Parabolic Orbits Research Articles

Aerographite: a Candidate Material for Interstellar Photon Sailing

Aerographite has been suggested in a recent paper as a possible candidate for interstellar photon sailing. This paper begins by presenting known properties of this extremely low density, light absorptive, material. After a review of analytical tools, a number of possible interstellar missions are then considered. The first confirms that a thin-film Sun-accelerated probe deployed at the 0.4-AU perihelion of an initially parabolic solar orbit could reach Proxima/Alpha Centauri after a voyage duration of about two centuries. The next case examined is a thin-film probe accelerated to about 0.033 c by an in-space laser array. Finally, it is shown that a combined aerographite-graphene hollow-body solar-photon sail may have significant advantages in accelerating a generation ship to an interstellar cruise velocity in excess of 900 km/s. Some of the unknowns regarding this substance that must be addressed before this material can be applied to interstellar sail application, including the closest feasible perihelion distance and aerographite performance in the space environment, are also discussed. Keywords: Aerographite, Graphene, Photon Sailing, Interstellar Travel

Eddington Envelopes: The Fate of Stars on Parabolic Orbits Tidally Disrupted by Supermassive Black Holes

Abstract Stars falling too close to massive black holes in the centers of galaxies can be torn apart by the strong tidal forces. Simulating the subsequent feeding of the black hole with disrupted material has proved challenging because of the range of timescales involved. Here we report a set of simulations that capture the relativistic disruption of the star, followed by 1 yr of evolution of the returning debris stream. These reveal the formation of an expanding asymmetric bubble of material extending to hundreds of au—an outflowing Eddington envelope with an optically thick inner region. Such outflows have been hypothesized as the reprocessing layer needed to explain optical/UV emission in tidal disruption events but never produced self-consistently in a simulation. Our model broadly matches the observed light curves with low temperatures, faint luminosities, and line widths of 10,000–20,000 km s−1.

Underluminous tidal disruption events

Abstract We have evidence of X-ray flares in several galaxies consistent with a a star being tidally disrupted by a supermassive black hole (MBH). If the star starts on a nearly parabolic orbit relative to the MBH, one can derive that the fallback rate follows a t−5/3 decay. Depending on the penetration factor, β, a star will be torn apart differently, and relativistic effects play a role. We have modified the standard version of the smoothed-particle hydrodynamics (SPH) code Gadget to include a relativistic treatment of the gravitational forces between the gas particles of a main-sequence (MS) star and a MBH. We include non-spinning post-Newtonian corrections to incorpore the periapsis shift and the spin-orbit coupling up to next-to-lowest order. We find that tidal disruptions around MBHs in the relativistic cases are underluminous for values starting at β≧2.25; i.e. the fallback curves produced in the relativistic cases are progressively lower compared to the Newtonian simulations as the penetration parameter increases. While the Newtonian cases display a total disruption, we find that all relativistic counterparts feature a survival core for penetration factors going to values as high as 12.05. We perform a additional dynamical numerical study which shows that the geodesics of the elements in the star converge at periapsis. We confirm these findings with an analytical study of the geodesic separation equation. The luminosity of TDEs must be lower than predicted theoretically due to the fact that the star will partially survive when relativistic effects are taken into account. A survival core should consistently emerge from any TDE with β≧2.25.

The Dynamics and Gravitational-wave Signal of a Binary Flying Closely by a Kerr Supermassive Black Hole

Recent astrophysical models predict that stellar-mass binary black holes (BBHs) could form and coalesce within a few gravitational radii of a supermassive black hole (SMBH). Detecting the gravitational waves (GWs) from such systems requires numerical tools that can track the dynamics of the binaries while capturing all the essential relativistic effects. This work develops upon our earlier study of a BBH moving along a circular orbit in the equatorial plane of a Kerr SMBH. Here we modify the numerical method to simulate a BBH falling toward the SMBH along a parabolic orbit of arbitrary inclination with respect to the equator. By tracking the evolution in a frame freely falling alongside the binary, we find that the eccentricity of the BBH is more easily excited than it is in the previous equatorial case, and that the cause is the asymmetry of the tidal tensor imposed on the binary when the binary moves out of the equatorial plane. Since the eccentricity reaches maximum around the same time as the BBH becomes the closest to the SMBH, multiband GW bursts could be produced that are simultaneously detectable by space- and ground-based detectors. We show that the effective spin parameters of such GW events also undergo significant variation due to the rapid reorientation of the inner BBHs during their interaction with SMBHs. These results demonstrate the richness of three-body dynamics in the region of strong gravity, and highlight the necessity of building new numerical tools to simulate such systems.

