A Cepheid variable (often shortened to Cepheid) is a type of variable star that varies in temperature and luminosity with in a regular cycle. They are named after the first such star identified, Delta Cephei. There are relationships between their period and stellar characteristics that can be measured or determined, which allows Cepheids to be used as a standard candle, as part of the cosmic distance ladder. Some relationships:
There are two populations, classical Cepheids (aka Type I Cepheids) or Type II Cepheids, each with its own period/brightness relation, so which of these populations it falls in must be determined to use it to determine distance. They can be observed in nearby galaxies, allowing determination of distances for galaxies not providing good data by Type Ia supernovae or redshifts. Periods vary from a day to fifty or more.
Classical Cepheid variables are yellow giants. Their period/brightness relation is:
Mv = (-2.43 ± 0.12)(log10(P)-1) - (4.05 ± -0.02)