Unbound Orbits Research Articles

Exploring the Origin of Stars on Bound and Unbound Orbits Causing Tidal Disruption Events

Tidal disruption events (TDEs) provide a clue to the properties of a central supermassive black hole (SMBH) and an accretion disk around it, and to the stellar density and velocity distributions in the nuclear star cluster surrounding the SMBH. Deviations of TDE light curves from the standard occurring at a parabolic encounter with the SMBH depend on whether the stellar orbit is hyperbolic or eccentric and the penetration factor (β, the tidal disruption radius to the orbital pericenter ratio). We study the orbital parameters of bound and unbound stars being tidally disrupted by comparison of direct N-body simulation data with an analytical model. Starting from the classical steady-state Fokker–Planck model of Cohn & Kulsrud, we develop an analytical model of the number density distribution of those stars as a function of orbital eccentricity (e) and β. To do so, fittings of the density and velocity distribution of the nuclear star cluster and of the energy distribution of tidally disrupted stars are required and obtained from N-body data. We confirm that most of the stars causing TDEs in a spherical nuclear star cluster originate from the full loss-cone region of phase space, derive analytical boundaries in eccentricity-β space, and find them confirmed by N-body data. Since our limiting eccentricities are much smaller than critical eccentricities for full accretion or the full escape of stellar debris, we conclude that those stars are only very marginally eccentric or hyperbolic, close to parabolic.

Dynamics investigation and chaos-based application of a novel no-equilibrium system with coexisting hidden attractors

This work presents a novel three-dimensional system with multiple types of coexisting attractors (including chaotic, periodic, quasi-periodic, and unbound divergent orbit) that are categorized as hidden attractors and investigates its dynamics via the Lyapunov exponent spectrum, phase diagrams, and basins of attraction. The mechanism of the emergence of chaos is explored through numerical simulation. Under some conditions, the periodic orbits embedded in the new system without equilibria are studied using the variational method, and effective symbolic coding with four letters is successfully established to classify all short cycles. The symbols proposed by the method are highly consistent with the calculated results. Furthermore, the analogous circuit implementation is executed to demonstrate the flexibility and validity of the new system that possesses coexisting attractors. Finally, chaos-based applications of the new system, including synchronization, offset boosting control, and image encryption, are presented to show system’s feasibility.

Oort cloud perturbations as a source of hyperbolic Earth impactors

The observation of interstellar objects 1I/’Oumuamua and 2I/Borisov suggests the existence of a larger population of smaller projectiles that impact our planet with unbound orbits. We analyze an asteroidal grazing meteor (FH1) recorded by the Finnish Fireball Network on October 23, 2022. FH1 displayed a likely hyperbolic orbit lying on the ecliptic plane with an estimated velocity excess of ∼0.7 kms−1 at impact. FH1 may either be an interstellar object, indicating a high-strength bias in this population, or an Oort cloud object, which would reinforce migration-based solar system models. Furthermore, under the calculated uncertainties, FH1 could potentially be associated with the passage of Scholz’s binary star system. Statistical evaluation of uncertainties in the CNEOS database and study of its hyperbolic fireballs reveals an anisotropic geocentric radiant distribution and low orbital inclinations, challenging the assumption of a randomly incoming interstellar population. Orbital integrations suggest that the event on March 9, 2017 (IM2) from CNEOS may have experienced gravitational perturbation during the Scholz fly-by, contingent upon velocity overestimation within the expected range. These findings suggest that apparent interstellar meteors may, in fact, be the result of accelerated meteoroid impacts caused by close encounters with massive objects within or passing through our solar system.

Extending Gibbons-Werner method to bound orbits of massive particles

The Gibbons-Werner method for the gravitational deflection angle of unbound particles in static spherically symmetric spacetimes is based on the Jacobi metric and Gauss-Bonnet theorem. When it is extended to bound massive particles, there exist two difficulties: (a) Bound orbits may overlap with themselves azimuthally. To extend the definition of deflection angle for unbound orbits to bound orbits, we divide the bound orbit into multiple segments such that each segment does not overlap with itself azimuthally and can be regarded as an unbound orbit. (b) The infinite region constructed for unbound orbits in the Gibbons-Werner method is invalid for bound orbits, since the Jacobi metric of bound massive particles is singular at the far region. To construct a suitable region for bound orbits, we adopt the generalized Gibbons-Werner method proposed in our last work [Huang and Cao, Phys. Rev. D 106, 104043 (2022)], so that the unphysical region in Jacobi space is avoided. What is more, taking the Schwarzschild spacetime as an example, we show the details of the calculation and obtain an analytical expression of the deflection angle between two arbitrary points on the orbit.

