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

We determine the distance to the Sculptor Dwarf Spheroidal via three Population II stellar distance indicators: (a) the Tip of the Red Giant Branch (TRGB), (b) RR Lyrae variables (RRLs), and (c) the ridgeline of the blue horizontal branch (HB). High signal-to-noise, wide-field VI imaging that covers an area $48^{\prime} \,\times \,48^{\prime} $ and reaches a photometric depth approximately 2 mag fainter than the HB was acquired with the Magellan-Baade 6.5 m telescope. The true modulus derived from Sculptor's TRGB is found to be ${\mu }_{o}^{\mathrm{TRGB}}=19.59\,\pm \,{0.07}_{\mathrm{stat}}\,\pm \,{0.05}_{\mathrm{sys}}$ mag. Along with periods adopted from the literature, newly acquired RRL phase points are fit with template light curves to determine ${\mu }_{{W}_{I,V-I}}^{\mathrm{RRL}}=19.60\pm {0.01}_{\mathrm{stat}}\pm {0.05}_{\mathrm{sys}}$ mag. Finally, the HB distance is found to be ${\mu }_{o}^{\mathrm{HB}}\,=19.54\pm {0.03}_{\mathrm{stat}}\pm {0.09}_{\mathrm{sys}}$ mag. Absolute calibrations of each method are anchored by independent geometric zero-points, utilize a different class of stars, and are determined from the same photometric calibration. *Based in part on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. These observations are associated with program No. 13691. Additional observations are credited to the Observatories of the Carnegie Institution of Science for the use of Magellan-Baade IMACS.