within this slice. The ISM flow reaches the disc after $\approx$ 100 years and the computational domain contains $\approx 6N_{\rm disc}$ ISM-particles when it is completely filled.

### Disc {#sec:disc_eda1}

In the case of a disc in a steady state, the mid-plane temperature profile follows a simple power-law, $T_c \propto r^{-p}$, and the surface density profile, $\Sigma$, is proportional to $r^{p-\frac{3}{2}}$, assuming a constant viscosity parameter $\alpha_{\nu}$ in the @shakura73 formalism [see e.g. @armitage11]. Since we assume a constant temperature in the whole disc, $p = 0$ and $\Sigma \propto r^{-\frac{3}{2}}$, which corresponds to a minimum mass solar nebula [@Weidenschilling77; @hayashi81] and is also assumed in e.g. M09 and @rosotti14. The typical temperature of a protoplanetary disc at radii $> 10$ AU is roughly consistent with a temperature of 25 K [$\approx$ 20K, see e.g. @armitage11]. Although heating of the outer layers of the disc may cause photoevaporation, the mid-plane of the disc is shielded. At approximately 10 AU, the disc has to be heated to temperatures $> 10^3$ K to effectively lose mass due to photoevaporation. An $0.4\,{\mbox{$\mathrm{M}_{\odot}$}}$ star has an effective temperature of $3\times 10^3$ K, which is not high enough to unbind gas from the surface layer 