Tip of the Red Giant Branch Distances with JWST: An Absolute Calibration in NGC 4258 and First Applications to Type Ia Supernova Hosts

The tip of the red giant branch (TRGB) allows for the measurement of precise and accurate distances to nearby galaxies, based on the brightest ascent of low-mass red giant branch stars before they undergo the helium flash. With the advent of JWST, there is great promise to utilize the technique to measure galaxy distances out to at least 50 Mpc, significantly further than HST's reach of 20 Mpc. However, with any standard candle, it is first necessary to provide an absolute reference. Here we use Cycle 1 data to provide an absolute calibration in the F090W filter. F090W is most similar to the F814W filter commonly used for TRGB measurements with HST, which had been adopted by the community due to minimal dependence from the underlying metallicities and ages of stars. The imaging we use was taken in the outskirts of NGC 4258, which has a direct geometrical distance measurement from the Keplerian motion of its water megamaser. Utilizing several measurement techniques, we find $M_{TRGB}^{F090W}$ = -4.362 $\pm$ 0.033 (stat) $\pm$ 0.045 (sys) mag (Vega) for the metal-poor TRGB. We also perform measurements of the TRGB in two Type Ia supernova hosts, NGC 1559, and NGC 5584. We find good agreement between our TRGB distances and previous distance determinations to these galaxies from Cepheids ($\Delta$ = 0.01 $\pm$ 0.06 mag), with these differences being too small to explain the Hubble tension ($\sim$0.17 mag). As a final bonus, we showcase the serendipitous discovery of a faint dwarf galaxy near NGC 5584.