Circular Orbit Research Articles

Is WR 104 a face-on, colliding-wind binary?

ABSTRACT Two decades of extensive spectroscopic monitoring of WR 104 is used to confront what we think we understand about this iconic prototype of the dust-producing pinwheel stars. Convincing SB1 orbital solutions are obtained for both the WC9d star and its OB companion. The period ($241.54 \pm 0.14$ d) and circular orbit agree perfectly with results from modelling images of the rotating dust spiral. Contrary to those results though, the orbit is found to be significantly inclined instead of face-on. The two SB1 solutions each indicate $i \sim 45^{\circ }$ but could be as low as $\sim 34^{\circ }$. This result naturally provides an explanation for the long puzzling photometric and emission line strength variations but is difficult to reconcile with the imaging. Confirmation that colliding winds are present is found by the detection of variable excess emission in two of the lines where it would be most expected. The changing shapes of this excess emission are not perfectly phase-locked though, which will complicate future modelling.

Carroll geodesics

Using effective field theory methods, we derive the Carrollian analog of the geodesic action. We find that it contains both “electric” and “magnetic” contributions that are in general coupled to each other. The equations of motion descending from this action are the Carrollian pendant of geodesics, allowing surprisingly rich dynamics. As an example, we derive Carrollian geodesics on a Carroll–Schwarzschild background and discover an effective potential similar to the one appearing in geodesics on Schwarzschild backgrounds. However, the Newton term in the potential turns out to depend on the Carroll particle’s energy. As a consequence, there is only one circular orbit localized at the Carroll extremal surface, and this orbit is unstable. For large impact parameters, the deflection angle is half the value of the general relativistic light-bending result. For impact parameters slightly bigger than the Schwarzschild radius, orbits wind around the Carroll extremal surface. For small impact parameters, geodesics get reflected by the Carroll black hole, which acts as a perfect mirror.

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.

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.

Space-time structures, light trajectories and shadows for Kerr-Newman-AdS black hole with surrounding perfect fluid matter in Rastall gravity

We present the horizon structures and the shadows for Kerr-Newman-AdS black hole located in perfect fluid matter field in Rastall gravity. By considering the Hamilton-Jacobi equation and Carter constant separable method, we obtain the null geodesic equations of the black hole space-time as well as the unstable circular photon orbits in terms of the impact parameters. The horizon structures of the space-time are calculated numerically. The results show that there are four roots for a general case of the horizon equation (the Cauchy horizon r−h , the event horizon r+h , the cosmological horizon r q of Rastall gravity and the cosmological horizon r c of cosmological constant), which lead to a specific characteristic with the subregions of the space-time. The influences of the cosmological horizons r q and r c on the light trajectories around the black hole are also investigated. Furthermore, we study the effects of the parameters, including the perfect fluid matter intensity N s , the Rastall parameter k λ, the cosmological constant Λ, the black hole spin a and the black hole charge Q on black hole shadows in detail.

Symmetric twin paradox for free-falling frames: Argument against the relativistic time dilation?

The twin paradox, a classical puzzle in Special Relativity (SR), is typically resolved by acknowledging the asymmetry introduced by the acceleration of one twin's frame, associated with a rocket's motion through space. A similar paradox arises without any accelerated system, involving three or more inertial systems. This is commonly resolved by employing the relativistic concepts of clock synchronization and simultaneity. Here, we reformulate the paradox for two free-falling systems, where the twins traverse identical circular orbits in opposite directions around a central mass with a spherically symmetric gravitational field. This redefined version of the paradox eliminates asymmetry inherent in the original problem. Since both frames are free-falling, they can be viewed as locally inertial according to Einstein's Equivalence Principle. Additionally, no synchronization with clocks in other frames is needed. We explore a potential resolution to the paradox and highlight that there may be a misinterpretation of the Lorentz transformation in SR.

