Fraction of kick-separated planetary orbits versus initial SMA. The kick distribution of K. El-Badry & H.-W. Rix (2018) is applied to the separation fraction calculated in Equation (4), resulting in the average expected separation fraction for a given planetary orbital SMA (red curve; the blue dots are from a numerical test). Note that, to allow direct comparisons to planetary systems orbiting MS stars, the SMAs shown are from the MS lifetime of the host star, before significant mass loss has occurred, while the kick is applied at the end of the AGB phase, after most mass loss has already taken place and the SMAs have expanded accordingly. In this example, the host star had an initial mass of 1 M_⊙, which reduced to 0.52 M_⊙ by the end of the AGB phase. The inset focuses on orbits closer than ∼100 au, relevant for the outer solar system planets.