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Paper: On the Dynamics of 4U 1820-30; Resonant Trapping and Tidal Dissipation Rate of the White Dwarf Secondary
Volume: 447, Evolution of Compact Binaries
Page: 257
Authors: Prodan, S.; Murray, N.
Abstract: The origin of the 170 day period in the light curve of the low mass X-ray binary 4U 1820-30 has been attributed to the presence of a third body with a large inclination to the binary orbit. In this work we interpret this long period motion as the period of libration around the stable fixed point in a Kozai resonance and demonstrate that mass transfer drives the system towards this fixed point. Our calculations, both analytic and numerical integrations, show that the period of libration is of order 170 days when the mutual inclination is near the Kozai critical value. Since the 170 day period results from libration, we require that the tidal dissipation of the white dwarf is such that the rate of change of the binary period is slower than that implied by standard mass transfer models, but, contrary to appearances, increasing with time. This results in a lower limit on the tidal dissipation factor (e/0.009)2Q/k2 ∼> 3.15 × 109, where k2 ≈ 0.01 is Love number and e = 0.009 is fiducial eccentricity of the inner binary. We argue that the observed negative period derivative does not result from the smaller than expected (but positive) value of dot P combined with the previously suggested acceleration of the system in the gravitational field of the host globular cluster NGC 6624.
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