Massless Test Particles Research Articles

More realistic planetesimal masses alter Kuiper belt formation models and add stochasticity

Much of the modern Kuiper belt is thought to be the result of Neptune’s migration through a primordial belt of planetesimals, possibly interrupted by an instability amongst the giant planets. While most prior work has employed massless test particles to study this Kuiper belt formation process, we perform simulations here that include the gravitational effects of the primordial planetesimal belt consisting of ∼105 massive bodies. In our simulations, Neptune unlocks from resonance with the other giant planets and begins to migrate outward due to interactions with planetesimals before a planetary orbital instability is triggered, and afterward, residual Neptunian migration completes the formation of the modern Kuiper belt. Compared to past simulations using massless test particles, our present work exhibits a number of notable differences. First, Neptune’s planetary resonance unlocking requires the Neptunian 3:2 mean motion resonance to sweep much of the primordial disk interior to 30 au prior to the giant planet instability. This generates a pre-instability population of planetesimals that is significantly lower in semimajor axis, eccentricity, and inclination than predicted by many prior models, and this effect persists after the instability. Second, direct scattering between Pluto-mass bodies and other small bodies removes material from Neptunian resonances significantly more efficiently than the resonant dropout resulting from small changes in Neptune’s semimajor axis during scattering between Pluto-mass bodies and Neptune. Consequently, the primordial population of Pluto-mass bodies may be as few as ∼200 objects. Finally, our simulation end states display a wide variety of orbital distributions, and straightforward relationships between final bulk Kuiper belt properties and Neptune’s migration or initial planetesimal properties largely elude us. In particular, we find that the rapid, stochastic planetary orbital evolution occurring during the giant planet instability can significantly alter final Kuiper belt properties such as its inclination dispersion and the prominence of resonant populations. This complicates efforts to use modern Kuiper belt properties to confidently constrain early solar system events and conditions, including planetary orbital migration and the primordial Kuiper belt’s characteristics.

Shadow and weak gravitational lensing of a rotating regular black hole in a non-minimally coupled Einstein-Yang-Mills theory in the presence of plasma

The null geodesics of the regular and rotating magnetically charged black hole in a non-minimally coupled Einstein-Yang-Mills theory surrounded by a plasma medium is studied. The effect of magnetic charge and Yang-Mills parameter on the effective potential and radius of photon orbits has investigated. We then study the shadow of a regular and rotating magnetically charged black hole along with the observables in presence of the plasma medium. The presence of plasma medium affects the apparent size of the shadow of a regular rotating black hole in comparison to vacuum case. Variation of shadow radius and deformation parameter with Yang-Mills and plasma parameter has examined. Furthermore, the deflection angle of the massless test particles in weak field approximation around this black hole spacetime in presence of homogeneous plasma medium is also investigated. Finally, we have compared the obtained results with Kerr-Newman and Schwarzschild black hole solutions in general relativity (GR).

The Transformation of Centaurs into Jupiter-family Comets

Centaurs are an ephemeral class of objects that can evolve into Jupiter-family comets (or JFCs) due to gravitational perturbations from the giant planets. In this work, we use numerical integration of massless test particles in the six-body problem (the Sun, four giant planets, and a test particle) to study the transformation of Centaurs into JFCs. We find that Centaurs can transform into JFCs via a rapid, continuous drop in perihelion or aphelion distance to a value below 5.2 au or 7 au, respectively, typically within 5 yr from the start of the drop. We call these JFC perihelion drops and JFC aphelion drops, respectively. These drops are correlated with close approaches to Jupiter. For such perihelion and aphelion drops, the maximum possible fractional change in the associated perihelion or aphelion distance increases with decreasing close-approach distance to Jupiter. A perihelion barrier may exist at 6.3 au. If so, then it must be crossed from above in order for a Centaur to transform into a JFC due to a single close approach to Jupiter. Currently, 93 (or 11%) of the known Centaurs have a perihelion distance, q, below 6.3 au. If the inclination of the orbit of the Centaur to the ecliptic plane is above 10.°2, then orbits with q > 6.3 au and 2 < T J < 3 can exist, where T J is the Tisserand parameter with respect to Jupiter. Small bodies in such orbits could be classified as either Centaurs or JFCs.

