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Ruling out chaos in compact binary systems.

J D Schnittman1, F A Rasio

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

Physical Review Letters
|October 3, 2001
PubMed
Summary

This study on compact binary systems found no evidence of chaotic orbits during inspiral. The calculations suggest that orbital chaos will not hinder the detection of these gravitational wave events.

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Area of Science:

  • Astrophysics
  • General Relativity
  • Gravitational Waves

Background:

  • Compact binary systems, such as neutron stars and black holes, are key sources of gravitational waves.
  • The final inspiral phase before coalescence is crucial for gravitational wave emission.
  • Previous research suggested that spin-orbit and spin-spin couplings might induce chaotic behavior in these orbits.

Purpose of the Study:

  • To investigate the potential for chaotic orbits in compact binary systems during the final inspiral.
  • To determine if spin-orbit and spin-spin couplings lead to chaotic dynamics.
  • To assess the impact of potential chaos on the detectability of inspiral events.

Main Methods:

  • Integration of post-Newtonian equations of motion for compact binary systems.
  • Inclusion of spin-orbit and spin-spin coupling effects.
  • Calculation of trajectory divergence and estimation of the Lyapunov exponent (gamma) to quantify chaos.

Main Results:

  • No chaotic behavior was observed in the simulated compact binary systems.
  • A lower limit was established for the divergence time (t(L) = 1/gamma).
  • This divergence time was found to be significantly longer than the typical inspiral duration.

Conclusions:

  • The inclusion of spin-orbit and spin-spin couplings does not lead to chaotic orbits in compact binary inspirals.
  • The calculated long divergence time indicates that chaotic effects are unlikely to disrupt the inspiral process.
  • Gravitational wave signals from compact binary inspirals should be reliably detectable without adverse effects from orbital chaos.

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