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