Observations of young star-forming regions suggest that star clusters are born completely mass segregated. These initial conditions are, however, gradually lost as the star cluster evolves dynamically. For star clusters with single stars only and a canonical initial mass function, it has been suggested that traces of these initial conditions vanish at a time $tau_mathrm{v}$ between 3 and $3.5,t_mathrm{rh}$ (initial half-mass relaxation times). Since a significant fraction of stars are observed in binary systems and it is widely accepted that most stars are born in binary systems, we aim to investigate what role a primordial binary population (even up to $100,%$ binaries) plays in the loss of primordial mass segregation of young star clusters. We used numerical $N$-body models similar in size to the Orion Nebula Cluster (ONC) -- a representative of young open clusters -- integrated over several relaxation times to draw conclusions on the evolution of its mass segregation. We also compared our models to the observed ONC. We found that $tau_mathrm{v}$ depends on the binary star fraction and the distribution of initial binary parameters that include a semi-major axis, eccentricity, and mass ratio. For instance, in the models with $50,%$ binaries, we find $tau_mathrm{v} = (2.7 pm 0.8),t_mathrm{rh}$, while for $100,%$ binary fraction, we find a lower value $tau_mathrm{v} = (2.1 pm 0.6),t_mathrm{rh}$. We also conclude that the initially completely mass segregated clusters, even with binaries, are more compatible with the present-day ONC than the non-segregated ones.
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