A variable star is, quite simply, a star that changes brightness. A star is considered variable if its apparent magnitude (brightness) is altered in any way from our perspective on Earth. These changes can occur over years or just fractions of a second, and can range from onethousandth of a magnitude to 20 magnitudes. More than 100,000 variable stars are known and have been catalogued, and thousands more are suspected variables. Our own sun is a variable star; its energy output varies by approximately 0.1 percent, or one-thousandth of its magnitude, over an 11-year solar cycle. A star could be an intrinsic variable because it periodically swells and shrinks. A star could be an extrinsic variable because it has an orbiting companion that sometimes eclipses it.
Cepheid variable, one of a class of variable stars whose periods (i.e., the time for one cycle) of variation are closely related to their luminosity and that are therefore useful in measuring interstellar and intergalactic distances.
Cepheid variables, as seen by the Hubble Space Telescope. NASA - HQ - GRIN
This robust characteristic of classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt after studying thousands of variable stars in the Magellanic Clouds.
This discovery allows one to know the true luminosity of a Cepheid by simply observing its pulsation period. This in turn allows one to determine the distance to the star, by comparing its known luminosity to its observed brightness.
Cepheid stars have variable luminosity primarily because of helium in their outer layers. Neutral helium atoms have two electrons. When heated they may lose one electron to
become singly ionised. Heated further, they lose the second electron to become doubly ionised.
Doubly ionised helium atoms are more opaque than singly ionised atoms.
At the dimmest part of the cycle, the helium is doubly ionised, and so opaque. It absorbs the stars radiation and so heats up - which causes it to expand. As it expands it loses heat by the laws of thermodynamics. It becomes singly ionised, and thus less opaque, and the star therefore appears brighter. Because it has lost heat, the helium then contracts and is heated up, repeating the cycle.
It’s essentially a “standard candle” (or, almost, anyway) - that lets us determine distance.
When it comes to changing astronomers’ perception of the universe, the Cepheid variable V1 played one of the pivotal roles. The important variable star allowed American astronomer Edwin Hubble to determine that the filmy nebula in which it lay was, in fact, another galaxy entirely, demonstrating that the Milky Way did not contain the entire universe. "V1 is the most important star in the history of cosmology," astronomer Dave Soderblom of the Space Telescope Science Institute (STScI) in Maryland said in a statement.
"It's a landmark discovery that proved the universe is bigger and chock full of galaxies.”