Circular Orbit Research Articles

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.

Effect of the solar radiation pressure on the motion of satellites in almost circular Earth orbits

This paper considers the effect of the solar radiation pressure on the motion of a satellite in an almostcircular low-Earth orbit. The formulation of the problem is due to the need to determine the effect of solar radiation pressure forces on the motion of light commercial Earth remote sensing (ERS) satellites with large surface areas (solar batteries and antennas). The goal is to determine the main regularities of this effect, construct reasonably simple and accurate estimates of changes in orbital parameters for the orbits under consideration, and clarify their physics (cause-and-effect relations) The novelty of this study also lies in the use of variables specially introduced to describe a motion in almost circular orbits. The study assumes that the solar radiation pressure force is constant throughout the entire orbit, and it is concerned with dawn-dusk orbits, which are often used for ERS satellites with radar observation systems. The paper presents simple analytical expressions that describe the main regularities of short-term (several days) changes in orbital parameters. It is shown that the change in the orientation of the orbital plane is determined by the action of the gyroscopic moment. This moment balances the effect of the moment of external forces aimed at changing the orientation and the change in the orientation perpendicular to the direction of the applied moment of the external forces. The main effect of the solar radiation pressure is the excitation of forced oscillations of the orbital radius, whose amplitude linearly increases with time. The maximums of these oscillations (apogee) are at the point where the light pressure forces maximally slow down the motion of the satellite (directed oppositely to the velocity), and the minimums (perigee) are at the point of the maximum motion acceleration. It is shown that the annual movement of the Sun can qualitatively change the picture of the evolution of orbital parameters. For sun-synchronous dawn-dusk orbits, compact analytical solutions for changes in orbital parameters are constructed, and it is shown that the annual movement of the Sun’s declination reverses the direction of evolution of the orbital shape. The calculations showed a reasonably high accuracy of the analytical solutions at the initial stage. The obtained numerical estimates make it possible to evaluate the effect of the solar pressure on changes in orbital parameters.

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.

Searching For Optimal Areas of Circumlunar Space for Placement of Satellites Moving in Circular Orbits

Searching For Optimal Areas of Circumlunar Space for Placement of Satellites Moving in Circular Orbits

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 $h/r \sim 1$, 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.

Cone-beam CT with a noncircular (sine-on-sphere) orbit: imaging performance of a clinical system for image-guided interventions.

We aim to compare the imaging performance of a cone-beam CT (CBCT) imaging system with noncircular scan protocols (sine-on-sphere) to a conventional circular orbit. A biplane C-arm system (ARTIS Icono; Siemens Healthineers) capable of circular and noncircular CBCT acquisition was used, with the latter orbit (sine-on-sphere, "Sine Spin") executing a sinusoidal motion with tilt amplitude over the half-scan orbit. A test phantom was used for the characterization of image uniformity, noise, noise-power spectrum (NPS), spatial resolution [modulation transfer function (MTF) in axial and oblique directions], and cone-beam artifacts. Findings were interpreted using an anthropomorphic head phantom with respect to pertinent tasks in skull base neurosurgery. The noncircular scan protocol exhibited several advantages associated with improved 3D sampling-evident in the NPS as filling of the null cone about the spatial frequency axis and reduction of cone-beam artifacts. The region of support at the longitudinal extrema was reduced from 16 to at a radial distance of 6.5cm. Circular and noncircular orbits exhibited nearly identical image uniformity and quantum noise, demonstrating cupping of and overall noise of . Although both the radially averaged axial MTF ( ) and 45deg oblique MTF ( ) were lower for the noncircular orbit compared with the circular orbit at the default full reconstruction field of view (FOV), there was no difference in spatial resolution for the medium reconstruction FOV (smaller voxel size). Differences in the perceptual image quality for the anthropomorphic phantom reinforced the objective, quantitative findings, including reduced beam-hardening and cone-beam artifacts about structures of interest in the skull base. Image quality differences between circular and noncircular CBCT orbits were quantitatively evaluated on a clinical system in the context of neurosurgery. The primary performance advantage for the noncircular orbit was the improved sampling and elimination of cone-beam artifacts.

