DESCRIPCIÓN DE ESTADÍGRAFOS

Muzerolle et al. (2003) suggest that the increase in ˙M withM∗ arises from X-ray emission from the central star increasing the disc ionisation and therefore angu- lar momentum transfer. Higher mass pre-main sequence (PMS) stars have been observed to be more active in X-rays than lower mass PMS stars, with several

authors reporting a strong correlation between X-ray luminosity and stellar mass (Preibisch & Zinnecker 2002; Mokler & Stelzer 2002; Feigelson et al. 2003; Flac- comio et al. 2003a; Preibisch et al. 2005; Telleschi et al. 2007a). However, there is also several orders of magnitude difference in LX values at any given stellar

mass (see Fig. 1.9). Increased X-ray emission in higher mass stars may increase the ionisation of gas in their circumstellar discs (Glassgold et al. 1997). Increased disc ionisation leads to a more efficient magnetorotational instability (MRI), be- lieved to be the viscosity mechanism in accretion discs which allows the inward transfer of mass via the outward transfer of angular momentum (Balbus & Haw- ley 1991). Thus, higher mass T Tauri stars, with their increased X-ray emission, are likely to have higher mass accretion rates. Conversely, lower mass stars with their lower levels of disc ionisation are likely to have lower mass accretion rates. However, Muzerolle et al. (2003) and Natta et al. (2006) point out that it is not clear whether the observed increase in X-ray luminosity with stellar mass is large enough to explain a correlation as steep as ˙M _∝M2

∗. Mohanty et al. (2005a) also

comment that an increase in ionising flux with stellar mass does not explain the particular functional form of the correlation. Other authors claim that although X-ray emission from the central star may influence the calculated value of ˙M, it does not influence the observed trend with stellar mass (Alexander & Armitage 2006; Dullemond et al. 2006). However, it may be the case that the large scatter in LX values (see Fig. 1.9) could account for the large scatter in ˙M for a given

M∗ (Natta et al. 2006).

The roll of the MRI as it relates to the ˙M ₋M∗ correlation is discussed in detail by Hartmann et al. (2006), who suggest that different disc processes may be dominant depending on the mass of the star. The basic idea is that layered MRI accretion combined with the gravitational instability governs the mass accretion rate in the highest mass stars, with full viscous MRI accretion occurring in the lowest mass stars. In order for the MRI to operate the disc must

Figure 1.9: The increase in X-ray luminosity with stellar mass illustrated with data from the Chandra Orion Ultradeep Project. Based on a plot from Preibisch et al. (2005).

be highly ionised, but T Tauri discs are typically cold and thus have a low level of ionisation. A layered accretion model was proposed by Gammie (1996), where cosmic rays ionise the outermost layers of the disc, leaving a dead zone (a non- turbulent region) in the disc midplane. Further, as discussed above, X-rays from the central star can increase the level of disc ionisation (Glassgold et al. 1997). A layered disc model whereby the outer layers accrete material onto the star, with little contribution from regions in the disc midplane, may neither account for the large accretion rates derived for T Tauri stars, nor explain the observed correlation with stellar mass. However, Hartmann et al. (2006) demonstrate that the layered accretion model of Gammie (1996), where ˙M is independent of stellar mass, can be modified to include the effect of disc heating by irradiation from the central star, leading to a moderate dependence of ˙M on M∗, with ˙M _∝M∗. A relation of this form is consistent with the upper envelope of observations (Clarke & Pringle 2006; Hartmann et al. 2006). Accreting brown dwarfs, the lowest mass accretors, are found well below this upper envelope. Hartmann et al. (2006) argues that the discs of brown dwarfs are likely to be fully MRI-active. Since brown dwarfs have smaller accretion rates the layered accretion model of Gammie (1996) predicts that their disc surface densities are much lower that those of T Tauri discs. This leads to brown dwarfs having completely viscous discs (without non-accreting dead zones) as the disc material can be completely ionised by cosmic rays/X-rays. Thus full viscous MRI accretion may operate in brown dwarf discs. Accretion through the discs of higher mass stars may be somewhat different. Although the MRI may operate in the inner disc of higher mass stars, where thermal ionisation is high, there may be a dead zone at larger radii. The continuous accumulation of material from the outer disc may force the dead zone into gravitational instability (Hartmann et al. 2006). However a disc mass of at least 0.1M∗ is required for gravitational instabilities to operate (Pringle 1981). Andrews & Williams (2005) derived a median disc-to-star mass ratio of 0.5% from a comprehensive survey of the Taurus-Auriga star forming

region, suggesting that the typical masses of T Tauri discs are too low for any gravitational instabilities to develop. Hartmann et al. (2006) argues, however, that disc masses are likely to be underestimated and that perhaps more massive discs which are close to the limit for gravitational instability exist in at least the most massive T Tauri star systems.