Two-body Dynamics Research Articles

Redshift factor and the small mass-ratio limit in binary black hole simulations

We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to nonspinning, quasicircular binaries with mass ratios ranging from ${m}_{A}/{m}_{B}=1$ to ${m}_{A}/{m}_{B}=9.5$ we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order ${10}^{\ensuremath{-}5}$ from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from self-force calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with nonadiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a reexpansion in terms of the symmetric mass ratio $\ensuremath{\nu}$ does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, ${z}_{A}+{z}_{B}$, which is symmetric under the exchange of the masses, a reexpansion in $\ensuremath{\nu}$ accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.

Numerical-relativity validation of effective-one-body waveforms in the intermediate-mass-ratio regime

One of the open problems in developing binary black hole (BBH) waveforms for gravitational wave astronomy is to model the intermediate mass ratio regime and connect it to the extreme mass ratio regime. A natural approach is to employ the effective one body (EOB) approach to the two-body dynamics that, by design, can cover the entire mass ratio range and naturally incorporates the extreme mass ratio limit. Here we use recently obtained numerical relativity (NR) data with mass ratios $m_1/m_2=(7,15,\,32,\,64,\,128)$ to test the accuracy of the state-of-the-art EOB model TEOBResumS in the intermediate mass ratio regime. We generally find an excellent EOB/NR consistency around merger and ringdown for all mass ratios and for all available subdominant multipoles, except for the $\ell=m=5$ one. This mode can be crucially improved using the new large-mass ratio NR data of this paper. The EOB/NR inspirals are also consistent with the estimated NR uncertainties. We also use several NR datasets taken by different public catalogs to probe the universal behavior of the multipolar hierarchy of waveform amplitudes at merger, that smoothly connects the equal-mass BBH to the test-mass result. Interestingly, the universal behavior is strengthened if the nonoscillatory memory contribution is included in the NR waveform. Future NR simulations with improved accuracy will be necessary to further probe, and possibly quantitatively refine, the TEOBResumS transition from late inspiral to plunge in the intermediate mass ratio regime.

Hyperfine dependent atom-molecule loss analyzed by the analytic solution of few-body loss equations

We prepare mixtures of ultracold $^{39}$K atoms in various hyperfine spin states and $^{23}$Na$^{39}$K molecules in an optical dipole trap at a fixed magnetic field and study inelastic two-body atom-molecule collisions. We observe atom-molecule losses that are hyperfine dependent with a two-body loss rate far below the universal limit. We analyze the two-body loss dynamics based on the derivation of general and easy applicable analytic solutions for the differential equations describing the loss of an arbitrary number $\gamma$ of particles in a single collisional event.

Maximizing Dust Devil Follow-Up Observations on Mars Using Cubesats and On-Board Scheduling

Several million dust devil events occur on Mars every day. These events last, on average, about 30 minutes and range in size from meters to hundreds of meters in diameter. Designing low-cost missions that will improve our knowledge of dust devil formation and evolution, and their connection to atmospheric dynamics and the dust cycle, is fundamental to informing future crewed Mars lander missions about surface conditions. In this paper we present a mission for a constellation of low orbiting Mars cubesats, each carrying imagers with agile pointing capabilities. The goal is to maximize the number of dust devil follow-up observations through real-time, on-board scheduling. We study scenarios where cubesats are equipped with a 2.5 degree boresight angle camera that accommodates twenty-one slew positions (including nadir). We assume a concept of operations where the cubesats autonomously survey the surface of Mars and can autonomously detect dust devils from their surface imagery. When a dust devil is detected, the constellation is autonomously re-tasked through an onboard distributed scheduler to capture as many follow-on images of the event as possible, so as to study its evolution. The cubesat orbits are propagated assuming two-body dynamics and the ground tracks and camera field of view are computed assuming a spherical Mars. Realistic inter-agent communication link opportunities are computed and included in our optimization, which allow for real-time event detection information to be shared within the constellation. We compare against a powerful “omniscient” oracle which has a priori knowledge of all dust devil activity to show the gap between predicted performance and the best possible outcome. In particular, we show that the communications are especially important for acquiring follow-up observations, and that a realistic distributed scheduling mechanism is able to capture a large fraction of all dust devil observations that are possible for a given orbit configuration, significantly outperforming a nadir-pointing heuristic.

Quantum dynamics of few dipolar bosons in a double-well potential

We study the few-body dynamics of dipolar bosons in one-dimensional double-wells. Increasing the interaction strength, by investigating one-body observables, we study in the considered few-body systems tunneling oscillations, self-trapping and the regime exhibting an equilibrating behaviour. The corresponding two-body correlation dynamics exhibits a strong interplay between the interatomic correlation due to non-local nature of the repulsion and the inter-well coherence. We also study the link between the correlation dynamics and the occupation of natural orbitals of the one-body density matrix.

