The Near-Infrared Tip of the Red Giant Branch. I. A Calibration in the Isolated Dwarf Galaxy IC 1613

Based on observations from the \emph{FourStar} near-infrared camera on the 6.5m Baade-Magellan telescope at Las Campanas, Chile, we present calibrations of the $JHK$ luminosities of stars defining the tip of the red giant branch (TRGB) in the halo of the Local Group dwarf galaxy IC 1613. We employ metallicity-independent (rectified) T-band magnitudes---constructed using $J,H$ and $K$-band magnitudes and both $(J-H)~ \& ~(J-K)$ colors in order to flatten the upward-sloping red giant branch tips as otherwise seen in their apparent color-magnitude diagrams. We describe and quantify the advantages of working at these particular near-infrared wavelengths, which are applicable to both \emph{HST} and \emph{JWST}. We also note that these same wavelengths can be accessed from the ground for an eventual tie-in to \emph{Gaia} for absolute astrometry and parallaxes to calibrate the intrinsic luminosity of the TRGB. Adopting the color terms derived from the IC 1613 data, as well as the zero-points from a companion study of the Large Magellanic Cloud whose distance is anchored to the geometric distances of detached eclipsing binaries, we find a true distance modulus of 24.32 $\pm$ 0.02~ (statistical) $\pm$ 0.06~mag (systematic) for IC 1613, which compares favorably with the recently published multi-wavelength, multi-method consensus modulus of 24.30 $\pm$ 0.05~mag by Hatt et al. (2017).