pulsating variablesVariable stars that periodically brighten and fade as a result of large-scale and more or less rhythmical motions of their outer layers. Most stars evolve during their lifetime to a state where they naturally pulsate. The simplest motion is purely radial, a cycle of expansion and contraction in which the star remains spherical but changes volume. The idea that a periodic stellar expansion could lead to a variable light output was proposed by Shapley in 1914, with Eddington presenting the theory in 1918. The period of light variation is equal to the period of pulsation and is normally approximately constant. The spectrum of the star also changes periodically due to changes in surface temperature. The pulsation cycle is demonstrated by variations in radial velocity. All these variations are shown in the diagram at Cepheid variables. The pulsation period, P , was shown by Eddington to be related to mean stellar density, ρ, by the period-density relation and hence to the star's radius, R , and mass, M :
Combining this relation with Stefan's law and a mass-luminosity relation shows that pulsation period should be related to luminosity (see period-luminosity relation). Types of pulsating variable include the Cepheid variables, RR Lyrae stars, dwarf Cepheids, Delta Scuti stars, long-period Mira stars, semiregular variables (including RV Tauri stars), irregular variables, and Beta Cephei stars.
A star pulsates because there is a small imbalance between gravitational force and outward directed pressure so that it is not in hydrostatic equilibrium. When it pulsates it expands past its equilibrium size until the expansion is slowed and reversed by gravity. It then overshoots its equilibrium size again until the contraction is slowed and reversed by the increased gas pressure within the star. The fact that the pulsations do not die away as energy is dissipated means that some process is continuously providing mechanical energy to drive the pulsations. The center of the star is not involved in the pulsation. For most pulsating variables the driving force is a valve mechanism in the form of a region of changing opacity near the stellar surface where the pulsation amplitude is greatest. This region is an ionization zone in which atoms, mainly helium, are partially ionized. Normally atoms become transparent, letting heat escape, as they are compressed. In an ionization zone the opacity increases with compression and the zone effectively acts as a heat engine, storing energy (in the form of the second ionization of helium); the energy is released during the expansion stage (as the helium recombines). As long as the zone lies at the required depth below the surface it can drive the pulsations. If the zones are too close to the surface, as in a very hot star, or if too deep, then pulsations cannot occur. The period of pulsation is complicated by the fact that the gas is thought to be able to undergo oscillations (as in an open musical pipe) either in a fundamental mode or as a harmonic of the fundamental.
The distribution of pulsating variables on the Hertzsprung–Russell diagram differs from that of normal stars. Most lie on a nearly vertical band – the Cepheid instability strip – that extends upward from the main sequence (and possibly below it) and merges into a broader instability region at top right (see illustration). Stars reach these instability regions by various evolutionary paths and may turn up there several times during their evolution. The existence of such instability regions indicates that with certain combinations of stellar luminosity and effective temperature a state of pulsation rather than of rest is favoured.