Density contour plot of the thermal index of npeγ matter as a function of baryon density n_b and proton fraction Y_p. The three panels correspond to temperatures T = 5, 15, and 50 MeV from left to right. Contours are displayed in steps of 0.1. The dashed violet line represents the β-equilibrium trajectory, while the yellow line indicates the constraint (z_n, z_p) ≤ 0.3. The virial approximation is valid to the left of this line.