Distances to Local Group Galaxies via Population II, Stellar Distance Indicators. II. The Fornax Dwarf Spheroidal*

We determine three independent Population II distance moduli to the Fornax dwarf spheroidal (dSph) galaxy, using wide-field, ground-based $VI$ imaging acquired with Magellan-Baade telescope at Las Campanas Observatory. After subtracting foreground stars Gaia EDR3 proper motions, we measure an $I$-band tip of red giant branch (TRGB) magnitude $I_0^\mathrm{TRGB} = 16.753 \pm 0.03_\mathrm{stat} 0.037_\mathrm{sys}$ mag, a calibration based in LMC giving modulus $\mu_0^\mathrm{TRGB} 20.80 0.037_\mathrm{stat} 0.057_\mathrm{sys}$ mag. RR Lyrae (RRL) from template mean magnitudes, periods adopted literature. Adopting DR2 first overtone RRL period-luminosity and period-Wesenheit relations, find $\mu_0^\mathrm{PLZ} 20.74 0.01_\mathrm{stat} 0.12_\mathrm{sys}$ mag $\mu_0^\mathrm{PWZ} 20.68 0.02_\mathrm{stat} 0.07_\mathrm{sys}$ Finally, Fornax's horizontal (HB) two galactic globular cluster calibrators, $\mu_0^\mathrm{HB} 20.83 0.09_\mathrm{sys}$ These distances are each derived homogeneous IMACS photometry, anchored geometric zero-points, utilize different classes stars. therefore average over uncertainties report combined $\langle \mu_0\rangle 20.770 0.042_\mathrm{stat} 0.024_\mathrm{sys}$ (corresponding $143\pm3$ kpc).