On the Dynamics and Tidal Dissipation Rate of the White Dwarf in 4U 1820-30

TL;DR

This paper investigates the 170-day periodicity in the low mass X-ray binary 4U 1820-30, proposing it results from Kozai resonance libration, and explores implications for tidal dissipation and orbital period evolution.

Contribution

It demonstrates that the 170-day cycle arises from Kozai resonance libration and analyzes how mass transfer and tidal effects influence the system's orbital dynamics.

Findings

The 170-day period is consistent with Kozai resonance libration.

Tidal dissipation affects the rate of orbital period change.

The observed negative period derivative cannot be explained by current models.

Abstract

It has been suggested that the 170 day 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 170 days 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 170 day 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)^2Q/k_2 > 2.5 x 10^9, where k_2 = 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 \dot P 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 expected period derivative requires further investigation.