Context. Outbursting AM CVn stars exhibit outbursts similar to those observed in different types of dwarf novae. Their light-curves combine the characteristic features of SU UMa, ER UMa, Z Cam, and WZ Sge-type systems but also show a variety of properties never observed in dwarf novae. The compactness of AM CVn orbits and their unusual chemical composition make these systems valuable testbeds for outburst models. Aims. We aim for a better understanding of the role of helium in the accretion disc instability mechanism, testing the model for dwarf novae outbursts in the case of AM CVn stars, and aim to explain the outburst light-curves of these ultra-compact binaries. Methods. We calculated the properties of the hydrogen-free AM CVn stars using our previously developed numerical code adapted to the different chemical composition of these systems and supplemented with formulae accounting for mass transfer rate variations, additional sources of the disc heating, and the primary's magnetic field. Results. We discovered how helium-dominated discs react to the thermal-viscous instability and were able to reproduce various features of the outburst cycles in the light-curves of AM CVn stars. Conclusions. The AM CVn outbursts can be explained by the suitably adapted dwarf-nova disc instability model but, as in the case of its application to hydrogen-dominated cataclysmic variables, one has to resort to additional mechanisms to account for the observed superoutbursts, dips, cycling states, and standstills. We show that the enhanced mass-transfer rate, due presumably to variable irradiation of the secondary, must not only be taken into account but is a determining factor that shapes AM CVn star outbursts. The cause of the variable secondary's irradiation has yet to be understood; the best candidate is the precession of a tilted/warped disc.

We present the results of a two and a half year optical photometric monitoring programme covering 16 AM CVn binaries using the Liverpool Telescope on La Palma. We detected outbursts in seven systems, one of which (SDSS J0129) was seen in outburst for the first time. Our study coupled with existing data shows that ∼1/3 of these helium-rich accreting compact binaries show outbursts. The orbital period of the outbursting systems lies in the range 24-44 min and is remarkably consistent with disc-instability predictions. The characteristics of the outbursts seem to be broadly correlated with their orbital period (and hence mass transfer rate). Systems which have short periods (<30 min) tend to exhibit outbursts lasting 1-2 weeks and often show a distinct 'dip' in flux shortly after the onset of the burst. We explore the nature of these dips which are also seen in the near-ultraviolet. The longer period bursters show higher amplitude events (5 mag) that can last several months. We have made simulations to estimate how many outbursts we are likely to have missed.

Context. The physical mechanisms driving angular momentum transport in accretion discs are still unknown. Although it is generally accepted that, in hot discs, the turbulence triggered by the magneto-rotational instability is at the origin of the accretion process in Keplerian discs, it has been found that the values of the stress-to-pressure ratio (the α "viscosity" parameter) deduced from observations of outbursting discs are an order of magnitude higher than those obtained in numerical simulations. Aims. We test the conclusion about the observation-deduced value of α using a new set of data and comparing the results with model outbursts. Methods. We analyse a set of observations of dwarf-nova and AM CVn star outbursts and from the measured decay times determine the hot-disc viscosity parameter α h . We determine if and how this method is model dependent. From the dwarf-nova disc instability model we determine an amplitude vs. recurrence-time relation and compare it to the empirical Kukarkin-Parenago relation between the same, but observed, quantities. Results. We found that all methods we tried, including the one based on the amplitude vs. recurrence-time relation, imply α h ∼ 0.1−0.2 and exclude values an order of magnitude lower. Conclusions. The serious discrepancy between the observed and the MRI-calculated values of the accretion disc viscosity parameter α is therefore real since there can be no doubt about the validity of the values deduced from observations of disc outbursts.

The phenomenological Disc Instability Model has been successful in reproducing the observed light curves of dwarf nova outbursts by invoking an enhanced Shakura-Sunyaev α parameter ∼ 0.1 − 0.2 in outburst compared to a low value ∼ 0.01 in quiescence. Recent thermodynamically consistent simulations of magnetorotational (MRI) turbulence with appropriate opacities and equation of state for dwarf nova accretion discs have found that thermal convection enhances α in discs in outburst, but only near the hydrogen ionization transition. At higher temperatures, convection no longer exists and α returns to the low value comparable to that in quiescence. In order to check whether this enhancement near the hydrogen ionization transition is sufficient to reproduce observed light curves, we incorporate this MRI-based variation in α into the Disc Instability Model, as well as simulation-based models of turbulent dissipation and convective transport. These MRI-based models can successfully reproduce observed outburst and quiescence durations, as well as outburst amplitudes, albeit with different parameters from the standard Disc Instability Models. The MRIbased model lightcurves exhibit reflares in the decay from outburst, which are not generally observed in dwarf novae. However, we highlight the problematic aspects of the quiescence physics in the Disc Instability Model and MRI simulations that are responsible for this behavior.

We present multiwavelength observations of the helium-dominated accreting binary KL Dra which has an orbital period of 25 min. Our ground-based optical monitoring programme using the Liverpool Telescope has revealed KL Dra to show frequent outbursts. Although our coverage is not uniform, our observations are consistent with the outbursts recurring on a time-scale of ∼60 d. Observations made using Swift show that the outbursts occur with a similar amplitude and duration (2 weeks) at both UV and optical energies. Although KL Dra is a weak X-ray source, we find no significant evidence that the X-ray flux varies over the course of an outburst cycle. We can reproduce the main features of the 60-d outburst cycle using the disc instability model and a helium-dominated accretion flow. Although the outbursts of KL Dra are very similar to those of the hydrogen-accreting dwarf novae, we cannot exclude the fact that they are the AM CVn equivalent of WZ Sge-type outbursts. With outbursts occurring every ∼ 2 months, KL Dra is an excellent target to study helium-dominated accretion flows in general.