Stellar Structure

Abstract

A brief introduction to the basics of stellar structure is followed by discussion of some related topics, including stellar composition and stellar equilibrium, including a note on the mechanics of pulsating stars.

Keywords: stellar structure, stellar composition, stellar equilibrium, pulsating stars

Introduction

A star is structured in concentric shells or zones. At the centre lies the reaction zone, where the nuclear reactions which energise the star take place. The initial reaction is always the fusion of hydrogen to form helium. However, as stars evolve, helium accumulates at the centre and the hydrogen fusion zone moves out, forming a shell around a core of helium. Later, if the star is sufficiently massive, helium fusion may commence at the centre. It is possible for two, and possibly more reaction shells to exist simultaneously.

Radial Structure

The Core

At the centre lies the core; the reaction zone where the nuclear reactions which energise the star take place. The initial reaction is always the fusion of hydrogen to form helium. However, as stars evolve, helium accumulates at the centre and the hydrogen fusion zone moves out, forming a shell around a core of helium. Later, if the star is sufficiently massive, helium fusion may commence at the centre. It is possible for two, and possibly more reaction shells to exist simultaneously.

Convective and Conductive Zones

Around the reaction zone are the convective and, farther out, conductive zones. Nuclear reactions do not occur in these zones – they are too cool – but energy from the core moves outwards through these areas to the photosphere.

Photosphere and Chromosphere

The photosphere is the visible part of the star we can see. The photosphere is characterised by emission spectra.

A rarefied chromosphere, characterised by selective absorption, surrounds the photosphere.

Corona

Outermost is the corona, a tenuous, wispy phenomenon extending for several stellar diameters into space. In a memorable note, George Gamow (1964, p. 87) says of the solar corona "To the present author it looks very much like the hair of Albert Einstein in his old age."

The solar corona (and probably stellar coronae in general) is hotter than the surface of the star. A theory developed by Martin Schwarzschild to explain this phenomenon was that convective motion near the solar surface caused sound waves to propagate into the outermost layers of the Sun. As the waves moved outwards into areas of decreasing density they steepened into shock waves which then dissipated, heating the corona. This idea has since fallen from favour and the present view is that the corona may be heated by magneto-hydrodynamic waves or other magnet phenomena (Tayler 1994, pp. 170 - 171).

Stellar Composition

Stellar composition is usually described in terms of three components: hydrogen (X), helium (Y), and heavier elements (Z) collectively known as ‘metals.’

Stellar Equilibrium

Except for brief intervals, stars must exist in both mechanical and thermal equilibrium.

Mechanical equilibrium is maintained by the weight of stellar matter, falling towards the centre under the influence of gravity, being supported by the radial pressure of the compressed stellar gas below. Kippenhahn 1992 (pp. 105 - 109) uses the analogy of a heavy piston, wherein the weight of the piston acting downwards (gravity) is held at rest at a certain distance from the bottom of the cylinder by the gas pressure of the compressed air trapped underneath (gas pressure).

If the piston were to continue its descent, it would compress the gas too greatly, and the increased gas pressure would push it back to its equilibrium position. If the piston were above its rest position, the gas trapped beneath it, being less compressed, would have insufficient pressure to hold it up, so it would fall.

Thermal equilibrium is maintained indirectly, through the effects of pressure on both the rate of energy generation in the core, and the opacity of the outer layers. If a star began to cool significantly, the pressure supporting the outer layers would reduce, allowing the star to contract under the influence of gravity. As the star contracts, so pressure on the core is increased, driving the fusion reactions there to proceed more quickly. The increased rate of fusion in turn increases the temperature (thereby stopping the cooling) and pressure (thereby preventing further contraction). Moreover, as the star contracts, the increase of pressure in the outer layers causes them to become more opaque, thereby trapping more radiation inside the star, slowing any further cooling.

Pulsating Stars

Returning to the piston analogy given above, if the piston is pushed down from its equilibrium position and suddenly released, it begins to oscillate. At first it moves upwards, driven by the excessively compressed air beneath. However, the inertia of the heavy piston carries it beyond the equilibrium point, overshooting the rest position. Now the gas is insufficiently compressed to support the weight of the piston, so it begins to fall again.

In an ideal closed system, it oscillates forever, but in both our analogy and in most real stars, energy is continually radiated away; the equilibrium position is overshot by a smaller amount with each iteration, until the oscillations cease altogether.

However, if the system is kept energetic, e.g. by irradiation, the oscillations can continue indefinitely. This is the basis of the Eddington-Zhevakhin model for cepheid variables. "In 1953 Zhevakhin ... showed that in the case of a Delta Cephei star the effects of opacity properties of surface regions [which prevents energetic radiation from the core escaping] were sufficiently strong to overcome the damping effect in the rest of the star and to allow the star to oscillate" (Kippenhahn 1992, p. 109).

References

Böhm-Vitense, Erika (1989b): Introduction to Stellar Astrophysics. Volume 2 – Stellar Atmospheres. Cambridge.

Chiosi, C.; Wood, P.R.; Capitanio, N. (1993): Theoretical Models of Cepheid variables and their BVI_C Colors and Magnitudes.  The Astrophysical Journal Supplement Series, 86: 541-598, June 1993.

Gamow, George (1964): A Star Called the Sun. Macmillan.

Kippenhahn, Rudolph (1992): 100 Billion Suns: The Birth, Life, and Death of the Stars. Princeton University Press.

Tayler, R. J. (1994): The Stars: their Structure and Evolution (2nd ed.) Cambridge University Press, 241 pp.