Calibration of the Tip of the Red Giant Branch

The tip of the red giant branch (TRGB) method provides one of the most accurate and precise means of measuring the distances to nearby galaxies. Here we present a multi-wavelength, VIJHK absolute calibration of the TRGB based on observations of TRGB stars in the Large Magellanic Cloud (LMC), grounded on a geometric distance, determined by detached eclipsing binaries (DEBs). This paper presents a more detailed description of the method first presented by Freedman et al. for measuring corrections for the total line-of-sight extinction and reddening to the LMC. In this method, we use a differential comparison of the red giant population in the LMC, first with red giants in the Local Group galaxy IC 1613, and then with those in the Small Magellanic Cloud (SMC). As a consistency check, we derive an independent calibration of the TRGB sequence using the SMC alone, invoking its geometric distance also calibrated by DEBs. An additional consistency check comes from near-infrared observations of Galactic globular clusters covering a wide range of metallicities. In all cases we find excellent agreement in the zero-point calibration. We then examine the recent claims by Yuan et al., demonstrating that, in the case of the SMC, they corrected for extinction alone while neglecting the essential correction for reddening. In the case of IC 1613, we show that their analysis contains an incorrect treatment of (over-correction for) metallicity. Using our revised (and direct) measurement of the LMC TRGB extinction, we find a value of H ₀ = 69.6 ± 0.8 (±1.1% stat) ± 1.7 (±2.4%