Correspondence of Concept of Circular Orbits in Schwarzschild Metric and Kerr Metric to those in Tidally Evolving Binaries in Weak Gravitational Regime and its Application in Determination of Spin of Supermassive Black Hole

This paper rederives diameters of the Innermost Stable Circular Orbits (ISCO) in Schwarzschild Metric (RDISCO = 6RSch for non-rotating BH with a =0) and in Kerr metric with particular reference to recently studied Super Massive Black Hole in NGC1365 (RDISCO = 9RSch for retrograde orbits and RDISCO = 1RSch for prograde orbits around maximally spinning BH of a=1). Next the same derivations are made in tidally evolving binaries based on kinematic model. Kinematic Model derivation corresponds to the derivations made in Kerr Metric for Circular Orbits in all its details at weak gravitation regime. At strong gravitation regime in Kerr metric, the two orbits converge to Innermost Stable Circular Orbit due to the Space-Time Curvature and Frame-Dragging Effect in the vicinity of SMBH. Kinematic model fails to arrive at ISCO since it has not included the relativistic mechanics.

Feedback Control for Directional Rendezvous Using Constant-Magnitude Low Thrust

Feedback control for close-range orbital rendezvous, which permits choosing the direction of the final approach, is beneficial for numerous space missions. However, developing such a feedback controller for satellites operating with constant-magnitude low thrust without introducing chattering is nontrivial due to the underactuated nature of the dynamics. This paper develops a feedback control law for rendezvous with a target on a nearly circular orbit, assuming that the chaser satellite utilizes constant-magnitude low thrust. Based on the Clohessy–Wiltshire (CW) model, a sliding surface is chosen on which the states approach the origin. A feedback law driving given initial states to the sliding surface is developed first. Close to the origin, a bang-bang type controller is then employed, which drives the state errors to zero in finite time while allowing to choose the final approach direction along the R-, V-, or H-bar. Solutions to the state trajectories are obtained in closed form, except for the case of the R-bar approach, which is proven to be finite-time stable. It is shown that the higher-order dynamics neglected in the CW equations can be handled through dynamic inversion combined with a hopping maneuver.

Warm start for optimal transfer between close circular orbits with first generation E-sail

The Electric Solar Wind Sail (E-sail) is a propellantless propulsion system for deep space navigation that exploits the dynamic pressure of the solar wind to generate thrust using a web of long, conducting tethers. The heliocentric trajectory of an E-sail-based spacecraft in a classic transfer between two Keplerian orbits is usually analyzed, in an optimal framework, by minimizing the total flight time. This paper discusses an analytical, approximate procedure for solving the two-point boundary value problem associated with the trajectory optimization process in a heliocentric, two-dimensional scenario involving a first-generation E-sail. The procedure is applied in a typical transfer between two coplanar circular orbits whose (assigned) radii are sufficiently close to each other. Paralleling the approach proposed in the recent literature, the mathematical model presented in this paper discusses a set of analytical equations that give an accurate approximation of both the minimum flight time and the (unknowns) initial adjoint variables. The paper also analyzes a set of mission applications, which involve interplanetary transfers to some near-Earth asteroids whose orbits have a very small value of both eccentricity and inclination.

Energy extraction via magnetic reconnection in magnetized black holes

The Comisso-Asenjo mechanism is a novel mechanism proposed recently to extract energy from black holes through magnetic reconnection of the surrounding charged plasma, in which the magnetic field plays a crucial role. In this work, we revisit this process by taking into account the backreaction of the magnetic field on the black hole's geometry. We employ the Kerr-Melvin metric to describe the local near-horizon geometry of the magnetized black hole. By analyzing the circular orbits in the equatorial plane, energy extraction conditions, power and efficiency of the energy extraction, we found that while a stronger magnetic field can enhance plasma magnetization and aid energy extraction, its backreaction on the spacetime may hinder the process, with a larger magnetic field posing a greater obstacle. Balancing these effects, an optimal moderate magnetic field strength is found to be most conducive to energy extraction. Moreover, there is a maximum limit to the magnetic field strength associated with the black hole's spin, beyond which circular orbits in the equatorial plane are prohibited, thereby impeding energy extraction in the current scenario.

