arXiv subjects

Ygal Y. Klein

Publications and source records attributed to Ygal Y. Klein.

9 recordsLinked to original sources

arXiv2026

Short-Range Forces Can Catalyze Extreme Orbital Evolution in Hierarchical Triples

Hierarchical triples are promising environments for producing exotica such as black hole mergers and hot Jupiters, because of the von Zeipel-Lidov-Kozai (ZLK) effect, whereby a distant tertiary can torque an inner binary to high eccentricity over secular timescales. In the double-averaged (DA) approximation to ZLK, this eccentricity excitation is suppressed by apsidal precession due to "short-range forces" (SRFs) like relativity and tidal/rotational bulges. Here we show that, when the DA approximation breaks down, SRFs often catalyze, rather than suppress, extreme eccentricity behavior. This occurs because SRFs can drive large, discrete jumps in the binary's effective "adiabatic invariants" during high-eccentricity episodes. These nonadiabatic jumps can dramatically alter the maximum/minimum eccentricity and secular period of astrophysically relevant triples, including some for which SRFs were previously thought irrelevant. Even the angular momentum component j_z evolves secularly -- to our knowledge, this is the first time such evolution has been demonstrated from a test-particle quadrupole-order, three-body mechanism. In short, binaries may explore much more of phase space than is implied by any (semi-)analytic ZLK theory of which we are aware. We demonstrate this at the test-particle quadrupole level; in a companion work we show how even more-extreme behavior occurs when the jumps are combined with octupolar ZLK evolution.

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arXiv2026

Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum, IV: Octupole for Librating Kozai-Lidov Cycles

We solve analytically the long-term octupole evolution of \textit{librating} Kozai-Lidov cycles - those with a negative Kozai constant, in which the argument of pericenter librates - in the double-averaged restricted hierarchical three-body problem. Librating cycles reach extreme eccentricities when the normal component of the orbital angular momentum vanishes, just as rotating cycles do, but their slow dynamics was left unsolved: as noted by Katz, Dong \& Malhotra (2011), the azimuth of the eccentricity vector jumps by half a turn every cycle, so the leading-order octupole kick alternates in sign and cancels pairwise. We show that the surviving dynamics, at second order in the octupole strength, is a simple pendulum with explicit coefficients. The pendulum predicts slow oscillations of the normal angular momentum with amplitude linear in the octupole strength, evolving on a timescale of order the secular timescale divided by the octupole strength, together with an explicit criterion for orbital flips. At octupole strengths typical of hierarchical triples, these amplitudes are comparable to - and in part of the librating window can exceed - those of rotating cycles, provided one waits the correspondingly longer timescale. The analytic model agrees with numerical integrations of the double-averaged equations across the librating window, for octupole strengths typical of the hierarchical triples in which the eccentric Kozai-Lidov effect is studied - from hot-Jupiter formation to gravitational-wave sources.

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arXiv2025

Kozai Lidov Cycles = Simple Pendulum

The quadrupole Kozai mechanism, which describes the hierarchical three-body problem in the leading order, is shown to be equivalent to a simple pendulum where the change in the eccentricity squared equals the height of the pendulum from its lowest point: $e_{\text{max}}^2-e^2=h=l\left(1-\cosθ\right)$. In particular, this results in useful expressions for the KLC period, and the maximal and minimal eccentricities in terms of orbital constants. We derive the equivalence using the vector coordinates $\boldsymbolα=\textbf{j}+\textbf{e}, \boldsymbolβ=\textbf{j}-\textbf{e}$ for the inner Keplerian orbit, where $\textbf{j}$ is the normalized specific angular momentum, and $\textbf{e}$ is the eccentricity vector. The equations of motion for $\boldsymbolα$ and $\boldsymbolβ$ simplify to $\dot{\boldsymbolα}=2\partial_{\boldsymbolα} ϕ\times \boldsymbolα$ and $\dot{\boldsymbolβ}=2\partial_{\boldsymbolβ} ϕ\times \boldsymbolβ$, where $ϕ$ is the normalized averaged interaction potential and are symmetric to replacing $\boldsymbolα$ and $\boldsymbolβ$ for the KLC quadratic potential. Their constraints simplify to $\boldsymbolα^2=\boldsymbolβ^2=1$, and they are distributed uniformly and independently on the unit sphere for a uniform distribution in phase space (with a fixed energy).

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arXiv2024

Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum III: Precessing Quadrupole

The very long-term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is investigated analytically and solved for both rotating and librating Kozai-Lidov cycles (KLCs) with high eccentricities. We describe the finding of a striking similarity between librating and rotating KLCs for some range of precession rates. We show that the main effect occurs in both categories when the KLC frequency is equal to the precession rate of the perturbing potential. We solve the resonant dynamics analytically and show that it is equivalent to a simple pendulum model allowing us to map the strikingly rich structures that arise for precession rates similar to the Kozai-Lidov timescale (ratio of a few) and explain the similarity and when it vanishes. Additionally, we show that the regular KLCs at high eccentricities can also be described using a simple pendulum.

