ON THE DYNAMICS AND TIDAL DISSIPATION RATE OF THE WHITE DWARF IN 4U 1820-30

Abstract

It has been suggested that the 170 day period in the light curve of the low\nmass X-ray binary 4U 1820-30 arises from the presence of a third body with a\nlarge inclination to the binary orbit. We show that this long period motion\narises if the system is librating around the stable fixed point in a Kozai\nresonance. We demonstrate that mass transfer drives the system toward this\nfixed point, and calculate, both analytically and via numerical integrations,\nthat the period of libration is of order 170 days when the mutual inclination\nis near the Kozai critical value. The non-zero eccentricity of the binary,\ncombined with tidal dissipation, implies that the rate of change of the binary\nperiod would be slower than, or even of opposite sign to, that implied by\nstandard mass transfer models. If the 170 day period results from libration,\nthen, contrary to appearances, the orbital period of the inner binary is\nincreasing with time; in that case, (e/0.009)^2Q/k_2 > 2.5 x 10^9, where k_2 =\n0.01 is the tidal Love number and e = 0.009 is the fiducial eccentricity of the\ninner binary. It appears unlikely that the observed negative period derivative\nresults from the smaller than expected (but positive) value of \\dot P combined\nwith the previously suggested acceleration of the system in the gravitational\nfield of the host globular cluster NGC 6624. The discrepancy between the\nobserved and expected period derivative requires further investigation.\n