Rick's Cosmology Tutorial: Chapter 11 Abstract

Stellar Structure Part 1 - Hydrostatic Equilibrium and the Clayton Model

An amateur's foray into elementary cosmology might charitably be regarded as merely ambitious. In this Chapter, however, we consider the astrophysics of stars. Stars are complicated beasts. Possibly this might go beyond ambition into foolishness. Unfortunately it is absolutely necessary for our purpose to have some understanding of stellar structure. It is only under stellar conditions that the chemical elements are forged which give rise to the possibility of life. This Chapter is the first of a sequence - ending in Chapter 19 - which together derive,

Attention is generally confined to main sequence, hydrogen-burning stars, although Chapter 17 provides a purely descriptive treatment of the development of stars beyond the main sequence. The formation of stars is more difficult, and far less well understood. This is left to later Chapters, if at all. The Hertzsprung-Russell graphic at the bottom of this page may be helpful in illustrating the remarks of the Introduction to this Chapter. It shows the evolution of a solar mass star.

In this Chapter the most basic requirement for a star, that of hydrostatic equlibrium is discussed and several different, equivalent, equations are derived which impose this condition. The polytropic equation of state for the stellar medium is introduced. The non-linear differential equation (the structure equation) which results from combining hydrostatic equilibrium and polytropic behaviour, is derived but not used further.

Instead, this Chapter follows Clayton in guessing an approximate algebraic form for the density as a function of radius. Imposing hydrostatic equilibrium yields closed-form expressions for the density, pressure and temperature provided that some data are 'given', e.g. the central density.

The Clayton model is only accurate near the centre of the star. However, it has the advantage of showing how the rapid reduction in the pressure, density and temperature away from the centre are virtually inevitable consequences of hydrostatic equlilibrium. This Chapter therefore forms an introduction to the more detailed models of Chapter 18.

Read Chapter 11 (pdf): Stellar Structure: Part 1

Go to Next Chapter Abstract

Go back to Chapter Selection page

Go to Rick's Cosmology FAQ

Go to Rick's Critique of the Cosmic Coincidences

Go back to Rick's Home Page (Main Menu)

Contact me and other links

The Hertzsprung-Russell diagram: Luminosity versus surafce temperature (increasing to the left). The main sequence covers virtually the whole range of possible initial masses. The track off the main sequence, via the red giant stages, is for a star initially of solar mass