Probability distributions of mass and radius obtained with our MC sampling for 4U 1820–30. Between two distance measurements for this source, we chose to use the larger one, namely, D = 8.4 ± 0.6 kpc, for the result shown here. In all panels, the 68% (solid white lines) and 95% (dot-dashed white lines) confidence contours are drawn. The color bar on the right reflects the relative probabilities the details of which are given in the text. The general relativistic causality limit (β_limit = 1/2.94) is drawn as a black straight line. From top to bottom: h = 2, h = 1 and h = 0, which correspond to r_ph = R (top), r_ph = 2R (middle), and r_ph ≫ R (bottom), respectively. From left to right: X = 0.1 (left), X = 0.3 (middle), and X = 0.7 (right). We note that the relative probabilities P_i of all distributions are normalized by ∫P_idRdM = 1. For comparison, we also plot the mass–radius curves predicted from nine equation of state (EoS) models. See the text for the detailed description of these EoS models.