Innermost Circular Orbit Research Articles

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.

Particle and light motion in Lyra–Schwarzschild spacetime

Abstract In this paper we recall the static and spherically symmetric solution derived within LyST gravity. LyST stands for “Lyra Scalar-Tensor” and is a scalar-tensor proposal for the gravitational interaction modifying general relativity by adopting Lyra manifold as the spacetime substrate. Lyra manifold is characterized both by the metric tensor gµν(x) and the scale φ(x); the latter being an integral part of the definition of reference frame. In a previous work, we have launched the formal geometrical basis of LyST, we have proposed an associated action integral for the gravitational interaction, we have derived the field equations generalizing Einstein field equation, and we have solved these equation to obtain the generalized version of Schwarzschild line element in Lyra manifold. This lead us to Lyra-Schwarzschild spacetime, which is further explored in the present paper. Herein, the trajectories of test particles is thoroughly studied. This is done for both massive particles and massless particles. The geodesic equations are built and solved. The effective potential associated to the motion of these particles around the source is determined and characterized. The possible trajectories include gravitational capture, scattering, bounded orbits, stable and unstable circular orbits, near-horizon motion. The innermost circular orbit allowed for massive particles is determined and compared to the one predicted by GR. The last photon orbit is also calculated for Lyra-Schwarzschild metric. The equation for the periastron shift in the context of Lyra-Schwarzschild solution is constructed; its application to observational data could be useful to constrain the parameters typical of LyST, telling it apart from GR.

Explaining QPOs data for black holes in the Starobinsky–Bel–Robinson gravity

In this work we explore the properties of the spacetime around the Schwarzschild-like black hole in the Starobinsky–Bel–Robinson gravity through a test particle motion and its quasi periodic oscillations (QPOs) in the circular orbits in the close vicinity of the black hole horizon. We show how the extra spacetime parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} affects the effective potential, energy, angular momentum, inner most circular orbit (ISCO) radius, and trajectory of a test particle. Next, we focus on the QPOs of particles and explore it in the relativistic precision model. Finally, we apply our analysis to explain the observational data obtained for several black hole candidates including GRO J1655-40, GRS 1915+105, XTE J1859+226, and XTE J1550-564 and get constraints on their spacetime parameters by employing the Markov Chain Monte Carlo analysis methodology.

The Search for the Origin of the Quantum Conditions under the Paradigm of Absolute Space

This study deals with the physical (not the mathematical) origin of the quantum conditions. The assumption of an absolute space together with the speed of 369.5 km/s of the sun leads to cycloidal or helical orbits of the electron around the proton. This kind of orbits is a previously unnoticed fact and not compatible with the model of a closed circular standing wave. It is the aim of this study to search for alternative models. The Alternating Field model (AFM) assumes the existence of alternating fields for both the proton and the electron. The Higgs-field provides the energy requirements. By Puthoff’s effect, adapted for the electrostatic field, the electron changes its Compton frequency according to its position in the field. The interference of the alternating fields of the proton and the electron causes beats that are integer multiples of the orbital frequencies when the electron moves on Bohr’s orbits. Important results of this study are: The electrostatic Schwarzschild-radius is exactly half the value of the classical electron radius. Bohr’s first three principal quantum numbers, 1, 2, 3, are reproduced as 1.000052, 2.000214, and 3.000685. A two-dimensional simulation shows that the AFM causes orbits with ribbon shape. A formula, using only the orbital frequencies of the two innermost circular orbits, can predict the shortest wavelength of the Lyman series. The AFM is still incomplete. E.g., it does not prevent illegal orbits, but only indicates them. Also, the AFM does not use the magnetic core field of the proton. On the other hand, the model has produced results showing that Newton’s absolute space and the QM are compatible.

