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The instability strip refers to the region of the H-R diagram in which stars are unstable such that they oscillate in luminosity. They are pulsating stars, which constitute some of the types of variable stars, including Cepheid variables and RR Lyrae variables. On the diagram, it is a diagonal strip leading away from the main-sequence line, between giant stars and supergiants.
The basic instability mechanism is an example of the kappa mechanism: a helium layer at a temperature such that singly and doubly ionized states exist, the latter deeper, at the higher temperature. Any expansion allows recombination from doubly to singly ionized, which reduces opacity, allowing energy to escape more rapidly so at that depth, the star cools and contracts. The contraction, in turn, promotes ionization, increasing opacity and thus temperature, triggering expansion again. A star within this strip theoretically could sit at a perfect balance point between the two tendencies, but in such a condition, some slight inhomogeneity would result in a distinct oscillation that would spread, making such oscillation inevitable.