To zeroth order a gap will be formed in a disc if the wind is faster at removing material from a given region than accretion is at pushing new material into it. It is classically assumed that for the largest part of their lives, the evolution of the surface density of discs can be well described by simple viscous theory [ 92 , 93 ]. These models predict a slow, homogeneous dispersal of the disc. These observations have motivated the development of theoretical models able to match this two-timescale and inside-out dispersal modus.
Photoevaporation from the central star is currently accepted as an important player in the late evolution of discs and has seen several dedicated theoretical efforts [ 94 — ]. All models of photoevaporation show that radiation from the central star heats the disc atmosphere, where a thermal wind is established. The mass loss rate of the wind must exceed the accretion rate in the disc for dispersal to set in. Young discs accrete at a vigorous rate, which naturally decreases as time goes by, until, after a few million years accretion rates fall to values smaller than the wind rates, allowing photoevaporation to take over the further evolution of the disc.
This scenario is based on the assumption that the mass accretion rate is radially constant throughout. While the community seems to agree on this broad brush picture, quantitatively speaking, the dispersal mechanism is still largely unconstrained. In fact, photoevaporation by energetic radiation from the central star is not the only way to produce a disc wind. Extended magnetically launched disc winds appear to be necessary to explain the properties of jets in young stars [ ] and models have been developed since the s [ ].
However, only recently non-ideal MHD effects have been incorporated, albeit with computational costs that have mostly limited the calculation to small regions of the disc. Some of these recent models, based on local simulations, suggest that even a weak vertical magnetic field can launch a wind [ ]. The wind can be so vigorous as to compete with photoevaporation for the dispersal of the disc and may even provide an efficient channel to remove angular momentum from the material in the disc, hence driving the accretion process.
Global MHD discs simulations have until very recently only been possible in the ideal limit [ , ], or including only Ohmic diffusion [ , ]. The most recent simulations in the ideal limit [ ], which improve on resolution and convergence compared to previous work, do not show winds that significantly contribute to the evolution of the surface density of the disc under the assumption made.
At the time of writing only one set of global simulations of protoplanetary discs including all three non-ideal MHD effects Ohmic and ambipolar diffusions, and the Hall drift has been performed [ ]. Discs are found to accrete in which case a disc wind is also present only for given configurations of the large-scale magnetic field, which thus remains an important uncertainty. The nature of disc accretion and the driving mechanisms behind disc winds are currently a rapidly developing and very active area of research.
An attempt at summarizing the state of the art at the time of writing follows. The source of the viscosity is, however, still a matter of debate. The standard paradigm for circumstellar disc accretion invokes the magneto-rotational instability MRI to drive turbulence [ ].
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The conditions to trigger MRI are that the gas is sufficiently ionized, that the disc is weakly, but non-negligibly magnetized and that the angular frequency decreases with radius. While the last two conditions are always satisfied in discs, there are uncertainties about the ionization structure of the gas. It is indeed often pointed out in the literature that large disc regions may be actually MRI-inactive, due to poor coupling of the gas to the magnetic fields.
Accretion in these cases is thought to happen in the outer layers surrounding the dead zones. These regions, however, may be dominated by non-ideal MHD effects e. Recent non-ideal MHD simulations [ , ] show that in the presence of even a weak net vertical magnetic field threading the disc, MRI is completely suppressed. As a result however a vigorous magnetocentrifugal wind is launched in these simulations.
The wind in this case also removes angular momentum from the disc and can thus drive accretion. Based on this approach, recent work has found that accretion is completely dominated by winds in most regions of the disc, with the MRI perhaps only playing a part in the outer regions, e.
The dispersal of planet-forming discs: theory confronts observations
In this scenario, the accretion and wind mass loss processes are strongly coupled by the field strength which drives both. While the suggestion of MHD winds driving accretion in discs is certainly tantalizing, it is currently too early to assess its validity. In particular, all attempts at constructing global models for the evolution of discs rely on a number of important assumptions about how critical parameters scale with radius [ ] and are sensitive to the amount of magnetic flux assumed to thread the disc.
