Numerical simulations of accretion discs - I. Superhumps : a tidal phenomenon of accretion discs.

Numerical simulations of the SU UMa star Z Cha in outburst are presented which demonstrate the role of the secondary's tidal influence upon the accretion flow and provide explanations for the superhumps seen in SU UMa stars. The results show that for a system with an extreme mass-ratio q = 0.15, the disk is tidally unstable and can become asymmetric and slowly rotate in the inertial frame of reference. The tidal stresses raised in this disk by the secondary produce a peak in the light curve which is interpreted as the superhump. Such behavior will occur only for systems with mass-ratios more extreme than approximately 4:1, which is consistent with the known mass-ratio of SU UMa stars and other cataclysmic variables. It is suggested that outbursts are periods of high disk viscosity, while in quiescence the disk is in a low-viscosity state.