of the disc at radii $> 10$ AU. At radii $< 10$ AU extreme-ultraviolet radiation from the star may cause mass loss from the disc in the order of $10^{-11}-10^{-10}\,{\mbox{$\mathrm{M}_{\odot}$}}/$yr [@armitage11; @font04]. This is 2 to 3 orders of magnitude less than the mass loss rates found in this work and we conclude that taking heating by the star into account would not affect our results.

The stability of differentially rotating gaseous discs against self-gravity can be expressed in terms of the Toomre parameter $Q$ [@toomre64], which is defined as: $$Q = \frac{c_s \Omega}{\pi G \Sigma}$$ where $\Omega$ is the angular frequency. A disc becomes unstable if $Q$ is less than unity at the outer edge of the disc. In our set-up, $Q$ has a value of $\approx 44$. Self-gravity is therefore not expected to lead to instabilities. As in M09, we assume that the initial mass of the disc is 1% of the mass of the star and we set the outer radius of the disc to 100 AU and the inner radius to 10 AU. Realistically, the disc should probably extend inwards towards the radius of the star, but it is computationally very expensive to simulate the disc 