Tidal generation of gravitational waves from orbiting Newtonian stars. I - General formalism

Details Tidal generation of gravitational waves from orbiting Newtonian stars. I - General formalism Tidal generation of gravitational waves from orbiting Newtonian stars. I - General formalism

Sep 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977apj...216..914t&link_type=abstract

Astrophysical Journal, Part 1, vol. 216, Sept. 15, 1977, p. 914-929.

Astronomy and Astrophysics

Astrophysics

12

Binary Stars, Gravitational Fields, Gravitational Waves, Tides, Harmonic Oscillators, Perturbation Theory, Quadrupoles, Spectrum Analysis, Vibration Mode

Scientific paper

A general formalism is presented for calculating the gravitational radiation produced by tidally generated internal motions in a system of two Newtonian and isentropic stars that are static and spherically symmetric when unperturbed. The tidally induced internal motions of one star are computed by a linear normal-mode analysis and then used to calculate the tidally produced gravitational-radiation potential (hTT) by a multipole analysis in the Newtonian limit. The differential equations for the normal modes of the star are evaluated, and the tidal perturbation potential is expanded in a Fourier integral. The results obtained show that the nature of the radiation falls into two categories if the damping time for l = 2 oscillations of the star is assumed to be much greater than the time scale of the tidal perturbation. It is found that if the damping time is much less than the time between periastron passages, the frequency spectrum of hTT will consist only of the l = 2 eigenfrequencies near the fundamental l = 2 eigenfrequency. However, if the damping time is much greater than the time between periastron passages, the gravitational-radiation spectrum will be similar to that resulting from the orbital motion.

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