What internal mechanism drives the rhythmic swelling and shrinking observed in variable stars?

Answer

An instability related to the opacity of the outer layers acting as a feedback loop.

Variable stars undergo pulsations driven by internal instability where a layer of gas becomes opaque when compressed (trapping heat and expanding), then becomes transparent when expanded and cooled (allowing heat escape and subsequent compression).

What internal mechanism drives the rhythmic swelling and shrinking observed in variable stars?
instabilitystar