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A Cepheid variable (/ ˈ s ɛ f i. ɪ d, ˈ s iː f i -/) is a type of variable star that pulsates radially, varying in both diameter and temperature. It changes in brightness, with a well-defined stable period and amplitude.

Cepheids are important cosmic benchmarks for scaling galactic and extragalactic distances. A strong direct relationship exists between a Cepheid variable's luminosity and its pulsation period. Cepheids change brightness due to the κ–mechanism, which occurs when opacity in a star increases with temperature rather than decreasing. The main gas involved is thought to be helium. First, the outer layer of the star contracts, heating due to compression until the helium doubly ionizes, becoming much more opaque. This causes it to accumulate heat, causing a build-up of pressure that forces the layer back out again until it cools enough to become singly ionized again. The helium, now transparent and not accumulating as much heat and pressure, contracts again to restart the cycle. Cepheid variables become dimmest during the part of the cycle when the helium is doubly ionized.

This characteristic of classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt after studying thousands of variable stars in the Magellanic Clouds. The discovery establishes the true luminosity of a Cepheid by observing its pulsation period. This in turn gives the distance to the star by comparing its known luminosity to its observed brightness, calibrated by directly observing the parallax distance to the closest Cepheids such as RS Puppis and Polaris.

The term Cepheid originates from Delta Cephei in the constellation Cepheus, identified by John Goodricke in 1784. It was the first of its type to be identified.