Top: depth of the gas envelope (in Earth radius), as a function of the planetary mass, for the three models presented in Sect. 3.4, for a pure H₂ envelope. The red solid line is the convective-isothermal model, the black dashed line is the radiative-convective model without irradiation, and the blue dotted line is the radiative-convective model with irradiation effect. The red thin solid line is similar to the red solid line, except that we use the opacities of Freedman et al. (2008), for the low metallicity case, to derive the planetary radius. Middle: the mass-radius relationship for the four same models. Bottom: the mass-radius relationship for the convective-isothermal model, assuming three compositions. The red solid line is for pure H₂, the black dashed line is for a mixture of H and He in solar proportions, and the blue dotted line is for CO₂ (not including condensation). For the three panels, the planetary interior model is computed as in Sect. 3.2, and the surface temperature and pressure are equal to 375 K and 1 GPa respectively.