Deceleration of kicked objects due to the Galactic potential

Context. Various stellar objects experience a velocity kick at some point in their evolution. These include neutron stars and black holes at their birth, or binary systems when one of the two components goes supernova. For most of these objects, the magnitude of the kick and its impact on the object dynamics remains a topic of debate. Aims. We investigate how kicks alter the velocity distribution of objects born in the Milky Way disc, both immediately after the kick and at later times, and whether these kicks are encoded in the observed population of Galactic neutron stars. Methods. We simulated the Galactic trajectories of point masses on circular orbits in the disc after being perturbed by an isotropic kick, with a Maxwellian distribution where σ = 265 km s−1. Then, we simulated the motion of these point masses for 200 Myr. These trajectories were then evaluated, either for the Milky Way population as a whole or for those passing within two kiloparsecs of the Sun, to get the time evolution of the velocities. Results. During the first 20 Myr, the bulk velocity of kicked objects becomes temporarily aligned with the cylindrical radius, implying an anisotropy in the velocity orientations. Beyond this age, the velocity distribution shifts towards lower values and settles to a median of ∼200 km s−1. Around the Sun, the distribution also loses its upper tail, primarily due to unbound objects escaping the Galaxy. We compared this to the velocities of Galactic pulsars and find that pulsars show a similar evolution with characteristic age. Conclusions. The shift in the velocity distribution is due to bound objects spending most of their orbits at larger radii after the kick. They are, therefore, decelerated by the Galactic potential. We find the same deceleration for nearby objects and the total population, and conclude that it is also observed in Galactic pulsars. Because of this effect, the (scalar) speeds of old neutron stars provide little information about their kicks at birth.

Forming off-center massive black hole binaries in dwarf galaxies through Jacobi capture

It is well established that black holes reside in the central regions of virtually all types of known galaxies. Recent observational and numerical studies however challenge this picture, suggesting that intermediate-mass black holes in dwarf galaxies may be found on orbits far from the center. In particular, constant-density cores minimize orbital energy losses due to dynamical friction, and allow black holes to settle on stable off-center orbits. Using controlled simulations, we study the dynamics of off-center black holes in dwarf galaxies with such cores. We propose a new scenario to describe off-center mergers of massive black holes, starting with a Jacobi capture. We focus on initially circular and co-planar black hole orbits and explore a large parameter space of black hole masses and orbital parameters. We find that Jacobi captures are a complex and chaotic phenomenon that occurs in about 13% of cases in this simplified setup, and we quantify how the likelihood of capture depends on the simulation parameters. We note that this percentage is likely an upper limit of the general case. Nevertheless, we show that Jacobi captures in cored dwarf galaxies can facilitate the formation of off-center black hole binaries, and that this process is sufficiently common to have a substantial effect on black hole growth. While our setup only allows for temporary captures, we expect dissipative forces from baryons and post-Newtonian corrections to maintain the captures over time and to lead to the formation of stable binary systems. This motivates future studies of the effectiveness of such dissipative forces, within stripped nuclei or globular clusters, in forming stable bound systems.

Possible signatures of higher dimension in thin accretion disk around brane world black hole

We probe deeply into the characteristics of thin accretion disk surrounding black hole within the brane world paradigm. We investigate how model parameters affect the physical properties of the disk. Our findings indicate that as the tidal charge parameter inherited from the higher dimension increases, the energy flux, the radiation temperature, the spectral cutoff frequency, the spectral luminosity, and the conversion efficiency of the disk all increase, but the radius of the innermost stable circular orbit decreases. Compared to cases of the Kerr and Schwarzschild black holes, the disk is hotter and more luminous for positive tidal charge parameter, while it is cooler and less luminous for negative tidal charge parameter, which suggests the potential for probing possible signatures of higher dimension.

