Prior probability distributions for PSR J0030+0451 transformed to the joint space of central pressure and central energy density (upper panels), and the space of mass and radius (lower panels), for the PP (left panels) and CS parameterization (right panels). The dotted and dashed contours bound the highest-density two-dimensional regions respectively containing 68% and 95% of the prior mass. The peak in the CS model just above 1.97 M_⊙ is due to how the model is constructed: all EoSs are forced to soften at high densities to comply with causality and at asymptotic densities with the constraint from pQCD, causing all mass–radius sequences to have ∂M/∂R ≲ 0 near the maximum mass, thereby overlapping each other (see Greif et al. 2019). Note that these priors are specifically for PSR J0030+0451 because adjustments are made to match the priors in the analysis in Riley et al. (2019); i.e., M ∈ [1.0, 3.0] M_⊙ and R ∈ [3r_g, 16] km where r_g(M) = GM/c². For comparison the three representative EoSs from Hebeler et al. (2013) are shown as solid curves: HLPS Soft, Intermediate, and Stiff. Note that the discernible small-scale structure is due to: (i) the behavior of the (numerical) transformation from interior matter parameters to exterior spacetime parameters; and (ii) finite sampling noise.