Low-mass red giants as binary stars without angular momentum

Low-mass red giants may be viewed as stars - or even binary stars - with 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. This two-centre or two-star perspective leads to an explicit, analytic, asymptotic theory of low-mass red-giant structure. In this theory, both rho(sh)/rhoc and rhosh . rhoc prove to be important quantities. I present new theorems and results involving these quantities, and then sketch a viewpoint which (i) links the structural and evolutionary behaviour of stars from the main-sequence through horizontal branch phases of evolution, and (ii) also has implications for post-main-sequence developments in more massive stars.