Stability curve with the positions indicated of the three warm absorbers from our best fit for Ark 564. The absence of a region with negative slope on the S-curve indicates there are no unstable regions i.e. gas can exist in equilibrium throughout the curve. This is likely due to the steep soft-excess seen in Ark 564, which allows gas to cool efficiently by lowering the Compton temperature. (Marker size exaggerated to show against small error bars in green.)