Each symbol in the SFR vs. ECMF slope β (Eq. (2)) plane corresponds to a solution that reproduces the low binary fraction for the retrograde stellar population if typical star cluster half-mass radii were only r_h = 0.1 pc. All symbols inside one of the grey boxes have the SFR indicated by the arrow on the left of each box. Each row of symbols in a box corresponds to the minimum mass of the cluster (M_ecl, min) that was able to form. The SFRs on the left ordinate correspond to a maximum cluster mass, M_ecl, max, on the right ordinate using Eq. (3). The binary fraction for the retrograde population is ≈10% if the SFR in the ω Cen galaxy was large, the ECMF has been top-heavy (low β), and low-mass star cluster formation was suppressed (large M_ecl, min).