Partial Tidal Disruptions of Main-sequence Stars by Intermediate-mass Black Holes

We study close encounters of a 1 M ⊙ middle-age main-sequence star (modeled using MESA) with massive black holes through hydrodynamic simulations, and explore in particular the dependence of the outcomes on the black hole mass. We consider here black holes in the intermediate-mass range, M BH = 100–104 M ⊙. Possible outcomes vary from a small tidal perturbation for weak encounters all the way to partial or full disruption for stronger encounters. We find that stronger encounters lead to increased mass loss at the first pericenter passage, in many cases ejecting the partially disrupted star on an unbound orbit. For encounters that initially produce a bound system, with only partial stripping of the star, the fraction of mass stripped from the star increases with each subsequent pericenter passage and a stellar remnant of finite mass is ultimately ejected in all cases. The critical penetration depth that separates bound and unbound remnants has a dependence on the black hole mass when M BH ≲ 103 M ⊙. We also find that the number of successive close passages before ejection decreases as we go from the stellar-mass black hole to the intermediate-mass black hole regime. For instance, after an initial encounter right at the classical tidal disruption limit, a 1 M ⊙ star undergoes 16 (5) pericenter passages before ejection from a 10 M ⊙ (100 M ⊙) black hole. Observations of periodic flares from these repeated close passages could in principle indicate signatures of a partial tidal disruption event.

Exciting spiral arms in protoplanetary discs from flybys

ABSTRACT Spiral arms are observed in numerous protoplanetary discs. These spiral arms can be excited by companions, either on bound or unbound orbits. We simulate a scenario where an unbound perturber, i.e. a flyby, excites spiral arms during a periastron passage. We run three-dimensional hydrodynamical simulations of a parabolic flyby encountering a gaseous protoplanetary disc. The perturber mass ranges from $10\, \rm M_J$ to $1\, \rm {\rm M}_{\odot }$. The perturber excites a two-armed spiral structure, with a more prominent spiral feature for higher mass perturbers. The two arms evolve over time, eventually winding up, consistent with previous works. We focus on analysing the pattern speed and pitch angle of these spirals during the whole process. The initial pattern speed of the two arms are close to the angular velocity of the perturber at periastron, and then it decreases over time. The pitch angle also decreases over time as the spiral winds up. The spirals disappear after several local orbital times. An inclined prograde orbit flyby induces similar disc substructures as a coplanar flyby. A solar-mass flyby event causes increased eccentricity growth in the protoplanetary disc, leading to an eccentric disc structure which dampens over time. The spirals’ morphology and the disc eccentricity can be used to search for potential unbound stars or planets around discs where a flyby is suspected. Future disc observations at high resolution and dedicated surveys will help to constrain the frequency of such stellar encounters in nearby star-forming regions.

Testing the Galaxy-collision-induced Formation Scenario for the Trail of Dark-matter-deficient Galaxies with the Susceptibility of Globular Clusters to the Tidal Force

It has been suggested that a trail of diffuse galaxies, including two dark-matter-deficient galaxies (DMDGs), in the vicinity of NGC 1052 formed because of a high-speed collision between two gas-rich dwarf galaxies, one bound to NGC 1052 and the other one on an unbound orbit. The collision compresses the gas reservoirs of the colliding galaxies, which in turn triggers a burst of star formation. In contrast, the dark matter and preexisting stars in the progenitor galaxies pass through it. Since the high pressures in the compressed gas are conducive to the formation of massive globular clusters (GCs), this scenario can explain the formation of DMDGs with large populations of massive GCs, consistent with the observations of NGC 1052-DF2 (DF2) and NGC 1052-DF4. A potential difficulty with this “mini bullet cluster” scenario is that the observed spatial distributions of GCs in DMDGs are extended. GCs experience dynamical friction causing their orbits to decay with time. Consequently, their distribution at formation should have been even more extended than that observed at present. Using a semianalytic model, we show that the observed positions and velocities of the GCs in DF2 imply that they must have formed at a radial distance of 5–10 kpc from the center of DF2. However, as we demonstrate, the scenario is difficult to reconcile with the fact that the strong tidal forces from NGC 1052 strip the extendedly distributed GCs from DF2, requiring 33–59 massive GCs to form at the collision to explain observations.

