It is now widely accepted that most ultraluminous X-ray sources (ULXs) are binary systems whose large (above $10^{39}$ erg s$^{-1}$) apparent luminosities are explained by super-Eddington accretion onto a stellar-mass compact object. Many of the ULXs
, especially those containing magnetized neutron stars, are highly variable; some exhibit transient behaviour. Large luminosities might imply large accretion discs that could be therefore prone to the thermal-viscous instability known to drive outbursts of dwarf novae and low-mass X-ray binary transient sources. The aim of this paper is to extend and generalize the X-ray transient disc-instability model to the case of large (outer radius larger than $10^{12}$ cm) accretion discs and apply it to the description of systems with super-Eddington accretion rates at outburst and, in some cases, super-Eddington mass transfer rates. We have used our disc-instability-model code to calculate the time evolution of the accretion disc and the outburst properties. We show that, provided that self-irradiation of the accretion disc is efficient even when the accretion rate exceeds the Eddington value, possibly due to scattering back of the X-ray flux emitted by the central parts of the disc on the outer portions of the disc, heating fronts can reach the discs outer edge generating high accretion rates. We also provide analytical approximations for the observable properties of the outbursts. We have reproduced successfully the observed properties of galactic transients with large discs, such as V404 Cyg, as well as some ULXs such as M51 XT-1. Our model can reproduce the peak luminosity and decay time of ESO 243-39 HLX-1 outbursts if the accretor is a neutron star. Observational tests of our predicted relations between the outburst duration and decay time with peak luminosity would be most welcome.
I review the basics of the disc instability model (DIM) for dwarf novae and soft-X-ray transients and its most recent developments, as well as the current limitations of the model, focusing on the dwarf nova case. Although the DIM uses the Shakura-Su
nyaev prescription for angular momentum transport, which we know now to be at best inaccurate, it is surprisingly efficient in reproducing the outbursts of dwarf novae and soft X-ray transients, provided that some ingredients, such as irradiation of the accretion disc and of the donor star, mass transfer variations, truncation of the inner disc, etc., are added to the basic model. As recently realized, taking into account the existence of winds and outflows and of the torque they exert on the accretion disc may significantly impact the model. I also discuss the origin of the superoutbursts that are probably due to a combination of variations of the mass transfer rate and of a tidal instability. I finally mention a number of unsolved problems and caveats, among which the most embarrassing one is the modelling of the low state. Despite significant progresses in the past few years both on our understanding of angular momentum transport, the DIM is still needed for understanding transient systems.
FO Aquarii, an asynchronous magnetic cataclysmic variable (intermediate polar) went into a low-state in 2016, from which it slowly and steadily recovered without showing dwarf nova outbursts. This requires explanation since in a low-state, the mass-t
ransfer rate is in principle too low for the disc to be fully ionized and the disc should be subject to the standard thermal and viscous instability observed in dwarf novae. We investigate the conditions under which an accretion disc in an intermediate polar could exhibit a luminosity drop of 2 magnitudes in the optical band without showing outbursts. We use our numerical code for the time evolution of accretion discs, including other light sources from the system (primary, secondary, hot spot). We show that although it is marginally possible for the accretion disc in the low-state to stay on the hot stable branch, the required mass-transfer rate in the normal state would then have to be extremely high, of the order of 10$^{19}$ gs$^{-1}$ or even larger. This would make the system so intrinsically bright that its distance should be much larger than allowed by all estimates. We show that observations of FO Aqr are well accounted for by the same mechanism that we have suggested as explaining the absence of outbursts during low states of VY Scl stars: during the decay, the magnetospheric radius exceeds the circularization radius, so that the disc disappears before it enters the instability strip for dwarf nova outbursts. Our results are unaffected, and even reinforced, if accretion proceeds both via the accretion disc and directly via the stream during some intermediate stages; the detailed process through which the disc disappears still needs investigations.
Recent observations of two unusual Z Cam systems, V513 Cas and IW And have shown light curves that seem to contradict the disc-instability model for dwarf novae: outbursts are appearing during standstills of the system when according to the model, th
e disc is supposed to be in a hot quasi-equilibrium state. We investigate what additional physical processes need to be included in the model to reconcile it with observations of such anomalous Z Cam systems. We used our code for modeling thermal-viscous outbursts of the accretion discs and determined what types of mass-transfer variations reproduce the observed light curves. Outbursts of mass transfer (with a duration of a few days, with a short rise time and an exponential decay) from the stellar companion will account for the observed properties of V513 Cas and IW And, provided they are followed by a short but significant mass-transfer dip. The total mass involved in outbursts is of the order of 10$^{23}$g. We studied the possible origins of these mass transfer outbursts and showed that they most probably result from a giant flare near the secondary star surface, possibly due to the absence of star spots in the $L_1$ region.
The study of outer disc radius variations in close binary systems is important for understanding the structure and evolution of accretion discs. These variations are predicted by models of both quasi steady and time-dependent discs, and these predict
ions can be confronted with observations. We consider theoretical and observational consequences of such variations in cataclysmic variables and low mass X-ray binaries. We find that the action of tidal torques, that determine the outer radius at which the disc is truncated, must be important also well inside the tidal radius. We conclude that it is doubtful that the tidal-thermal instability is responsible for the superoutburst/superhump phenomena in dwarf novae, and confirm that it cannot be the reason for the outbursts of soft X-ray transients. It is likely that tidal torques play a role during superoutbursts of very-low mass-ratio systems but they cannot be the main and only cause of superhumps.
