skip to main content

Title: Secular chaos in white dwarf planetary systems: origins of metal pollution and short-period planetary companions

Secular oscillations in multiplanet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This ‘secular chaos’ readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets’ properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-scales spanning several orders of magnitude in a given system. We apply our results to the evolution of planetary systems around white dwarfs (WDs), specifically the tidal disruption and high-eccentricity migration of planetesimals and planets. We find that secular chaos in a planetesimal belt driven by large (≳10 M⊕), distant ($\gtrsim 10 \, \mathrm{au}$) planets can sustain metal accretion on to a WD over Gyr time-scales. We constrain the total mass of planetesimals initially present within the chaotic zone by requiring that the predicted mass delivery rate to the Roche limit be consistent with the observed metal accretion rates of WDs with atmospheric pollution throughout the cooling sequence. Based on the occurrence of more » long-period exoplanets and exo-asteroid belts, we conclude that secular chaos can be a significant (perhaps dominant) channel for polluting solitary WDs. Secular chaos can also produce short-period planets and planetesimals around WDs in concert with various circularization mechanisms. We discuss prospects for detecting exoplanets driving secular chaos around WDs using direct imaging and microlensing.

« less
; ;
Publication Date:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Page Range or eLocation-ID:
p. 4178-4195
Oxford University Press
Sponsoring Org:
National Science Foundation
More Like this

    Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term evolution of model planetary systems, made up of three equal mass giant planets on initially eccentric orbits. The range of separations studied is dominated by secular processes, but intersects chains of high-order mean-motion resonances. Over time-scales of 108 orbits, the secular evolution of the simulated systems is predominantly regular. High-order resonant chains, however, can be a significant source of angular momentum deficit (AMD), leading to instability. Using a time series analysis based on a Hilbert transform, we associate instability with broad islands of chaotic evolution. Previous work has suggested that first-order resonances could modify the AMD of nominally secular systems and facilitate secular chaos. We find that higher order resonances, when present in chains, can have similar impacts.

  2. Abstract

    The dynamical evolution of the solar system is chaotic with a Lyapunov time of only ∼5 Myr for the inner planets. Due to the chaos it is fundamentally impossible to accurately predict the solar system’s orbital evolution beyond ∼50 Myr based on present astronomical observations. We have recently developed a method to overcome the problem by using the geologic record to constrain astronomical solutions in the past. Our resulting optimal astronomical solution (called ZB18a) shows exceptional agreement with the geologic record to ∼58 Ma (Myr ago) and a characteristic resonance transition around 50 Ma. Here we show that ZB18a and integration of Earth’s and Mars’ spin vector based on ZB18a yield reduced variations in Earth’s and Mars’ orbital inclination and Earth’s obliquity (axial tilt) from ∼58 to ∼48 Ma—the latter being consistent with paleoclimate records. The changes in the obliquities have important implications for the climate histories of Earth and Mars. We provide a detailed analysis of solar system frequencies (gandsmodes) and show that the shifts in the variation in Earth’s and Mars’ orbital inclination and obliquity around 48 Ma are associated with the resonance transition and caused by changes in the contributions to the superposition ofsmodes, plusgsmode interactionsmore »in the inner solar system. Thegsmode interactions and the resonance transition (consistent with geologic data) are unequivocal manifestations of chaos. Dynamical chaos in the solar system hence not only affects its orbital properties but also the long-term evolution of planetary climate through eccentricity and the link between inclination and axial tilt.

    « less
  3. ABSTRACT Partial condensation of dust from the Solar nebula is likely responsible for the diverse chemical compositions of chondrites and rocky planets/planetesimals in the inner Solar system. We present a forward physical–chemical model of a protoplanetary disc to predict the chemical compositions of planetary building blocks that may form from such a disc. Our model includes the physical evolution of the disc and the condensation, partial advection, and decoupling of the dust within it. The chemical composition of the condensate changes with time and radius. We compare the results of two dust condensation models: one where an element condenses when the mid-plane temperature in the disc is lower than the 50 per cent condensation temperature ($\rm T_{50}$) of that element and the other where the condensation of the dust is calculated by a Gibbs free energy minimization technique assuming chemical equilibrium at local disc temperature and pressure. The results of two models are generally consistent with some systematic differences of ∼10 per cent depending upon the radial distance and an element’s condensation temperature. Both models predict compositions similar to CM, CO, and CV chondrites provided that the decoupling time-scale of the dust is of the order of the evolution time-scale of the disc ormore »longer. If the decoupling time-scale is too short, the composition deviates significantly from the measured values. These models may contribute to our understanding of the chemical compositions of chondrites, and ultimately the terrestrial planets in the Solar system, and may constrain the potential chemical compositions of rocky exoplanets.« less

    Exoplanetary observations reveal that the occurrence rate of hot Jupiters is correlated with star clustering. In star clusters, interactions between planetary systems and close flyby stars can significantly change the architecture of primordially coplanar, circular planetary systems. Flybys can impact hot Jupiter formation via activation of high-eccentricity excitation mechanisms such as the Zeipel–Lidov–Kozai (ZLK) effect and planet–planet scattering. Previous studies have shown that, for a two-planet system, close flybys, especially at high incidence angles, can efficiently activate the ZLK mechanism, thus triggering high-eccentricity tidal migration and ultimately form hot Jupiters. Here, we extend our previous study with a multiplanet (triple) system. We perform high-precision, high-accuracy few-body simulations of stellar flybys and subsequent planetary migration within the perturbed planetary systems using the code spacehub. Our simulations demonstrate that a single close flyby on a multiplanet system can activate secular chaos and ultimately lead to hot Jupiter formation via high-eccentricity migration. We find that the hot Jupiter formation rate per system increases with both the size of the planetary system and the mass of the outer planet, and we quantify the relative formation fractions for a range of parameters. Hot Jupiters formed via secular chaos are expected to be accompanied bymore »massive companions with very long periods. Our study further shows that flyby-induced secular chaos is preferred in low-density clusters where multiplanet systems are more likely to survive, and that it contributes a significant fraction of hot Jupiter formation in star clusters compared to the flyby-induced ZLK mechanism.

    « less

    We develop a rapid algorithm for the evolution of stable, circular, circumbinary discs suitable for parameter estimation and population synthesis modelling. Our model includes disc mass and angular momentum changes, accretion on to the binary stars, and binary orbital eccentricity pumping. We fit our model to the post-asymptotic giant branch (post-AGB) circumbinary disc around IRAS 08544−4431, finding reasonable agreement despite the simplicity of our model. Our best-fitting disc has a mass of about $0.01\, \mathrm{M}_{\odot }$ and angular momentum $2.7\times 10^{52}\, \mathrm{g}\, \mathrm{cm}^{2}\, \mathrm{s}^{-1}\simeq 9 \,\mathrm{M}_{\odot }\, \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{au}$, corresponding to 0.0079 and 0.16 of the common-envelope mass and angular momentum, respectively. The best-fitting disc viscosity is αdisc = 5 × 10−3 and our tidal torque algorithm can be constrained such that the inner edge of the disc Rin ∼ 2a. The inner binary eccentricity reaches about 0.13 in our best-fitting model of IRAS 08544−4431, short of the observed 0.22. The circumbinary disc evaporates quickly when the post-AGB star reaches a temperature of $\sim \! 6\times 10^4\, \mathrm{K}$, suggesting that planetismals must form in the disc in about $10^{4}\, \mathrm{yr}$ if secondary planet formation is to occur, while accretion from the disc on to the stars at ∼10 times the inner-edge viscous rate canmore »double the disc lifetime.

    « less