arXiv subjects

Hanno Rein

Publications and source records attributed to Hanno Rein.

At least 37 records · Page 2Linked to original sources

arXiv2023

WHFast512: A symplectic N-body integrator for planetary systems optimized with AVX512 instructions

We describe the implementation of the symplectic N-body integrator WHFast512 using Single Instruction Multiple Data (SIMD) parallelism and 512-bit Advanced Vector Extensions (AVX512). We are able to speed up integrations of planetary systems by up to 4.7x compared to the non-vectorized version of WHFast. WHFast512 can integrate the Solar System with 8 planets for 5 billion years in less than 1.4 days. To our knowledge, this makes WHFast512 the fastest direct N-body integrator for systems of this kind. As an example, we present an ensemble of 40-Gyr integrations of the Solar System. Ignoring the Sun's post-main sequence evolution, we show that the instability rate is well captured by a diffusion model. WHFast512 is freely available within the REBOUND package.

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arXiv2023

ASSIST: An Ephemeris-Quality Test Particle Integrator

We introduce ASSIST, a software package for ephemeris-quality integrations of test particles. ASSIST is an extension of the REBOUND framework and makes use of its IAS15 integrator to integrate test particle trajectories in the field of the Sun, Moon, planets, and 16 massive asteroids, with the positions of the masses coming from the JPL DE441 ephemeris and its associated asteroid perturber file. The package incorporates the most significant gravitational harmonics and general relativistic corrections. ASSIST also accounts for position- and velocity-dependent non-gravitational effects. The first order variational equations are included for all terms to support orbit fitting and covariance mapping. This new framework is meant to provide an open-source package written in a modern language to enable high-precision orbital analysis and science by the small body community. ASSIST is open source, freely distributed under the GNU General Public license, version 3.

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arXiv2023

General relativistic precession and the long-term stability of the solar system

The long-term evolution of the solar system is chaotic. In some cases, chaotic diffusion caused by an overlap of secular resonances can increase the eccentricity of planets when they enter into a linear secular resonance, driving the system to instability. Previous work has shown that including general relativistic contributions to the planets' precession frequency is crucial when modelling the solar system. It reduces the probability that the solar system destabilizes within 5 Gyr by a factor of 60. We run 1280 additional N-body simulations of the solar system spanning 12.5 Gyr where we allow the GR precession rate to vary with time. We develop a simple, unified, Fokker-Planck advection-diffusion model that can reproduce the instability time of Mercury with, without, and with time-varying GR precession. We show that while ignoring GR precession does move Mercury's precession frequency closer to a resonance with Jupiter, this alone does not explain the increased instability rate. It is necessary that there is also a significant increase in the rate of diffusion. We find that the system responds smoothly to a change in the precession frequency: There is no critical GR precession frequency below which the solar system becomes significantly more unstable. Our results show that the long-term evolution of the solar system is well described with an advection-diffusion model.

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arXiv2023

Self-Consistent Spin, Tidal and Dynamical Equations of Motion in the REBOUNDx Framework

We have introduced self-consistent spin, tidal and dynamical equations of motion into REBOUNDx, a library of additional effects for the popular N-body integrator REBOUND. The equations of motion used are derived from the constant time lag approximation to the equilibrium tide model of tidal friction. These effects will allow the study of a variety of systems where the full dynamical picture cannot be encapsulated by point particle dynamics. We provide several test cases and benchmark the code's performance against analytic predictions. The open-source code is available in the most recent release of REBOUNDx.

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arXiv2023

Thermal hysteresis and front propagation in dense planetary rings

Saturn's rings are composed of icy grains, most in the mm to m size ranges, undergoing several collisions per orbit. Their collective behaviour generates a remarkable array of structure over many orders of magnitude, much of it not well understood. On the other hand, the collisional properties and parameters of individual ring particles are poorly constrained; usually N-body simulations and kinetic theory employ hard-sphere models with a coefficient of restitution $ε$ that is constant or a decreasing function of impact speed. Due to plastic deformation of surface regolith, however, it is likely that $ε$ will be more complicated, at the very least a non-monotonic function. We undertake N-body simulations with the REBOUND code with non-monotonic $ε$ laws to approximate surfaces that are friable but not sticking. Our simulations reveal that such ring models can support two thermally stable steady states for the same (dynamical) optical depth: a cold and a warm state. If the ring breaks up into radial bands of one or the other state, we find that warmer states tend to migrate into the colder states via a coherent travelling front. We also find stationary `viscous' fronts, which connect states of different optical depth, but the same angular momentum flux. We discuss these preliminary results and speculate on their implications for structure formation in Saturn's B and C-rings, especially with respect to structures that appear in Cassini images but not in occultations.

