Daniel Tamayo

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 Brouwers 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.

Consequences of an eccentric orbit for Fomalhaut b

Fomalhaut b is currently the least massive, directly imaged exoplanet candidate. New observation epochs reveal this object to be moving on a highly eccentric orbit (Kalas et al. 2013), which sets important new constraints. I consider scenarios where Fomalhaut b is the only object interacting with the debris disk, and ones involving an additional unseen planet. I also investigate the possibility that Fomalhaut b is merely a transient dust cloud in light of the revised eccentric orbit. I argue that the scenario best able to match the observational constraints is a super-Earth Fomalhaut b surrounded by a vast cloud of dust that is generated by a population of irregular satellites, with an undetected

DYNAMICAL INSTABILITIES IN HIGH-OBLIQUITY SYSTEMS

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Convergent Migration Renders TRAPPIST-1 Long-lived

Saturn-mass planet orbiting interior to the disk and driving the secular dynamics. Testable predictions are summarized that could differentiate between this scenario and other possibilities.

Chaotic dust dynamics and implications for the hemispherical color asymmetries of the Uranian satellites

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations—large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. found that, for planets with obliquities >68. ◦ 875, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we find that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68. ◦ 875. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting–Robertson drag through any unstable range. For low-eccentricity orbits in the equilibrium Laplace plane, we find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this occurs because radiation pressure modifies the equilibrium Laplace plane.

TATOOINE’S FUTURE: THE ECCENTRIC RESPONSE OF KEPLER’S CIRCUMBINARY PLANETS TO COMMON-ENVELOPE EVOLUTION OF THEIR HOST STARS

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

COULD JUPITER OR SATURN HAVE EJECTED A FIFTH GIANT PLANET

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A MACHINE LEARNS TO PREDICT THE STABILITY OF TIGHTLY PACKED PLANETARY SYSTEMS

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 (

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

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The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star

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