Recurrence plots for the analysis of complex systems

Acknowledgements Foreword Introduction I BACKGROUND Long-term astrophysical processes Evolution theory and the future of humanity Millenial tendencies in responses to apocalyptic threats Cognitive biases potentially affecting judgement of global risks Observation selection effects and global catastrophic risks Systems-based risk analysis Catastrophes and insurance Public policy towards catastrophe II RISKS FROM NATURE Super-volcanism and other geophysical processes of catastrophic import Hazards from comets and asteroids Influence of Supernovae, gamma-ray bursts, solar flares, and cosmic rays on the terrestrial environment III RISKS FROM UNINTENDED CONSEQUENCES Climate change and global risk Plagues and pandemics: past, present, and future Artificial Intelligence as a positive and negative factor in global risk Big troubles, imagined and real IV RISKS FROM HOSTILE ACTS Catastrophe, social collapse, and and human extinction The continuing threat of nuclear war Catastrophic nuclear terrorism: a preventable peril Biotechnology and biosecurity Nanotechnology as global catastrophic risk The totalitarian threat Author's biographies Index

Global Catastrophic Risks

Prior work has found that a variety of terrestrial planetary compositions are expected to occur within known extrasolar planetary systems. However, such studies ignored the effects of giant planet migration, which is thought to be very common in extrasolar systems. Here we present calculations of the compositions of terrestrial planets that formed in dynamical simulations incorporating varying degrees of giant planet migration. We used chemical equilibrium models of the solid material present in the disks of five known planetary host stars: the Sun, GJ 777, HD4203, HD19994, and HD213240. Giant planet migration has a strong effect on the compositions of simulated terrestrial planets as the migration results in large-scale mixing between terrestrial planet building blocks that condensed at a range of temperatures. This mixing acts to (1) increase the typical abundance of Mg-rich silicates in the terrestrial planets' feeding zones and thus increase the frequency of planets with Earth-like compositions compared with simulations with static giant planet orbits, and (2) drastically increase the efficiency of the delivery of hydrous phases (water and serpentine) to terrestrial planets and thus produce waterworlds and/or wet Earths. Our results demonstrate that although a wide variety of terrestrial planet compositions can still be produced, planets with Earth-like compositions should be common within extrasolar planetary systems.

https://iopscience.iop.org/article/10.1088/0004-637X/715/2/1050/pdf

The compositional diversity of extrasolar terrestrial planets. i. in situ simulations

Extrasolar planet host stars have been found to be enriched in key planet-building elements. These enrichments have the potential to drastically alter the composition of material available for terrestrial planet formation. Here we report on the combination of dynamical models of late-stage terrestrial planet formation within known extrasolar planetary systems with chemical equilibrium models of the composition of solid material within the disk. This allows us to determine the bulk elemental composition of simulated extrasolar terrestrial planets. A wide variety of resulting planetary compositions are found, ranging from those that are essentially "Earth-like", containing metallic Fe and Mg-silicates, to those that are dominated by graphite and SiC. This shows that a diverse range of terrestrial planets may exist within extrasolar planetary systems.

The Compositional Diversity of Extrasolar Terrestrial Planets: I. In-Situ Simulations

We investigate the stability regions of hypothetical terrestrial planets around the Lagrangian equilibrium points L4 and L5 in some specific extrasolar planetary systems. The problem of their stability can be treated in the framework of the restricted three body problem where the host star and a massive Jupiter-like planet are the primary bodies and the terrestrial planet is regarded as being massless. From these theoretical investigations one cannot determine the extension of the stable zones around the equilibrium points. Using numerical experiments we determined their largeness for three test systems chosen from the table of the know extrasolar planets, where a giant planet is moving close to the so-called habitable zone around the host star in low eccentric orbits. The results show the dependence of the size and structure of this region, which shrinks significantly with the eccentricity of the known gas giant.

