We do find that the decoupling of the two instabilities can happen much more easily in ULMR systems than in other SU UMa stars. However, the tidal instability stops almost immediately after the end of the thermal-viscous instability (delay less than a day), because the disc shrinks very rapidly after the departure of a cooling wave. We estimate that it takes only a few days for the disc to return to a circular shape after the cessation of the tidal instability. This is still insufficient to explain late superhumps that are found tens of days after the superoutburst in some systems.
We propose instead that the discs in ER UMa systems are permanently eccentric, and that they should therefore have permanent superhumps; there are observational indications of this (Gao et al. 1999). The short supercycle is then due to either an alternation of narrow and wide outbursts as in SS Cyg (see Buat-Ménard et al. 2001), or to the effects of irradiation (see Hameury et al. 2000). Further observations of late superhumps should confirm their permanence in ER UMa stars.
As in Hameury et al. (1997), we propose that WZ Sge stars are in a stable cold state during quiescence. The superoutburst is then triggered by an enhancement of mass transfer rate, and echo outbursts are triggered while the mass transfer rate is still high after the superoutburst. However, simulated light curves are still somewhat different from observations; this might be due to our crude treatment of the secondary illumination.
Acknowledgements
This work was supported in part by a grant from Programme National de Physique Stellaire of the CNRS. We thank J. P. Lasota for a very careful reading of the manuscript and for helpful comments. We are grateful to the referee, Prof. Y. Osaki, for pointing out an error in one of the sets of parameters used.
Copyright ESO 2002