Shadow and photon ring of black hole in asymptotically safe gravity

In this paper, we discuss the influence of thin disk accretion and asymptotically safe (AS) gravity correction parameters on the shadow and photon ring of black hole. For the thin disk accretion, the dark region is the shadow of the black hole, and the bright photon ring is composed of direct image, lensing ring, and photon ring. For the specific intensity of the radiation source of the accretion disk, we consider three different emission profile models. For the second-order attenuation function model in which the emission starts from the innermost circular orbit, direct image, lensing ring, and photon ring can be clearly distinguished. The direct image contributes most of the brightness, and the lensing ring contributes a small portion, while the contribution of the photon ring can almost be ignored. And the observed corresponding intensity peak decreases with the increase of the AS gravity parameter, that is, the corresponding brightness of the photon ring darkens as correction parameter increases. For the third-order attenuation function model in which the emission begins at the radius of the photon sphere, lensing ring and photon ring are superimposed on the direct radiation. Thus a new extreme value of the observed intensity emerges, and the extreme value increases with the increase of the AS gravity parameter, which leads to a brighter observed photon ring. For the anti-trigonometric attenuation function model in which the radiation starts from the event horizon, the superposition range of lensing ring and photon ring on the direct radiation becomes larger, which makes photon ring wider. The smaller the AS gravity parameter, the more difficult it is to distinguish between the lensing ring and photon ring, and the brighter the photon ring turns. In short, the results show that the shadow radius decreases with the increase of the AS correction parameter. For different AS gravity correction parameters, the light intensities of emission source, especially emission profiles of the observed intensity are significantly different, resulting in obvious differences in observed emission intensity between the shadow of the black hole and the bright photon ring of the black hole.

Epicyclic Oscillations and Circular Orbits in Hairy Black Holes: Testing by High-Frequency Quasi-Periodic Oscillations Observed in Microquasars

Recently, Ovalle and his collaborators proposed an exact solution to Einstein’s equations. In this study, we investigate the main characteristics of the spherically symmetric spacetime determined by the hair parameter l, with a specific focus on circular orbits, particularly the innermost circular orbits (ISCOs), and the epicyclic oscillatory motion along these orbits. To assess the validity of this novel geometry, we employ the frequencies derived from the epicyclic resonance model of high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars, as well as the ISCOs. By analyzing the observed data from three selected microquasars, we establish constraints on the parameter l. Our findings suggest that this geometric framework can encompass the phenomena associated with HF QPOs and offer a partial explanation for the observed shift in the ISCOs, which is commonly attributed to the rotation of the black hole.

Shadow and photon ring of black hole in asymptotically safe gravity

In this paper, we focus on discussing the influence of thin disk accretion and asymptotically safe (AS) gravity correction parameter on the shadow and photon ring of black holes. For the thin disk accretion, the dark region is the shadow of the black hole, and the bright photon ring is composed of Direct image, lensing ring and Photon ring. For the specific intensity of the radiation source of the accretion disk, we consider three different emission profile models. For the second-order attenuation function model in which emission starts from the innermost circular orbit, Direct image, lensing ring and Photon ring can be clearly distinguished. The Direct image contributes most of the brightness, and the lensing ring contributes a small portion, while the contribution of the Photon ring can almost be ignored. And the peak value of the corresponding observed intensity decreases with the increase of the AS gravity parameter, that is, the corresponding brightness of the photon ring darkens as correction parameter increases. For the third-order attenuation function model in which the emission begins at the radius of the photon sphere, lensing ring and Photon ring are superimposed on the direct radiation. Thus a new extreme value of the observed intensity emerges, and the extreme value increases with the increase of the AS gravity parameter, which leads to observed photon ring brighter. For the anti-trigonometric attenuation function model in which the radiation starts from the event horizon, the superposition range of lensing ring and Photon ring on the direct radiation becomes larger, which makes photon ring wider. The smaller the AS gravity parameter is, the more difficult it is to distinguish the lensing ring and Photon ring, and the photon ring gets brighter. In short, the results show that the shadow radius decreases with the increase of the AS correction parameter. For different AS gravity correction parameters, the light intensity of emission source, especially emission profiles of the observed intensity are significantly different, resulting in obvious differences for the shadow and bright photon ring of the black hole.

Quasiperiodic oscillation around charged black holes in Einstein–Maxwell-scalar theory

In the present paper, first, we study the event horizon properties of charged black holes (BHs) in Einstein Maxwell-scalar (EMS) gravity. Then, we investigate the circular motion of test particles’ around the BH in the EMS gravity. We also analyze the effects of the EMS parameters on the position of innermost circular orbits (ISCOs), energy, and angular momentum of the test particles corresponding to circular orbits. We provide detailed studies of the efficiency of energy release from EMS BHs based on the Hartle–Thorne model and fundamental frequencies of oscillations of particles along their circular stable orbits. Moreover, we have explored possible values of upper and lower frequencies of twin-peak quasiperiodic oscillations (QPOs) around the BHs. Finally, we obtain relationships between the BH charge and the EMS parameters using observational data from the QPOs detected in the microquasars: GRS 1905+105, GRO J 1655-40, H 1745+322, and XTE 1550-564.

