Secular Behavior of Exoplanets: Self-Consistency and Comparisons with the Planet-Planet Scattering Hypothesis

If mutual gravitational scattering among exoplanets occurs, then it may produce unique orbital properties. For example, two-planet systems that lie near the boundary between circulation and libration of their periapses could result if planet-planet scattering ejected a former third planet quickly, leaving one planet on an eccentric orbit and the other on a circular orbit. We first improve upon previous work that examined the apsidal behavior of known multiplanet systems by doubling the sample size and including observational uncertainties. This analysis recovers previous results that demonstrated that many systems lay on the apsidal boundary between libration and circulation. We then performed over 12,000 three-dimensional N-body simulations of hypothetical three-body systems that are unstable, but stabilize to two-body systems after an ejection. Using these synthetic two-planet systems, we test the planet-planet scattering hypothesis by comparing their apsidal behavior, over a range of viewing angles, to that of the observed systems and find that they are statistically consistent regardless of the multiplicity of the observed systems. Finally, we combine our results with previous studies to show that, from the sampled cases, the most likely planetary mass function prior to planet-planet scattering follows a power law with index -1.1. We find that this pre-scattering mass function predicts a mutual inclination frequency distribution that follows an exponential function with an index between -0.06 and -0.1.Comment: 29 pages, 3 figures, accepted for publication in A

A Systematic Survey of Moon-forming Giant Impacts. I. Nonrotating Bodies

In the leading theory of lunar formation, known as the giant impact hypothesis, a collision between two planet-size objects resulted in a young Earth surrounded by a circumplanetary debris disk from which the Moon later accreted. The range of giant impacts that could conceivably explain the Earth–Moon system is limited by the set of known physical and geochemical constraints. However, while several distinct Moon-forming impact scenarios have been proposed—from small, high-velocity impactors to low-velocity mergers between equal-mass objects—none of these scenarios have been successful at explaining the full set of known constraints, especially without invoking controversial post-impact processes. In order to bridge the gap between previous studies and provide a consistent survey of the Moon-forming impact parameter space, we present a systematic study of simulations of potential Moon-forming impacts. In the first paper of this series, we focus on pairwise impacts between nonrotating bodies. Notably, we show that such collisions require a minimum initial angular momentum budget of approximately 2 J $_{EM}$ in order to generate a sufficiently massive protolunar disk. We also show that low-velocity impacts (v $_{∞}$ ≲ 0.5 v $_{esc}$) with high impactor-to-target mass ratios (γ → 1) are preferred to explain the Earth–Moon isotopic similarities. In a follow-up paper, we consider impacts between rotating bodies at various mutual orientations

Halbarath/disk_finder_timpe2023: Release for Paper

This repository contains a demonstration version of the disk finding algorithm used in Timpe et al. (2023). This disk finder is intended for use with smooth-particle hydrodynamics simulations of pairwise collisions between planetary-size objects (i.e., "giant impacts")

Machine learning applied to simulations of collisions between rotating, differentiated planets

In the late stages of terrestrial planet formation, pairwise collisions between planetary-sized bodies act as the fundamental agent of planet growth. These collisions can lead to either growth or disruption of the bodies involved and are largely responsible for shaping the final characteristics of the planets. Despite their critical role in planet formation, an accurate treatment of collisions has yet to be realized. While semi-analytic methods have been proposed, they remain limited to a narrow set of post-impact properties and have only achieved relatively low accuracies. However, the rise of machine learning and access to increased computing power have enabled novel data-driven approaches. In this work, we show that data-driven emulation techniques are capable of classifying and predicting the outcome of collisions with high accuracy and are generalizable to any quantifiable post-impact quantity. In particular, we focus on the dataset requirements, training pipeline, and classification and regression performance for four distinct data-driven techniques from machine learning (ensemble methods and neural networks) and uncertainty quantification (Gaussian processes and polynomial chaos expansion). We compare these methods to existing analytic and semi-analytic methods. Such data-driven emulators are poised to replace the methods currently used in N-body simulations, while avoiding the cost of direct simulation. This work is based on a new set of 14,856 SPH simulations of pairwise collisions between rotating, differentiated bodies at all possible mutual orientations