A potential mass-gap black hole in a wide binary with a circular orbit

A potential mass-gap black hole in a wide binary with a circular orbit

Twenty-three new Heartbeat Star systems discovered based on TESS data

ABSTRACT Heartbeat stars (HBSs) are ideal astrophysical laboratories to study the formation and evolution of binary stars in eccentric orbits and the internal structural changes of their components under strong tidal action. We discover 23 new HBSs based on TESS photometric data. The orbital parameters, including orbital period, eccentricity, orbital inclination, argument of periastron, and epoch of periastron passage of these HBSs, are derived by using a corrected version of Kumar et al.'s model based on the Markov Chain Monte Carlo (MCMC) method. The preliminary results show that these HBSs have orbital periods in the range from 2.7 to 20 d and eccentricities in the range from 0.08 to 0.70. The eccentricity-period relation of these objects shows a positive correlation between eccentricity and period and also shows the existence of orbital circularization. The Hertzsprung–Russell diagram shows that the HBSs are not all located in a particular area. The distribution of the derived parameters suggests a selection bias within the TESS survey towards HBSs with shorter periods. These objects are a very useful source to study the structure and evolution of eccentricity orbit binaries and to extend the TESS HBS catalog.

Stability Analysis of Stable Circular Orbit in Multi-Static Black Hole Spacetime

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.

Galactic Stellar Black Hole Binaries: Spin Effects on Jet Emissions of High-Energy Gamma-Rays

In the last few decades, galactic stellar black hole X-ray binary systems (BHXRBs) have aroused intense observational and theoretical research efforts specifically focusing on their multi-messenger emissions (radio waves, X-rays, γ-rays, neutrinos, etc.). In this work, we investigate jet emissions of high-energy neutrinos and gamma-rays created through several hadronic and leptonic processes taking place within the jets. We pay special attention to the effect of the black hole’s spin (Kerr black holes) on the differential fluxes of photons originating from synchrotron emission and inverse Compton scattering and specifically on their absorption due to the accretion disk’s black-body radiation. The black hole’s spin (dimensionless spin parameter a*) enters into the calculations through the radius of the innermost circular orbit around the black hole, the RISCO parameter, assumed to be the inner radius of the accretion disk, which determines its optical depth τdisk. In our results, the differential photon fluxes after the absorption effect are depicted as a function of the photon energy in the range 1GeV ≤E≤103GeV. It is worth noting that when the black holes’ spin (α*) increases, the differential photon flux becomes significantly lower.

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.

Reachable Set Computation with Terminal Velocity Constraints

This work establishes a general-purpose method for computing the exact boundary of the reachable set in a specified direction, with additional constraints imposed on the terminal velocities. Reachable sets with rest boundary conditions, that is, zero-velocity constraints imposed at initial and final times, are of interest for formation flying and spacecraft rendezvous and docking applications. The rest-to-rest reachability problem is extended to compute reachable neighboring circular orbits and a modified problem formulation is developed to exclusively compute the maximum and minimum reachable circular orbits. Reachable sets are computed by applying classical optimal control techniques to a maximum position optimization problem. A solution method for the optimization problem is outlined, which makes use of a Newton’s method solving schema. Additional constraints are added to the problem to compute maxima along specified directions, allowing for the characterization of the reachable set in as many directions as desired. Example reachable sets are computed to illustrate the use of this method on various systems, including an application to relative motion.

An effective model for the tidal disruption of satellites undergoing minor mergers with axisymmetric primaries

According to the hierarchical formation paradigm, galaxies form through mergers of smaller entities and massive black holes (MBHs), if present at their centers, migrate to the nucleus of the newly formed galaxy, where they form binary systems. The formation and evolution of MBH binaries, and in particular their coalescence timescale, is highly relevant for current and future facilities aimed at detecting the gravitational wave signal produced by the MBHs close to coalescence. While most of the studies targeting this process are based on hydrodynamic simulations, the high computational cost makes a complete parameter space exploration prohibitive. Semianalytic approaches represent a valid alternative, but they require ad hoc prescriptions for the mass loss of the merging galaxies in minor mergers due to tidal stripping, which is not commonly considered or is at best modelled assuming very idealised geometries. In this work we propose a novel, effective model for the tidal stripping in axisymmetric potentials, to be implemented in semi-analytic models. We validated our semi-analytic approach against N-body simulations considering different galaxy sizes, inclinations, and eccentricities, finding only a moderate dependence on the orbit eccentricity. In particular, we find that, for almost circular orbits, our model mildly overestimates the mass loss, and this is due to the adjustment of the stellar distribution after the mass is removed. Nonetheless, the model exhibits a very good agreement with simulations in all the considered conditions, and thus represents an extremely powerful addition to semi-analytic calculations.