A Meteor of Apparent Interstellar Origin in the CNEOS Fireball Catalog

The earliest confirmed interstellar object, ‘Oumuamua, was discovered in the solar system by Pan-STARRS in 2017, allowing for a calibration of the abundance of interstellar objects of its size ∼100 m. This was followed by the discovery of Borisov, which allowed for a similar calibration of its size ∼0.4–1 km. One would expect a much higher abundance of significantly smaller interstellar objects, with some of them colliding with Earth frequently enough to be noticeable. Based on the CNEOS catalog of bolide events, we identify the ∼0.45 m meteor detected at 2014 January 8 17:05:34 UTC as originating from an unbound hyperbolic orbit. The U.S. Department of Defense has released an official letter stating that “the velocity estimate reported to NASA is sufficiently accurate to indicate an interstellar trajectory,” which we rely on here as confirmation of the object’s interstellar trajectory. Based on the data provided by CNEOS, we infer that the meteor had an asymptotic speed of v ∞ ∼ 42.1 ± 5.5 km s−1 outside of the solar system. Note that v ∞ here refers to the velocity of the meteor outside the solar system, not the velocity of the meteor outside the atmosphere. Its origin is approximately toward R.A. 49.°4 ± 4.°1 and decl. 11.°2 ± 1.°8, implying that its initial velocity vector was 58 ± 6 km s−1 away from the velocity of the local standard of rest (LSR).

Study of null and time-like geodesics in the exterior of a Schwarzschild black hole with quintessence and cloud of strings

Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has been done in Mustafa and Hussain (Eur Phys J C 81:419, 2021). In this paper, we complete the aforementioned study by investigating possible analytical solutions to the equations of motion for other types of bound orbits, beside taking into account the cases of unbound orbits. This requires an extensive study of the corresponding effective potentials that categorize the test particle motion. We follow the standard Lagrangian dynamics to parametrize the radial and angular geodesics and the resultant (hyper-)elliptic integrals of motion are treated accordingly. We also simulate the orbits which correspond to different levels of energy in the effective potentials.

Fate of observers in circular motion

In Newtonian physics or in general relativity, energy dissipation causes observers moving along circular orbits to slowly spiral towards the source of the gravitational field. We show that the loss of energy has the same effect in any theory of gravity respecting the weak equivalence principle, by exhibiting an intimate relation between the energy of a massive test particle and the stability of its orbit. Ultimately, massive particles either plunge, or are driven towards minima of the generalized Newtonian potential, where they become static. In addition, we construct a toy metric which displays an unbound innermost stable circular orbit, allowing particles that reach this orbit to be expelled away.

Spin Dynamics of Moving Bodies in Rotating Black Hole Spacetimes

AbstractThe dynamics of spinning test bodies, moving in rotating black hole (Kerr, Bardeen‐like and Hayward‐like) spacetimes, are investigated. In Kerr spacetime, all the spherical, zoom‐whirl and unbound orbits are considered numerically. Along spherical orbits and for high spin, an amplitude modulation is found in the harmonic evolution of the spin precessional angular velocity, caused by the spin‐curvature coupling. Along the discussed zoom‐whirl and unbound orbits, the test body approaches the center so much that it passes through the ergosphere. Near and inside the ergosphere, the variation of the spin direction can be very rapid. The effects of the spin‐curvature coupling is also investigated. The initial values are chosen such a way, that the body and its spin move in the equatorial plane of the coordinate space and of the comoving frame, respectively. Hence, a clear effect of the spin‐curvature coupling is observed as the orbit and the spin vector leave the equatorial plane. Additional effects in the spin precessional angular velocity and in the evolution of the Boyer–Lindquist coordinate components of the spin vector is also considered. Finally, in case of different regular black holes, the spin‐curvature coupling influences differently the orbit and the spin evolutions.

Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order

Accurate waveform models are crucial for gravitational-wave data analysis, and since spin has a significant effect on the binary dynamics, it is important to improve the spin description in these models. In this paper, we derive the spin-orbit (SO) coupling at the fifth-and-a-half post-Newtonian (5.5PN) order. The method we use splits the conservative dynamics into local and nonlocal-in-time parts, and then relates the local-in-time part to gravitational self-force results by exploiting the simple mass-ratio dependence of the post-Minkowskian expansion of the scattering angle. We calculate the nonlocal contribution to the 5.5PN SO dynamics to eighth order in the small-eccentricity expansion for bound orbits, and to leading order in the large-eccentricity expansion for unbound orbits. For the local contribution, we obtain all of the 5.5PN SO coefficients from first-order self-force results for the redshift and spin-precession invariants, except for one unknown that could be fixed in the future by second-order self-force results. However, by incorporating our 5.5PN results in the effective-one-body formalism and comparing its binding energy to numerical relativity, we find that the remaining unknown has a small effect on the SO dynamics, demonstrating an improvement in accuracy at that order.

