• Cluster Dynamics
• core collapse
• N-body
• Numerical Codes
• SPH simulation
• Turbulence

There has been a growing interest in the community working on star formation and early evolution on the interaction between
clusters and their embedding nascent environment. Since such systems are born in dense giant gaseous structures, any study of clusters
as if they are isolated from the beginning (classical $N$-body analyses) may be too serious a simplification of their dynamical evolution.
By creating a fluctuating tidal potential, turbulent dense structures passing nearby
are going to perturb the cluster, injecting energy into the system and removing
less bound stars.
By creating a fluctuating tidal potential, turbulent dense structures passing nearby are going to perturb the cluster, injecting energy into the system and removing less bound stars. Physical modelling of this effect has become possible numerically only recently thanks the growth of computational power and new algorithmic environments.

In this work, we studied the interplay of the internal cluster stellar dynamics and the external perturbations caused by the medium in which they originated using modern numerical techniques, computational tools available within the Astrophysical Multipurpose Software Environment
(AMUSE Portegies Zwart et al., 2010). We coupled an $N$-body code (PeTar; Wang et al., 2020) and a smoothed particles hydrodynamics code (Gadget-2; Springel, 2005) to conduct a series of simulations in which both the dynamical evolution of the cluster
and the hydrodynamics of the medium were followed simultaneously.
We modelled the gaseous environment as a periodic box, in which a driven
turbulent field was developed according to realistic physical conditions that can
be found in the interstellar medium (ISM). After an in-depth study of the relevant
properties of the medium arising from the pure hydrodynamics simulations, we
introduced a star cluster at the box centre, initialized according to a Plummer (1911)
profile, and let it evolve with the gas. Its initial density and stellar population mass function were varied among the runs to study how these properties affect
the interaction with the environment.
In addition, to isolate the effect of the environmental harassment, we performed control runs of isolated clusters with a mass
function for the stellar dynamics alone and equal mass clusters embedded into the medium
for the harassment.

Comparing our simulations to the control runs, we found that
when both the processes are included, they couple in a complex fashion. Evidence
of the coupling was found studying the mass lost by the cluster throughout the simulations
and the outer density distribution of the cluster. Moreover, in agreement with one of the few published studies of the scenario Gnedin et al. (1999), we found that the tidal field generated by turbulent structures accelerates its internal evolution, and the cluster undergoes
core collapse more rapidly. Finally, we conducted a study of the properties of
the binaries formed after the core collapse. Slight differences were found in their
number and binding energy, showing that tidally forced clusters tend to form more,
but less bound, binary systems. Our statistical analysis was limited by the relatively small number of cases we were able to compute but the results point in a fruitful direction for more complete physical simulations.