Top panel: temperature and density profiles for example models approaching the instability, i.e., the first time ⟨Γ₁⟩−4/3 = 0.01. The filled circles mark the central conditions at this stage. The green, yellow, and blue lines show examples of PPI+CC, PISN, and CC above the mass gap, respectively. All three examples are labeled according to their M_He, init. The red area marks the region of the EOS where pair-production results in an (local) instability. Bottom panel: values of the adiabatic index in the center when approaching the instability for the entire grid. The thin vertical lines mark the M_CO of the examples models of the corresponding color in the top panel.