Accretion disks around a static black hole in f(R) gravity

We provide a description of a thin accretion disc for a static spherically symmetric black holes in $f(R)$ gravity. In this regard, we first study the horizons of black holes in $f(R)$ gravity. The equation of motion and effective potential are also computed which eventually leads to possible existence of innermost circular orbits of accretion disc. We derive the specific energy, specific angular momentum and angular velocity of the particles moving in circular orbits also. A comparative study of various parameters are also presented. The locations of the event horizon, cosmological horizon, innermost and outermost stable circular orbits are also pointed out.

Analytical time-like geodesics in modified Hayward black hole space-time

The properties of modified Hayward black hole space-time can be investigated through analyzing the particle geodesics. By means of a detailed analysis of the corresponding effective potentials for a massive particle, we find all possible orbits which are allowed by the energy levels. The trajectories of orbits are plotted by solving the equation of orbital motion numerically. We conclude that whether there is an escape orbit is associated with $b$ (angular momentum). The properties of orbital motion are related to $b$, $\alpha$ ($\alpha$ is associated with the time delay) and $\beta$ ($\beta$ is related to 1-loop quantum corrections). There are no escape orbits when $b$ $<$ $4.016M$, $\alpha$ = 0.50 and $\beta$ = 1.00. For fixed $\alpha$ = 0.50 and $\beta$ = 1.00, if $b$ $<$ $3.493M$, there only exist unstable orbits. Comparing with the regular Hayward black hole, we go for a reasonable speculation by mean of the existing calculating results that the introduction of the modified term makes the radius of the innermost circular orbit (ISCO) and the corresponding angular momentum larger.

Magnetic field strength at the innermost circular orbit in accretion disk of supermassive black hole in active galactic nuclei: comparison with the equipartition value

In this paper we present the results of the determination of the magnetic field strength at the innermost stable circular orbit (ISCO) of an active galactic nuclei (AGN) derived from the polarimetric data for radiation emerging from broad line regions (BLR). These results are obtained by the radiative transfer method that takes into account the effect of Faraday rotation depolarization. The observed polarization degree allows to estimate the value of the magnetic field in the BLR and then to derive the ISCO magnetic field strength using the standard accretion disk model (Shakura and Sunyaev in Astron. Astrophys. 24:337, 1973). We used the polarimetric data obtained by Smith et al. (Mon. Not. R. Astron. Soc. 335:773, 2002) to calculate the values of relativistic jet kinetic power of AGN from the derived values of the magnetic field strength at the ISCO radius.

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries — binary star systems composed of neutron stars and/or black holes in their late stage of evolution — require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries — moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

The X-ray spectrum of the black hole candidate Swift J1753.5−0127

We present a spectral analysis of the black hole candidate and X-ray transient source Swift J1753.5 0127 making use of simultaneous observations of XMM-Newton and Rossi X-ray Timing Explorer (RXTE) in 2006, when the source was in outburst. The aim of this paper is to test whether a thermal component due to the accretion disc is present in the X-ray spectrum. We fit the data with a range of spectral models, and we find that for all of these models the fits to the X-ray energy spectra significantly require the addition of the disc black-body component. We also find a broad iron emission line at around 6.5 keV, most likely due to iron in the accretion disc. Our results confirm the existence of a cool inner disc extending near or close to the innermost circular orbit (ISCO).We further discovered broad emission lines of NVII and OVIII at ~ 0.52 keV and 0.65 keV, respectively in the RGS spectrum of Swift J1753.5-0127.

ROTATING QUARK STAR IN CHIRAL COLOUR DIELECTRIC MODEL

The properties of rotating quark star are studied using the equation of state obtained from chiral colour dielectric model. The results are compared with those obtained from MIT bag model equation of state. The frequencies in the corotating innermost circular orbits for different central densities are evaluated and compared with the observed data.

Orbital dynamics of Sun-facing solar sails under the constraint of constant sail temperature

The orbital dynamics of Sun-facing solar sails is investigated considering a constraint of constant sail temperature at the limit of the sail material. Although solar sails can normally be articulated so as to provide thrust with both a transverse and radial component, a Sunfacing attitude with the center of solar pressure behind the center of gravity may be preferred for very large or gossamer sails in order to achieve Sun-facing attitude stability. The proposed Sun-facing solar sails are applicable to space weather and geo-storm warning missions for monitoring the inner solar system environment by in-situ measurement of solar wind plasma and high-energy particle events. Constraining the temperature of the sail to the temperature limit of the sail material allows the innermost circular orbits to be attained thereby maximizing scientific returns. The stability of the heliocentric circular orbit under such radial thrust with the constant temperature constraint is investigated, and the stability conditions are obtained as functions of the radius of circular orbit and the solar sail lightness number accounting for optical/thermal properties.

