Binary disruption during the early phase of open clusters

The binary fraction in young open clusters exceeds that of field stars, making the study of binary dynamical evolution in clusters essential for understanding the origins and evolution of field binaries. Using N-body simulations based on Gaia DR3 open cluster observations and assuming a 100\% primordial binary fraction, we investigated the early evolution of binary survival fractions in open clusters. We find that binary disruption has two stages, an initial rapid decline followed by a slower decrease, well described by two piecewise linear functions. The early disruption rate, $k_1$, follows a power-law relation with the cluster's initial density ($\rho_\mathrm{0}$), with an index of approximately 0.56, driven by the disruption of wide binaries via close encounters. The transition time between the two phases, $t_\mathrm{b}$, also exhibits a power-law dependence on $\rho_\mathrm{0}$ with an index of about -0.46. The disruption rate also depends on binary parameters: high-$q$ and wide binaries are disrupted faster, while the dependence on eccentricity $e$ is less clear, likely due to its strong evolution. We developed and publicly released a Python tool to predict binary survival fraction evolution based on $\rho_0$, $P$ and $q$. Additionally, we also investigate how open cluster binaries contribute to the field population, and find that the escaped stars have a systematically lower binary fraction, likely due to mass segregation. Both populations show similar distributions of $P$ and $e$, but lower-$q$ systems preferentially remain bound within clusters, the origin of which remains uncertain.