At the end of the 1960s it was noted that T Tauri stars showed an unusual infrared excess, which was interpreted as due to circumstellar dust around the YSO (Mendoza V., 1966, 1968), responsible for the absorption of optical light and re-emission at longer wavelengths. At first it was not clear whether the dust surrounding the star was distributed in shells, discs or outflows. Lynden-Bell & Pringle (1974) argued that the material around the newly born stars should be in the shape of a disc. The model they proposed, the Boundary Layer model, was later superseded, but the basic idea of a disc is still valid. The formation of the
disc would be a consequence of some initial angular momentum, present in the collapsing cloud, which would not allow the material to fall directly onto the star, but would cause it to create in a disc (Terebey et al., 1984; Adams & Shu, 1986). Only later in the 1980s, infrared observations especially with the satellite IRAS confirmed the presence of discs, having sizes of the order of 100 AU, and solely at the end of 2014 great image details were achieved with Atacama Large Millimeter Array (ALMA). In the beginning, instead, the structure of protoplanetary discs was inferred mainly from the SED. By analysing the emitted light at various wavelengths, it is possible to trace different parts of the disc. For a typical T Tauri stars having T = 4000 K and M = 1-2 M⊙, the innermost region
between the star and 0.1 AU, emits in the UV and optical; the middle region between 0.1 and 20 AU is traced by near and mid infrared radiation; while the external region beyond 20 AU can be observed in far infrared. The sub-mm emission traces the coldest regions of the outer disc, especially the midplane (Dullemond et al., 2007; Carmona, 2010).
Several models have been developed since then to explain the observations and describe the disc structure and evolution. Two main categories can be highlighted: passive and active discs. In passive discs (e.g. Kenyon & Hartmann (1995); Chiang & Goldreich (1997); Dullemond et al. (2001)) most of the light is due to reprocessing of starlight, whereas in active discs (e.g. Lynden-Bell & Pringle (1974); Lin & Papaloizou (1980); Shu et al. (1987); Calvet et al. (1991); D’Alessio et al. (1998)) there is an intrinsic luminosity due to non negligible mass flow towards the star, which causes heating of the disc and consequently more thermal emission. In reality discs are not totally either passive or active, but a combination of the two cases coexists, where young discs tend to be more active and to accrete mass, while older discs are more passive.
In both cases discs are in Keplerian rotation and the absorbed stellar radiation is mostly re-emitted as thermal energy, i.e. they can be described as blackbodies. However, in both passive and active disc models the temperature profile scales as r−3
4 and the
spectral index α as r−4
3, so in these models the shape of the SED cannot provide any
information about the kind of disc (Adams et al., 1987). Discs are assumed to be thin, compared to their size, and initially they were depicted as flat. The disc vertical structure is considered in hydrostatic equilibrium, where there is a balance between the gravitational force and the gas pressure. In the radial direction, in passive discs the gravitational force is in equilibrium with centrifugal and pressure forces, while in active discs there is a more
1.5. Disc formation and structure
complex dynamics, because mass moves from the outer to the inner parts. However, since the angular momentum in a Keplerian rotating disc increases with radius, matter needs to lose angular momentum in order to accrete. Several mechanisms have been proposed to address this issue, the magneto-rotational instability (Balbus & Hawley, 1991) and the mass loss through disc wind (Blandford & Payne, 1982) being the most widely accepted.
From observations, however, it was noted that the SED profile was shallower than predicted. Kenyon & Hartmann (1987) explained the high infrared excess as due to flaring discs, i.e. discs whose height above the midplane increases at larger radii. A flared disc tends to intercept more light from the central star and consequently emits more in infrared than a flat disc. Dullemond & Dominik (2004) argued that protoplanetary discs can present a variety of shapes, from flared to self-shadowed and unstable discs, where dust settling would play an important role in determining the level of disc flatness. Flat discs would therefore be the evolution of flared ones.
First models described discs as a sum of annuli, each emitting as a blackbody, where the temperature and density followed a power law decline from the central star outwards (e.g. Beckwith et al. (1990)). However, the upper part which is directly irradiated by the star will be hotter than the inner one (Calvet et al., 1991). Chiang & Goldreich (1997) proposed a two-layer model for a passive disc, with a colder inner midplane and a hotter external layer, and where the stellar radiation impinging on the surface is re- emitted partly in space and partly into the inner regions of the disc. D’Alessio et al. (1998), instead, modelled an active disc into three zones, radius dependent. The outer one, far away from the star, is heated mainly by stellar irradiation, the inner one close to the star is characterised by viscous heating, while in the intermediate zone both processes can occur, with prevalence of viscous heating in the midplane and stellar irradiation on the surface.
Natta et al. (2001) and Dullemond et al. (2001) proposed a two-layer passive disc model with an inner hole, in order to explain the bump observed at 3µm, especially in the SED of Herbig stars. Other theories, however, explain the 3µm feature as due for example to turbulence caused by disc wind (Bans & K¨onigl, 2012). The inner hole would be caused by dust evaporation and therefore would be composed only of gas. The dust inner disc close to the star is consequently truncated and presents a vertical surface. Since it is directly
illuminated by the star it is hotter and tends to increase in height, giving rise to a puffed inner rim (Natta et al., 2001). The shape of the puffed inner rim was further analysed and discussed by Isella & Natta (2005), who estimated it to have a curved instead of a vertical surface.
Other recent models, instead, simulate radiation transfer and can reproduce physical processes like scattering, polarisation and dust heating, offering an insight into the dynam- ics of discs in 2D, and also in 3D. They can either solve the radiative transfer equation analytically (e.g. Woitke et al., 2016) or make use of Monte Carlo techniques (Lefevre et al., 1982; Bjorkman & Wood, 2001; Pinte et al., 2006; Min et al., 2009).