning. The explanation for this seemingly contradictory result is that the disc is closer to the NS when a* = 0.2, and the resulting stronger irradiating flux offsets the weakening effect of spin on the PR drag. Hence, PR drag remains a viable explanation for the increased persistent emission and soft excess observed during X-ray bursts in spinning NS systems.

X-ray Spectroscopic Study of Low-Mass X-ray Binaries: A Review of Recent Progress via the Example of GX 339-4

Low-mass X-ray binaries (LMXB) serve as natural laboratories, where the predictions of general relativity can be tested in the strong field regime. The primary object of such sources can be a neutron star (NS) or a black hole (BH), and this object captures material from the secondary object through the inner Lagrange point via a process called Roche lobe overflow. Because of the angular momentum of the infalling matter, an accretion disk is formed, in which viscous effects transport the angular momentum radially outward. In the high/soft state of these sources, the accretion disk can extend all the way to the innermost stable circular orbit (ISCO); therefore, when the primary object is a BH, its X-ray spectrum contains information about the region very close to the event horizon. This paper aims to review the theoretical and observational works related to the X-ray spectroscopy of such sources via the example of GX 339-4, which is one of the most well-known and well-studied LMXBs.

Polarimetry and astrometry of NIR flares as event horizon scale, dynamical probes for the mass of Sgr A*

We present new astrometric and polarimetric observations of flares from Sgr A* obtained with GRAVITY, the near-infrared interferometer at ESO’s Very Large Telescope Interferometer (VLTI), bringing the total sample of well-covered astrometric flares to four and polarimetric flares to six. Of all flares, two are well covered in both domains. All astrometric flares show clockwise motion in the plane of the sky with a period of around an hour, and the polarization vector rotates by one full loop in the same time. Given the apparent similarities of the flares, we present a common fit, taking into account the absence of strong Doppler boosting peaks in the light curves and the EHT-measured geometry. Our results are consistent with and significantly strengthen our model from 2018. First, we find that the combination of polarization period and measured flare radius of around nine gravitational radii (9Rg ≈ 1.5RISCO, innermost stable circular orbit) is consistent with Keplerian orbital motion of hot spots in the innermost accretion zone. The mass inside the flares’ radius is consistent with the 4.297 × 106 M⊙ measured from stellar orbits at several thousand Rg. This finding and the diameter of the millimeter shadow of Sgr A* thus support a single black hole model. Second, the magnetic field configuration is predominantly poloidal (vertical), and the flares’ orbital plane has a moderate inclination with respect to the plane of the sky, as shown by the non-detection of Doppler-boosting and the fact that we observe one polarization loop per astrometric loop. Finally, both the position angle on the sky and the required magnetic field strength suggest that the accretion flow is fueled and controlled by the winds of the massive young stars of the clockwise stellar disk 1–5″ from Sgr A*, in agreement with recent simulations.

Test Particles and Quasiperiodic Oscillations around Gravitational Aether Black Holes

This paper is devoted to the analysis of the dynamics of test particles in the vicinity of a black hole within the framework of a gravitational aether model. First, we explored the structure of spacetime by analyzing the curvature scalars. Then, we studied particle dynamics around a black hole using the Hamilton–Jacobi equation.The influence of the aether on the effective potential of the radial motion of test particles around the black hole has been investigated. The dependence of the innermost stable circular orbits (ISCO) on the aether parameter has also been investigated. We also considered particle collision near the black hole in the presence of aether, and studied the fundamental frequencies of the orbital motion of the test particles around the black hole in the presence of aether. Further, we applied the obtained results to the analysis of the upper and lower frequencies of twin-peaked quasiperiodic oscillations (QPOs) occurring near black holes. Finally, we use theoretical and numerical results to obtain constraints on model parameters using observation data in QPO.