Timing and scintillation studies of PSR J1439−5501

Context. PSR J1439−5501 is a mildly recycled pulsar in a 2.12-day circular orbit around a heavy white dwarf. A white dwarf cooling model has estimated the companion mass to be between 1 and 1.3 M⊙ and the inclination angle to be greater than 55°. Such high mass and inclination are expected to induce a Shapiro delay, namely, a relativistic time delay in the signal propagation caused by the curved space-time induced by the companion. Until now, however, no Shapiro delay has been measured in this system. Aims. Our aim is to detect the Shapiro delay and, thus, to independently measure the mass and inclination of PSR J1439−5501 by using data from the Parkes and MeerKAT radio telescopes. Methods. The Shapiro delay parameters were measured through pulsar timing, which coherently accounts for every rotation of the pulsar. These measurements were then used to estimate the masses of the component stars and the inclination angle of the binary. A scintillation analysis was additionally performed by investigating the secondary spectra, which are the Fourier-transformed observed scintillation patterns. The obtained secondary spectral variations were analyzed in terms of the orbital motion and annual variation to estimate the ascending nodes, distance, and the location of the screen. Results. We obtained a highly significant measurement of the Shapiro delay, which allows estimates of the pulsar mass (1.57−0.26+0.30 M⊙), the white dwarf (WD) companion mass (1.27−0.12+0.13 M⊙), and inclination angle, (75(1)° or 105(1)°). These estimates assume that the companion mass cannot exceed the Chandrasekhar mass limit (1.48 M⊙), along with a lower limit of 1.17 M⊙ for NS masses. These results are consistent with previous studies, but the precision of the component masses has been improved significantly. The orbital and spin parameters and the large WD mass make this system very similar to that of PSR J2222−0137 and PSR J1528−3146, thereby suggesting a common evolutionary mechanism. The scintillation analysis suggests that the longitude of the ascending node is 16(7)° or −20(6)°, depending on the sense of the inclination angle. The screen distance is 260 ± 100 pc, potentially associated with the edge of the Local Bubble.

Forming Massive Terrestrial Satellites through Binary-exchange Capture

The number of planetary satellites around solid objects in the inner solar system is small either because they are difficult or unlikely to form or because they do not survive for astronomical timescales. Here we conduct a pilot study on the possibility of satellite capture from the process of collision-less binary exchange and show that massive satellites in the range 0.01–0.1 M ⊕ can be captured by Earth-sized terrestrial planets in a way already demonstrated for larger planets in the solar system and possibly beyond. In this process, one of the binary objects is ejected, leaving the other object as a satellite in orbit around the planet. We specifically consider satellite capture by an “Earth” in an assortment of hypothetical encounters with large terrestrial binaries at 1 au around the Sun. In addition, we examine the tidal evolution of captured objects and show that orbit circularization and long-term stability are possible for cases resembling the Earth–Moon system.

Powered–coasting–powered multi-phase mission reconfiguration method for launch vehicles under power system failures

For the final stage of a launch vehicle with powered–coasting–powered multi-phase flight, this paper investigates the joint reconfiguration method to determine subsequent flight trajectory and degraded orbit after power system failure in the first powered phase. While power system failures due to mass–flow–rate drop have been thoroughly studied in the existing literature, this paper focuses on the more challenging specific impulse drop failures, which result in loss of total launcher energy. This paper aims to design a fault-tolerant guidance method with onboard potential and to analyze the survivability and characteristics of the launcher in the event of such a failure. In the problem modeling, the strong nonlinearity of the orbital elements as terminal constraints is eliminated by analyzing the orbital properties in the orbital coordinate system to establish the primal trajectory optimization problem. For this multi-phase trajectory optimization problem, a joint optimization algorithm for the degradation orbit and the flight trajectory, based on convex optimization and Radau pseudospectral method, is designed to achieve autonomous mission reconfiguration. The algorithm introduces the relaxation–penalization idea, where the terminal constraints are relaxed and penalized in the performance index, allowing the algorithm to adaptively form an optimal degradation circular or elliptical orbit based on the remaining capacity of the launch vehicle. Simulation experiments demonstrate the effectiveness and superiority of the mission reconfiguration algorithm. Finally, the paper presents the first analysis of the optimal allocation of flight time between the first powered phase, the coasting phase, and the second powered phase in a propellant depletion scenario following the launcher power system failure.

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.