Low-Earth-Orbit Mega-Constellation Low-Redundancy Design: Rapid Performance Analysis and Adaptive Configuration Layering

Megaconstellations, which offer convenient communication and navigation services, are at the forefront of satellite application advancements. However, traditional constellations with a single uniform configuration fail to meet the various demands in different regions, thus leading to low utilization. In addition, satellite safety becomes a key consideration that megaconstellations cannot ignore. To address the aforementioned problems, this study proposes an adaptive method for designing layered megaconstellations under the assumptions of circular orbits, uniform distribution in each plane, and a pregiven altitude. Two novel methods are developed for evaluating the coverage performance and satellite safety. First, the longitude-coverage-ratio model is proposed based on the street of coverage theory, enhancing the constellation design for latitude-specific coverage needs. Next, a rapid method is derived for calculating the minimum angular distance between planes. Then, the study investigates the models to be used in subconstellation design techniques for assembling multilayer hybrid megaconstellations. Several hybrid megaconstellations are designed, demonstrating the applicability of the methodology for both nonuniform and global uniform coverage requirements. The results show that this method offers reduced redundancy and a lower number of satellites compared to a single Walker. The examples also suggest that low-Earth-orbit hybrid constellations can achieve global uniform coverage when reaching sufficient coverage folds.

The interface of gravity and dark energy

At sufficiently large radii dark energy modifies the behavior of (a) bound orbits around a galaxy and (b) virialized gas in a cluster of galaxies. Dark energy also provides a natural cutoff to a cluster’s dark matter halo. In (a) there exists a maximum circular orbit beyond which periodic motion is no longer possible, and orbital evolution near critical binding is analytically calculable using an adiabatic invariant integral. The finding implicates the study of wide galaxy pairs. In (b), dark energy necessitates the use of a generalized Virial Theorem to describe gas at the outskirts of a cluster. When coupled to the baryonic escape condition, aided by dark energy, the results is a radius beyond which the continued establishment of a hydrostatic halo of thermalized baryons is untenable. This leads to a theoretically motivated virial radius. We use this theory to probe the structure of a cluster’s baryonic halo and apply it to X-ray and weak-lensing data collected on cluster Abell 1835. We find that gas in its outskirts deviates significantly from hydrostatic equilibrium beginning at ∼1.3 Mpc , the ‘inner’ virial radius. We also define a model dependent dark matter halo cutoff radius to A1835. The dark matter cutoff gives an upper limit to the cluster’s total mass of ∼7×1015M⊙ . Moreover, it is possible to derive an ‘outer’ hydrostatic equilibrium cutoff radius given a dark matter cutoff radius. A region of cluster gas transport and turbulence occurs between the inner and outer cutoff radii.

The 2018 Outburst of MAXI J1820+070 as Seen by Insight-HXMT

We present an analysis of the whole 2018 outburst of the black hole X-ray binary MAXI J1820+070 with Insight-HXMT data. We focus our study on the temporal evolution of the parameters of the source. We employ two different models to fit the disk’s thermal spectrum: the Newtonian model diskbb and the relativistic model nkbb. These two models provide different pictures of the source in the soft state. With diskbb, we find that the inner edge of the disk is close to the innermost stable circular orbit of a fast-rotating black hole and the corona changes geometry from the hard to the soft state. With nkbb, we find that the disk is truncated in the soft state and that the coronal geometry does not change significantly during the whole outburst. However, the model with nkbb can predict an untruncated disk around a fast-rotating black hole if we assume that the disk inclination angle is around 30° (instead of ∼60°, which is the inclination angle of the jet and is usually adopted as the disk inclination angle in the literature) and we employ a high-density reflection model. In such a case, we measure a high value of the black hole spin parameter with observations in the soft state, in agreement with the high spin value found from the analysis of the reflection features and in disagreement with the low spin value found by previous continuum-fitting method measurements with the disk inclination angle set to the value of the jet inclination angle.

