Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2018 / S26 / 2 / d

Core-helium-burning stars populate the horizontal branch and red clump; hot subdwarf B stars provide examples with a helium-burning core of roughly half a solar mass and a very small remaining hydrogen envelope. Their high luminosity relative to mass, hot spectra and locations away from an ordinary hydrogen-burning main sequence are observational evidence for such evolved configurations.

A plausible history starts with a hydrogen-burning star. After central hydrogen exhaustion, hydrogen-shell burning builds a compact helium core and the envelope expands on the red giant branch. Sufficient core temperature ignites helium, often by a helium flash for a low-mass degenerate core. Strong mass loss or binary interaction can strip most of the hydrogen envelope, exposing a hot helium-burning remnant; retaining a substantial envelope instead gives an ordinary horizontal-branch or red-clump star.

The simple radiative Kramers scaling estimates a luminosity contrast but does not uniquely identify one evolutionary state or predict a real subdwarf luminosity precisely. A similarly low-mass helium white dwarf would be a cooling, degenerate object rather than the sustained high-temperature helium-burning configuration assumed here.