Stability diagram for a bipolar configuration. The gray region corresponds to unstable solutions, while the white region corresponds to stable states. The vertical axis represents the density contrast between the core of the AR and the external environment, while the horizontal axis corresponds to the reference plasma-β, β₀₀. In this plot, we have used a bipole with d = 0.25 and z₀ = 0.5 in the domain x_min = −2, x_max = 2, y_min = −2, y_max = 2, z_min = 0, and z_max = 4. The temperature contrast, T_AR = 2 T_C, is the same for all the points.