In the upper part of the Cepheid instability strip lie the CLASSICAL CEPHEIDS. These stars gave the instability strip its name; they are so called because they resemble the prototype 8 Cephei. This star can be found on almost any star map, and its brightness variations can normally be seen easily by the unaided eye. Cepheids are supergiant yellow stars, with periods of one to 100 days and ranges of about one magnitude. A few – notably Polaris – have ranges which are much smaller. In fact, there may be many other micro-variable Cepheids like Polaris, but the search for them has only just begun.

There is an important relation between the period of pulsation of a Cepheid and its luminosity, which is usually expressed as a relation between the logarithm of the period, and the absolute magnitude. The relation is then a linear one. The period also depends to a slight extent on the colour of the star, and this dependence introduces some of the scatter in the relation.

The Cepheid period-luminosity relation is a specific example of a much more general relation which applies to all pulsating variables. The physical explanation for this relation was determined in 1917 by Sir Arthur Eddington. He derived a wave equation, which like the wave equation that describes the vibration of a string, describes the vibration of the star. Roughly, the period of pulsation is the time required for a vibration to travel from the surface of the star to the centre and back again. The bigger the star, the longer this time will be. More precisely, the wave equation says that for a given class of pulsating variables, the period is inversely proportional to the square root of the average density of the star. Large, distended stars therefore have longer periods than small, compact stars. Since the luminosity of the star is also dependent on the size of the star, the period is related to the luminosity also. The fact that the luminosity of the star also depends on its temperature or colour, explains why the period is furthermore slightly dependent on the colour. Stars with the same luminosity may have slightly different colours, and hence slightly different periods.

The period-luminosity relation for Cepheids was discovered in 1908 by Henrietta Leavitt, who noted that in the Small Magellanic Cloud (SMC), a nearby galaxy to our own, the brightest Cepheids had the longest periods. Since all the SMC Cepheids are at roughly the same distance, the apparently brightest ones are the most luminous. The route from this observation to the present period-luminosity relation was not an easy one. It required a detailed study of Cepheids whose distances were known: Cepheids in binary systems, in galactic star clusters and in nearby galaxies. Most of these studies were made in the 1960s.

From the period-luminosity relation, astronomers can deter¬mine the absolute magnitude, and hence the distance of any Cepheid for which period and apparent magnitude can be measured. Fortunately, Cepheids are extremely luminous, and can be seen at great distances. They have been used to establish the size and structure of our own Galaxy, and of nearby galaxies, and they are one of the fundamental tools of observational cosmology.

The Understanding of cepheids, and of the period –luminosity relation ,became much clearer in the late 1940s when walter Baade discovered that there were two POPULATIONS of cepheids the classical cepheids ,and the POPULATION 2 CEPHEIDS or w VIRGINIS STARS .Both population share the same part of the HR diagram ,and have similar light curves.Nevertheless ,the two populations are fundamentally different : whereas the classical cepheids are massive ,young stars ,the Population 2 cepheids are two magnitude fainter for the period –luminosity law are obvious !

Although Population II Cepheids are found throughout our Galaxy and other galaxies, they are particularly conspicuous in globular clusters. These enormous clusters which were formed billions of years ago consist entirely of Population II stars, of low mass. On a single photograph of a globular cluster, thousands of stars, including hundreds of variables, may be recorded.

Population II Cepheids are stars that have exhausted most of their supply of hydrogen fuel, and are now ‘burning’ helium. The shorter-period variables are in a relatively quiescent phase of evolution, but the longer-period variables are evolving rapidly through the instability strip, and are subject to abrupt changes in their period and range. The most bizarre case is RU Camelopardalis, which in the 1960s stopped pulsating completely! Several times, it made half-hearted attempts to recover its pulsation, but it has always stopped again.

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