Fallback Rates in Partial Tidal Disruptions of White Dwarfs by Intermediate-mass Black Holes

The fallback rate of debris after the partial tidal disruption of a star by an intermediate-mass black hole (IMBH) might provide important signatures of such black holes rather than supermassive ones. Here using smoothed particle hydrodynamics methods, we provide a comprehensive numerical analysis of this phenomenon. We perform numerical simulations of single partial tidal disruptions of solar-mass white dwarfs in parabolic orbits, with a nonspinning 103 M ⊙ IMBH for various values of the impact parameter, and determine the core mass fractions and fallback rates of debris into the IMBH. For supermassive black holes, in full disruption processes, it is known that the late-time fallback rate follows a power law t −5/3, whereas for partial disruptions, such a rate has recently been conjectured to saturate at a steeper power law t −9/4, independent of the mass of the remnant core. We show here that for IMBHs, partial disruptions significantly alter this conclusion. That is, the fallback rate at late times does not asymptote to a t −9/4 power law, and this rate is also a strong function of the core mass. We derive a robust formula for the late-time fallback rate as a function of the core mass fraction, which is independent of the mass of the white dwarf, as we verify numerically by varying it.

Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the $$(n+2)$$-Body Problem

Invariant Manifolds of Degenerate Tori and Double Parabolic Orbits to Infinity in the $$(n+2)$$-Body Problem

Gravitational wave peeps from EMRIs and their implication for LISA signal confusion noise

Scattering events around the center of massive galaxies will occasionally toss a stellar-mass compact object into an orbit around the massive black hole (MBH) at the center, beginning an extreme mass ratio inspiral (EMRI). The early stages of such a highly eccentric orbit are not likely to produce detectable gravitational waves (GWs), as the source will only be in a suitable frequency band briefly when it is close to periapsis during each long-period orbit. This repeated burst of emission, firmly in the millihertz band, is the GW peep. While a single peep is not likely to be detectable, if we consider an ensemble of such subthreshold sources, spread across the Universe, together they may produce an unresolvable background noise that could obscure sources otherwise detectable by the Laser Interferometer Space Antenna. Previous studies of the extreme mass ratio signal confusion background focused either on parabolic orbits near the MBH or events closer to merger. We seek to improve this characterization by implementing numerical kludge waveforms that can calculate highly eccentric orbits with relativistic effects. Our focus is on orbits at the point of capture that are farther away from the MBH. Here we present the waveforms and spectra of peeps generated from recent calculations of EMRIs/extreme mass ratio bursts capture parameters and discuss how these can be used to estimate the signal confusion noise generated by such events. We demonstrate the effects of changing the orbital parameters on the resulting spectra as well as showing direct comparisons to parabolic orbits and why the GW ‘peep’ needs to be studied further. The results of this study will be expanded upon in a further paper that aims to provide an update on the EMRI signal confusion noise problem.

Scattered disc dynamics: the mapping approach

ABSTRACT We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericentre of the parabolic orbit. The map shows excellent agreement with direct numerical integrations and elucidates how the dynamics depends on perturber mass and pericentre distance. We also use the map to explore the onset of chaos, statistical descriptions of chaotic transport, and sticking in mean-motion resonances. We discuss implications of our mapping model for the dynamical evolution of the Solar system’s scattered disc and other highly eccentric trans-Neptunian objects.

