Asymptotic giant branch stars in the Fornax dwarf spheroidal galaxy

We report on a multi-epoch study of the Fornax dwarf spheroidal galaxy, made with the Infrared Survey Facility, over an area of about 42 x 42 arcmin(2). The colour-magnitude diagram shows a broad well-populated giant branch with a tip that slopes downwards from red to blue, as might be expected given Fornax's known range of age and metallicity. The extensive asymptotic giant branch (AGB) includes seven Mira variables and 10 periodic semiregular variables. Five of the seven Miras are known to be carbon rich. Their pulsation periods range from 215 to 470 d, indicating a range of initial masses. Three of the Fornax Miras are redder than typical Large Magellanic Cloud (LMC) Miras of similar period, probably indicating particularly heavy mass-loss rates. Many, but not all, of the characteristics of the AGB are reproduced by isochrones from Marigo et al. for a 2 Gyr population with a metallicity of Z = 0.0025. An application of the Mira period-luminosity relation to these stars yields a distance modulus for Fornax of 20.69 +/- 0.04 (internal), +/- 0.08 (total) (on a scale that puts the LMC at 18.39 mag) in good agreement with other determinations. Various estimates of the distance to Fornax are reviewed.