Distribution of stellar encounters in the model (left column of plots) and what we expect to observe from this model given the selection function (right column). Top row of plots: two-dimensional PDFs P_mod(t_ph,d_ph) (left) and (right) on a colour scale in units Myr^-1 pc^-1. The colour scale covers the full range of densities plotted (and is different in the two cases, being a factor of 4.4 larger for the model). Middle row: one-dimensional conditional PDFs over perihelion distance for different values of t_ph ranging from 100 kyr to 5 Myr in steps of 20 kyr. These are vertical cuts through the two-dimensional PDF (and re-normalized, as given by Eq. (17) for the model distribution). Bottom row: one-dimensional conditional PDFs over perihelion time for different values of d_ph ranging from 0.1 pc to 10 pc in steps of 0.1 pc. Only the positive perihelion times are shown for the four conditional plots, which also use different density scales (vertical axes).