Exogenous delivery of water to Mercury

Radar and spacecraft observations show the permanently shadowed regions around Mercury’s North Pole to contain water ice and complex organic material. One possible source of this material are impacts by interplanetary dust particles (IDPs), asteroids, and comets.We have performed numerical simulations of the dynamical evolution of asteroids and comets over the few Myr and checked for their impacts with Mercury. We use the N-body integrator RMVS/Swifter to propagate the Sun and the eight planets from their current positions. We add comets and asteroids to the simulations as massless test particles, based on their current orbital distributions. Asteroid impactors are assigned a probability of being water-rich (C-class) based on the measured distribution of taxonomic types. For comets, we assume a constant water fraction. For IDPs, we use a dynamical meteoroid model to compute the dust flux on Mercury. Relative to previous work on asteroid and comet impacts (Moses et al., 1999), we leverage 20 years of progress in minor body surveys.Immediate post-impact ejection of impactor material into outer space is taken into account as is the migration efficiency of water across Mercury’s surface to the polar cold traps.We find that asteroids deliver ∼1×103kg/yr of water to Mercury, comets deliver ∼1×103kg/yr and IDPs deliver ∼16×103kg/yr within a factor of several. Over a timescale of ∼1Gyr, this is enough to deliver the minimum amount of water required by the radar and MESSENGER observations.While other sources of water on Mercury are not ruled out by our analysis, we show that they are not required to explain the currently available observational lower limits.

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent

We study the dynamics of test particle and stability of circular geodesics in the gravitational field of a non-commutative geometry-inspired Schwarzschild black hole spacetime. The coordinate time Lyapunov exponent ( $$\lambda _{c}$$ ) is crucial to investigate the stability of equatorial circular geodesics of massive and massless test particles. The stability or instability of circular orbits is discussed by analyzing the variation of Lyapunov exponent with radius of these orbits for different values of non-commutative parameter ( $$\alpha $$ ). In the case of null circular orbits, the instability exponent is calculated and presented to discuss the instability of null circular orbits. Further, by relating parameters corresponding to null circular geodesics (i.e., angular frequency and Lyapunov exponent), the quasinormal modes for a massless scalar field perturbation in the eikonal approximation are evaluated and also visualized by relating the real and imaginary parts. The nature of scalar field potential, by varying the non-commutative parameter ( $$\alpha $$ ) and angular momentum of perturbation (l), is also observed and discussed.

Stability analysis of circular orbits around a charged BTZ black hole spacetime in a nonlinear electrodynamics model via Lyapunov exponents

We investigate the existence and stability of both the timelike and null circular orbits for a (2 + 1)-dimensional charged BTZ black hole in Einstein-nonlinear Maxwell gravity with a negative cosmological constant. The stability analysis of orbits is performed to study the possibility of chaos in geodesic motion for a special case of black hole so-called conformally invariant Maxwell spacetime. The computations of both proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] are useful to determine the stability of these circular orbits. We observe the behavior of the ratio [Formula: see text] as a function of radius of circular orbits for the timelike case in view of different values of charge parameter. However, for the null case, we calculate only the coordinate time Lyapunov exponent [Formula: see text] as there is no proper time for massless test particles. More specifically, we further analyze the behavior of the ratio of [Formula: see text] to angular frequency [Formula: see text], so-called instability exponent as a function of charge [Formula: see text] and parameter related to cosmological constant [Formula: see text] for the particular values of other parameters.

