Innermost Stable Circular Orbit Research Articles

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

Quasi periodic oscillations around Kerr-type black hole in the Starobinsky–Bel–Robinson theory of gravity

In this study of Kerr-type black hole within the Starobinsky–Bel–Robinson gravity, we unveil intriguing dynamics. We observe that the black hole spin weakens the effective potential, while the stringy parameter β of the Starobinsky–Bel–Robinson gravity, strengthens it, notably near the black hole. We further see that the deviations from the Kerr paradigm affect Innermost Stable Circular Orbit (ISCO) and Outermost Stable Circular Orbit (OSCO) regions. Moreover, the fundamental frequencies reveal the dominance of the β parameter near the black hole. Our analysis provides valuable insights into the possible black hole mass and β parameter for GRO J1655-40, XTE J1550-564, XTE J1859+226, GRS 1915+105 and H1743-322 under the Starobinsky–Bel–Robinson gravity, highlighting the role of quasi periodic oscillations behavior and black hole spin in defining these constraints. These findings have significant implications, highlighting the potential of the parameter β to rival or surpass the influence of the spin of the black hole, offering new insights into the behavior of black hole and spacetime beyond General Relativity.

Accretion disks properties around regular black hole solutions obtained from non-linear electrodynamics

We investigate a family of spherically symmetric, static, charged regular black hole solutions derived within the framework of Einstein-nonlinear electrodynamics. Our study focuses on examining the characteristics of accretion disks in the spacetimes described by the Dymnikova and Fan-Wang solutions. We explore circular geodesics of test particles and calculate various properties, including the radius of the innermost stable circular orbit, radiant energy, temperature, and conversion efficiency of accretion mass into radiation. We employ the Novikov-Thorne-Page thin accretion disk model as a background. By comparing our findings with those obtained in the Schwarzschild black hole case, we reveal significant modifications in the overall spectral properties. Specifically, we observe an increase in the energy emitted from the disk surface, resulting in higher temperatures for the accretion disks under certain values of the free parameters. Consequently, we note an enhanced efficiency of mass conversion into radiation compared to the Schwarzschild spacetime.

Observational appearances of hairy black holes in the framework of gravitational decoupling

Abstract We investigate the observational appearance of static and spherically symmetric hairy black holes in the framework of gravitational decoupling with the weak energy condition (WEC). Two types of thin illumination conditions are studied: 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, the lensing ring and the photon ring. Employing four types of astrophysical disk luminosity model, we investigate the appearance of halos and note that their luminosities do not superimpose when the source is on or beyond the innermost stable circular orbit.

The three-dimensional structure of black hole accretion flows within the plunging region

Abstract We analyse, using new analytical models and numerical general relativistic magnetohydrodynamic simulations, the three-dimensional properties of accretion flows inside the plunging region of black hole spacetimes (i.e., at radii smaller than the innermost stable circular orbit). These simulations are of thick discs, with aspect ratios of order unity h/r ∼ 1, and with a magnetic field geometry given by the standard low-magnetization ‘SANE’ configuration. This work represents the first step in a wider analysis of this highly relativistic region. We show that analytical expressions derived in the ‘thin disc’ limit describe the numerical results remarkably well, despite the large aspect ratio of the flow. We further demonstrate that accretion within this region is typically mediated via spiral arms, and that the geometric properties of these spiral structures can be understood with a simple analytical model. These results highlight how accretion within the plunging region is fundamentally two dimensional in character, which may have a number of observational implications. We derive a modified theoretical description of the pressure within the plunging region which accounts for turbulent heating and may be of use to black hole image modelling.

Quantum gravity modifications to the accretion onto a Kerr black hole

In the framework of the Asymptotic Safety scenario for quantum gravity, we analyze quantum gravity modifications to the thermal characteristics of a thin accretion disk spiraling around a renormalization group improved (RGI-) Kerr black hole in the low energy regime. We focused on the quantum effects on the location of the innermost stable circular orbit (ISCO), the energy flux from the disk, the disk temperature, the observed redshifted luminosity, and the accretion efficiency. The deviations from the classical general relativity due to quantum effects are described for a free parameter that arises in the improved Kerr metric as a consequence of the fact that the Newton constant turns into a running coupling G(r) depending on the energy scale. We find that, both for rapid and slow rotating black holes with accretion disks in prograde and retrograde circulation, increases in the value of this parameter are accompanied by a decreasing of the ISCO, by a lifting of the peaks of the radiation properties of the disk and by an increase of the accretion mass efficiency, as compared with the predictions of general relativity. Our results confirm previously established findings in Zuluaga and Sánchez (Eur Phys J C 81:840, 2021) where we showed that these quantum gravity effects also occur for an accretion disk around a RGI-Schwarzschild black hole.