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arXiv2022

On the long-term stability of the Solar System in the presence of weak perturbations from stellar flybys

The architecture and evolution of planetary systems are shaped in part by stellar flybys. Within this context, we look at stellar encounters which are too weak to immediately destabilize a planetary system but are nevertheless strong enough to measurably perturb the system's dynamical state. We estimate the strength of such perturbations on secularly evolving systems using a simple analytic model and confirm those estimates with direct N-body simulations. We then run long-term integrations and show that even small perturbations from stellar flybys can influence the stability of planetary systems over their lifetime. We find that small perturbations to the outer planets' orbits are transferred between planets, increasing the likelihood that the inner planetary system will destabilize. Specifically, our results for the Solar System show that relative perturbations to Neptune's semi-major axis of order 0.1% are strong enough to increase the probability of destabilizing the Solar System within 5 Gyrs by one order of magnitude.

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arXiv2022

An Implementation of Stochastic Forces for the N-body code REBOUND

We describe the implementation of a new module which can be used to simulate physical systems in which the motion of particles is affected by stochastic forces. Such forces are expected to be present in turbulent circumstellar disks or remnant planetesimal disks. Our implementation offers a convenient way to generate correlated noise with a user-specified amplitude and auto-correlation time for each particle. The module has minimal memory requirements and is freely available within the REBOUNDx additional effects library.

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arXiv2022

The vertical structure of debris disks and the impact of gas

The vertical structure of debris disks provides clues about their dynamical evolution and the collision rate of the unseen planetesimals. Thanks to the ever-increasing angular resolution of contemporary instruments and facilities, we are beginning to constrain the scale height of a handful of debris disks, either at near-infrared or millimeter wavelengths. Nonetheless, this is often done for individual targets only. We present here the geometric modeling of eight disks close to edge-on, all observed with the same instrument (SPHERE) and using the same mode (dual-beam polarimetric imaging). Motivated by the presence of CO gas in two out of the eight disks, we then investigate the impact that gas can have on the scale height by performing N-body simulations including gas drag and collisions. We show that gas can quickly alter the dynamics of particles (both in the radial and vertical directions), otherwise governed by gravity and radiation pressure. We find that, in the presence of gas, particles smaller than a few tens of microns can efficiently settle toward the midplane at the same time as they migrate outward beyond the birth ring. For second generation gas ($M_\mathrm{gas} \leq 0.1$ $M_\oplus$), the vertical settling should be best observed in scattered light images compared to observations at millimeter wavelengths. But if the gas has a primordial origin ($M_\mathrm{gas} \geq 1$ $M_\oplus$), the disk will appear very flat both at near-infrared and sub-mm wavelengths. Finally, far beyond the birth ring, our results suggest that the surface brightness profile can be as shallow as $\sim -2.25$.

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arXiv2021

BEBOP III. Observations and an independent mass measurement of Kepler-16 (AB) b -- the first circumbinary planet detected with radial velocities

The radial velocity method is amongst the most robust and most established means of detecting exoplanets. Yet, it has so far failed to detect circumbinary planets despite their relatively high occurrence rates. Here, we report velocimetric measurements of Kepler-16A, obtained with the SOPHIE spectrograph, at the Observatoire de Haute-Provence's 193cm telescope, collected during the BEBOP survey for circumbinary planets. Our measurements mark the first radial velocity detection of a circumbinary planet, independently determining the mass of Kepler-16~(AB)~b to be $0.313 \pm 0.039\,{\rm M}_{\rm Jup}$, a value in agreement with eclipse timing variations. Our observations demonstrate the capability to achieve photon-noise precision and accuracy on single-lined binaries, with our final precision reaching $\rm 1.5~m\,s^{-1}$ on the binary and planetary signals. Our analysis paves the way for more circumbinary planet detections using radial velocities which will increase the relatively small sample of currently known systems to statistically relevant numbers, using a method that also provides weaker detection biases. Our data also contain a long-term radial velocity signal, which we associate with the magnetic cycle of the primary star.

