Joint posterior probability densities of ﹩{f}_{\perp }\cos (2{\theta }_{\perp })﹩ and ﹩{f}_{\perp }\sin (2{\theta }_{\perp })﹩. Black contours are 0.5σ, 1.0σ, 1.5σ, and 2.0σ joint confidence levels. Marginalized posteriors and their KDE approximations are shown on the top and right axes. The constraints on each planet’s oblateness depend sensitively on the planet’s unknown obliquity. For intermediate values of θ_⊥, a Saturn-like f_⊥ is ruled out at ≳2σ significance for most of the systems. However, Saturn-like oblateness is allowed for other orientations. Even larger oblateness is allowed if θ_⊥  ≈  0^∘ or 90^∘, because the odd component of the signal vanishes.