Estimated semi-major axis (top) and the encounter time scale (bottom) of a binary star that can eject single stars from the core in a cluster of a given mass and half-mass radius. In this plot, we used Eqs. (8) and (9), for clusters containing stars of equal masses (m₃ = 1 M_⊙), one binary star with m₁ = m₂ = 30 M_⊙ at its centre, and v_∞ = 10 km s⁻¹. Time in the bottom panel is normalised by the half-mass relaxation time, Eq. (12).