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arXiv2021

A Bayesian neural network predicts the dissolution of compact planetary systems

Despite over three hundred years of effort, no solutions exist for predicting when a general planetary configuration will become unstable. We introduce a deep learning architecture to push forward this problem for compact systems. While current machine learning algorithms in this area rely on scientist-derived instability metrics, our new technique learns its own metrics from scratch, enabled by a novel internal structure inspired from dynamics theory. Our Bayesian neural network model can accurately predict not only if, but also when a compact planetary system with three or more planets will go unstable. Our model, trained directly from short N-body time series of raw orbital elements, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on compact resonant and near-resonant three-planet configurations, the model demonstrates robust generalization to both non-resonant and higher multiplicity configurations, in the latter case outperforming models fit to that specific set of integrations. The model computes instability estimates up to five orders of magnitude faster than a numerical integrator, and unlike previous efforts provides confidence intervals on its predictions. Our inference model is publicly available in the SPOCK package, with training code open-sourced.

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arXiv2020

A repository of vanilla long term integrations of the Solar System

We share the source code and a 121 GB dataset of 96 long-term N-body simulations of the Solar System. This dataset can be analyzed by itself to study the dynamics of the Solar System. In addition, our simulations can be the starting point for future studies wishing to explore different initial conditions or additional physical effects on the Solar System. Our simulations can also be used as a comparison and benchmark for new numerical algorithms.

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arXiv2020

Predicting the long-term stability of compact multiplanet systems

We combine analytical understanding of resonant dynamics in two-planet systems with machine learning techniques to train a model capable of robustly classifying stability in compact multi-planet systems over long timescales of $10^9$ orbits. Our Stability of Planetary Orbital Configurations Klassifier (SPOCK) predicts stability using physically motivated summary statistics measured in integrations of the first $10^4$ orbits, thus achieving speed-ups of up to $10^5$ over full simulations. This computationally opens up the stability constrained characterization of multi-planet systems. Our model, trained on $\approx 100,000$ three-planet systems sampled at discrete resonances, generalizes both to a sample spanning a continuous period-ratio range, as well as to a large five-planet sample with qualitatively different configurations to our training dataset. Our approach significantly outperforms previous methods based on systems' angular momentum deficit, chaos indicators, and parametrized fits to numerical integrations. We use SPOCK to constrain the free eccentricities between the inner and outer pairs of planets in the Kepler-431 system of three approximately Earth-sized planets to both be below 0.05. Our stability analysis provides significantly stronger eccentricity constraints than currently achievable through either radial velocity or transit duration measurements for small planets, and within a factor of a few of systems that exhibit transit timing variations (TTVs). Given that current exoplanet detection strategies now rarely allow for strong TTV constraints (Hadden et al., 2019), SPOCK enables a powerful complementary method for precisely characterizing compact multi-planet systems. We publicly release SPOCK for community use.

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arXiv2020

Embedded operator splitting methods for perturbed systems

It is common in classical mechanics to encounter systems whose Hamiltonian $H$ is the sum of an often exactly integrable Hamiltonian $H_0$ and a small perturbation $εH_1$ with $ε\ll1$. Such near-integrability can be exploited to construct particularly accurate operator splitting methods to solve the equations of motion of $H$. However, in many cases, for example in problems related to planetary motion, it is computationally expensive to obtain the exact solution to $H_0$. In this paper we present a new family of embedded operator splitting (EOS) methods which do not use the exact solution to $H_0$, but rather approximate it with yet another, embedded operator splitting method. Our new methods have all the desirable properties of classical methods which solve $H_0$ directly. But in addition they are very easy to implement and in some cases faster. When applied to the problem of planetary motion, our EOS methods have error scalings identical to that of the often used Wisdom-Holman method but do not require a Kepler solver, nor any coordinate transformations, or the allocation of memory. The only two problem specific functions that need to be implemented are the straight-forward kick and drift steps typically used in the standard second order leap-frog method.

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arXiv2019

On the accuracy of symplectic integrators for secularly evolving planetary systems

Symplectic integrators have made it possible to study the long-term evolution of planetary systems with direct N-body simulations. In this paper we reassess the accuracy of such simulations by running a convergence test on 20Myr integrations of the Solar System using various symplectic integrators. We find that the specific choice of metric for determining a simulation's accuracy is important. Only looking at metrics related to integrals of motions such as the energy error can overestimate the accuracy of a method. As one specific example, we show that symplectic correctors do not improve the accuracy of secular frequencies compared to the standard Wisdom-Holman method without symplectic correctors, despite the fact that the energy error is three orders of magnitudes smaller. We present a framework to trace the origin of this apparent paradox to one term in the shadow Hamiltonian. Specifically, we find a term that leads to negligible contributions to the energy error but introduces non-oscillatory errors that result in artificial periastron precession. This term is the dominant error when determining secular frequencies of the system. We show that higher order symplectic methods such as the Wisdom-Holman method with a modified kernel or the SABAC family of integrators perform significantly better in secularly evolving systems because they remove this specific term.