Circular orbit approximation for binary compact objects in general relativity

One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the calculation of innermost circular orbits to the construction of initial data for numerical relativity calculations. While this assumption is inconsistent with generic general relativistic astrophysical inspiral phenomena where the dissipative effects of gravitational radiation cause the separation of the compact objects to decrease in time, it is usually argued that the timescale of this dissipation is much longer than the orbital timescale so that the approximation of circular orbits is valid. Here, we quantitatively analyze this approximation using a post-Newtonian approach that includes terms up to order ({Gm/(rc^2)})^{9/2} for non-spinning particles. By calculating the evolution of equal mass black hole / black hole binary systems starting with circular orbit configurations and comparing them to the more astrophysically relevant quasicircular solutions, we show that a minimum initial separation corresponding to at least 6 (3.5) orbits before plunge is required in order to bound the detection event loss rate in gravitational wave detectors to < 5% (20%). In addition, we show that the detection event loss rate is > 95% for a range of initial separations that include all modern calculations of the innermost circular orbit (ICO).

Relativistic models for binary neutron stars with arbitrary spins

We introduce a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled Einstein field equations and equations of relativistic hydrodynamics are solved in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences of circular-orbit binaries of varying separation, keeping the rest mass and circulation constant along each sequence. Solutions are presented for configurations obeying an $n=1$ polytropic equation of state and spinning parallel and antiparallel to the orbital angular momentum. We treat stars with moderate compaction $[{(m/R)}_{\ensuremath{\infty}}=0.14]$ and high compaction $[{(m/R)}_{\ensuremath{\infty}}=0.19].$ For all but the highest circulation sequences, the spins of the neutron stars increase as the binary separation decreases. Our zero-circulation cases approximate irrotational sequences, for which the spin angular frequencies of the stars increases by 13% [11%] of the orbital frequency for ${(m/R)}_{\ensuremath{\infty}}=0.14$ $[{(m/R)}_{\ensuremath{\infty}}=0.19]$ by the time the innermost circular orbit is reached. In addition to leaving an imprint on the inspiral gravitational waveform, this spin effect is measurable in the electromagnetic signal if one of the stars is a pulsar visible from Earth.

Magnetized orbits around a Schwarzschild black hole

We study the motion of a magnetized particle orbiting around a supermassive Schwarzschild black hole, surrounded by a strong (asymptotically uniform) magnetic field. Using the Hamilton–Jacobi formalism, we solve in a fully analytical way the problem of finding the innermost circular orbits. We show that, for suitable values of the parameters controlling the magnetic interaction, these orbits may become stable near r = 3M, hence giving rise to a possible mechanism for particle confinement and energy storage. We argue that any sudden change in the above parameters could allow for abrupt release of large amounts of energy from such innermost orbits.

Innermost circular orbit of binary black holes at the third post-Newtonian approximation

The equations of motion of two point masses have recently been derived at the third post-Newtonian (3PN) approximation of general relativity. From that work we determine the location of the innermost circular orbit (ICO), defined by the minimum of the binary's 3PN energy as a function of the orbital frequency for circular orbits. We find that the post-Newtonian series converges well for equal masses. Spin effects appropriate to corotational black-hole binaries are included. We compare the result with a recent numerical calculation of the ICO in the case of two black holes moving on exactly circular orbits (helical symmetry). The agreement is remarkably good, indicating that the 3PN approximation is adequate to accurately locate the ICO of two black holes with comparable masses. This conclusion is reached with the post-Newtonian expansion expressed in the standard Taylor form, without using resummation techniques such as Pad\'e approximants and/or effective-one-body methods.

Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests

We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems such as spherical dust collapse, stability test of perturbed spherical stars, and preservation of (approximate) equilibrium states of rapidly rotating neutron star and/or corotating binary neutron stars. These test simulations confirm that simulations of coalescing binary neutron stars are feasible in a numerical relativity code. It is illustrated that using our numerical code, simulations of these problems, in particular those of corotating binary neutron stars, can be performed stably and fairly accurately for a couple of dynamical timescales. These numerical results indicate that our formulation for solving the Einstein field equation and hydrodynamic equations are robust and make it possible to perform a realistic simulation of coalescing binary neutron stars for a long time from the innermost circular orbit up to formation of a black hole or neutron star.