arXiv subjects

Hanno Rein

Publications and source records attributed to Hanno Rein.

At least 55 records · Page 3Linked to original sources

arXiv2018

Dimensionality and integrals of motion of the Trappist-1 planetary system

The number of isolating integrals of motion of the Trappist-1 system - a late M-dwarf orbited by seven Earth-sized planets - was determined numerically, using an adapted version of the correlation dimension method. It was found that over the investigated time-scales of up to 20 000 years the number of isolating integrals of motion is the same as one would find for a system of seven non-interacting planets - despite the fact that the planets in the Trappist-1 system are strongly interacting. Considering perturbed versions of the Trappist-1 system shows that the system may occupy an atypical part of phase-space with high stability. These findings are consistent with earlier studies.

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arXiv2018

Ejection of rocky and icy material from binary star systems: Implications for the origin and composition of 1I/`Oumuamua

In single star systems like our own Solar system, comets dominate the mass budget of bodies that are ejected into interstellar space, since they form further away and are less tightly bound. However 1I/`Oumuamua, the first interstellar object detected, appears asteroidal in its spectra and in its lack of detectable activity. We argue that the galactic budget of interstellar objects like 1I/`Oumuamua should be dominated by planetesimal material ejected during planet formation in circumbinary systems, rather than in single star systems or widely separated binaries. We further show that in circumbinary systems, rocky bodies should be ejected in comparable numbers to icy ones. This suggests that a substantial fraction of additional interstellar objects discovered in the future should display an active coma. We find that the rocky population, of which 1I/`Oumuamua seems to be a member, should be predominantly sourced from A-type and late B-star binaries.

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arXiv2018

The random walk of cars and their collision probabilities with planets

On February 6th, 2018 SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster's orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant.

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arXiv2017

JANUS: A bit-wise reversible integrator for N-body dynamics

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the new N-body integrator JANUS, for which we achieve exact time-reversal symmetry by combining integer and floating point arithmetic. JANUS is explicit, formally symplectic and satisfies Liouville's theorem exactly. Its order is even and can be adjusted between two and ten. We discuss the implementation ofJANUS and present tests of its accuracy and speed by performing and analyzing long-term integrations of the Solar System. We show that JANUS is fast and accurate enough to tackle a broad class of dynamical problems. We also discuss the practical and philosophical implications of running exactly time-reversible simulations.

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arXiv2017

Resonant structure, formation and stability of the planetary system HD155358

Two Jovian-sized planets are orbiting the star HD155358 near exact mean motion resonance (MMR) commensurability. In this work we re-analyze the radial velocity (RV) data previously collected by Robertson et al. (2012). Using a Bayesian framework we construct two models - one that includes and one that excludes gravitational planet-planet interactions (PPI). We find that the orbital parameters from our PPI and noPPI models differ by up to $2σ$, with our noPPI model being statistically consistent with previous results. In addition, our new PPI model strongly favours the planets being in MMR while our noPPI model strongly disfavours MMR. We conduct a stability analysis by drawing samples from our PPI model's posterior distribution and simulating them for $10^9$ years, finding that our best-fit values land firmly in a stable region of parameter space. We explore a series of formation models that migrate the planets into their observed MMR. We then use these models to directly fit to the observed RV data, where each model is uniquely parameterized by only three constants describing its migration history. Using a Bayesian framework we find that a number of migration models fit the RV data surprisingly well, with some migration parameters being ruled out. Our analysis shows that planet-planet interactions are important to take into account when modelling observations of multi-planetary systems. The additional information that one can gain from interacting models can help constrain planet migration parameters.

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arXiv2017

Convergent Migration Renders TRAPPIST-1 Long-lived

TRAPPIST-1 is a late M-dwarf orbited by seven Earth-sized planets with orbital period ratios near a chain of mean motion resonances. Due to uncertain system parameters, most orbital configurations drawn from the inferred posterior distribution are unstable on short timescales of $\sim$ 0.5 Myr, even when including the eccentricity damping effect of tides. By contrast, we show that most physically plausible resonant configurations generated through disk migration are stable even without tidal dissipation on timescales of at least 50 Myr ($10^{10}$ orbits), an increase of at least two orders of magnitude. This result, together with the remarkable chain of period ratios in the system, provide strong evidence for convergent migration naturally emplacing the system near an equilibrium configuration forced by the resonant chain. We provide an openly available database of physically plausible initial conditions for TRAPPIST-1 generated through parametrized planet-disk interactions, as well as bit-by-bit reproducible N-body integrations over $10^9-10^{10}$ orbits.