Dynamical classification of the asteroids in the Hungaria group: The objects affected by the exterior mean-motion resonance 2:3 with Mars

In this paper, we perform a dynamical study of the population of Hungaria asteroids, close to the exterior 2:3 mean-motion resonance (MMR) with Mars. The aim of this work is to initiate a catalog of asteroids captured in mean-motion resonances (MMRs) with Mars in the Hungaria region, by first identifying the minor bodies affected by the 2:3 MMR. To achieve our goal, we follow the temporal evolution of massless test particles by 2 Myr in the proximity of the 2:3 resonance considering the gravitational influence of all planets of the Solar System. We present a semi-analytical model to calculate the extension of the resonant region for a population with the dynamical characteristics of the Hungaria asteroids. We show that the resonance can disturb the asteroids in two ways: by capture or by indirect influence. We find 22 asteroids captured inside the 2:3 MMR and 89 asteroids which exhibit temporary librations around this resonance. The predictions of our model are in good agreement with the numerical results, which make it useful for the study of other MMRs in this region. For asteroids without determined synthetic proper elements, we use the results of our numerical simulations to calculate the mean orbital elements, which can be used as a first approximation of the proper elements.

Cylindrically symmetric unimodular f(R) black holes

In this paper, we examine massless scalar field by using unimodular [Formula: see text] theory. It is taken into account unimodular and cylindrically symmetric spacetime which provides convenience in researching black hole. The field equations in unimodular [Formula: see text] theory for given spacetime with massless scalar field and additional Bianchi identities are solved. Cylindrically symmetric anti-de Sitter (AdS)–Schwarzschild-like and AdS–Reissner–Nordström-like black hole spacetimes are achieved. Equations of motion are derived by using Hamiltonian. Orbits of massless test particles are depicted. Obtained line element asymptotically converges to dS/AdS spacetime. Weak and strong energy conditions of the massless scalar field are obtained with Raychaudhuri equations in unimodular [Formula: see text] theory. Also, stiff fluid interpretation of scalar field is reviewed.

The effects of ΛCDM dark matter substructure on the orbital evolution of star clusters

ABSTRACT We present a comprehensive study on how perturbations due to a distribution of Lambda cold dark matter (ΛCDM) dark matter subhalos can lead to star clusters deviating from their orbits. Through a large suite of massless test particle simulations, we find that (i) subhalos with masses less than 108 M⊙ negligibly affect test particle orbits, (ii) perturbations lead to orbital deviations only in environments with substructure fractions $f_{\mathrm{ sub}} \ge 1{{\ \rm per\ cent}}$, (iii) perturbations from denser subhalos produce larger orbital deviations, and (iv) subhalo perturbations that are strong relative to the background tidal field lead to larger orbital deviations. To predict how the variation in test particle orbital energy σe(t) increases with time, we test the applicability of theory derived from single-mass subhalo populations to populations where subhalos have a mass spectrum. We find σe(t) can be predicted for test particle evolution within a mass spectrum of subhalos by assuming subhalos all have masses equal to the mean subhalo mass and by using the local mean subhalo separation to estimate the change in test particle velocities due to subhalo interactions. Furthermore, the orbital distance variation at an orbital distance r can be calculated via $\sigma _r=2.98 \times 10^{-5} \pm 8 \times 10^{-8} (\rm kpc^{-1} km^{-2} s^{2}) \times r \times \sigma _e$ with a dispersion about the line of best-fitting equalling 0.08 kpc. Finally, we conclude that clusters that orbit within 100 kpc of Milky Way-like galaxies experience a change no greater than $2{{\ \rm per\ cent}}$ in their dissolution times.

Analytical solutions of the geodesic equation in the space-time of a black hole surrounded by perfect fluid in Rastall theory

In this paper, we investigate the geodesic motion of massive and massless test particles in the vicinity of a black hole space-time surrounded by perfect fluid (quintessence, dust, radiation, cosmological constant and phantom) in Rastall theory. We obtain the full set of analytical solutions of the geodesic equation of motion in the space-time of this black hole. For all cases of perfect fluid, we consider some different values of Rastall coupling constant $k\lambda$ so that the equations of motion have integer powers of $\tilde{r}$ and also can be solved analytically. These analytical solutions are presented in the form of elliptic and also hyperelliptic functions. In addition, using obtained analytical solution and also figures of effective potential and $L-E^2$ diagrams, we plot some examples of possibles orbits. moreover we use of the angular momentum, conserved energy, electrical charge and also Rastall parameter, to classify the different types of the possible gained orbits. Moreover, we show that when Rastall field structure constant becomes zero ($N=0$) our results are consistent with the analysis of a Reissner-Nordstr\"om black hole, however when both Rastall geometric parameter and electric charge vanish $(N=Q=0)$, the metric and results are same as analysis of a Schwarzschild black hole.