Analysis of the PPN two-Body Problem using non-osculating orbital elements

The parameterised post-Newtonian (PPN) formalism is a weak-field slow-motion approximation for both GR and some of its generalisations. It permits various parameterisations of the motion, among which are the Lagrange-type and Gauss-type orbital equations. Often, these equations are developed under the Lagrange constraint, which makes the evolving orbital elements parameterise instantaneous conics tangent to the orbit. Arbitrary mathematically, this choice of a constraint is convenient under perturbations dependent only on positions. Under perturbations dependent also on velocities (like relativistic corrections) the Lagrange constraint unnecessarily complicates solutions that can be simplified by introducing a freedom in the orbit parameterisation, which is analogous to the gauge freedom in electrodynamics and gauge theories. Geometrically, this freedom is the freedom of nonosculation, i.e. of the degree to which the instantaneous conics are permitted to be non-tangent to the actual orbit. Under the same perturbation, all solutions with different degree of nonosculation look mathematically different, though describe the same physical orbit. While non-intuitive, the modeling of an orbit with a sequence of nontangent instantaneous conics can at times simplify calculations. The appropriately generalised ("gauge-generalised") Lagrange-type equations, and their applications, appeared in the literature hitherto. We in this paper derive the gauge-generalised Gauss-type equations and apply them to the PPN two-body problem. Fixing the gauge freedom in three different ways (i.e. modeling an orbit with non-osculating elements of three different types) we find three parameterisations of the PPN two-body dynamics. These parameterisations render orbits with either a fixed non-osculating semimajor axis, or a fixed non-osculating eccentricity, or a fixed non-osculating argument of periastron.

Fast post-adiabatic waveforms in the time domain: Applications to compact binary coalescences in LIGO and Virgo

We present a computationally efficient (time-domain) multipolar waveform model for quasicircular spin-aligned compact binary coalescences. The model combines the advantages of the numerical-relativity informed, effective-one-body (EOB) family of models with a post-adiabatic solution of the equations of motion for the inspiral part of the two-body dynamics. We benchmark this model against other state-of-the-art waveforms in terms of efficiency and accuracy. We find a speed-up of one to two orders of magnitude compared to the underlying time-domain eob model for the total mass range $2--100\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. More specifically, for a low total-mass system, such as a binary neutron star with equal masses of $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, like GW170817, the computational speedup is around 100 times; for an event with total mass $\ensuremath{\sim}40\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and mass ratio $\ensuremath{\sim}3$, like GW190412, the speedup is by a factor of $\ensuremath{\sim}20$, while for a binary system of comparable masses and total mass of $\ensuremath{\sim}70\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, like GW150914, it is by a factor of $\ensuremath{\sim}10$. We demonstrate that the new model is extremely faithful to the underlying eob model with unfaithfulness less than 0.01% across the entire applicable region of parameter space. Finally, we present successful applications of this new waveform model to parameter estimation studies and tests of general relativity.

Radiative classical gravitational observables at mathcal{O} (G3) from scattering amplitudes

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and mathcal{N} =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at mathcal{O} (G3) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

Attitude Control of a Spacecraft during an Orbital Maneuver for Fast Rejecting of the Large Disturbance Torque without Using the Reaction Control System

During an impulsive orbital maneuver, thrust vector misalignment from the center of mass (C.M) generates a large exogenous disturbance torque that results in attitude deviation. This paper aims not to use the reaction control system (RCS) for the spacecraft attitude control. In order to reject the large disturbance very fast, a new control system is proposed. In this method, the large disturbance torque is rejected quickly while the RCS is not employed. The control system is based on one degree of freedom (1DoF) gimbaled-thruster, spin-stabilization, and two control moment gyros (CMG). The nonlinear two-body dynamics of the mentioned spacecraft is formulated. Because RCS is not used, this method is an efficient and implementable method for attitude control of small spacecraft. Numerical simulation shows that thrust vector deviation converges to zero despite disturbance torques. By this method, the disturbance is rejected very fast; thus an accurate orbital velocity change can be obtained. This method can eliminate the initial attitude deviation easily in addition to disturbance rejection. The results show the good performance and superiority of the proposed method compared to some other thrusting maneuver methods.

Near and far zones in two-body dynamics: An effective field theory perspective

We revisit several aspects of the interaction of self-gravitating, slowly varying sources with their own emitted radiation within the context of post-Newtonian approximation to General Relativity. We discuss and clarify the choice of boundary conditions of Green's functions used to determine conservative potentials, and the interplay between the so-called near and far zones, as well as the relation between far zone ultra-violet divergences and emitted power. Both near and far zone contributions are required for the computation of the conservative dynamics. Within a field-theory approach we rederive far-zone self-energy processes, known as tail and memory effects, generalising the calculation of their divergent part to arbitrary order in the post-Newtonian expansion.