Satellite impact on astronomical observations based on the elliptical orbit model

Space-based and ground-based telescopes have extensively documented the impact of satellites on astronomical observations. With the proliferation of satellite mega-constellation programmes, their influence on astronomical observations has become undeniable. Quantifying the impact of satellites on telescopes is crucial. To this end, we enhanced the circular orbit model for satellites and introduced a methodology based on two-line element orbit data. This involves constructing a satellite probability distribution model to evaluate the impact of satellites on telescopes. Using our method, we assessed the satellite impact on global grounded observatories. Our results indicate that the regions most severely affected by satellite interference at present are those near the equator, with latitudes of around ±50 and ±80 degrees experiencing the most significant impact from low-Earth-orbit satellites. Furthermore, we validated the reliability of our method using imaging data obtained from the focal surface acquisition camera of the LAMOST telescope.

The GAPS programme at TNG

Aims. We report the confirmation of a new transiting exoplanet orbiting the star TOI-5076. Methods. We present our vetting procedure and follow-up observations which led to the confirmation of the exoplanet TOI-5076b. In particular, we employed high-precision TESS photometry, high-angular-resolution imaging from several telescopes, and high-precision radial velocities from HARPS-N. Results. From the HARPS-N spectroscopy, we determined the spectroscopic parameters of the host star: Teff = (5070±143) K, log 𝑔 = (4.6±0.3), [Fe/H] = (+0.20±0.08), and [α/Fe] = 0.05±0.06. The transiting planet is a warm sub-Neptune with a mass mp = (16±2) M⊙, a radius rp =(3.2±0.l) R⊙ yielding a density ρp = (2.8±0.5) g cm−3. It revolves around its star approximately every 23.445 days. Conclusions. The host star is a metal-rich, K2V dwarf, located at about 82 pc from the Sun with a radius of R⋆ = (0.78±0.01) R⊙ and a mass of M⋆ = (0.80±0.07) M⊙. It forms a common proper motion pair with an M-dwarf companion star located at a projected separation of 2178 au. The chemical analysis of the host-star and the Galactic-space velocities indicate that TOI-5076 belongs to the old population of thin-to-thick-disk transition stars. The density of TOI-5076b suggests the presence of a large fraction by volume of volatiles overlying a massive core. We found that a circular orbit solution is marginally favored with respect to an eccentric orbit solution for TOI-5076b.

White dwarf magnetospheres: Shielding volatile content of icy objects and implications for volatile pollution scarcity

Context. About 25–50% of white dwarfs are found to be contaminated by heavy elements, which are believed to originate from external sources such as planetary materials. Elemental abundances suggest that most of the pollutants are rocky objects and only a small fraction of white dwarfs bear traces of volatile accretion. Aims. In order to account for the scarcity of volatile pollution, we investigate the role of the white dwarfs’ magnetospheres in shielding the volatile content of icy objects. Methods. We estimated the volatile sublimation of inward drifting exocomets. We assume the orbits of the exocomets are circularized by the Alfvén wing drag that is effective for long-period comets. Results. Volatile material can sublimate outside the corotation radius and be shielded by the magnetic field. The two conditions for this volatile-shielded mechanism are that the magnetosphere radius must be larger than the corotation radius and that the volatiles are depleted outside the corotation radius, which requires a sufficiently slow orbital circularization process. We applied our model to nine white dwarfs with known rotational periods, magnetic fields, and atmosphere compositions. Our volatile-shielded model may explain the excess of volatile elements such as C and S in the disk relative to the white dwarf atmosphere in WD2326+049 (G29-38). Nevertheless, given the sensitivity of our model to the circularization process and material properties of icy objects, there remains considerable uncertainty in our results. Conclusions. We emphasize the importance of white dwarfs’ magnetic fields in preventing the accretion of volatile gas onto them. Our work suggests a possible explanation for the scarcity of volatile-accretion signatures among white dwarfs. We also identify a correlation between the magnetic field strength, the spin period, and the composition of pollutants in white dwarf atmospheres. However, given the uncertainties in our model, more observations are necessary to establish more precise constraints on the relevant parameters.