Regardless of the detailed process es that provide the viscosity needed to drive accretion in discs, if the phenomenologically formulated alpha-description is roughly correct, then one expects the surface density to decrease as a power law of time and the radius to increase, as a result of viscous draining and spreading, i.
The implication is that viscously evolving discs should become progressively faint simultaneously at all wavelengths as a function of time. Owing to the temporal power law, the evolution should become progressively slower, such that discs should spend most of their lifetime in a homogeneously draining transition phase. To date there is no convincing observational evidence of any homogeneously draining disc. Viscosity is thus not the end of the story, rather an additional dispersal process must take over at advanced stages of disc evolution.
Mass loss via a disc wind, driven by photoevaporation by the central star, likely plays an important role, such that the evolution of the surface density of a disc switches from an accretion-dominated to a wind-dominated regime, marking the beginning of the final, rapid disc dispersal phase. However, if MHD winds dominate angular momentum transport in a significant part of the disc, the evolution of the surface density and of the mass accretion rate is unlikely to be well described by an alpha-formalism [ , ].
Theoretical work on photoevaporation has been recently reviewed by a number of authors [ 83 , , ]. We will only summarize the main mechanisms here, focusing on the current open questions and uncertainties, as well as on the specific predictions and the predictive power of current models.
Radiation from the central star penetrates the disc atmosphere and deposits energy in i. To zeroth order a thermal wind is established if the temperature of the gas at a given location becomes higher than the local escape temperature. The FUV and soft X-rays are thus expected to drive the strongest winds [ 97 — , ]. This is a fundamental question as the mass-loss rates implied by the different models can differ by orders of magnitude. Mass-loss rates crucially determine the timescales of disc dispersal for given initial disc conditions.
Attenuation of a model coronal spectrum through columns of neutral hydrogen. The spectra are in arbitrary units. Figure adapted from [ ]. Thus, the mass-loss rates predicted by the XEUV model for solar-type stars may vary strongly depending on the X-ray property of the central object.
X-ray surveys of young stars show approximately 2 orders of magnitude scatter in the X-ray luminosities of young solar-mass stars. The contribution of short term variability to the observed scatter is minor [ ], with intrinsic differences in stellar rotational velocities or internal structure being instead the dominant factor. The same scatter will then be reflected in the mass-loss rates, and thus in the expected lifetimes of their discs.
The same is not true for an EUV-only scenario where the dependence of the mass-loss rate on the EUV luminosity is much weaker. These models, however, do not perform a hydrodynamical calculation to obtain a solution for the wind. It is difficult to estimate the uncertainty introduced by the method, thus a comparison with hydrodynamical models [ 96 , 98 — ] is of limited relevance.
The wind profile, which determines the region of the disc that is most affected by photoevaporation, is also very different in each scenario [ 83 , ]. The X-ray profile is more extended than the EUV profile, which predicts mass loss only from a vary narrow range of disc radii, centred at the gravitational radius. The FUV model is again very different, showing mass loss from the outer regions of the disc and predicting in some cases an outside-in mode of dispersal.
The detailed profile of the photoevaporative wind has important consequences for the formation and migration of planets in the wind. As an example, it has recently been shown that changing the wind profile yields completely different distributions for the semi-major axes of giant planet in otherwise equal populations of discs losing mass globally at the same rate [ 5 ]. While the physics of photoevaporation is reasonably well understood, all current models are somewhat incomplete. The available FUV models focus on chemistry, but do not perform hydrodynamical calculations [ , ].
Current radiation hydrodynamic calculations of X-ray driven winds use realistic gas temperatures obtained from X-ray photoionization calculations [ ], but they do not include chemistry and ignore the dust phase [ 98 — ]. Indeed none of the existing models take into account dust evolution in the underlying disc and entrainment of grains in the wind self-consistently. Table 1 summarizes the main ingredients included by the models, as discussed above.