Erratum: Hereditary terms at next-to-leading order in two-body gravitational dynamics [Phys. Rev. D 101 , 064033 (2020)

Erratum: Hereditary terms at next-to-leading order in two-body gravitational dynamics [Phys. Rev. D <b>101</b> , 064033 (2020)

Creep stability of the DART/Hera mission target 65803 Didymos: II. The role of cohesion

The binary asteroid 65803 Didymos-Dimorphos is the target of the first asteroid deflection test (NASA's Double Asteroid Redirection Test, DART) and the first binary asteroid system that will be characterized by a rendezvous mission (ESA's Hera). The cohesive strength of the fast-spin-primary Didymos is a key factor that could affect the impact outcome and stability of this system. To support the preparation and data interpretation of these missions and gain a better understanding of the formation and evolution of this system, we investigate the structural stability and cohesive strength of Didymos based on current observational information. We use the Didymos radar shape model to construct rubble-pile models consisting of ~40,000 to ~100,000 particles with different arrangements and size distributions. To investigate the effect of cohesion on the structural stability and dynamical behaviors of Didymos, we explicitly simulate the YORP spin-up process of these rubble-pile models from a slow spin state to Didymos' current spin state using a high-efficiency soft-sphere-discrete-element-model code, pkdgrav. We test the creep stability of Didymos' rubble-pile representation with different values of cohesion and derive the critical amount of cohesion to maintain stability. The results show that Didymos should at least have a minimum bulk cohesion on the order of 10 Pa to maintain its structural stability if the interparticle tensile strength is uniformly distributed. Since the surface particles are less bonded by cohesive contacts than the interior particles, the internal macroscopic cohesion is about three times the surface macroscopic cohesion. We find that the bulk density and particle arrangement and size distribution of Didymos have significant influences on its critical cohesion and failure behaviors, indicating different binary formation pathways. With the critical cohesion, Didymos is at the edge of maintaining a stable shape, and a rapid small decrease in its spin period would excite its rubble-pile structure and lead to reshaping or mass shedding. Whether the DART impact could partially or globally destabilize this system requires further investigation of the full two-body gravitational dynamics and the ejecta evolution. With the expected measurements returned by DART's onboard cubesat LICIACube in 2022 and Hera in 2027, the correlations between Didymos' physical properties and failure behaviors found in this study may be possible to constrain the mechanical properties and evolutionary history of this binary system.

Weak Transitions in Light Nuclei

Nuclei are used for high-precision tests of the Standard Model and for searches of physics beyond the Standard Model. Without a thorough understanding of nuclei, we will not be able to meaningfully interpret the growing body of experimental data nor will we be able to disentangle new physics signals from underlying nuclear effects. This calls for accurate calculations of nuclear structure and reactions. In this work, we focus on electroweak decays in nuclei with mass number $A\, \le 10$ and report on {\it ab initio} Quantum Monte Carlo calculations of reduced matrix elements entering beta decays and electron captures in nuclei with mass number $A\, \le 10$. The many-body wave functions are calculated using selected Norfolk two- and three-nucleon potential models and associated one- and two-body axial currents at tree-level obtained from a chiral effective field theory with pions, nucleons and $\Delta$. The agreement with the experimental data is satisfactory with the exception of transitions in $A=8$ nuclei. In this specific case, the theory significantly underpredicts the experimental data, which indicates the need of further improvements in the corresponding nuclear wave functions. In this study, emphasis is given to the contributions from two-body axial currents that are carefully analyzed using two-body transition densities. This allow us to study the spatial distribution and short-range behavior of two-body dynamics. In particular, the transition densities when scaled to peak at 1.0 exhibit the universal short-range behavior across the considered nuclei, while they differ in the long range tails.

Classical gravitational self-energy from double copy

We apply the classical double copy to the calculation of self-energy of composite systems with multipolar coupling to gravitational field, obtaining next-to-leading order results in the gravitational coupling GN by generalizing color to kinematics replacement rules known in literature. When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and then re-absorbed by the same source. These processes contribute to the conservative two-body dynamics and the present work represents a decisive step towards the systematic use of double copy within the multipolar post-Minkowskian expansion.

