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. They show that for a system with an extreme mass-ratio q=0.15, the disc is tidally unstable and can become asymmetric and slowly rotate in the inertial frame of reference. The tidal stresses raised in this disc by the secondary produce a peak in the light curve of order 30 per cent which recurs with a period 3.5 per cent longer than that of the orbit. This is interpreted as the superhump. Analytic considerations show that only for systems with mass-ratios more extreme than approximately 4 :: 1 will such behaviour occur, which is consistent with the known mass-ratio of SU UMa stars and other cataclysmic variables. Arguments based on the observed occurrence of superhumps in SU UMa stars are advanced which suggest that outbursts are periods of high disc viscosity whereas in quiescence the disc is in a low-viscosity state. This supports the general predictions of disc-instability models over mass-transfer driven bursts. It is, however, found to be likely that mass-transfer is high during the superoutburst of SU UMa stars.