Energetic processes and thermodynamic analysis of the spinning Kiselev black hole with cloud of strings

Here we study the impact of the string clouds, the quintessence dark energy and other spacetime parameters on the center-of-mass energy, Penrose-process and thermodynamic properties of a stationary black hole solution of the Einstein field equations. We observe that the three distinct horizons i.e the Cauchy horizon, the event horizon and the cosmological horizon exist when the spin parameter a of the black hole is less than its extremal value aE. Interestingly we see that the infinite redshift surface of the black hole is not much sensitive to the quintessence parameter γ. It is sensitive to the parameter a and it increases as the parameter a increases. Further, we notice that an increase in the string cloud parameters b, quintessence parameter γ and a make the radius of the ergosphere of the black hole larger. We also notice that a rise in the parameter a makes the innermost stable circular orbits (ISCO) smaller and for an increase in the parameter b and γ the ISCO becomes larger than that for the Kerr spacetime. For the center-of-mass energy of the spinning black hole with quintessence and cloud of strings we observe that it can be arbitrarily high only for the extremal case of the black hole for a specific range of values of the angular momentum of the colliding particles. We notice that the Penrose-process is more efficient for smaller values of the string cloud parameter b and the parameter γ has no significant impact on this process. Moreover we see that an increase in the parameters b, γ and a cause the Helmholtz free energy to increase and opposite is true for the temperature of this type of rotating black hole. We learn that the area and entropy of the black hole are also depend on the parameters b, γ and a, and their effect make the entropy smaller. Interestingly we find a range of the horizon radius for the thermodynamic stability of the black hole. To get more information about the thermodynamic quantities of the rotating black hole with quintessence and cloud of strings, we plot them for different ranges of the spacetime parameters.

Infinitely degenerate slowly rotating solutions in f(R) gravity

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)=(α0+α1R)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.

Precessing and periodic timelike orbits and their potential applications in Einsteinian cubic gravity

Einsteinian cubic gravity (ECG) is the most general theory up to cubic order in curvature, which has the same graviton spectrum as the Einstein theory. In this paper, we investigate the geodesic motions of timelike particles around the four dimensional asymptotically flat black holes in ECG, and discuss their potential applications when connecting them with recent observational results. We first explore the effects of the cubic couplings on the marginally bound orbits (MBO), innermost stable circular orbits (ISCO) and on the periodic orbits around the Einsteinian cubic black hole. We find that comparing to Schwarzschild black hole in general relativity, the cubic coupling enhances the energy as well as the angular momentum for all the bound orbits of the particles. Then, we derive the relativistic periastron precessions of the particles and give a preliminary bound on the cubic coupling employing the observational result of the S2 star’s pericenter precession in SgrA*. Finally, after calculating the periodic orbits’ configurations, we preliminarily evaluate the gravitational waveform radiated from several periodic orbits in one complete period of a test object which orbits a supermassive Einsteinian cubic black hole. Our studies could be helpful for us to better understand the gravitational structure of the theory with high curvatures.

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

Kinematic Model Yields Two Geo-Synchronous Orbits of E-M System and M-P-D System Validated by Total Energy Analysis

In Black Holes (BH) studies , a well-tested method of total energy analysis is used by which the radius of Innermost Stable Circular Orbit (ISCO) around the central BH is analyzed and the dimensionless spin parameter of BH is extracted. The same total energy analysis is utilized in case of E-M and M-P planet-satellite pairs and their extremum points are obtained. The energy maxima happens to be the inner unstable co-rotational orbit (aG1) and the energy minima happens to be outer stable corotational orbit(aG2) in case of E-M and M-P systems and their values from KM correspond to those obtained from Energy Analysis. This vindicates KM of binary pairs

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-yr 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 d, corresponding to a Kerr black hole mass of MBH = (1.5 ± 1.2) × 109 and (1.5 ± 1.3) × 109 M⊙, 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.