Why do Cepheid stars pulsate? Why are these stars important to astronomers who study galaxies beyond the Milky Way?

Cepheid stars pulsate due to a process called the Eddington valve, or κ-mechanism, where the outer hydrogen layer of the star is ionized and then recombines. This process of ionization and recombination causes the star to expand and contract, leading to the observed pulsations. This mechanism occurs because the opacity of the star's outer layers to radiation interior to them increases with a rise in temperature. This increased opacity traps the star's interior radiation, leading to higher pressure from the trapped heat below causing the outer layer to move outward. As these layers expand, they cool down, opacity reduces, and the radiation trapped underneath is then able to escape, significantly reducing the pressure underneath, thus allowing the outer layers to fall back again which starts a new pulsation cycle.

Cepheid stars are important to astronomers as 'standard candles' to measure cosmic distances. This is primarily because of the reliable relationship between their pulsation periods and intrinsic luminosities, which is known as the Cepheid period-luminosity relation. By observing the period of a Cepheid’s pulsations and using the period-luminosity relation, astronomers can determine its intrinsic brightness. By comparing this with the star's apparent brightness, astronomers can infer the distance of the Cepheid, thus providing a method to measure the scale of the universe and study galaxies beyond the Milky Way.