Cluster dynamics largely shapes protoplanetary disc sizes
  It is still on open question to what degree the cluster environment
influences the sizes of protoplanetary discs surrounding young stars.
Particularly so for the short-lived clusters typical for the solar
neighbourhood in which the stellar density and therefore the influence of the
cluster environment changes considerably over the first 10 Myr. In previous
studies often the effect of the gas on the cluster dynamics has been neglected,
this is remedied here. Using the code NBody6++ we study the stellar dynamics in
different developmental phases - embedded, expulsion, expansion - including the
gas and quantify the effect of fly-bys on the disc size. We concentrate on
massive clusters ($M_{\text{cl}} \geq 10^3 - 6 \cdot 10^4 M_{\text{Sun}}$),
which are representative for clusters like the Orion Nebula Cluster (ONC) or
NGC 6611. We find that not only the stellar density but also the duration of
the embedded phase matters. The densest clusters react fastest to the gas
expulsion and drop quickly in density, here 98% of relevant encounters happen
before gas expulsion. By contrast, discs in sparser clusters are initially less
affected but as they expand slower 13% of discs are truncated after gas
expulsion. For ONC-like clusters we find that usually discs larger than 500 AU
are affected by the environment, which corresponds to the observation that 200
AU-sized discs are common. For NGC 6611-like clusters disc sizes are cut-down
on average to roughly 100 AU. A testable hypothesis would be that the discs in
the centre of NGC 6611 should be on average ~20 AU and therefore considerably
smaller than in the ONC.
