Love number k₂ and core mass of two-layer models (squares connected by dashed lines), three-layer models with metal-free envelopes (triangles), and three-layer models with low-metallicity envelopes (diamonds) of GJ 436b. Color-coded circles are for interior models of Jupiter (red), Saturn (yellow), and Neptune (blue), and a 20M_⊕ water planet (black). Adding the mass of the water layer to the mass of the rocky core shifts 3L models solutions from filled to open triangles, and the Neptune model to the position as indicated by an arrow. For each of the dashed lines (which are for different isothermal atmospheres of 300 K (blue), 700 K (cyan), and 1300 K (orange)), the squares indicate solutions for Z₁ = 0, 0.5, and the highest possible value when M_core = 0. On the left hand side of the gray dashed line at k₂ = 0.2, the models are highly degenerate, and on the right hand side, no metal-free envelope models were found.