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The Araucaria Project: The distance to the Carina Dwarf Galaxy from infrared photometry of RR Lyrae stars

We obtained single-phase near-infrared (NIR) magnitudes in the $J$- and $K$-band for a sample of 33 RR Lyrae stars in the Carina dSph galaxy. Applying different theoretical and empirical calibrations of the NIR period-luminosity-metallicity relation for RR Lyrae stars, we find consistent results and obtain a true, reddening-corrected distance modulus of 20.118 $\pm$ 0.017 (statistical) $\pm$ 0.11 (systematic) mag. This value is in excellent agreement with the results obtained in the context of the Araucaria Project from NIR photometry of Red Clump stars (20.165 $\pm$ 0.015) and Tip of Red Giant Branch (20.09 $\pm$ 0.03 $\pm$ 0.12 mag in $J$-band, 20.14 $\pm$ 0.04 $\pm$ 0.14 mag in $K$-band), as well as with most independent distance determinations to this galaxy. The near-infrared RR Lyrae method proved to be a reliable tool for accurate distance determination at the 5 percent level or better, particularly for galaxies and globular clusters that lack young standard candles, like Cepheids.