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We have computed 8, 10, and 12 Gyr isochrones and physically consistent models of zero-age red horizontal branch stars for stellar masses between 0.55 and 1.3~M$_\odot$, all at [Fe/H] $=+0.15$. Comparison to the NGC~6791 BVI photometry of Ka{\l}u\.zny \& Udalski (1992, Acta Astron., 42, 29) and Montgomery, Janes \& Phelps (1994, AJ, 108, 585) yields an age of $10\pm0.5$ Gyr at an apparent distance modulus $ 13.49 < (m-M)_v < 13.70$. The color offsets required to fit the isochrones, combined with the spectroscopic results of Friel \& Janes (1993, A\&A, 267,75), imply that the foreground reddening to NGC~6791 lies in the range $0.24 >$ E(B$-$V) $ >0.19$ with $+0.27 <$ [Fe/H] $<+0.44$. These results are derived using a technique by which we predict color shifts and apply these to the isochrones to simulate progressively higher metallicities.
The zero-age horizontal branch models suggest that the red horizontal branch stars of NGC~6791 have masses $ \lesssim 0.7$M$_\odot$. This is similar to the results found for the M67 red horizontal branch stars by Tripicco, Dorman \& Bell (1993, AJ, 106, 618), and for globular cluster branch stars, even though the M67 progenitors are $\sim 0.2$ M$_\odot$ more massive, and the globular cluster progenitors similarly less massive. This suggests the presence of a mechanism, not strongly dependent on metallicity, which reduces stellar envelopes on the zero-age horizontal branch to a given mass rather than by a given amount.
