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.