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arXiv2024

Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum II: Octupole including Brown's Hamiltonian

The very long-term evolution of the hierarchical restricted three-body problem with a massive perturber is analyzed analytically in the high eccentricity regime. Perturbations on the time scale of the outer orbit can accumulate over long timescales and be comparable to the effect of the octupole term. These perturbations are described by Brown's Hamiltonian - having different forms in the literature. We show that at the high eccentricity regime - the effect of Brown's Hamiltonian is an azimuthal precesssion of the eccentricity vector and can be solved analytically. In fact, the dynamics are equivalent to a simple pendulum model allowing an explicit flip criterion.

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arXiv2024

Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum

The gradual evolution of the restricted hierarchical three body problem is analyzed analytically, focusing on conditions of Kozai-Lidov Cycles that may lead to orbital flips from prograde to retrograde motion due to the octupole (third order) term which are associated with extremely high eccentricities. We revisit the approach described by Katz, Dong and Malhotra (\href{https://doi.org/10.1103/PhysRevLett.107.181101}{Phys. Rev. Lett. 107, 181101 (2011)}) and show that for most initial conditions, to an excellent approximation, the analytic derivation can be greatly simplified and reduces to a simple pendulum model allowing an explicit flip criterion. The resulting flip criterion is much simpler than the previous one but the latter is still needed in a small fraction of phase space. We identify a logical error in the earlier derivation but clarify why it does not affect the final results.

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arXiv2024

Librating Kozai-Lidov Cycles with a Precessing Quadrupole Potential are Analytically Approximately Solved

The very long-term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is investigated analytically for librating Kozai-Lidov cycles (KLCs). \citet{klein2023} presented an analytic solution for the approximate dynamics on a very long timescale developed in the neighborhood of the KLCs fixed point where the eccentricity vector is close to unity and aligned (or anti aligned) with the quadrupole axis and for a precession rate equal to the angular frequency of the secular Kozai-Lidov Equations around this fixed point. In this Letter, we generalize the analytic solution to encompass a wider range of precession rates. We show that the analytic solution approximately describes the quantitative dynamics for systems with librating KLCs for a wide range of initial conditions, including values that are far from the fixed point which is somewhat unexpected. In particular, using the analytic solution we map the strikingly rich structures that arise for precession rates similar to the Kozai-Lidov timescale (ratio of a few).

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arXiv2023

Construction of a Multidimensional Parallel Adaptive Mesh Refinement Special Relativistic Hydrodynamics Code for Astrophysical Applications

We have developed a new computer code, RELDAFNA, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. We have implemented a characteristic-wise, finite volume Godunov scheme using the full characteristic decomposition of the SRHD equations, to achieve second and third order accuracy in space (both PLM and PPM reconstruction). For time integration, we use the method of directional splitting with symmetrization, which is second order accurate in time. We have also implemented second and third order Runge-Kutta time integration scheme for comparison. In addition to the hydrodynamics solvers we have implemented approximate Riemann solvers along with an exact Riemann solver. We examine the ability of RELDAFNA to accurately simulate special relativistic flows efficiently in number of processors, computer memory and over all integration time. We show that a wide variety of test problems can be solved as accurately as solved by higher order programs, such as RAM, GENESIS, or PLUTO, but with a less number of variables kept in memory and computer calculations than most schemes, an advantage which is crucial for 3D high resolution simulations to be of practical use for scientific research in computational astrophysics. RELDAFNA has been tested in one, two and three dimensions and in Cartesian, cylindrical and spherical geometries. We present the ability of RELDAFNA to assist with the understanding of open questions in high energy astrophysics which involve relativistic flows.

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arXiv2023

Analytic understanding of the resonant nature of Kozai Lidov Cycles with a precessing quadrupole potential

The very long-term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is studied analytically. This problem describes the evolution of a star and a planet which are perturbed either by a (circular and not too inclined) binary star system or by one other star and a second more distant star, as well as a perturbation by one distant star and the host galaxy or a compact-object binary system orbiting a massive black hole in non-spherical nuclear star clusters \citep{hamers2017,petrovich2017}. Previous numerical experiments have shown that when the precession frequency is comparable to the Kozai-Lidov time scale, long term evolution emerges that involves extremely high eccentricities with potential applications for a broad scope of astrophysical phenomena including systems with merging black holes, neutron stars or white dwarfs. By averaging the secular equations of motion over the Kozai-Lidov Cycles (KLCs) we solve the problem analytically in the neighborhood of the KLC fixed point where the eccentricity vector is close to unity and aligned with the quadrupole axis and for a precession rate similar to the Kozai Lidov time scale. In this regime the dynamics is dominated by a resonance between the perturbation frequency and the precession frequency of the eccentricity vector. While the quantitative evolution of the system is not reproduced by the solution far away from this fixed point, it sheds light on the qualitative behaviour.

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