The role of chaos in the circularization of tidal capture binaries. I. The chaos boundary

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Abstract

A self-consistent model for binary evolution devised by Gingold & Monaghan (1980) is used to show that two distinctly different types of behavior are possible for close eccentric binaries. The model is based on a linear adiabatic normal mode analysis of the problem, which allows detailed examination of the transfer of energy from the orbit to the tides. We show that for most binaries, energy is exchanged quasi-periodically, with the system regulating itself so that the maximum tidal energy always remains small, and no circulation takes place. In contrast, for a range of eccentricities and periastron separations chaotic behavior prevails, with the eccentricity following a random walk and with the energy transferred to the tides during a single periastron passage being up to an order of magnitude larger than that transferred during the initial periastron passage. These results have important consequences for the study of tidal capture binaries. The standard model (McMillan, McDermott, & Taam 1987; Ray, Kembhavi, & Antia 1987) assumes that the energy transferred to the tides during a periastron encounter is independent of the oscillatory state of the stars, and that the amount of tidal energy present at any time can be calculated using a formula which (accurately) gives the amount deposited after the first encounter (Press & Teukolsky 1977). The calculations presented here show that a self-consistent treatment is necessary in order to study the dynamical evolution of tidal capture binaries.

Original languageEnglish
Pages (from-to)722-731
Number of pages10
JournalThe Astrophysical Journal
Volume450
Issue number2
DOIs
Publication statusPublished - 10 Sep 1995

Keywords

  • Binaries: close
  • Celestial mechanics
  • Chaos
  • Globular clusters: general
  • Pulsars: individual (PSR J0045 - 7319)
  • Stellar dynamics
  • X-rays: stars

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