Posteriors for the two population model. Top left: the posterior for κ₁ (subpopulation with semimajor axis a ≤ a_cutoff). The mode and 68% HDPI is ﹩{\kappa }_{1}=4{8}_{-32}^{+194}﹩, corresponding to spin–orbit angles peaking at ﹩\psi ={{8}_{-4}^{+6}}^\circ ﹩. Top right: 1000 ψ distributions shown as green curves, each corresponding to samples from the κ₁ posterior. The black curve is the ψ distribution for κ₁ = 48, peaking at 10°, indicating highly aligned spin–orbit angles. Bottom: same as the top two panels, but for κ₂ (when a > a_cutoff). The mode and 68% HDPI is ﹩{\kappa }_{2}={6}_{-2}^{+4}﹩, corresponding to peak ﹩\psi ={2{3}_{-5}^{+5}}^\circ ﹩, indicating weak but not random spin–orbit alignment.