Nonlinear Damping of Oscillations in Tidal-Capture Binaries

Pawan Kumar; Jeremy Goodman

doi:10.1086/177565

paper

Nonlinear Damping of Oscillations in Tidal-Capture Binaries

arXiv:astro-ph/9509112 · doi:10.1086/177565

Abstract

We calculate the damping of quadrupole f and low order g modes (primary modes) by nonlinear coupling to other modes of the star. This damping is orders of magnitude more rapid than direct radiative damping when the primary amplitude is large, as in tidal capture. Primary modes destabilize high degree g-modes of half their frequency (daughter modes) by 3-mode coupling in radiative zones. In sunlike stars, the growth time $\equiv η^{- 1} \approx 4 E_{0, 42}^{- 1/2}$ days, where $E_{0, 42}$ is the initial energy of the primary mode in units of $1 0^{42}$ erg, and of order $1 0^{10} E_{0, 42}^{5/4}$ daughters are unstable. The growth rate is approximately equal to the angular frequency of the primary mode times its dimensionless radial amplitude, $δ R / R_{*} \approx 0.002 E_{0, 42}^{1/2}$ . Although the daughter modes are limited by their own nonlinearities, collectively they absorb most of the primary mode's energy after a time $\sim 10 η^{- 1}$ provided $E_{0}> 10^{40}~\mbox{erg}$. In fact nonlinear mode interaction may be the dominant damping process if $E_0\gtrsim 10^{37}~\mbox{erg}$. Our results have application to tidally captured main sequence globular cluster stars of mass $\ge 0.5 M_{\sun}$; the tidal energy is dissipated in the radiative core of the star in about a month, which is less than the initial orbital period.

AASTeX, 25 pages, plus 4 figures in compressed postscript. Revised only to wrap lines longer than 80 characters

Nonlinear Damping of Oscillations in Tidal-Capture Binaries

Abstract

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