Astrophysical Distance Scale: The AGB J-band Method. I. Calibration and a First Application

A near-infrared, color-selected subset of carbon-rich asymptotic giant branch (C-AGB) stars is found to have tightly constrained luminosities in the near-infrared J band. Based on JK photometry of some 3300 C-AGB stars in the bar of the Large Magellanic Cloud (LMC) we find that these stars have a constant absolute magnitude of < M-J > = -6.22 mag, adopting the detached eclipsing binary (DEB) distance to the LMC of 18.477 +/- 0.004 (stat) +/- 0.026 (sys). Undertaking a second, independent calibration in the Small Magellanic Cloud, which also has a DEB geometric distance, we find < M-J > = - 6.18. 0.01 (stat) +/- 0.05.(sys) mag. For the LMC the scatter is +/- 0.27 mag for single-epoch observations, (falling to +/- 0.15 mag for multiple observations averaged over a window of more than one year). We provisionally adopt < M-J > = -6.20 mag +/- 0.01.(stat) +/- 0.04.(sys) mag for the mean absolute magnitude of these stars. Applying this calibration to stars recently observed in the galaxy NGC.253, we determine a distance modulus of 27.66 +/- 0.01(stat) +/- 0.04 mag (syst), corresponding to a distance of 3.40 +/- 0.06 Mpc.(stat). This is in excellent agreement with the average tip of the red giant branch (TRGB) distance modulus of 27.68 +/- 0.05 mag, assuming M-I = -4.05 mag for the TRGB zero-point.