Geodesics from classical double copy

We extend the Kerr-Schild double copy to the case of a probe particle moving in the Kerr-Schild background. In particular, we solve Wong's equations for a test color charge in a Coulomb non-Abelian potential ($\sqrt{\text{Schw}}$) and on the equatorial plane for the potential generated by a rotating disk of charge known as the single copy of the Kerr background ($\sqrt{\text{Kerr}}$). The orbits, as the corresponding geodesics on the gravity side, feature elliptic, circular, hyperbolic and plunge behavior for the charged particle. We then find a new double copy map between the conserved charges on the gauge theory side and the gravity side, which enables us to fully recover geodesic equations for Schwarzschild and Kerr. Interestingly, the map works naturally for both bound and unbound orbits.

Introduction of Near to Far Infrared Range Direct Band Gaps in Graphene: A First Principle Insight.

Lack of band gaps hinders application of graphene in the fields like logic, optoelectronics, and sensing despite its various extraordinary properties. In this work, we have done systematic investigations on direct band gap opening in graphene by hydrogenation and fluorination of carbon vacancies using the density functional theory computational approach. We have seen that although a carbon vacancy (void) opens an indirect band gap in graphene, it also creates unwanted mid gap (trap) states, which is attributed to unbound orbitals of the nearest unsaturated carbon atoms at the vacant site. The unsaturated carbon atoms and corresponding trap states can degrade the stability of graphene and create band gaps particularly for large size vacancies. We have proposed that hydrogenation or fluorination of the unsaturated carbon atoms near the vacant site helps in disappearance of the trap states while contributing to promising direct band gaps in graphene. The opened band gap is tunable in the infrared regime and persists for different sizes and densities of hydrogenated or fluorinated patterns. In addition, we have also found that the proposed approach is thermodynamically favorable as well as stable. This keeps the planar nature of the graphene monolayer, despite creation of defects and subsequent functionalization, thereby making it useful for 2D material-based electronics, optoelectronics, and sensing applications.

Spherical orbits around a Kerr black hole

A special class of orbits known to exist around a Kerr black hole are spherical orbits -- orbits with constant coordinate radii that are not necessarily confined to the equatorial plane. Spherical time-like orbits were first studied by Wilkins almost 50 years ago. In the present paper, we perform a systematic and thorough study of these orbits, encompassing and extending previous works on them. We first present simplified forms for the parameters of these orbits. The parameter space of these orbits is then analysed in detail; in particular, we delineate the boundaries between stable and unstable orbits, bound and unbound orbits, and prograde and retrograde orbits. Finally, we provide analytic solutions of the geodesic equations, and illustrate a few representative examples of these orbits.

Near‐horizon structure of escape zones of electrically charged particles around weakly magnetized rotating black hole: Case of oblique magnetosphere

AbstractWe study the effects of large‐scale magnetic fields on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on geodesic orbits in the equatorial plane become ionized, and hence they are destabilized by the charging process. Fraction of charged particles are then accelerated out of the equatorial plane and then follow jet‐like trajectories with relativistic velocities. We explore nonaxisymmetric systems in which the magnetic field is inclined with respect to the black hole spin. We study the system numerically in order to locate the zones of escaping trajectories and compute the terminal escape velocity. By breaking the axial symmetry, we notice increasing fraction of unbound orbits which allow for acceleration to ultrarelativistic velocities.

