2002A&A...386..891B

We include the tidal instability due to the 3:1 resonance in the disc instability model developed by Hameury et al. (1998MNRAS.298.1048H) and modified by Buat-Menard et al. (2001A&A...366..612B). We confirm earlier results by Osaki (1989PASJ...41.1005O) that the tidal instability can account for the SU UMa light curves. We show that in ultra-low mass ratio systems such as ER UMa stars and WZ Sge stars, the superoutburst ends while the disc is still eccentric, as proposed by Hellier (2001). However, since the disc shrinks rapidly once a cooling wave has started, the eccentricity should stop shortly after the end of a superoutburst. This result disagrees with the suggestion by Hellier that decoupling the thermal and tidal instability in the TTI model can account for late superhumps and echo outbursts in ultra-low mass ratio systems. We propose instead that ER UMa short supercycles can be explained either by the alternation of narrow and wide outbursts similar to those occurring in SS Cyg, or by the effects of irradiation (Hameury et al., 2000A&A...353..244H). In both cases, we predict that superhumps should be permanent, which is suggested by observations (Gao et al., 1999ApJ...527L..55G). We can also reproduce light curves similar to those of EG Cnc, varying the mass transfer rate in a TTI model including both irradiation and the presence of an inner hole in the disc.