The discovery of a flux excess in the far-ultraviolet (FUV) spectrum of elliptical galaxies was a major surprise in 1969. While it is now clear that this UV excess is caused by an old population of hot helium-burning stars without large hydrogen-rich envelopes, rather than young stars, their origin has remained a mystery. Here we show that these stars most likely lost their envelopes because of binary interactions, similar to the hot subdwarf population in our own Galaxy. We have developed an evolutionary population synthesis model for the FUV excess of elliptical galaxies based on the binary model developed by Han et al. for the formation of hot subdwarfs in our Galaxy. Despite its simplicity, it successfully reproduces most of the properties of elliptical galaxies with a UV excess: the range of observed UV excesses, both in (1550 - V) and (2000 - V), and their evolution with redshift. We also present colour-colour diagrams for use as diagnostic tools in the study of elliptical galaxies. The model has major implications for understanding the evolution of the UV excess and of elliptical galaxies in general. In particular, it implies that the UV excess is not a sign of age, as had been postulated previously, and predicts that it should not be strongly dependent on the metallicity of the population, but exists universally from dwarf ellipticals to giant ellipticals.
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