SPH simulations of tidally unstable accretion discs in cataclysmic variables

We numerically study the precessing disc model for superhumps in the SU UMa subclass of cataclysmic variables, using a two-dimensional SPH code specifically designed for thin disc problems. Two disc simulations for a binary with mass ratio q = 3/17 (similar to OY Car) are performed, in order to investigate the Lubow tidal resonance instability mechanism. In the first calculation, a disc evolves under steady mass transfer from L(1). In the second simulation, mass is added in a Keplerian orbit to the inner disc. The two discs follow similar evolutionary paths. However the L(1) stream-disc interaction is found to slow the disc's radial expansion and to circularize gas orbits. The initial eccentricity growth in our simulations is exponential at a rate slightly less than predicted by Lubow. We do not observe the clearing of material from the resonance region, via the disc's tidal response to the m = 2 component of the binary potential, described by Lubow. Instead the m = 2 response weakens as the disc eccentricity increases. Both discs reach an eccentric equilibrium state in which they undergo prograde precession. The rate of viscous energy dissipation in the discs has a periodic excess with a period matching the period of the discs' rotation in the frame corotating with the binary. The source is a large region in the outer disc. The mechanism by which the excess is produced is identified. The time taken for the periodic excess to develop is consistent with the first appearance of superhumps in a superoutburst.