Absolute Magnitude Calibration for Red Giants based on the
  Colour-Magnitude Diagrams of Galactic Clusters. III-Calibration with 2MASS
  We present two absolute magnitude calibrations, $M_{J}$ and $M_{K_s}$, for
red giants with the colour magnitude diagrams of five Galactic clusters with
different metallicities i.e. M92, M13, M71, M67, and NGC 6791. The combination
of the absolute magnitudes of the red giant sequences with the corresponding
metallicities provides calibration for absolute magnitude estimation for red
giants for a given colour. The calibrations for $M_{J}$ and $M_{K_s}$ are
defined in the colour intervals $1.3\leq(V-J)_{0}\leq2.8$ and $1.75 \leq
(V-K_{s})_{0}\leq 3.80$ mag, respectively, and they cover the metallicity
interval $-2.15 \leq \lbrack Fe/H \rbrack \leq +0.37$ dex. The absolute
magnitude residuals obtained by the application of the procedure to another set
of Galactic clusters lie in the intervals $-0.08<\Delta M_{J}\leq +0.34$ and
$-0.10< \Delta M_{K_s}\leq +0.27$ mag for $M_{J}$ and $M_{K_s}$, respectively.
The means and standard deviations of the residuals are $<\Delta M_{J}>= 0.137$
and $\sigma_{M_J}=0.080$, and $<\Delta M_{K_s}>=0.109$ and
$\sigma_{M_{K_{s}}}=0.123$ mag. The derived relations are applicable to stars
older than 4 Gyr, the age of the youngest calibrating cluster.
