The Araucaria Project: The Distance to the Fornax Dwarf Galaxy from Near-infrared Photometry of RR Lyrae Stars

We have obtained single-phase near-infrared (NIR) magnitudes in the J and K bands for 77 RR Lyrae (RRL) stars in the Fornax Dwarf Spheroidal Galaxy. We have used different theoretical and empirical NIR period-luminosity-metallicity calibrations for RRL stars to derive their absolute magnitudes, and found a true, reddening-corrected distance modulus of 20.818 +/- 0.015(statistical) +/- 0.116(systematic) mag. This value is in excellent agreement with the results obtained within the Araucaria Project from the NIR photometry of red clump stars (20.858 +/- 0.013 mag), the tip of the red giant branch (20.84 +/- 0.04 +/- 0.14 mag), as well as with other independent distance determinations to this galaxy. The effect of metallicity and reddening is substantially reduced in the NIR domain, making this method a robust tool for accurate distance determination at the 5% level. This precision is expected to reach the level of 3% once the zero points of distance calibrations are refined thanks to the Gaia mission. NIR period-luminosity-metallicity relations of RRL stars are particularly useful for distance determinations to galaxies and globular clusters up to 300 kpc, that lack young standard candles, like Cepheids.