Tidal Disruption Flares from Stars on Marginally Bound and Unbound Orbits

Abstract We study the mass fallback rate of tidally disrupted stars on marginally bound and unbound orbits around a supermassive black hole (SMBH) by performing three-dimensional smoothed particle hydrodynamic simulations with three key parameters. The star is modeled by a polytrope with two different indexes (n = 1.5 and 3). The stellar orbital properties are characterized by five orbital eccentricities ranging from e = 0.98 to 1.02, and five different penetration factors ranging from β = 1 to 3, where β represents the ratio of the tidal disruption to pericenter distance radii. We derive analytic formulae for the mass fallback rate as a function of the stellar density profile, orbital eccentricity, and penetration factor. Moreover, two critical eccentricities to classify tidal disruption events (TDEs) into five different types: eccentric ( ), marginally eccentric ( ), purely parabolic (e = 1), marginally hyperbolic ( ), and hyperbolic ( ) TDEs, are reevaluated as and , where q is the ratio of the SMBH to stellar masses and 0 < k ≲ 2. We find the asymptotic slope of the mass fallback rate varies with the TDE type. The asymptotic slope approaches −5/3 for the parabolic TDEs, is steeper for the marginally eccentric TDEs, and is flatter for the marginally hyperbolic TDEs. For the marginally eccentric TDEs, the peak of mass fallback rates can be about one order of magnitude larger than the parabolic TDE case. For marginally hyperbolic TDEs, the mass fallback rates can be much lower than the Eddington accretion rate, which can lead to the formation of a radiatively inefficient accretion flow, while hyperbolic TDEs lead to failed TDEs. Marginally unbound TDEs could be an origin of a very low-density gas disk around a dormant SMBH.

Ab Initio Nonadiabatic Molecular Dynamics with Hole-Hole Tamm-Dancoff Approximated Density Functional Theory.

The study of photoinduced dynamics in chemical systems necessitates accurate and computationally efficient electronic structure methods, especially as the systems of interest grow larger. The linear response hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory method was recently proposed to satisfy such demands. The N-electron electronic states are obtained by means of double annihilations on a doubly anionic (N + 2)-electron reference state, allowing for the ground and excited states to be formed on the same footing and thus enabling the correct description of conical intersections. Dynamic electron correlation effects are incorporated by means of the exchange-correlation functional. The accuracy afforded by the simultaneous treatment of static and dynamic correlation in addition to the relatively low computational cost, comparable to that of time-dependent density functional theory (TDDFT), makes it a promising ab initio electronic structure method for on-the-fly generation of potential energy surfaces in nonadiabatic dynamics simulations of photochemical systems, particularly those for which the nπ* and ππ* electronic excitations are most relevant. Here, we apply the hh-TDA method to nonadiabatic dynamics simulations of prototypical photochemical processes. First, we demonstrate the ability of hh-TDA to adequately describe conical intersection geometries. We next examine its ability to describe the ultrafast excited state dynamics of photoexcited ethylene through an ab initio multiple spawning (AIMS) dynamics simulation. Finally, we present an alternative variant of the hh-TDA method, which uses orbitals from a fractional occupation number Kohn-Sham (FON-KS) calculation applied to an ensemble with N-electrons. The resulting method is termed floating occupation molecular orbital hh-TDA (FOMO-hh-TDA). This scheme allows us to combine hh-TDA with global hybrid functionals and allows us to avoid unbound valence orbitals that may result from an (N + 2)-electron self-consistent field (SCF) procedure. FOMO-hh-TDA-BHLYP faithfully reproduces the nonadiabatic dynamics of trans-azobenzene (TAB) and is used to characterize the excited state decay pathways from the first (nπ*) excited state.

Gravitational Spin-Orbit Coupling through Third-Subleading Post-Newtonian Order: From First-Order Self-Force to Arbitrary Mass Ratios.

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.

Evidence that 1I/2017 U1 (‘Oumuamua) was Composed of Molecular Hydrogen Ice

Abstract ‘Oumuamua (I1 2017) was the first macroscopic (l ∼ 100 m) body observed to traverse the inner solar system on an unbound hyperbolic orbit. Its light curve displayed strong periodic variation, and it showed no hint of a coma or emission from molecular outgassing. Astrometric measurements indicate that ‘Oumuamua experienced nongravitational acceleration on its outbound trajectory, but energy balance arguments indicate this acceleration is inconsistent with a water ice sublimation-driven jet of the type exhibited by solar system comets. We show that all of ‘Oumaumua’s observed properties can be explained if it contained a significant fraction of molecular hydrogen (H2) ice. H2 sublimation at a rate proportional to the incident solar flux generates a surface-covering jet that reproduces the observed acceleration. Mass wasting from sublimation leads to monotonic increase in the body axis ratio, explaining ‘Oumuamua’s shape. Back-tracing ‘Oumuamua’s trajectory through the solar system permits calculation of its mass and aspect ratio prior to encountering the Sun. We show that H2-rich bodies plausibly form in the coldest dense cores of giant molecular clouds, where number densities are of order n ∼ 105, and temperatures approach the T = 3 K background. Post-formation exposure to galactic cosmic rays implies a τ ∼ 100 Myr age, explaining the kinematics of ‘Oumuamua’s inbound trajectory.