Analytic Transformation Between Osculating and Mean Elements in the J2 Problem

This work presents an analytical perturbation method to study the dynamics of an orbiting object subject to the term from the gravitational potential of the main celestial body. In particular, this paper focuses on the generation of the analytical transformations between osculating and mean elements under this perturbation. This is done using a power series expansion in the perturbation constant on all the variables of the system, and a time regularization based on the argument of latitude of the orbit. This enables the generation of analytic approximate solutions without the need to control the perturbed frequency of the system. The resultant approximations provide the osculating behavior of the problem as well as the transformations between osculating and mean elements for orbits at any eccentricity, including near-circular, elliptic, parabolic, and hyperbolic orbits. Several examples of application are presented to show the accuracy of the perturbation approach and their related transformations.

The Mass Fallback Rate of the Debris in Relativistic Stellar Tidal Disruption Events

Highly energetic stellar tidal disruption events (TDEs) provide a way to study black hole characteristics and their environment. We simulate TDEs with the Phantom code in a general relativistic and Newtonian description of a supermassive black hole’s gravity. Stars, which are placed in parabolic orbits with different β parameters, are constructed with the stellar evolution code MESA and therefore have realistic stellar density profiles. We study the mass fallback rate of the debris and its dependence on β, stellar mass, and age as well as the supermassive black hole’s spin and the choice of the gravity description. We calculate the peak value , time to peak t peak, duration of the super-Eddington phase t Edd, time during which , early rise-time τ rise, and late-time slope n ∞. We recover the trends of , t peak, τ rise, and n ∞ with β, stellar mass, and age which were obtained in previous studies. We find that t Edd, at a fixed β, scales primarily with the stellar mass, while scales with the compactness of stars. The effect of the SMBH’s rotation depends on the orientation of its rotational axis relative to the direction of the stellar motion in the initial orbit. Encounters in prograde orbits result in narrower curves with higher , while the opposite occurs for retrograde orbits. We find that disruptions, at the same pericenter distance, are stronger in a relativistic tidal field than in a Newtonian one. Therefore, relativistic curves have higher , and shorter t peak and t Edd.

Tidal Disruption Events from Eccentric Orbits and Lessons Learned from the Noteworthy ASASSN-14ko

Stars grazing supermassive black holes (SMBHs) on bound orbits may survive tidal disruption, causing periodic flares. Inspired by the recent discovery of the periodic nuclear transient ASASSN-14ko, a promising candidate for a repeating tidal disruption event (TDE), we study the tidal deformation of stars approaching SMBHs on eccentric orbits. With both analytical and hydrodynamic methods, we show the overall tidal deformation of a star is similar to that in a parabolic orbit provided that the eccentricity is above a critical value. This allows one to make use of existing simulation libraries from parabolic encounters to calculate the mass fallback rate in eccentric TDEs. We find the flare structures of eccentric TDEs show a complicated dependence on both the SMBH mass and the orbital period. For stars orbiting SMBHs with relatively short periods, we predict significantly shorter-lived duration flares than those in parabolic TDEs, which can be used to predict repeating events if the mass of the SMBH can be independently measured. Using an adiabatic mass-loss model, we study the flare evolution over multiple passages, and show the evolved stars can survive many more passages than main-sequence stars. We apply this theoretical framework to the repeating TDE candidate ASASSN-14ko and suggest that its recurrent flares originate from a moderately massive (M ≳ 1 M ⊙), extended (likely ≈10 R ⊙), evolved star on a grazing, bound orbit around the SMBH. Future hydrodynamic simulations of multiple tidal interactions will enable realistic models on the individual flare structure and the evolution over multiple flares.

Rapid capture trajectories from parabolic orbit with modulated radial thrust

The aim of this paper is to analyze the performance of a radially-accelerated spacecraft in a capture mission scenario, in which a space vehicle transfers from a parabolic approaching trajectory of assigned semilatus rectum to a target circular orbit around a generic celestial body. The radial propulsive acceleration provided by the spacecraft propulsion system can be modulated within a suitable given range, and the radial thrust can be either inward- or outward-directed. The transfer mission performance is analyzed in an optimal framework, by minimizing the total flight time with an indirect approach. In this context, the paper proposes a semi-analytical method to reduce the computation time required to solve the optimal control problem. Using a proper description of the spacecraft dynamics in a dimensionless form, the paper reports a set of graphs and tables that allow the designer to obtain a rapid approximation of the optimal mission performance with an accuracy consistent with that of a preliminary trajectory design. Finally, the proposed approach is used to describe the minimum time capture trajectories in a mission scenario towards Ceres.

