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A partial ionization zone is a portion (layer) of some stars where the gas is partly ionized, i.e., the material at the edge between "gas" and plasma. Any added heat, such as resulting from compression, is largely absorbed by the conversion to ions, analogous to the absorption of considerable heat in the conversion of liquid water to steam. In the case of ionization, this absorbed energy is that necessary to extract electrons from their orbits.
In such a zone, added heat can increase opacity (more freed electrons, which scatter EMR), which reduces the escape of energy so heat builds up, leading to an unstable situation incompatible with hydrostatic equilibrium. The instability results in an expansion of this part of the star, which dilutes the heat, until eventually the lower temperature (and decreasing ionization) allows the reverse of this process to occur. The result is a physical pulse (increase, then decrease) in the star's size and luminosity. This tendency to go back and forth between the increasing and decreasing states is termed the kappa mechanism, which is one of the phenomena that result in variable stars.