Deflection of light around a rotating BTZ black hole

We present a detailed study of gravitational lensing around a rotating Bañados–Teitelboim–Zanelli (BTZ) black hole in (2 + 1)-dimensional gravity. The study of orbits for massless test particle around this BH spacetime is performed to describe the nature of cosmological constant in lower dimensions. We study the effect of cosmological constant on the photon orbit in view of other critical parameters. The bending angle of light is studied in view of different values of cosmological constant for direct and retrograde motion of test particles. It is being observed that the bending angle slightly decreases as the value of cosmological constant increases in the negative region.

A New Formulation of a Hénon–Heiles Potential with Additional Singular Gravitational Terms

We examine the orbital dynamics in a new Hénon–Heiles system with an additional gravitational potential, by classifying sets of starting conditions of trajectories. Specifically, we obtain the results on how the total orbital energy along with the transition parameter influence the overall dynamics of the massless test particle, as well as the respective time of escape/collision. By using modern diagrams with color codes we manage to present the different types of basins of the system. We show that the character of the orbits is highly dependent on the energy and the transition parameter.

Stability in the most external region of the Oort Cloud: evolution of the ejected comets

ABSTRACTIn this paper, we present a study of the dynamical effects of the Galaxy on the external region of the Oort Cloud. The aims of this paper are: (i) to determine an outer limit for the Oort Cloud; and (ii) to analyse the dynamical behaviour of the most external objects of the Oort Cloud and how they are ejected from the Solar system. To achieve these aims, we follow the temporal evolution of massless test particles in the Galactic environment of the solar neighbourhood. We show that the effect of the perturbations from the Galactic tide in the particles is similar to that found for the evolution of the population of wide binary stars. Moreover, in the Oort Cloud, we find a dynamical structure around 105 au conformed by objects unbound from the Sun. This structure allows us to define a transition region of stability and an outer boundary for the Oort Cloud, and it is also in agreement with previous results about the disruption of wide binary stars.

Orbit classification in the Copenhagen problem with oblate primaries

AbstractThis article aims to numerically investigate the orbital dynamics of the planar circular‐restricted three‐body problem, where the two primary bodies have equal masses and an oblate spheroid shape. By numerically integrating several large sets of initial conditions of both retrograde and prograde orbits, we classify them into three main categories: (a) bounded (regular or chaotic), (b) escaping, and (c) collision orbits. We reveal the motion of the test particle by presenting color‐coded diagrams, where the initial conditions are mapped to the orbit type and studied as a function of the total orbital energy (or equivalently of the Jacobi constant) as well as of the oblateness coefficient. Our numerical results are compared with related previous ones, corresponding to the classical version of the planar‐restricted three‐body problem. The presented outcomes have practical physical applications as they can be used for modeling the motion of a massless test particle in the gravitational field of a binary system of two oblate exoplanets.

Predicting multiple planet stability and habitable zone companions in the TESS era

Abstract We present an approach that is able to both rapidly assess the dynamical stability of multiple planet systems, and determine whether an exoplanet system would be capable of hosting a dynamically stable Earth-mass companion in its habitable zone (HZ). We conduct a suite of numerical simulations using a swarm of massless test particles (TPs) in the vicinity of the orbit of a massive planet, in order to develop a predictive tool which can be used to achieve these desired outcomes. In this work, we outline both the numerical methods we used to develop the tool, and demonstrate its use. We find that the TPs survive in systems either because they are unperturbed due to being so far removed from the massive planet, or due to being trapped in stable mean-motion resonant orbits with the massive planet. The resulting unexcited TP swarm produces a unique signature in (a, e) space that represents the stable regions within the system. We are able to scale and translate this stability signature, and combine several together in order to conservatively assess the dynamical stability of newly discovered multiple planet systems. We also assess the stability of a system’s HZ and determine whether an Earth-mass companion could remain on a stable orbit, without the need for exhaustive numerical simulations.