A NEW ORBIT FOR COMET C/1830 F1 (GREAT MARCH COMET)

Comet C/1830 F1 (Great March comet) is one of a large number of comets with parabolic orbits. Given that there are sufficient observations of the comet, (428 in right ascension and 424 in declination), it proves possible to calculate a better orbit. The calculations are based on a 12th order predictor-corrector method. The comet’s orbit is highly elliptical, e=0.99792 and, from calculated mean errors, statistically different from a parabola. The comet will not return for thousands of years and thus represents no immediate NEO threat.

Fractal zeta functions of orbits of parabolic diffeomorphisms

In this paper, we prove that fractal zeta functions of orbits of parabolic germs of diffeomorphisms can be meromorphically extended to the whole complex plane. We describe their set of poles (i.e. their complex dimensions) and their principal parts which can be understood as their fractal footprint. We study the fractal footprint of one orbit of a parabolic germ f and extract intrinsic information about the germ f from it, in particular, its formal class. Moreover, we relate complex dimensions to the generalized asymptotic expansion of the tube function of orbits with oscillatory "coefficients" as well as to the asymptotic expansion of their dynamically regularized tube function. Interestingly, parabolic orbits provide a first example of sets that have nontrivial Minkowski (or box) dimension and their tube function possesses higher order oscillatory terms, however, they do not posses non-real complex dimensions and are therefore not called fractal in the sense of Lapidus.

Homoclinic chaos in the Hamiltonian dynamics of extended test bodies

There is a long tradition of studying chaotic trajectories in systems whose integrability is broken by means of an external perturbation. Here we explore a different route to chaos, in the dynamics of extended bodies, which arises due to finite-size corrections to the otherwise integrable motion of a test particle. We find that cyclic changes in the overall shape of the body may lead to the onset of chaos. This is applied to the Duffing and Yukawa potentials. For Kepler’s potential, periodic deviations from spherical symmetry give rise to chaotic regions around the unperturbed parabolic orbit.

On survival of dust grains in the sublimation zone of cold white dwarfs

ABSTRACTWe consider a mechanism for the deposition of dust grains on to the surface of cold white dwarfs (WDs). Calculations show that grains can fall on to a cold WD directly, without reaching the phase of complete evaporation, if the parent bodies and the grains orbit on elongated, close to parabolic, orbits. To this end, we calculated the dynamics of evaporating silicate and graphite dust grains moving in circular and parabolic orbits around the white dwarf WD J1644−0449 with Teff ≈ 3830 K and M⋆ = 0.45 M⊙. The calculations accounted for the influence of radiation pressure and Poynting–Robertson drag on the grain dynamics. The results show that silicate grains of all sizes considered that leave the parent bodies on circular orbits evaporate completely at a distance of ∼3 stellar radii (R⋆) from the star. The boundary of the dust-free zone for graphite grains is closer to the star, ∼1.5R⋆, and is represented confidently only for larger grains with radius > 0.5 ${\mu m}$. We determined the lower limits of the radius for grains capable of reaching the stellar surface. For comparison, we analysed the dependences of lower size limits for infalling silicate grains for a set of WDs within the temperature range 3000–5000 K. We conclude that silicate grains with an initial size ≥ 300 ${\mu m}$ can reach the surface of WD J1644−0449. For stars with temperatures in the range 3000–5000 K, the corresponding grain size range is 0.016 μm–5 cm.

