What causes the pulsation of a cepheid-type variable star?

The Cephied Variable stage lies between the Horizontal Giant Branch and the Asymptotic Giant Phase in a sun-like star's life cycle, and stars entering and exiting it can momentarily (on a star's life scale) create the conditions necessary to pulsate. In ordinary stars, hydrostatic equllibrium diminishes these pulsations.

In essence, stars in this stage are able to produce conditions that trap their radiated energy in the outer layers; pressure builds to the point where the outer layers expand, becoming less hot and dense as a result, which causes gravity to compress the star and the cycle to repeat.

I apologize for any misspellings.

When a star undergoes periodic expansions and contractions due to pressure from nuclear fusion reactions pushing outward, it is known as a Cepheid-type variable star. The pulsation period of a Cepheid-type variable star is directly proportional to the star's intrinsic luminosity, making Cepheid variables useful for measuring astronomical distances.