Engineering topics

Hadden, Sam

Publications and source records attributed to Hadden, Sam.

5 records

DOE OSTI2024

Mercury’s Chaotic Secular Evolution as a Subdiffusive Process

Abstract Mercury’s orbit can destabilize, generally resulting in a collision with either Venus or the Sun. Chaotic evolution can causeg 1 to decrease to the approximately constant value ofg 5 and create a resonance. Previous work has approximated the variation ing 1 as stochastic diffusion, which leads to a phenomological model that can reproduce the Mercury instability statistics of secular andN-body models on timescales longer than 10 Gyr. Here we show that the diffusive model significantly underpredicts the Mercury instability probability on timescales less than 5 Gyr, the remaining lifespan of the solar system. This is becauseg 1 exhibits larger variations on short timescales than the diffusive model would suggest. To better model the variations on short timescales, we build a new subdiffusive phenomological model forg 1 . Subdiffusion is similar to diffusion but exhibits larger displacements on short timescales and smaller displacements on long timescales. We choose model parameters based on the behavior of theg 1 trajectories in theN-body simulations, leading to a tuned model that can reproduce Mercury instability statistics from 1–40 Gyr. This work motivates fundamental questions in solar system dynamics: why does subdiffusion better approximate the variation ing 1 than standard diffusion? Why is there an upper bound ong 1 , but not a lower bound that would prevent it from reachingg 5 ?

Astronomy & Astrophysics↗

DOE OSTI2021

Rare Event Sampling Improves Mercury Instability Statistics

Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury's orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare-event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately 10 –4 in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Mildly Hierarchical Triple Dynamics and Applications to the Outer Solar System

Three-body interactions are ubiquitous in astrophysics. For instance, Kozai–Lidov oscillations in hierarchical triple systems have been studied extensively and applied to a wide range of astrophysical systems. However, mildly hierarchical triples also play an important role, but they are less explored. In this work, we consider the secular dynamics of a test particle in a mildly hierarchical configuration. We find the limit within which the secular approximation is reliable when the outer perturber is in a circular orbit. In addition, we present resonances and chaotic regions using surface-of-section plots, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer Solar System. We focus on the distribution of extreme trans-Neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet 9), and find that in addition to a low-inclination Planet 9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Chaotic Dynamics of Trans-Neptunian Objects Perturbed by Planet Nine

Observations of clustering among the orbits of the most distant trans-Neptunian objects (TNOs) has inspired interest in the possibility of an undiscovered ninth planet lurking in the outskirts of the solar system. Numerical simulations by a number of authors have demonstrated that, with appropriate choices of planet mass and orbit, such a planet can maintain clustering in the orbital elements of the population of distant TNOs, similar to the observed sample. However, many aspects of the rich underlying dynamical processes induced by such a distant eccentric perturber have not been fully explored. We report the results of our investigation of the dynamics of coplanar test-particles that interact with a massive body on an circular orbit (Neptune) and a massive body on a more distant, highly eccentric orbit (the putative Planet Nine). We find that a detailed examination of our idealized simulations affords tremendous insight into the rich test-particle dynamics that are possible. In particular, we find that chaos and resonance overlap plays an important role in particles’ dynamical evolution. We develop a simple mapping model that allows us to understand, in detail, the web of overlapped mean-motion resonances explored by chaotically evolving particles. We also demonstrate that gravitational interactions with Neptune can have profound effects on the orbital evolution of particles. Our results serve as a starting point for a better understanding of the dynamical behavior observed in more complicated simulations that can be used to constrain the mass and orbit of Planet Nine.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

The Gold Standard: Accurate Stellar and Planetary Parameters for Eight Kepler M Dwarf Systems Enabled by Parallaxes

We report parallaxes and proper motions from the Hawaii Infrared Parallax Program for eight nearby M dwarf stars with transiting exoplanets discovered by Kepler. We combine our directly measured distances with mass–luminosity and radius–luminosity relationships to significantly improve constraints on the host stars’ properties. Our astrometry enables the identification of wide stellar companions to the planet hosts. Within our limited sample, all the multi-transiting planet hosts (three of three) appear to be single stars, while nearly all (four of five) of the systems with a single detected planet have wide stellar companions. By applying strict priors on average stellar density from our updated radius and mass in our transit fitting analysis, we measure the eccentricity probability distributions for each transiting planet. Planets in single-star systems tend to have smaller eccentricities than those in binaries, although this difference is not significant in our small sample. In the case of Kepler-42bcd, where the eccentricities are known to be ≃0, we demonstrate that such systems can serve as powerful tests of M dwarf evolutionary models by working in L{sub &lowast;}--ρ{sub &lowast;} space. The transit-fit density for Kepler-42bcd is inconsistent with model predictions at 2.1σ (22%), but matches more empirical estimates at 0.2σ (2%), consistent with earlier results showing model radii of M dwarfs are underinflated. Gaia will provide high-precision parallaxes for the entire Kepler M dwarf sample, and the Transiting Exoplanet Survey Satellite will identify more planets transiting nearby, late-type stars, enabling significant improvements in our understanding of the eccentricity distribution of small planets and the parameters of late-type dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