The frequency of Kozai-Lidov disc oscillation driven giant outbursts in Be/X-ray binaries

Giant outbursts of Be/X-ray binaries may occur when a Be-star disc undergoes strong eccentricity growth due to the Kozai-Lidov (KL) mechanism. The KL effect acts on a disc that is highly inclined to the binary orbital plane provided that the disc aspect ratio is sufficiently small. The eccentric disc overflows its Roche lobe and material flows from the Be star disc over to the companion neutron star causing X-ray activity.With N-body simulations and steady state decretion disc models we explore system parameters for which a disc in the Be/X-ray binary 4U 0115+634 is KL unstable and the resulting time-scale for the oscillations. We find good agreement between predictions of the model and the observed giant outburst time-scale provided that the disc is not completely destroyed by the outburst. This allows the outer disc to be replenished between outbursts and a sufficiently short KL oscillation time-scale. An initially eccentric disc has a shorter KL oscillation time-scale compared to an initially circular orbit disc. We suggest that the chaotic nature of the outbursts is caused by the sensitivity of the mechanism to the distribution of material within the disc. The outbursts continue provided that the Be star supplies material that is sufficiently misaligned to the binary orbital plane.We generalize our results to Be/X-ray binaries with varying orbital period and find that if the Be star disc is flared, it is more likely to be unstable to KL oscillations in a smaller orbital period binary, in agreement with observations.