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

Tamayo, Daniel; Silburt, Ari; Valencia, Diana; Menou, Kristen; Ali-Dib, Mohamad; Petrovich, Cristóbal; Huang, Chelsea X.; Rein, Hanno; Laerhoven, Christa Van; Paradise, Adiv; Obertas, Alysa; Murray, Norman

doi:10.3847/2041-8205/832/2/l22

Cited by 79 publications

(49 citation statements)

References 26 publications

(28 reference statements)

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“…Having found a practical method for identifying outlier initial conditions with sharply peaked distributions of instability times, we now focus on characterizing the limiting lognormal distributions that we argue are plausible outcomes of long random walks with many steps. While predicting the mean of these distributions is a difficult and unsolved problem (e.g., Chambers et al 1996;Tamayo et al 2016;Obertas et al 2017), we can see in Fig. 1 that the standard deviations of the lognormal distributions tend to be similar to one another.…”

Section: A Universal Width For the Lognormal Distribution Of Instabilmentioning

confidence: 97%

Fundamental limits from chaos on instability time predictions in compact planetary systems

Hussain

Tamayo

2019

Monthly Notices of the Royal Astronomical Society

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Instabilities in compact planetary systems are generically driven by chaotic dynamics. This implies that an instability time measured through direct N-body integration is not exact, but rather represents a single draw from a distribution of equally valid chaotic trajectories. In order to characterize the 'errors' on reported instability times from direct N-body integrations, we investigate the shape and parameters of the instability time distributions (ITDs) for ensembles of shadow trajectories that are initially perturbed from one another near machine precision. We find that in the limit where instability times are long compared to the Lyapunov (chaotic) timescale, ITDs approach remarkably similar lognormal distributions with standard deviations ≈ 0.43±0.16 dex, despite the instability times varying across our sample from 10 4 −10 8 orbits. We find excellent agreement between these predictions, derived from ≈ 450 closely packed configurations of three planets, and a much wider validation set of ≈ 10, 000 integrations, as well as on ≈ 20, 000 previously published integrations of tightly packed five-planet systems, and a seven-planet resonant chain based on TRAPPIST-1, despite their instability timescales extending beyond our analyzed timescale. We also test the boundary of applicability of our results on dynamically excited versions of our Solar System. These distributions define the fundamental limit imposed by chaos on the predictability of instability times in such planetary systems. It provides a quantitative estimate of the instrinsic error on an N-body instability time imprinted by chaos, approximately a factor of 3 in either direction.

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Section: A Universal Width For the Lognormal Distribution Of Instabilmentioning

confidence: 97%

Fundamental limits from chaos on instability time predictions in compact planetary systems

Hussain

Tamayo

2019

Monthly Notices of the Royal Astronomical Society

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“…As an alternative method to estimate the correlation between various features and simulation results, we turn to a machine learning (ML) approach akin to that of Tamayo et al (2016). The purpose of this method is to look for correlations not found by either of the previous methods.…”

Section: Statistics and Machine Learningmentioning

confidence: 99%

Exo-Milankovitch Cycles. II. Climates of G-dwarf Planets in Dynamically Hot Systems

Deitrick

Barnes

Bitz

et al. 2018

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Using an energy balance model with ice sheets, we examine the climate response of an Earth-like planet orbiting a G dwarf star and experiencing large orbital and obliquity variations. We find that ice caps couple strongly to the orbital forcing, leading to extreme ice ages. In contrast with previous studies, we find that such exo-Milankovitch cycles tend to impair habitability by inducing snowball states within the habitable zone. The large amplitude changes in obliquity and eccentricity cause the ice edge, the lowest latitude extent of the ice caps, to become unstable and grow to the equator. We apply an analytical theory of the ice edge latitude to show that obliquity is the primary driver of the instability. The thermal inertia of the ice sheets and the spectral energy distribution of the G dwarf star increase the sensitivity of the model to triggering runaway glaciation. Finally, we apply a machine learning algorithm to demonstrate how this technique can be used to extend the power of climate models. This work illustrates the importance of orbital evolution for habitability in dynamically rich planetary systems. We emphasize that as potentially habitable planets are discovered around G dwarfs, we need to consider orbital dynamics.

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“…As a result, it seems likely that truly stable solutions would require planets to be somewhat more widely spaced in such systems than our two-planet stability maps might otherwise suggest (e.g. Pu & Wu 2015Tamayo et al 2016). Additionally, previous studies have demonstrated that the ratio of two planet's masses has very little influence on stability.…”

Section: Systemmentioning

confidence: 76%

Predicting multiple planet stability and habitable zone companions in the TESS era

Agnew

Maddison

Horner

et al. 2019

Monthly Notices of the Royal Astronomical Society

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We present an approach that is able to both rapidly assess the dynamical stability of multiple planet systems, and determine whether an exoplanet system would be capable of hosting a dynamically stable Earth-mass companion in its habitable zone. We conduct a suite of numerical simulations using a swarm of massless test particles in the vicinity of the orbit of a massive planet, in order to develop a predictive tool which can be used to achieve these desired outcomes. In this work, we outline both the numerical methods we used to develop the tool, and demonstrate its use. We find that the test particles survive in systems either because they are unperturbed due to being so far removed from the massive planet, or due to being trapped in stable mean motion resonant orbits with the massive planet. The resulting unexcited test particle swarm produces a unique signature in (a,e) space that represents the stable regions within the system. We are able to scale and translate this stability signature, and combine several together in order to conservatively assess the dynamical stability of newly discovered multiple planet systems. We also assess the stability of a system's habitable zone and determine whether an Earth-mass companion could remain on a stable orbit, without the need for exhaustive numerical simulations.

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

Cited by 79 publications

References 26 publications

Fundamental limits from chaos on instability time predictions in compact planetary systems

Fundamental limits from chaos on instability time predictions in compact planetary systems

Exo-Milankovitch Cycles. II. Climates of G-dwarf Planets in Dynamically Hot Systems

Predicting multiple planet stability and habitable zone companions in the TESS era

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