Quasiperiodic Oscillations and Dynamics of Test Particles around Quasi- and Non-Schwarzschild Black Holes

One of the open problems in black hole physics is testing spacetime around black holes through astrophysical observations in the strong field regime. In fact, black holes cannot produce radiation themselves in the electromagnetic spectrum. However, a black hole’s gravity plays an important role in the production of the radiation of the accretion disc around it. One may obtain valuable information from the electromagnetic radiation of accretion discs about the gravitational properties of the spacetime around black holes. In this work, we study particle dynamics in the spacetime of quasi- and non-Schwarzschild black holes. We compare the gravitational effects of the spacetime deformation parameters of both black hole solutions on the innermost stable circular orbit (ISCO) radius, position, energy, and angular momentum of test particles at the ISCO, together with the energy efficiency of the accretion disc in the thin Novikov–Thorn model. Furthermore, we study the frequencies of particle oscillations in the radial and angular directions along circular stable orbits around both deformed black holes. Furthermore, we investigate quasiperiodic oscillations around the black holes in the relativistic precession model. We show the dependence of the deviation parameters on the orbits of twin peak QPOs with the frequency ratio 3:2. In the obtained results, we compare the gravitational effects of deviation parameters with the spin of a rotating Kerr black hole. Finally, we obtain constraints on the values of the deviation parameter of the spacetime around the black hole at the center of the microquasars GRO J1655-40 and GRS 1915-105 and their mass, using the χ2 method.

Charged particles and quasiperiodic oscillations around magnetized Schwarzschild black holes

We study the motion of charged particles around Schwarzschild black holes immersed in external (i) asymptotically uniform, (ii) dipolar, and (iii) parabolic-like magnetic fields. The effect of the different magnetic-field configurations on the position of innermost stable circular orbits (ISCOs) for test-charged particles is analyzed. Furthermore, we investigated frequencies of radial and vertical oscillations of the charged particles along their stable circular orbits together with the Keplerian one. As an astrophysical application, we explore quasiperiodic oscillations (QPOs) observed in microquasars sourced by black hole candidates in the frame of the relativistic precession (RP) model. In order to obtain constraints on the values of the magnetic parameter and black hole mass for the microquasars GRO J1655-40 and GRS 1915-105, we use the method so-called chi ^2 in the Bayesian approach. Also, we get constraints on the magnetic field around the black hole in the microquasars by treating electrons and protons as oscillating test-charged particles in the accretion disc. Our performed analyses show that the masses of black hole candidates in the above-mentioned objects and magnetic parameters are different for the uniform and dipolar magnetic field configurations. However, no constraints on the magnetic field and black hole masses are obtained in the case of a parabolic magnetic field configuration. The obtained results on the black hole masses are compared with the measurements in independent astrophysical observations of these black hole masses.

Accretion disc evolution in GRO J1655−40 and LMC X-3 with relativistic and non-relativistic disc models

ABSTRACT Black hole X-ray binaries are ideal environments to study the accretion phenomena in strong gravitational potentials. These systems undergo dramatic accretion state transitions and analysis of the X-ray spectra is used to probe the properties of the accretion disc and its evolution. In this work, we present a systematic investigation of ∼1800 spectra obtained by Rossi X-Ray Timing Explorer Proportional Counter Array observations of GRO J1655−40 and LMC X-3 to explore the nature of the accretion disc via non-relativistic and relativistic disc models describing the thermal emission in black hole X-ray binaries. We demonstrate that the non-relativistic modelling throughout an outburst with the phenomenological multicolour disc model DISKBB yields significantly lower and often unphysical inner disc radii and correspondingly higher (∼50–60 per cent) disc temperatures compared to its relativistic counterparts KYNBB and KERRBB. We obtained the dimensionless spin parameters of a* = 0.774 ± 0.069 and a* = 0.752 ± 0.061 for GRO J1655−40 with KERRBB and KYNBB, respectively. We report a spin value of a* = 0.098 ± 0.063 for LMC X-3 using the updated black hole mass of 6.98 M⊙. Both measurements are consistent with the previous studies. Using our results, we highlight the importance of self-consistent modelling of the thermal emission, especially when estimating the spin with the continuum-fitting method which assumes the disc terminates at the innermost stable circular orbit at all times.