Cepheids

A Cepheid is a member of a class of pulsating stars. The first variable of the type to be discovered was Delta Cephei. It is also called Yellow giant or supergiant pulsating variable star, so called because Cepheids pulsate in a particularly regular manner.

During this brief period in their lives, these stars oscillate, alternately expanding and contracting so that in each cycle a star may change in size by as much as 30%. These regular, rhythmic changes in size are accompanied by changes in luminosity. The surface temperature also changes in the course of each cycle of variations in brightness, being at its lowest when the star is at minimum and at its highest when the star is brightest. This temperature change may equal 1500 K for a typical Cepheid. A change in temperature also means a change in spectral type, so that the star may be F2 at maximum, becoming the later type, G2, at minimum, changing in a regular manner as the temperature falls or rises. A Cepheid may continue to pulsate in this manner for a million years, which is a comparatively short time compared to the life span of a star.

Most massive stars spend at least some time as Cepheid variables. Stars like Delta Cephei have amplitudes of around 0.5 mag. and periods usually not longer than 7 days; there are, however, Cepheids with larger amplitudes and longer periods, which form a separate subtype. This subtype includes the naked-eye stars 1 Carinae, Doradus and  Pavonis. The period of light changes is related to the average luminosity of the star. This means that the absolute magnitude of a Cepheid variable may be found by measuring the period of the light cycle. The apparent magnitude may be obtained directly. Once period, apparent and absolute magnitude are known, it becomes possible to determine the distance to the star.

Cepheids are visible in external galaxies, but their value as distance indicators is compounded by the fact that there are two types. Both follow a period–luminosity relationship, but their light-curves are different. First, there are the classical Cepheids, such as Delta Cephei itself, which are yellow supergiants of Population I. The second type, the W Virginis Stars, are Population II stars found in globular clusters and in the centre of the Galaxy. In using Cepheids to determine distances it is necessary to know which type is being observed. At the time Cepheids were first used to determine distances it was not known that there were Cepheids with different period–luminosity values. This resulted in erroneously applying the value for type II to classical Cepheids.

The period–luminosity relationship means that the longer the period, the brighter the visual absolute magnitude. A comparison of the curves shows that classical Cepheids are about one magnitude brighter than type II Cepheids. The light-curves may be arranged in groups, according to their shapes, which progressively become more pronounced in each group as the period lengthens. Most Cepheid light-curves fall into one of about 15 such divisions, each with a longer average period. They all follow a period–luminosity relationship, which commences with the RR Lyrae stars of very short period and, after a break, is continued by the Mira Stars. This regular progression – the longer the period, the later the spectral type is called the Great Sequence. A typical Cepheid would have a surface temperature varying between 6000 and 7500 K and an absolute luminosity that is ten thousand times that of the Sun.

Questions to Ponder

• What is a Cepheid variable?
• What is the size of the largest Cephei discovered?