The Araucaria Project. Multi-band calibrations of the TRGB absolute
  magnitude
  We present new empirical calibrations of the absolute magnitude of the tip of
the red giant branch (TRGB) in the optical I and near-infrared J, H, and K
bands in terms of the (V-K)_0, (V-H)_0, and (J-K)_0 colors of the red giant
branch. Our calibrations are based on the measurements in 19 fields in the
Large and Small Magellanic Clouds, which span a wide (V-K)_0 color range of the
brightest part of the red giant branch. We use a simple edge detection
technique based on the comparison of the star count difference in two adjacent
bins with the estimated Poisson noise. Further, we include the reddening and
geometrical corrections, as well as the precise and accurate to 2% distance to
the Large Magellanic Cloud. The calibration based on a (V-K) colors can be a
robust tool to calculate with a great precision the absolute magnitude of the
TRGB.
