Nonlinear damping of oscillations in tidal-capture binaries

Pawan Kumar, Jeremy Goodman

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83 Scopus citations


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 ≈ 4E0.42-1/2 days, where E0,42 is the initial energy of the primary mode in units of 1042 ergs, and the number of daughter modes N ∼ 1010E0,425/4. The growth rate is approximately equal to the angular frequency of the primary mode times its dimensionless radial amplitude, δR/R* ≈ 0.002E0,421/2. 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 E0 > 1040 ergs. This is orders of magnitude smaller than usual radiative damping time. In fact, nonlinear mode interaction may be the dominant damping process if E0> ≳ 1037 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/E0; this damping time is about 30 days for E0 ≈ 1045 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 languageEnglish (US)
Pages (from-to)946-956
Number of pages11
JournalAstrophysical Journal
Issue number2 PART I
StatePublished - 1996

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Binaries: close
  • Stars: interiors
  • Stars: oscillations


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