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).
