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Cepheid variable stars are stars whose luminosity varies periodically from a minimum to a maximum periodically, with rapid brightening followed by gradual dimming. When a star uses up its main supply of hydrogen fuel it becomes unstable and pulsates. The periods are typically from a couple of days to a couple of months. Cepheid variables are found in the region of a H-R diagram known as the instability strip.
Cepheid variables are important because they can be used as distance indicators (standard candles) because the period of their pulsation varies proportionally to their luminosity. The graph below shows how the luminosity of the 'original' Cepheid star Delta Cephei varies with time. The period is about 5.4 days.
At the beginning of the 20th century American astronomer Henrietta Leavitt measured the period of 25 variable stars in the Small Magellanic Cloud and made the discovery that the period (of brightness variation) of Cepheids is directly related to their luminosity - the more luminous the star the longer the period.
Forces-of-Nature_Henrietta-Swan-Leavitt.pdf
There are in fact two types of Cepheids, I and II. They differ in their spectral characteristics and their light curves, but their luminosity-period relation is of the same form. The graph below shows a copy of Henrietta Leavitt’s original data. The x-axis shows period in days and the y-axis shows absolute magnitude (an alternative measurement of luminosity). The top curve shows type I Cepheids while the bottom curve shows type II.
The relation for type I Cepheid variables is shown in the luminosity-period graph below, where the axes are logarithmic.
The graph can be used to determine the luminosity of a Cepheid variable star. Since the period of pulsation of Delta Cephei is 5.4 days, its luminosity is approximately 2000 Lsun.
Henrietta Leavitt’s discovery means that the relative distances of stars within our galaxy can be measured. The period of a Cepheid may, for example, show that it should have a luminosity that is twice as bright as another in our galaxy. By comparing their apparent brightnesses the relative distance from earth can be calculated.
This method depends on the fact that the distances to some Cepheids must be known already in order to compare with them. The Cepheid star, Delta Cephei, is close enough that its distance has been measured by parallax. Stars with a known luminosity like this are called standard candles. Other such candle stars are found in the Hyades cluster. The Hyades cluster is a known distance of about 40 parsecs away and contains hundreds of stars approximately the same distance away but with different colours and brightnesses.
The distance to another galaxy can also be found using this method if a Cepheid variable star can be found in that galaxy. The distance can be determined by measuring the period of pulsation and the apparent brightness.
The type I Cepheid variable star Zeta Geminorum has a pulsation period of 10.1 days and a peak apparent brightness of 7.2 x 10-10 W m-2.
a. Use the period-luminosity relationship below to determine the luminosity of Zeta Geminorum. The luminosity is given in terms of the luminosity of the Sun of 3.9 x 1026 W.
L=3000×Lsun =3000×3.9×1026=1.17×1030 W
b. Hence calculate the distance to this variable star in pc.
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