/pdf/extrasolar-trojan-planets-close-to-habitable-zones-kw9gizz066.pdf

Extrasolar Trojan planets close to habitable zones

We have undertaken a thorough dynamical investigation of five extrasolar planetary systems using extensive numerical experiments. The systems Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question of whether they could host terrestrial like planets in their habitable zones (=HZ). First we investigated the mean motion resonances between fictitious terrestrial planets and the existing gas giants in these five extrasolar systems. Then a fine grid of initial conditions for a potential terrestrial planet within the HZ was chosen for each system, from which the stability of orbits was then assessed by direct integrations over a time interval of 1 million years. The computations were carried out using a Lie-series integration method with an adaptive step size control. This integration method achieves machine precision accuracy in a highly efficient and robust way, requiring no special adjustments when the orbits have large eccentricities. The stability of orbits was examined with a determination of the Renyi entropy, estimated from recurrence plots, and with a more straight forward method based on the maximum eccentricity achieved by the planet over the 1 million year integration. Additionally, the eccentricity is an indication of the habitability of a terrestrial planet in the HZ; any value of e>0.2 produces a significant temperature difference on a planet's surface between apoapse and periapse. The results for possible stable orbits for terrestrial planets in habitable zones for the five systems are summarized as follows: for Gl 777 A nearly the entire HZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survive for a sufficiently long time, while for Gl 614 our results exclude terrestrial planets moving in stable orbits within the HZ.

/pdf/stability-of-terrestrial-planets-in-the-habitable-zone-of-gl-x557pc429j.pdf

Stability of Terrestrial Planets in the Habitable Zone of Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208

Received; accepted Abstract. We have undertaken a thorough dynamical investigation of five extrasolar planetary systems using extensive numerical experiments on the supercomputer of the Max Planck Institute for Gravitational Physics (Albert Einstein Institute). This work was performed as part of the Helmholtz Institute for Supercomputational Physics Summer School on "Chaos and Stability in Planetary Systems" (2003). The systems Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question of whether they could host terrestrial like planets in their habitable zones (=HZ). First we investigated the mean motion resonances between fictitious terrestrial planets and the existing gas giants in these five extrasolar systems. Then a fine grid of initial conditions for a potential terrestrial planet within the HZ was chosen for each system, from which the stability of orbits was then assessed by direct integrations over a time interval of 1 million years. For each of the five systems the 2-dimensional grid of initial conditions contained 80 eccentricity points for the Jovian planet and up to 160 semimajor axis points for the fictitious planet. The computations were carried out using a Lie-series integration method with an adaptive step size control. This integration method achieves machine precision accuracy in a highly efficient and robust way, requiring no special adjustments when the orbits have large eccentricities. The stability of orbits was examined with a determination of the Renyi entropy, estimated from recurrence plots, and with a more straight forward method based on the maximum eccentricity achieved by the planet over the 1 million year integration. Additionally, the eccentricity is an indication of the habitability of a terrestrial planet in the HZ; any value of e > 0.2 produces a significant temperature difference on a planet's surface between apoapse and periapse. The results for possible stable orbits for terrestrial planets in habitable zones for the five systems are summarized as follows: for Gl 777 A nearly the entire HZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survive for a sufficiently long time,while for Gl 614 our results exclude terrestrial planets moving in stable orbits within the HZ. Studies such as this one are of primary interest to future space missions dedicated to finding habitable terrestrial planets in other stellar systems. Assessing the likelihood of other habitable planets, and more generally the possibility of other life, is the central question of astrobiology today. Our investigation indicates that, from the dynamical point of view, habitable terrestrial planets seem to be quite compatible with many of the currently discovered extrasolar systems.

/pdf/stability-of-terrestrial-planets-in-the-habitable-zone-of-gl-34iq7wqi55.pdf

Stability of terrestrial planets in the habitable zone of Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208

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Stability of Terrestrial Planets in the Habitable Zone of Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208

Stability of terrestrial planets in the habitable zone of Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208