Love numbers k₂ and core masses of two-layer models of HAT-P-13b for different 1 kbar temperatures (color coded). For pressures  <1 kbar the temperature profile is either adiabatic (colored solid) or isothermal (colored dashed). The metallicity increases along a line, reaching its maximum value for M_core/M_p = 0. The zero metallicity line for fully adiabatic models (brown solid) separates the region of all possible planetary models (white) from the prohibited area (light gray). Vertical black dashed lines indicate the allowed interval for k₂-values derived by BBL. Based on that interval we find a maximum possible core mass of 0.32   M_p ≈ 87 M_⊕. Our new k₂ interval is shown with vertical black dot-dashed lines. It lowers the uncertainty of the planet’s core mass down to 0.1   M_p ≈ 27 M_⊕. The other black lines show our models that are based on our model atmosphere with a fully adiabatic envelope (solid black) and P_ad of 5 bar (dotted black), 10 bar (dashed black), 50 bar (dot-dashed black), and 72 bar (black triangle).