Capturing the experimental behaviour of a point-absorber WEC by simplified numerical models

The paper presents a wave basin experiment of a direct-driven point-absorber wave energy converter moving in six degrees of freedom. The goal of the work is to study the dynamics and energy absorption of the wave energy converter, and to verify under which conditions numerical models restricted to heave can capture the behaviour of a point-absorber moving in six degrees of freedom. Several regular and irregular long-crested waves and different damping values of the power take-off system have been tested. We collected data in terms of power output, device motion in six degrees of freedom and wave elevation at different points of the wave basin. A single-body numerical model in the frequency domain and a two-body model in the time domain are used in the study. Motion instabilities due to parametric resonance observed during the experiments are discussed and analysis of the buoy motion in terms of the Mathieu instability is also presented. Our results show that the simplified models can reproduce the body dynamics of the studied converter as long as the transverse non-linear instabilities are not excited, which typically is the case in irregular waves. The performance of the more complex time domain model is able to reproduce both the buoy and PTO dynamics, while the simpler frequency domain model can only reproduce the PTO dynamics for specific cases. Finally, we show that the two-body dynamics of the studied wave energy converter affects the power absorption significantly, and that common assumptions in the numerical models, such as stiff mooring line or that the float moves only in heave, may lead to incorrect predictions for certain sea states.

Two-body quench dynamics of harmonically trapped interacting particles

We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate time-dependent observables such as the overlap between initial and final states and the expectation value of the separation between the two atoms. In the case where the interaction is quenched from the non-interacting regime to the strongly interacting regime, or vice versa, we are able to obtain analytic results. Examining the overlap between the initial and final states we show that when the interaction is quenched from the non-interacting to strongly interacting regimes the early time dependence dynamics are consistent with theoretical work in the single impurity many-body limit. When the system is quenched from the strongly to non-interacting regime we predict large oscillations in the separation between the two atoms, which arises from a logarithmic divergence due to the zero-range nature of the interaction potential.

Sixth post-Newtonian local-in-time dynamics of binary systems

Using a recently introduced method [Phys.\ Rev.\ Lett.\ {\bf 123}, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a non-local-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging. The full functional structure of the local 6PN Hamiltonian (which involves 151 numerical coefficients) is derived, but contains four undetermined numerical coefficients. Our 6PN-accurate results are complete at orders $G^3$ and $G^4$, and the derived $O(G^3)$ scattering angle agrees, within our 6PN accuracy, with the computation of [Phys.\ Rev.\ Lett.\ {\bf 122}, no. 20, 201603 (2019)]. All our results are expressed in several different gauge-invariant ways. We highlight, and make a crucial use of, several aspects of the hidden simplicity of the mass-ratio dependence of the two-body dynamics.

A benchmarking and sensitivity study of the full two-body gravitational dynamics of the DART mission target, binary asteroid 65803 Didymos

NASA's Double Asteroid Redirection Test (DART) is designed to be the first demonstration of a kinetic impactor for planetary defense against a small-body impact hazard. The target is the smaller component of the binary asteroid 65,803 Didymos. We have conducted high-fidelity rigid full two-body simulations of the mutual dynamics of this system in a broad benchmarking exercise to find the best simulation methodologies, and to understand the sensitivity of the system to initial conditions. Due to the non-spherical shapes of the components and their close proximity, the components cannot be treated as point masses and so the dynamics differ significantly from a simple Keplerian orbit, necessitating the use of numerical simulations to fully capture the system's dynamics. We find that the orbit phase (angular position or true anomaly) of the secondary is highly sensitive to the initial rotation phase of the primary, making prediction of the secondary's location from numerical simulation challenging. Finally, we show that the DART impact should induce significant free and forced librations on the secondary. If this libration can be measured by ESA's recently approved follow-up spacecraft, Hera, it may be possible to constrain properties of the secondary's interior structure.

The Lagrange coefficients of Vinti theory

The existence of Lagrange coefficients under two-body dynamics is well known, and the concept forms the basis of robust algorithms for solving a variety of fundamental astrodynamics problems. The Lagrange coefficients are generalized to Vinti theory in the present work, where the Vinti potential describes the dynamics of small objects like spacecraft orbiting an oblate body. Exact expressions for the coefficients are provided in various forms alongside detailed derivations. Useful properties and geometrical interpretations are also established.

Logarithmic tail contributions to the energy function of circular compact binaries

We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of General Relativity. The logarithms come from the conservative part of non linear gravitational-wave tails and their iterations. Explicit, original expressions are found for conservative dynamics logarithmic tail terms up to 6PN order by adopting both traditional PN calculations and effective field theory (EFT) methods. We also determine all logarithmic terms at 7PN order, fixing a sub-leading logarithm from a tail-of-tail-of-tail process by comparison with self-force (SF) results. Moreover, we use renormalization group techniques to obtain the leading logarithmic terms to generic power $n$, appearing at $(3n+1)$PN order, and we resum the infinite series in a closed form. Half-integer PN orders enter the conservative dynamics starting at 5.5PN, but they do not generate logarithmic contributions up to next-to-next-to-leading order included. We nevertheless present their contribution at leading order in the small mass ratio limit.