Physics
Scientific paper
Jan 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aas...21340311l&link_type=abstract
American Astronomical Society, AAS Meeting #213, #403.11; Bulletin of the American Astronomical Society, Vol. 41, p.195
Physics
Scientific paper
This work continues previous explorations of the effects of turbulence on mean motion resonances in extrasolar planetary systems. Turbulence is expected to be present in the circumstellar disks that give rise to planets, and these fluctuations act to compromise resonant configurations. We study how interactions between the planets affect mean motion resonance, both by direction numerical integrations of the 3-body problem with additional forcing due to turbulence, and with Fokker-Planck equations that describe the time evolution of an ensemble of such systems. With this combined approach, we elucidate the basic physics of how turbulence can remove extrasolar planetary systems from mean motion resonance. Ensembles of these systems exhibit two regimes of behavior, where the fraction of the bound states decreases as a power-law or as an exponential. We propose a model which explains both behaviors. For systems that have weak interactions between the planets, the model reduces to that of a stochastic pendulum, and the fraction of bound states decreases as a power-law. For highly interactive systems, however, the dynamics are more complicated and the fraction of bound states decreases exponentially with time. We show how planetary interactions lead to drift terms in the Fokker-Planck equation and account for this exponential behavior. In addition to clarifying the physical processes involved, these findings strengthen the original claim that turbulence implies that mean motions resonances should be rare.
Adams Fred C.
Bloch T. M.
Lecoanet Daniel
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