Cluster dynamics largely shapes protoplanetary disc sizes

Abstract: 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.