hotter horizontal branch stars being less luminous than cooler ones.

The hottest horizontal-branch stars, referred to as extreme horizontal branch, have temperatures of 20,000-30,000 K. This is far beyond what would be expected for a normal core helium burning star. Theories to explain these stars include binary interactions, and "late thermal pulses", where a thermal pulse that asymptotic giant branch (AGB) stars experience regularly, occurs after fusion has ceased and the star has