There are further important differences in the implementation of the various heating channels, as well as on assumptions made by the different codes. A full technical discussion of the different choices adopted and their influence of the derived mass loss rates and profiles is still at this stage, since not all ingredients are included in all models. A benchmarking exercise would be nevertheless useful at this stage in order to converge on a roadmap for future development. Including a comprehensive discussion of these early works is beyond the scope of this review.
Here we will focus on MHD winds only in the context of disc dispersal. Classically, MHD simulations in a local shearing box have been used to study the properties of turbulence driven by the MRI [ ]. More recently, vertically stratified local shearing box simulations have been used to investigate the possibility of MRI-driven disc winds [ , ]. Their model differed from previous work, that used initially toroidal and zero-net vertical flux magnetic fields [ ], by assuming vertical magnetic fields and outgoing boundary conditions.
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This was motivated by the assumption that discs may be threaded by net vertical magnetic fields that are connected to their parental molecular cloud. These rather short timescales, which are clearly in contrast with disc observations, do not account for global viscous accretion, which would slow down the process. Very recent work expands on these results to present one-dimensional models of disc evolution including the effects of viscous heating, in addition to the loss of mass and angular moment by the disc wind [ ]. The focus of this work is more on the early stages of evolution, when accretion heating is important and can give rise to density structures which show a positive radial slope for the surface density in the inner disc regions.
While this may have important implications for planetesimal formation and migration models, its relevance to the dispersal of discs is limited. The latest global ideal MHD simulation performed, at the time of writing this review, is for thin accretion discs threaded by net vertical magnetic fields [ ]. This work suggests that only very weak and episodic disc winds can be driven and these are not efficient at carrying angular momentum.
As mentioned in the previous section, however, local non-ideal MHD simulations suggest instead that in the presence of a weak net vertical magnetic field, MRI is completely suppressed, while a strong magnetocentrifugal wind is launched, which carries away disc angular momentum so efficiently to account for the measured accretion rates [ ]. One-dimensional, vertically integrated, disc evolution models including angular momentum redistribution and wind angular momentum loss have been constructed using a parametrization of the wind stress parameter from the vertically stratified ambipolar disc simulations [ , ].
For low initial magnetic field strengths discs are almost inviscid and very long lived. The behaviour of MHD dispersal models depends upon the radial evolution of the net field and how this couples to disc evolution, which is currently unknown [ ]. This study shows that, under the assumptions made, wind-driven accretion and mass loss, rather than MRI, dominate disc evolution.
Later work also tries to incorporate some thermodynamical effects using simplified prescriptions for disc temperature and the depth of the FUV penetration [ ]. In this work it is found that, while FUV penetration can have significant effects on the wind-driven accretion rates and fractional wind mass loss rates, the key parameter controlling the disc evolution timescales in their models is the amount of magnetic flux threading the disc.
This depends both on the initial strength of the magnetic field and its evolution with respect to the surface density evolution of the disc. This is in agreement with previous assessment [ ], and it shows that understanding the behaviour of magnetic fields in discs is key to predicting the impact of MHD winds in the evolution and dispersal of discs.
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Gas flowing into a wind has a very clear non-Keplerian kinematical signature, which can be observed in the profile of emission lines that are produced within it. The physics of photoevaporative winds is relatively well understood and detailed calculations of wind structures, that will improve the ability of models to confront observations, are slowly maturing. Examples of predicted emission line profiles for four different orientations of a full disc figure 4 , left panels and one with an inner cavity of approximately 14 AU figure 4 , right panels are shown in figure 4 , which is a re-rendering of previous radiation-hydrodynamics calculations [ ].
On the other hand, MHD wind models that try to predict the mass and angular momentum loss profiles and flow topology from the disc rely on a number of assumptions about how critical parameters scale with radius [ ]. Furthermore, as discussed in the previous section, these models are extremely sensitive to details of the magnetic field strength, topology and evolution that are poorly known.
As such, a detailed comparison with candidate wind diagnostics is still lacking.