the radius of the sink particle is 5% of the Bondi-Hoyle accretion radius, $R_{\rm A}$, defined as [see also @Bondi52; @shima85]:

$$\label{eq:ra_eda1}
R_{\rm A} = \frac{2GM_{*}}{c_s^2 +v_{\rm ISM}^2}\\$$

in which $M_{*}$ is the mass of the star, $c_s$ is the sound speed and $v_{\rm ISM}$ the velocity of the ISM (with respect to the star). Using the values mentioned above, gives us an accretion radius of 1.8 AU, which is significantly smaller than in M09, where $R_{\rm A} \approx 2 R_{\rm disc}$.

Artificial viscosity {#sec:visc_eda1}
--------------------

Since the typical velocity dispersion in a GC is highly supersonic, it is important to resolve shocks. In order to do so, SPH codes introduce a numerical viscosity which is characterised by the parameters $\alpha_{\rm SPH}$ and $\beta_{\rm SPH}$, where $\beta_{\rm SPH}$ has been introduced to prevent particle interpenetration in shocks with high Mach numbers [@springel10]. Typical values for the parameters are $\alpha_{\rm SPH} \simeq 0.5-1$ and $\beta_{\rm SPH}=2\alpha_{\rm SPH}$.

The numerical (shear) viscosity can also be used to model the physical viscous transport of matter in an accretion disc [@artymowicz94], but this implies lower values of $\alpha_{\rm SPH}$. This value can be derived using @artymowicz94 to relate the artificial viscosity parameter $\alpha_{\rm SPH}$ 