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In the nearby galaxy NGC 4258, the well-modeled orbital motion of H$_2$Omasers about its supermassive black hole provides the means to measure aprecise geometric distance. As a result, NGC 4258 is one of a few "geometricanchors" available to calibrate the true luminosities of stellar distanceindicators such as the Tip of the Red Giant Branch (TRGB) or the CepheidLeavitt law. In this paper, we present a detailed study of the apparentmagnitude of the TRGB within NGC 4258 using publicly-available HST observationsoptimally situated in the gas- and dust-free halo along the minor axis,spanning distances ranging from 8 to 22 kpc in projected galactocentric radius.We undertake a systematic evaluation of the uncertainties associated withmeasuring the TRGB in this galaxy, based on an analysis of 54 arcmin$^2$ ofHST/ACS imaging. After quantifying these uncertainties, we measure the TRGB inNGC 4258 to be F814W$_0$ = 25.347 $\pm$ 0.014(stat) $\pm$ 0.042(sys) mag.Combined with a recent 1.5% megamaser distance to NGC 4258, we determine theabsolute luminosity of the TRGB to be $M_{F814W}^{TRGB}$ = -4.050 $\pm$0.028(stat) $\pm$ 0.048(sys) mag. This new calibration agrees to better than 1%with an independent calibration presented in Freedman et al. (2019, 2020) thatwas based on detached eclipsing binaries (DEBs) located in the LMC.

The Carnegie-Chicago Hubble Program. IX. Calibration of the Tip of the Red Giant Branch Method in the Mega-Maser Host Galaxy, NGC4258 (M106)