Fred Hoyle, Red Giants and Beyond

Abstract

The impact of Fred Hoyle’s work on the structure and evolution of red giants, particularly his breakthrough contribution with Martin Schwarzschild (1955), is described and assessed. Working with his students in the early 1960s, Hoyle presented new physical ways of understanding some of the approximations used, and results obtained, in that seminal paper. His initial viewpoint on the critical role of the outer surface boundary condition was replaced by a more subtle, if related one, which emphasized the peculiar difficulty of storing much mass outside a dense stellar core. That viewpoint that — low-mass red giants are essentially white dwarfs with a serious mass-storage problem — is still extremely fruitful.

Recently, I have extended Hoyle’s approach to explain not only many of the structural properties of red giants themselves, but also to link and unify the structures of low-mass stars from the main sequence through both the red giant and horizontal branch phases of evolution. Many aspects of these stars that had remained mysterious for decades have now fallen into place, and some questions have been answered that were not even posed before.

With red giants as the simplest example, this recent work emphasizes that stars, in general, may have at least two distinct but very important centres: (i) a geometrical centre, and (ii) a separate nuclear centre, residing in a shell outside a zero-luminosity dense core for example. This two-centre perspective leads to an explicit, analytic, asymptotic theory of low-mass red giant structure. In this theory, there arises a naturally important in situ measure of central compactness: the parameter ${\rho _{sh}}\sqrt {{\rho _c}}$. That parameter, like others, is derived self-consistently and explicitly, and can be used to show how close a given model’s properties are to ultimate asymptotic relationships.

The results obtained also imply that the problem of understanding why such stars become red giants is one of anticipating a remarkable yet natural structural bifurcation which occurs in them. In the resulting theory, both the ratio ${\rho _{sh}}\sqrt {{\rho _c}}$ and products like ${\rho _{sh}}.{\bar \rho _c}$ Pc prove to be important, self-consistently derived quantities.

Two striking theorems involving such quantities express between them the very essence of red giant behaviour, proving analytically for the first time that stars with dense cores are necessarily (i) extremely luminous, and (ii) very large. Perhaps the most astonishingly unexpected single result is that for the very value Nature provides for the relevant nuclear energy-generating temperature exponent (CNO’s η = 15), ρ _sh and ${\bar \rho _c}$ behave in a well-defined, precisely inverse manner. This emphasizes that the internal behaviour of such stars is definitely anti-homologous rather than homologous, thus showing how very unfortunate the term ‘shell homology’ is. Finally, I sketch a viewpoint which (i) links the structural and evolutionary behaviour of stars from the main-sequence through horizontal branch phases of evolution, and also (ii) has implications for post-main-sequence developments in more massive stars.

The final text of this contribution was not received (The Editors).