Initial period distributions adopted in our models. The vertical axis represents the binary fraction in each period bin, i.e. f_{log P}. The solid black line represents our default initial distribution of separations, which is flat in log₁₀ a_i between 5 R_⊙ and 5 × 10⁶ R_⊙, with f_{log P} = 0.11 over this interval. The dashed brown line shows the prescription of Moe & Di Stefano (2017), adopted in set M13, for a 1.0 M_⊙ primary and mass ratio M_2,i/M_1,i > 0.1. The shape and maximum of the distribution of Moe & Di Stefano (2017) depend on the primary mass and mass ratio. The dotted green line shows a period distribution flat in log₁₀ P_i and with f_{log P} = 0.15 in the period range [10, 2 × 10⁴] days, which we adopt in our model set M14. The integral of each curve represents the total binary fraction over the period interval.