Constraining the initial conditions of NGC 2264 using ejected stars found in Gaia DR2

Fast, ejected stars have been found around several young star-forming regions, such as the Orion Nebula Cluster (ONC). These ejected stars can be used to constrain the initial density, spatial and kinematic substructure when compared to predictions from $N$-body simulations. We search for runaway and slower walkaway stars using $Gaia$ DR2 within 100 pc of NGC 2264, which contains subclustered regions around higher-mass OB-stars (S Mon, IRS 1 and IRS 2). We find five runaways and nine walkaways that trace back to S Mon and six runaways and five walkaways that trace back to IRS 1/2 based on their 3D-kinematics. We compare these numbers to a range of $N$-body simulations with different initial conditions. The number of runaways/walkaways is consistent with initial conditions with a high initial stellar density ($\sim$10 000 M$_{\odot}$ pc$^{-3}$), a high initial amount of spatial substructure and either a subvirial or virialised ratio for all subclusters. We also confirm the trajectories of our ejected stars using the data from $Gaia$ EDR3, which reduces the number of runaways from IRS 1/2 from six to four but leaves the number of runaways from S Mon unchanged. The reduction in runaways is due to smaller uncertainties in the proper motion and changes in the parallax/distance estimate for these stars in $Gaia$ EDR3. We find further runaway/walkaway candidates based on proper motion alone in $Gaia$ DR2, which could increase these numbers once radial velocities are available. We also expect further changes in the candidate list with upcoming $Gaia$ data releases.