Hyperbolic comets as an indicator of a hypothetical planet 9 in the solar system

In this study, we assess whether a dynamic relationship exists between hyperbolic comets (HCs) with osculating orbit elements and a hypothetical planet 9 (HP9). We have found strong statistical evidence that HCs and parabolic comets are two independent sets of long-periodic comets; thus, HCs can be used as an independent set in this analysis. We have applied numerical integration, minimal orbit intersectional distance (MOID) calculations, close encounter phenomena, and the descending and ascending node distributions of comets to investigate the possible dynamic relationship between planet candidates and HCs. Transitions between the two groups (from a hyperbolic orbit to a parabolic orbit or vice versa) of these comets require a strong perturbation from a massive body. Notable clusters have been obtained for the descending and ascending node distributions of HCs for distances of 250–300 AU and 200–250 AU with respect to the ecliptic, accordingly, and for distances of 260–400 AU relative to the predicted HP9 plane at Ωp = 2710.6 and ip = 840.3. These clusters may arise from perturbations caused by HP9 near these distances.Our findings show that the MOID values of 30 comets are lower than the Hill sphere radius of HP9 sub-models. The changing eccentricity of comet C/2007J A21 (LINEAR) and its close encounter with the orbit of the HP9 sub-model were demonstrated by numerical integration and MOID calculation methods. We also assessed the possible dynamic perturbation of HCs caused by massive trans-Neptunian objects using MOID value analysis.

Existence of a Smooth Hamiltonian Circle Action near Parabolic Orbits and Cuspidal Tori

We show that every parabolic orbit of a two-degree of freedom integrable system admits a $C^\infty$-smooth Hamiltonian circle action, which is persistent under small integrable $C^\infty$ perturbations. We deduce from this result the structural stability of parabolic orbits and show that they are all smoothly equivalent (in the non-symplectic sense) to a standard model. Our proof is based on showing that every symplectomorphism of a neighbourhood of a parabolic point preserving the integrals of motion is Hamiltonian whose generating function is smooth and constant on the connected components of the common level sets.

Hidden toric symmetry and structural stability of singularities in integrable systems

The goal of the paper is to develop a systematic approach to the study of (perhaps degenerate) singularities of integrable systems and their structural stability. As the main tool, we use "hidden" system-preserving torus actions near singular orbits. We give sufficient conditions for the existence of such actions and show that they are persistent under integrable perturbations. We find toric symmetries for several infinite series of singularities and prove, as an application, structural stability of Kalashnikov's parabolic orbits with resonances in the real-analytic case. We also classify all Hamiltonian $k$-torus actions near a singular orbit on a symplectic manifold $M^{2n}$ (or on its complexification) and prove that the normal forms of these actions are persistent under small perturbations. As a by-product, we prove an equivariant version of the Vey theorem (1978) about local symplectic normal form of nondegenerate singularities.

Global simulations of tidal disruption event disc formation via stream injection in GRRMHD

ABSTRACT We use the general relativistic radiation magnetohydrodynamics code KORAL to simulate the accretion disc formation resulting from the tidal disruption of a solar mass star around a supermassive black hole (BH) of mass 106 M⊙. We simulate the disruption of artificially more bound stars with orbital eccentricity e ≤ 0.99 (compared to the more realistic case of parabolic orbits with e = 1) on close orbits with impact parameter β ≥ 3. We use a novel method of injecting the tidal stream into the domain, and we begin the stream injection at the peak fallback rate in this study. For two simulations, we choose e = 0.99 and inject mass at a rate that is similar to parabolic TDEs. We find that the disc only becomes mildly circularized with eccentricity e ≈ 0.6 within the 3.5 d that we simulate. The rate of circularization is faster for pericenter radii that come closer to the BH. The emitted radiation is mildly super-Eddington with $L_{\rm {bol}}\approx 3{-}5\, L_{\rm {Edd}}$ and the photosphere is highly asymmetric with the photosphere being significantly closer to the inner accretion disc for viewing angles near pericenter. We find that soft X-ray radiation with Trad ≈ 3–5 × 105 K may be visible for chance viewing angles. Our simulations suggest that TDEs should be radiatively inefficient with η ≈ 0.009–0.014.