Excitation and Depletion of the Asteroid Belt in the Early Instability Scenario

Abstract Containing only a few percentages of the mass of the moon, the current asteroid belt is around three to four orders of magnitude smaller than its primordial mass inferred from disk models. Yet dynamical studies have shown that the asteroid belt could not have been depleted by more than about an order of magnitude over the past ∼4 Gyr. The remainder of the mass loss must have taken place during an earlier phase of the solar system’s evolution. An orbital instability in the outer solar system occurring during the process of terrestrial planet formation can reproduce the broad characteristics of the inner solar system. Here, we test the viability of this model within the constraints of the main belt’s low present-day mass and orbital structure. Although previous studies modeled asteroids as massless test particles because of limited computing power, our work uses graphics processing unit acceleration to model a fully self-gravitating asteroid belt. We find that depletion in the main belt is related to the giant planets’ exact evolution within the orbital instability. Simulations that produce the closest matches to the giant planets’ current orbits deplete the main belt by two to three orders of magnitude. These simulated asteroid belts are also good matches to the actual asteroid belt in terms of their radial mixing and broad orbital structure.

A stringy test of the Scalar Weak Gravity Conjecture

We prove a version of the Weak Gravity Conjecture for 6d F-theory or heterotic string compactifications with 8 supercharges. This sharpens our previous analysis by including massless scalar fields. The latter are known to modify the Weak Gravity Conjecture bound in two a priori independent ways: First, the extremality condition of a charged black hole is modified, and second, the test particles required to satisfy the Weak Gravity Conjecture are subject to additional Yukawa type interactions. We argue on general grounds that at weak coupling, the two types of effects are equivalent for a tower of asymptotically massless charged test particles predicted by the Swampland Distance Conjecture.We then specialize to F-theory compactified on elliptic Calabi–Yau three-folds and prove that the precise numerical bound on the charge-to-mass ratio is satisfied at weak coupling. This amounts to an intriguing coincidence of two a priori different notions of extremality, namely one based on the balance of gauge, gravitational and scalar forces for extremal (non-BPS) black holes, and the other encoded in the modular properties of certain Jacobi forms. In the presence of multiple abelian gauge group factors, the elliptic genus counting these states is a lattice quasi-Jacobi form of higher rank, and we exemplify this in a model with two abelian gauge group factors.

Particle Motion around Charged Black Holes in Generalized Dilaton-Axion Gravity

The behaviour of massive and massless test particles around asymptotically flat and spherically symmetric, charged black holes in the context of generalized dilaton-axion gravity in four dimensions is studied. All the possible motions are investigated by calculating and plotting the corresponding effective potential for the massless and massive particles as well. Further, the motion of massive (charged or uncharged) test particles in the gravitational field of charged black holes in generalized dilaton-axion gravity for the cases of static and nonstatic equilibrium is investigated by applying the Hamilton-Jacobi approach.

Strong lensing and observables around 5D Myers–Perry black hole spacetime

We study the motion of massless test particles in a five-dimensional (5D) Myers–Perry black hole spacetime with two-spin parameters. The behavior of the effective potential in view of different values of black hole parameters is discussed in the equatorial plane. The frequency shift of photons is calculated which is found to depend on the spin parameter of black hole and the observed redshift is discussed accordingly. The deflection angle and the strong deflection limit coefficients are also calculated and their behavior with the spin parameters is analyzed in detail. It is observed that the behaviors of both deflection angle and strong field coefficient differs from Kerr black hole spacetime in four dimensions in General Relativity (GR), which is mainly due to the presence of two-spin parameters in higher dimension.

Null geodesics and red–blue shifts of photons emitted from geodesic particles around a noncommutative black hole space–time

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space–time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.