### Abstract

We calculate the damping of quadrupole f- and low-order g-modes (primary modes) by nonlinear coupling to other modes of the star. Primary modes destabilize high-degree g-modes of half their frequency (daughter modes) by 3-mode coupling in radiative zones. For Sun-like stars, the growth time ≡η^{-1} ≈ 4E_{0.42}^{-1/2} days, where E_{0,42} is the initial energy of the primary mode in units of 10^{42} ergs, and the number of daughter modes N ∼ 10^{10}E_{0,42}^{5/4}. The growth rate is approximately equal to the angular frequency of the primary mode times its dimensionless radial amplitude, δR/R* ≈ 0.002E_{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 ∼10η^{-1} provided E_{0} > 10^{40} ergs. This is orders of magnitude smaller than usual radiative damping time. In fact, nonlinear mode interaction may be the dominant damping process if E_{0}> ≳ 10^{37} ergs. These results have obvious application to tidally captured main-sequence globular cluster stars of mass ≥0.5 M_{⊙}; the tidal energy is dissipated in the radiative core of the star in about a month, which is less than the. initial orbital period. Nonlinear mode coupling is a less efficient damping process for fully convective stars, which lack g-modes. In convective stars, most of the tidal energy is in the quadrupole f-modes, which nonresonantly excite high-order p-modes of degree 0, 2, and 4. The resultant short-wavelength waves are more efficiently dissipated. The nonlinear damping time for f-modes is shown to be proportional to 1/E_{0}; this damping time is about 30 days for E_{0} ≈ 10^{45} ergs expected in tidal captures. However, at such a large energy the system is very nonlinear: 4-mode and higher order couplings are as important as 3-mode couplings.

Original language | English (US) |
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Pages (from-to) | 946-956 |

Number of pages | 11 |

Journal | Astrophysical Journal |

Volume | 466 |

Issue number | 2 PART I |

DOIs | |

State | Published - Jan 1 1996 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

- Binaries: close
- Stars: interiors
- Stars: oscillations

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## Cite this

*Astrophysical Journal*,

*466*(2 PART I), 946-956. https://doi.org/10.1086/177565