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We show that discs accreting onto the magnetosphere of a rotating star can end up in a trapped state, in which the inner edge of the disc stays near the corotation radius, even at low and varying accretion rates. The accretion in these trapped states can be steady or cyclic; we explore these states over wide range of parameter space. We find two distinct regions of instability, one related to the buildup and release of mass in the disk outside corotation, the other to mass storage within the transition region near corotation. With a set of calculations over long time scales we show how trapped states evolve from both nonaccreting and fully accreting initial conditions, and also calculate the effects of cyclic accretion on the spin evolution of the star. Observations of cycles such as found here would provide important clues on the physics of magnetospheric accretion. Recent observations of cyclic and other unusual variability in T Tauri stars (EXors) and X-ray binaries are discussed in this context.
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The Eclipse Mapping Method is an indirect imaging technique that transforms the shape of the eclipse light curve into a map of the surface brightness distribution of the occulted regions. Three decades of application of this technique to the investigation of the structure, the spectrum and the time evolution of accretion discs around white dwarfs in cataclysmic variables have enriched our understanding of these accretion devices with a wealth of details such as (but not limited to) moving heating/cooling waves during outbursts in dwarf novae, tidally-induced spiral shocks of emitting gas with sub-Keplerian velocities, elliptical precessing discs associated to superhumps, and measurements of the radial run of the disc viscosity through the mapping of the disc flickering sources. This chapter reviews the principles of the method, discusses its performance, limitations, useful error propagation procedures, as well as highlights a selection of applications aimed at showing the possible scientific problems that have been and may be addresses with it.
It is quite likely that self-gravity will play an important role in the evolution of accretion discs, in particular those around young stars, and those around supermassive black holes. We summarise, here, our current understanding of the evolution of such discs, focussing more on discs in young stellar system, than on discs in active galactic nuclei. We consider the conditions under which such discs may fragment to form bound objects, and when they might, instead, be expected to settle into a quasi-steady, self-regulated state. We also discuss how this understanding may depend on the mass of the disc relative to the mass of the central object, and how it might depend on the presence of external irradiation. Additionally, we consider whether or not fragmentation might be stochastic, where we might expect it to occur in an actual protostellar disc, and if there is any evidence for fragmentation actually playing a role in the formation of planetary-mass bodies. Although there are still a number of outstanding issue, such as the convergence of simulations of self-gravitating discs, whether or not there is more than one mode of fragmentation, and quite what role self-gravitating discs may play in the planet formation process, our general understanding of these systems seems quite robust.
Rings and gaps have been observed in a wide range of protoplanetary discs, from young systems like HLTau to older discs like TW Hydra. Recent disc simulations have shown that magnetohydrodynamic (MHD) turbulence (in the ideal or non-ideal regime) can lead to the formation of rings and be an alternative to the embedded planets scenario. In this paper, we investigate how these ring form in this context and seek a generic formation process, taking into account the various dissipative regimes and magnetizations probed by the past simulations. We identify the existence of a linear and secular instability, driven by MHD winds, and giving birth to rings of gas having a width larger than the disc scale height. We show that the linear theory is able to make reliable predictions regarding the growth rates, ring/gap contrast and spacing, by comparing these predictions to a series of 2D (axisymmetric) and 3D MHD numerical simulations. In addition, we demonstrate that these rings can act as dust traps provided that the disc is sufficiently magnetised, with plasma beta lower than $10^4$. Given its robustness, the process identified in this paper could have important implications, not only for protoplanetary discs but also for a wide range of accreting systems threaded by large-scale magnetic fields.
Dust plays a key role in the formation of planets and its emission also provides one of our most accessible views of protoplanetary discs. If set by radiative equilibrium with the central star, the temperature of dust in the disc plateaus at around $10-20$K in the outer regions. However sufficiently nearby massive stars can heat the outer disc to substantially higher temperatures. In this paper we study the radiative equilibrium temperature of discs in the presence of massive external sources and gauge the effect that it has on millimetre dust mass estimates. Since millimetre grains are not entrained in any wind we focus on geometrically simple 2D-axisymmetric disc models using radiative transfer calculations with both the host star and an external source. Recent surveys have searched for evidence of massive stars influencing disc evolution using disc properties as a function of projected separation. In assuming a disc temperature of $20$K for a disc a distance $D$ from a strong radiation source, disc masses are overestimated by a factor that scales with $D^{-1/2}$ interior to the separation that external heating becomes important. This could significantly alter dust mass estimates of discs in close proximity to $theta^1$C in the Orion Nebular Cluster. We also make an initial assessment of the effect upon snow lines. Within a parsec of an O star like $theta^1$C a CO snow line no longer exists, though the water snow line is virtually unaffected except for very close separations of $leq0.01,$pc.
The migration of low-mass planets is driven by the differential Lindblad torque and the corotation torque in non-magnetic viscous models of protoplanetary discs. The corotation torque has recently received detailed attention as it may slow down, stall, or reverse migration. In laminar viscous disc models, the long-term evolution of the corotation torque is intimately related to viscous and thermal diffusion processes in the planets horseshoe region. This paper examines the properties of the corotation torque in discs where MHD turbulence develops as a result of the magnetorotational instability, considering a weak initial toroidal magnetic field. We present results of 3D MHD simulations carried out with two different codes. Non-ideal MHD effects and the discs vertical stratification are neglected, and locally isothermal disc models are considered. The running time-averaged torque exerted by the disc on a fixed planet is evaluated in three disc models. We first present results with an inner disc cavity (planet trap). As in viscous disc models, the planet is found to experience a positive running time-averaged torque over several hundred orbits, which highlights the existence of an unsaturated corotation torque maintained in the long term in MHD turbulent discs. Two disc models with initial power-law density and temperature profiles are also adopted, in which the time-averaged torque is found to be in decent agreement with its counterpart in laminar viscous disc models with similar viscosity at the planet location. Detailed analysis of the averaged torque density distributions indicates that the differential Lindblad torque takes very similar values in MHD turbulent and laminar viscous discs, and there exists an unsaturated corotation torque in MHD turbulent discs. This analysis also reveals the existence of an additional corotation torque in weakly magnetized discs.
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