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arXiv2019

REBOUNDx: A Library for Adding Conservative and Dissipative Forces to Otherwise Symplectic N-body Integrations

Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences of incorporating such forces into otherwise symplectic schemes is not always clear. We show that moving to a general framework of non-commutative operators (dissipative or not) clarifies many of these questions, and that several important properties of symplectic schemes carry over to the general case. In particular, we show that explicit splitting schemes generically exploit symmetries in the applied external forces which often strongly suppress integration errors. Furthermore, we demonstrate that so-called `symplectic correctors' (which reduce energy errors by orders of magnitude at fixed computational cost) apply equally well to weakly dissipative systems and can thus be more generally thought of as `weak splitting correctors.' Finally, we show that previously advocated approaches of incorporating additional forces into symplectic methods work well for dissipative forces, but give qualitatively wrong answers for conservative but velocity-dependent forces like post-Newtonian corrections. We release REBOUNDx, an open-source C library for incorporating additional effects into REBOUND N-body integrations, together with a convenient Python wrapper. All effects are machine-independent and we provide a binary format that interfaces with the SimulationArchive class in REBOUND to enable the sharing and reproducibility of results. Users can add effects from a list of pre-implemented astrophysical forces, or contribute new ones.

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arXiv2019

Dynamical Interactions in the Planetary System GJ4276

GJ4276 is an M4.0 dwarf star with an inferred Neptune mass planet from radial velocity (RV) observations. We reanalyse the RV data for this system and focus on the possibility of a second, super earth mass, planet. We compute the timescale for fast resonant librations in the eccentricity to be $\sim 2\,000\,\mathrm{days}$. Given that the observations were taken over $700\,\mathrm{days}$, we expect to see the effect of these librations in the observations. We perform a fully dynamical fit to test this hypothesis. Similar to previous results, we determine that the data could be fit by two planets in a 2:1 mean motion resonance. However, we also find solutions near the 5:4 mean motion resonance which are not present when planet-planet interactions are ignored. Using the MEGNO indicator, we analyze the stability of the system and find that our solutions lie in a stable region of parameter space. We also find that though out of resonance solutions are possible, the system favours a configuration which is in a first order mean motion resonance. The existence of mean motion resonances has important implications in many planet formation theories. Although we do not attempt to distinguish between the one and two planet models in this work, in either case, the predicted orbital parameters are interesting enough to merit further study. Future observations should be able to distinguish between the different scenarios within the next $5\,\mathrm{years}$.

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arXiv2019

High order symplectic integrators for planetary dynamics and their implementation in REBOUND

Direct N-body simulations and symplectic integrators are effective tools to study the long-term evolution of planetary systems. The Wisdom-Holman (WH) integrator in particular has been used extensively in planetary dynamics as it allows for large timesteps at good accuracy. One can extend the WH method to achieve even higher accuracy using several different approaches. In this paper we survey integrators developed by Wisdom et al. (1996), Laskar & Robutel (2001, and Blanes et al. (2013). Since some of these methods are harder to implement and not as readily available to astronomers compared to the standard WH method, they are not used as often. This is somewhat unfortunate given that in typical simulations it is possible to improve the accuracy by up to six orders of magnitude (!) compared to the standard WH method without the need for any additional force evaluations. To change this, we implement a variety of high order symplectic methods in the freely available N-body integrator REBOUND. In this paper we catalogue these methods, discuss their differences, describe their error scalings, and benchmark their speed using our implementations.

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arXiv2019

Hybrid Symplectic Integrators for Planetary Dynamics

Hybrid symplectic integrators such as MERCURY are widely used to simulate complex dynamical phenomena in planetary dynamics that could otherwise not be investigated. A hybrid integrator achieves high accuracy during close encounters by using a high order integration scheme for the duration of the encounter while otherwise using a standard 2nd order Wisdom-Holman scheme, thereby optimizing both speed and accuracy. In this paper we reassess the criteria for choosing the switching function that determines which parts of the Hamiltonian are integrated with the high order integrator. We show that the original motivation for choosing a polynomial switching function in MERCURY is not correct. We explain the nevertheless excellent performance of the MERCURY integrator and then explore a wide range of different switching functions including an infinitely differentiable function and a Heaviside function. We find that using a Heaviside function leads to a significantly simpler scheme compared to MERCURY, while maintaining the same accuracy in short term simulations.

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