Direct imaging of molten protoplanets in nearby young stellar associations

During their formation and early evolution, rocky planets undergo multiple global melting events due to accretionary collisions with other protoplanets. The detection and characterization of their post-collision afterglows (magma oceans) can yield important clues about the origin and evolution of the solar and extrasolar planet population. Here, we quantitatively assess the observational prospects to detect the radiative signature of forming planets covered by such collision-induced magma oceans in nearby young stellar associations with future direct imaging facilities. We have compared performance estimates for near- and mid-infrared instruments to be installed at ESO’s Extremely Large Telescope (ELT), and a potential space-based mission called Large Interferometer for Exoplanets (LIFE). We modelled the frequency and timing of energetic collisions using N-body models of planet formation for different stellar types, and determine the cooling of the resulting magma oceans with an insulating atmosphere. We find that the probability of detecting at least one magma ocean planet depends on the observing duration and the distribution of atmospheric properties among rocky protoplanets. However, the prospects for detection significantly increase for young and close stellar targets, which show the highest frequencies of giant impacts. For intensive reconnaissance with a K band (2.2 μm) ELT filter or a 5.6 μm LIFE filter, the β Pictoris, Columba, TW Hydrae, and Tucana-Horologium associations represent promising candidates for detecting a molten protoplanet. Our results motivate the exploration of magma ocean planets using the ELT and underline the importance of space-based direct imaging facilities to investigate and characterize planet formation and evolution in the solar vicinity. Direct imaging of magma oceans will advance our understanding of the early interior, surface and atmospheric properties of terrestrial worlds

The Initial Mass Distribution For Exoplanetary Systems

The initial mass distribution for exoplanet systems, prior to the onset of planet-planet scattering, has yet to be adequately constrained. Scattering has previously explained a broad range of observed properties, such as large eccentricities, packing, and mean motion resonances, and hence is a promising theory. We present the results of numerical simulations of scattering-produced multiple planet systems arising from different initial power law mass distributions. Each simulation begins with 5-26 planets on nearly coplanar and circular orbits. We explore which of these power law distributions most accurately reproduces the observed mass distribution, thereby constraining the initial mass function

The Initial Mass Distribution for Exoplanetary Systems

Abstract (2,250 Maximum Characters): The initial mass distribution for exoplanet systems, prior to the onset of planet-planet scattering, has yet to be adequately constrained. Scattering has previously explained a broad range of observed properties, such as large eccentricities, packing, and mean-motion resonances, and hence is an appealing theory. Likewise, a new study has shown that planet-planet scattering is also capable of reproducing the apsidal behavior of observed systems. Scattering is strongly dependent on the initial distribution of planetary masses, which recent results suggest may follow a power law relation. We present the results of numerical simulations of scattering-produced multiple planet systems arising from different initial power law mass distributions, extending down to 1 Earth mass. We test which of these power law distributions most accurately reproduces the observed mass distribution. We find that our simulations are able to reproduce the observed mass distribution, but fail to reproduce the observed eccentricity distribution. We repeat our analysis at increasing initial mutual inclinations, but find that our results do not vary significantly as a result. This suggests that the initial mass distribution is described by a relation more intricate than a global power law, and therefore we explore more complex approaches with which we might constrain the initial mass distribution

The Initial Mass Distribution for Exoplanetary Systems

Abstract (2,250 Maximum Characters): The initial mass distribution for exoplanet systems, prior to the onset of planet-planet scattering, has yet to be adequately constrained. Scattering has previously explained a broad range of observed properties, such as large eccentricities, packing, and mean-motion resonances, and hence is an appealing theory. Likewise, a new study has shown that planet-planet scattering is also capable of reproducing the apsidal behavior of observed systems. Scattering is strongly dependent on the initial distribution of planetary masses, which recent results suggest may follow a power law relation. We present the results of numerical simulations of scattering-produced multiple planet systems arising from different initial power law mass distributions, extending down to 1 Earth mass. We test which of these power law distributions most accurately reproduces the observed mass distribution. We find that our simulations are able to reproduce the observed mass distribution, but fail to reproduce the observed eccentricity distribution. We repeat our analysis at increasing initial mutual inclinations, but find that our results do not vary significantly as a result. This suggests that the initial mass distribution is described by a relation more intricate than a global power law, and therefore we explore more complex approaches with which we might constrain the initial mass distribution