Why do stars pulsate ? The fact that pulsating variables are not distributed randomly in the HR diagram strongly suggests that certain combinations of luminosity and effective surface temperature favour a state of pulsation as opposed to a state of rest. Sir Arthur Eddington made the first serious attempts to explain the cause of stellar pulsation. By 1917, he had derived the wave equation that described the mechanical (but not the thermodynamic) aspects of the pulsation. This equation provided an explanation for the period-luminosity relation. It also showed that the relative amplitude of pulsation decreased very rapidly from the surface of the star to the centre, because the density at the centre is so high. As a result, the centre of the star neither affects nor is affected by the pulsation.

This has two important consequences . It means that when we try to understand pulsation, we do not have to know about or to understand the complicated changes in chemical composition which may have occurred at the centre of the star, due to thermonuclear reactions. It also means that thermonuclear reactions at the centre are not likely to be the direct cause of pulsation. Eddington realized this and looked elsewhere for the cause of stellar pulsation. He reasoned that if a star pulsated then it must somehow have acquired mechanical energy, both to begin to pul¬sate and to maintain the pulsation against dissipative or frictional forces. The star must therefore function as a thermodynamic HEAT ENGINE, converting a small fraction of its abundant supply of radiant energy into motion. The basic requirement of a heat engine is that it must absorb excess heat when compressed (at high temperature); this heat is released as mechanical energy during the expansion phase of the pulsation. Eddington suggested that there might be a ‘valve’ near the surface of the star, where the relative pulsation amplitude was greatest. If the valve closed, trapping heat, when the star was hottest and most compressed, and opened, releasing heat, when the star was coolest and most expanded, then the requirements for a heat engine would be satisfied. Eddington considered that the natural opacity of the atoms in a star might provide the valve. Normally, they do not: they become more transparent when compressed, letting heat escape. Therefore, most stars do not pulsate. However, in a region of a star in which atoms of a particular element are partially ionized (called an IONIZATION ZONE), the atoms do become more opaque when compressed. lonization zones are the direct cause of pulsation in stars. The most effective ionization zones are those of the abundant elements hydrogen and helium. In stars with an effective surface temperature of about 7000 K (those near the Cepheid instability strip), these ionization zones are close enough to the surface so that the relative pulsation amplitude is large, but deep enough in the star so that the density is high and the zones contain appreciable mass.

Eddington did not identify these ionization zones as the true cause of stellar pulsation because, in his time, it was believed (incorrectly) that hydrogen and helium were rather rare in stars. In the last two decades, by use of better estimates of the chemical composition of the stars, astronomers have completely verified Eddington’s ideas. Computers have figured prominently in this work. They have made it possible to calculate accurately the opacity of stellar material and to build mathematical models of pulsating stars. These models can duplicate most of the observed properties of stars in the Cepheid instability strip. They also provide clues about such properties as mass, absolute magnitude and helium content, that are difficult to observe directly. For example, the presence of helium and its ionization zones make pulsation possible in stars with effective surface temperatures of about 9000K; without helium, this temperature would be about 6000K. The fact that the oldest pulsating variables, the RR Lyrae and Population II Cepheid variables, have effective surface temperatures as high as 9000 K tells us that these stars contain 30 per cent helium by mass in their outer layers. Helium must there¬fore have been present when they were formed and must therefore be a primordial element from an earlier phase of the Universe. According to evolutionary cosmological theories, helium was synthesized in the big bang. We see that pulsating variables even provide information for cosmology!

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