On the dynamics and tidal dissipation rate of the white dwarf in 4U 1820-30

Abstract

It has been suggested that the 170day period in the light curve of the low-mass X-ray binary 4U 1820-30 arises from the presence of a third body with a large inclination to the binary orbit. We show that this long-period motion arises if the system is librating around the stable fixed point in a Kozai resonance. We demonstrate that mass transfer drives the system toward this fixed point and calculate, both analytically and via numerical integrations, that the period of libration is of order 170days when the mutual inclination is near the Kozai critical value. The non-zero eccentricity of the binary, combined with tidal dissipation, implies that the rate of change of the binary period would be slower than, or even of opposite sign to, that implied by standard mass transfer models. If the 170day period results from libration, then, contrary to appearances, the orbital period of the inner binary is increasing with time; in that case, (e/0.009)2 Q/k2 ≳ 2.5 × 10 9, where k2 ≈ 0.01 is the tidal Love number and e = 0.009 is the fiducial eccentricity of the inner binary. It appears unlikely that the observed negative period derivative results from the smaller than expected (but positive) value of combined with the previously suggested acceleration of the system in the gravitational field of the host globular cluster NGC 6624. The discrepancy between the observed and the expected period derivative requires further investigation. © 2012 The American Astronomical Society. All rights reserved.