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We present a quantitative analysis of the UV radiation from evolved low mass hot stars. We use a new, extensive grid of horizontal branch (HB) and post-HB models (Dorman, Rood, \& O'Connell 1993, preprint), which concentrates on extreme HB stars and their progeny, post-Early AGB and AGB-Manqu\'e stars, and post-AGB evolutionary sequences. The models cover the metallicity range $\rm -2.3 < [Fe/H] < 0.6$. We compute the lifetime-integrated UV energy emitted by each model from the Zero Age HB to late in the post-HB evolution, as a function of the ZAHB envelope mass $M_{\rm env}$. This UV energy is found to be a strong function of $M_{\rm env}$, but only a weak function of metallicity.
We use these sequences to compute the total UV luminosity of old stellar populations. We compare our synthetic UV color indices with the results of satellite observations of globular clusters, and also with IUE observations of elliptical galaxies and spiral galaxy bulges (Burstein et.~al., Ap.J. 328, 440 1988). The UV upturn (UVX) phenomenon in the spectra of galaxies such as NGC~4649 and NGC~1399 can be accounted for if only a fraction of the stars begin their helium-burning stages as ``Extreme HB stars.'' The weak dependence of the lifetime-integrated UV energy distributions on metallicity implies that the observed correlation between the UVX and metallicity can arise only if mass loss on the giant branch has a significant metallicity dependence for $\rm [Fe/H] > 0$. We also present sample UV spectra from our synthetic stellar populations and demonstrate the variation of the spectral energy distribution with the stellar mass distribution.