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arXiv2017

Connecting HL Tau to the Observed Exoplanet Sample

The Atacama Large Millimeter/submilimeter Array (ALMA) recently revealed a set of nearly concentric gaps in the protoplanetary disk surrounding the young star HL Tau. If these are carved by forming gas giants, this provides the first set of orbital initial conditions for planets as they emerge from their birth disks. Using N-body integrations, we have followed the evolution of the system for 5 Gyr to explore the possible outcomes. We find that HL Tau initial conditions scaled down to the size of typically observed exoplanet orbits naturally produce several populations in the observed exoplanet sample. First, for a plausible range of planetary masses, we can match the observed eccentricity distribution of dynamically excited radial velocity giant planets with eccentricities $>$ 0.2. Second, we roughly obtain the observed rate of hot Jupiters around FGK stars. Finally, we obtain a large efficiency of planetary ejections of $\approx 2$ per HL Tau-like system, but the small fraction of stars observed to host giant planets makes it hard to match the rate of free-floating planets inferred from microlensing observations. In view of upcoming GAIA results, we also provide predictions for the expected mutual inclination distribution, which is significantly broader than the absolute inclination distributions typically considered by previous studies.

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arXiv2017

A new paradigm for reproducing and analyzing N-body simulations of planetary systems

The reproducibility of experiments is one of the main principles of the scientific method. However, numerical N-body experiments, especially those of planetary systems, are currently not reproducible. In the most optimistic scenario, they can only be replicated in an approximate or statistical sense. Even if authors share their full source code and initial conditions, differences in compilers, libraries, operating systems or hardware often lead to qualitatively different results. We provide a new set of easy-to-use, open-source tools that address the above issues, allowing for exact (bit-by-bit) reproducibility of N-body experiments. In addition to generating completely reproducible integrations, we show that our framework also offers novel and innovative ways to analyze these simulations. As an example, we present a high-accuracy integration of the Solar System spanning 10Gyrs, requiring several weeks to run on a modern CPU. In our framework we can not only easily access simulation data at predefined intervals for which we save snapshots, but at any time during the integration. We achieve this by integrating an on-demand reconstructed simulation forward in time from the nearest snapshot. This allows us to extract arbitrary quantities at any point in the saved simulation exactly (bit-by-bit), and within seconds rather than weeks. We believe that the tools we present in this paper offer a new paradigm for how N-body simulations are run, analyzed, and shared across the community.

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arXiv2017

Planetary rings and other astrophysical disks

This chapter explores the physics shared by planetary rings and the various disks that populate the Universe. It begins with an observational overview, ranging from protoplanetary disks to spiral galaxies, and then compares and contrasts these astrophysical disks with the rings of the Solar System. Emphasis is placed on fundamental physics and dynamics, and how research into the two classes of object connects. Topics covered include disk formation, accretion, collisional processes, waves, instabilities, and satellite-disk interactions.

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arXiv2016

A Machine Learns to Predict the Stability of Tightly Packed Planetary Systems

The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing the complicated and multi-dimensional stability boundary of tightly packed systems is amenable to machine learning methods. We find that training an XGBoost machine learning algorithm on physically motivated features yields an accurate classifier of stability in packed systems. On the stability timescale investigated ($10^7$ orbits), it is 3 orders of magnitude faster than direct N-body simulations. Optimized machine learning classifiers for dynamical stability may thus prove useful across the discipline, e.g., to characterize the exoplanet sample discovered by the upcoming Transiting Exoplanet Survey Satellite (TESS). This proof of concept motivates investing computational resources to train algorithms capable of predicting stability over longer timescales and over broader regions of phase space.

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arXiv2016

Second-order variational equations for N-body simulations

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

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arXiv2015

Tides Alone Cannot Explain Kepler Planets Close to 2:1 MMR

A number of Kepler planet pairs lie just wide of first-order mean motion resonances (MMRs). Tides have been frequently proposed to explain these pileups, but it is still an ongoing discussion. We contribute to this discussion by calculating an optimistic theoretical estimate on the minimum initial eccentricity required by Kepler planets to explain the current observed spacing, and compliment these calculations with N-body simulations. In particular, we investigate 27 Kepler systems having planets within 6% of the 2:1 MMR, and find that the initial eccentricities required to explain the observed spacings are unreasonable from simple dynamical arguments. Furthermore, our numerical simulations reveal resonant tugging, an effect which conspires against the migration of resonant planets away from the 2:1 MMR, requiring even higher initial eccentricities in order to explain the current Kepler distribution. Overall, we find that tides alone cannot explain planets close to 2:1 MMR, and additional mechanisms are required to explain these systems.

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arXiv2015

High Order Harmonics in Light Curves of Kepler Planets

The Kepler mission was launched in 2009 and has discovered thousands of planet candidates. In a recent paper, Esteves et al. (2013) found a periodic signal in the light curves of KOI-13 and HAT-P-7, with a frequency triple the orbital frequency of a transiting planet. We found similar harmonics in many systems with a high occurrence rate. At this time, the origins of the signal are not entirely certain. We look carefully at the possibility of errors being introduced through our data processing routines but conclude that the signal is real. The harmonics on multiples of the orbital frequency are a result of non-sinusoidal periodic signals. We speculate on their origin and generally caution that these harmonics could lead to wrong estimates of planet albedos, beaming mass estimates, and ellipsoidal variations.

