Two Dynamical Classes of Centaurs

📝 Abstract

The Centaurs are a transient population of small bodies in the outer solar system whose orbits are strongly chaotic. These objects typically suffer significant changes of orbital parameters on timescales of a few thousand years, and their orbital evolution exhibits two types of behaviors described qualitatively as random-walk and resonance-sticking. We have analyzed the chaotic behavior of the known Centaurs. Our analysis has revealed that the two types of chaotic evolution are quantitatively distinguishable: (1) the random walk-type behavior is well described by so-called generalized diffusion in which the rms deviation of the semimajor axis grows with time t as ~t^H, with Hurst exponent H in the range 0.22–0.95, however (2) orbital evolution dominated by intermittent resonance sticking, with sudden jumps from one mean motion resonance to another, has poorly defined H. We further find that these two types of behavior are correlated with Centaur dynamical lifetime: most Centaurs whose dynamical lifetime is less than ~22 Myr exhibit generalized diffusion, whereas most Centaurs of longer dynamical lifetimes exhibit intermittent resonance sticking. We also find that Centaurs in the diffusing class are likely to evolve into Jupiter-family comets during their dynamical lifetimes, while those in the resonance-hopping class do not.

💡 Analysis

The Centaurs are a transient population of small bodies in the outer solar system whose orbits are strongly chaotic. These objects typically suffer significant changes of orbital parameters on timescales of a few thousand years, and their orbital evolution exhibits two types of behaviors described qualitatively as random-walk and resonance-sticking. We have analyzed the chaotic behavior of the known Centaurs. Our analysis has revealed that the two types of chaotic evolution are quantitatively distinguishable: (1) the random walk-type behavior is well described by so-called generalized diffusion in which the rms deviation of the semimajor axis grows with time t as ~t^H, with Hurst exponent H in the range 0.22–0.95, however (2) orbital evolution dominated by intermittent resonance sticking, with sudden jumps from one mean motion resonance to another, has poorly defined H. We further find that these two types of behavior are correlated with Centaur dynamical lifetime: most Centaurs whose dynamical lifetime is less than ~22 Myr exhibit generalized diffusion, whereas most Centaurs of longer dynamical lifetimes exhibit intermittent resonance sticking. We also find that Centaurs in the diffusing class are likely to evolve into Jupiter-family comets during their dynamical lifetimes, while those in the resonance-hopping class do not.

📄 Content

Two Dynamical Classes of Centaurs Brenae L. Baileya, Renu Malhotrab aProgram in Applied Mathematics, 617 N. Santa Rita, The University of Arizona, Tucson, AZ 85721 bLunar and Planetary Laboratory, 1629 E. University Blvd., The University of Arizona, Tucson, AZ 85721 Abstract The Centaurs are a transient population of small bodies in the outer so- lar system whose orbits are strongly chaotic. These objects typically suffer significant changes of orbital parameters on timescales of a few thousand years, and their orbital evolution exhibits two types of behaviors described qualitatively as random-walk and resonance-sticking. We have analyzed the chaotic behavior of the known Centaurs. Our analysis has revealed that the two types of chaotic evolution are quantitatively distinguishable: (1) the random walk-type behavior is well described by so-called generalized diffu- sion in which the rms deviation of the semimajor axis grows with time t as ∼tH, with Hurst exponent H in the range 0.22–0.95, however (2) orbital evolution dominated by intermittent resonance sticking, with sudden jumps from one mean motion resonance to another, has poorly defined H. We further find that these two types of behavior are correlated with Centaur dynamical lifetime: most Centaurs whose dynamical lifetime is less than ∼ 22 Myr exhibit generalized diffusion, whereas most Centaurs of longer dy- namical lifetimes exhibit intermittent resonance sticking. We also find that Centaurs in the diffusing class are likely to evolve into Jupiter-family comets during their dynamical lifetimes, while those in the resonance-hopping class do not.

1. Introduction The Centaurs are a dynamical class of small bodies in the outer solar system whose orbital parameters lie in a range intermediate between those Email addresses: bbailey@math.arizona.edu (Brenae L. Bailey), renu@lpl.arizona.edu (Renu Malhotra) Accepted for publication in Icarus arXiv:0906.4795v1 [astro-ph.EP] 25 Jun 2009 of the Kuiper belt and of the Jupiter-family comets. Numerical simulations have found that the Centaurs are typically removed from the solar system on timescales of only a few million years (Levison and Duncan, 1997; Dones et al., 1996; Tiscareno and Malhotra, 2003; Horner et al., 2004; Di Sisto and Brunini, 2007). These dynamical lifetimes are very short compared to the age of the solar system, implying that the Centaurs are a transitional population with a source elsewhere in the system. Likely source populations are the several dynamical subclasses of the Kuiper belt beyond Neptune (Levison and Duncan, 1997; Volk and Malhotra, 2008). Possible sinks of the Centaur population include the Kuiper belt’s scattered disk, the Jupiter- family comets, and the Oort cloud; Centaurs are also removed from the solar system by ejection on hyperbolic orbits or by collisions with a planet. Numerical analysis of their orbital evolution shows that these objects typi- cally suffer frequent close encounters with the giant planets and their orbits are strongly chaotic. Previous studies have provided detailed qualitative descriptions of the different types of chaotic behavior of Centaurs. The present study aims for a quantitative analysis of Centaur chaotic dynamics by using a generalized diffusion approach, which is a relatively new tool in solar system dynamics. Towards this end, we started with the known sample of Centaurs, and we carried out a 100 million year (Myr) numerical integration of their orbits under the perturbing influence of the four giant planets. (The length of this integration is more than ten times the median dynamical lifetimes of the ob- served Centaurs found in previous studies.) We then analyzed the Centaurs’ fluctuations in semimajor axis to determine how the root mean square fluc- tuations evolve over time. We found two distinct types of evolution of the semimajor axis fluctuations. The first is characterized by diffusion-like evo- lution, wherein the mean square fluctuations of the semimajor axis increase as a power law of time. The second type does not show this power law be- havior; instead, the fluctuations increase slowly at short timescales and more rapidly at larger timescales, suggesting that multiple processes are at work. These two types of behavior are strongly correlated with Centaur lifetime: with few exceptions, Centaurs exhibiting the diffusion-like behavior have dynamical lifetimes shorter than ∼22 Myr, whereas the second type have longer dynamical lifetimes. We also find that the latter group of Centaurs are strongly correlated with the ‘resonance-sticking’ behavior noted qualita- tively in previous studies, in which Centaurs become temporarily trapped in mean motion resonances with the giant planets; these Centaurs typically hop from one resonance to another for much of their dynamical lifetimes. Our analysis shows that the two types of behavior can be objectively and quan- 2 titatively distinguished, and suggests that the Centaurs may be comprised of two distinct dynamical

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