# Cepheid variables

Cepheid variables are one particular type of variable star (one whose brightness changes with time) called after delta Cephei, the first star of this type to be observed. The variation in brightness of this star was discovered by John Goodricke in 1784. Goodricke lived in York and was a promising young astronomer but tragically died at the age of twenty one. Since his discovery many other stars have since been found that vary in a similar way and the group of stars was called Cepheid variables.

These stars have a period of between one and fifty days and are giant yellow stars with a mass of between five and twenty times the mass of our Sun. Delta Cephei has a period of just under 5.4 days.

(There are actually two types of Cepheid variable but we will just consider one type here).

The brightness (luminosity) of a Cepheid variable changes because the size of the star is changing. When the star is small its density is large and the temperature and pressure inside the star increase. This makes the star expand. When the star is large gravity causes it to contract again and the cycle repeats itself.

The brightness of the star varied in a particular way (see Figure 1) and in 1912 Miss Henrietta Leavitt of Harvard College observatory discovered an important connection between the period and brightness. This is now known as the period-luminosity relationship. The longer the period of luminosity variation the more luminous the star.

The period-luminosity relation means that if you can measure the period of a Cepheid variable you can find its luminosity. Knowing how bright the star really is and then measuring how bright it appears to be will then give the distance of the star from the Earth. The discovery of Cepheid variables in the Andromeda nebula (M31) enabled its distance from Earth (over two million light years) to be found.

Two ways of presenting the period luminosity law are shown by the graphs in Figure 2.

Of course the period of a variable star in distant galaxies is really difficult to measure and so yet another method was needed to push back the limits of cosmic distance measurement.

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