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arXiv2015

WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations

We present WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler-solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps we achieve Brouwer's law, i.e. the energy error is dominated by an unbiased random walk due to floating-point round-off errors. We implement symplectic correctors up to order eleven that significantly reduce the energy error. We also implement a symplectic tangent map for the variational equations. This allows us to efficiently calculate two widely used chaos indicators the Lyapunov characteristic number (LCN) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). WHFast is freely available as a flexible C package, as a shared library, and as an easy-to-use python module.

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arXiv2015

Dynamical Stability of Imaged Planetary Systems in Formation: Application to HL Tau

A recent ALMA image revealed several concentric gaps in the protoplanetary disk surrounding the young star HL Tau. We consider the hypothesis that these gaps are carved by planets, and present a general framework for understanding the dynamical stability of such systems over typical disk lifetimes, providing estimates for the maximum planetary masses. We collect these easily evaluated constraints into a workflow that can help guide the design and interpretation of new observational campaigns and numerical simulations of gap opening in such systems. We argue that the locations of resonances should be significantly shifted in massive disks like HL Tau, and that theoretical uncertainties in the exact offset, together with observational errors, imply a large uncertainty in the dynamical state and stability in such disks. This presents an important barrier to using systems like HL Tau as a proxy for the initial conditions following planet formation. An important observational avenue to breaking this degeneracy is to search for eccentric gaps, which could implicate resonantly interacting planets. Unfortunately, massive disks like HL Tau should induce swift pericenter precession that would smear out any such eccentric features of planetary origin. This motivates pushing toward more typical, less massive disks. For a nominal non-resonant model of the HL Tau system with five planets, we find a maximum mass for the outer three bodies of approximately 2 Neptune masses. In a resonant configuration, these planets can reach at least the mass of Saturn. The inner two planets' masses are unconstrained by dynamical stability arguments.

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arXiv2015

Reanalysis of radial velocity data from the resonant planetary system HD128311

The multi-planetary system HD128311 hosts at least two planets. Its dynamical formation history has been studied extensively in the literature. We reanalyse the latest radial velocity data for this system with the affine-invariant Markov chain Monte Carlo sampler EMCEE. Using the high order integrator IAS15, we perform a fully dynamical fit, allowing the planets to interact during the sampling process. A stability analysis using the MEGNO indicator reveals that the system is located in a stable island of the parameter space. In contrast to a previous study, we find that the system is locked in a 2:1 mean motion resonance. The resonant angle $φ_1$ is librating with a libration amplitude of approximately 37°. The existence of mean motion resonances has important implication for planet formation theories. Our results confirm predictions of models involving planet migration and stochastic forces.

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arXiv2014

IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits

We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gauß-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can automatically choose an optimal timestep. The algorithm can handle close encounters and high-eccentricity orbits. The systematic errors are kept well below machine precision and long-term orbit integrations over $10^9$ orbits show that IAS15 is optimal in the sense that it follows Brouwer's law, i.e. the energy error behaves like a random walk. Our tests show that IAS15 is superior to a mixed-variable symplectic integrator (MVS) and other popular integrators, including high-order ones, in both speed and accuracy. In fact, IAS15 preserves the symplecticity of Hamiltonian systems better than the commonly-used nominally symplectic integrators to which we compared it. We provide an open-source implementation of IAS15. The package comes with several easy-to-extend examples involving resonant planetary systems, Kozai-Lidov cycles, close encounters, radiation pressure, quadrupole moment, and generic damping functions that can, among other things, be used to simulate planet-disc interactions. Other non-conservative forces can be added easily.

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arXiv2014

Some inconvenient truths about biosignatures involving two chemical species on Earth-like exoplanets

The detection of strong thermochemical disequilibrium in the atmosphere of an extrasolar planet is thought to be a potential biosignature. In this article we present a new kind of false positive that can mimic a disequilibrium or any other biosignature that involves two chemical species. We consider a scenario where the exoplanet hosts a moon that has its own atmosphere and neither of the atmospheres is in chemical disequilibrium. Our results show that the integrated spectrum of the planet and the moon closely resembles that of a single object in strong chemical disequilibrium. We derive a firm limit on the maximum spectral resolution that can be obtained for both directly-imaged and transiting planets. The spectral resolution of even idealized space-based spectrographs that might be achievable in the next several decades is in general insufficient to break the degeneracy. Both chemical species can only be definitively confirmed in the same object if absorption features of both chemicals can be unambiguously identified and their combined depth exceeds 100%.

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