Space Motions of the Dwarf Spheroidal Galaxies Draco and Sculptor based
  on HST Proper Motions with ~10-year Time Baseline
  We present new proper motion (PM) measurements of the dwarf spheroidal
galaxies (dSphs) Draco and Sculptor using multi-epoch images obtained with the
Hubble Space Telescope ACS/WFC. Our PM results have uncertainties far lower
than previous measurements, even made with the same instrument. The PM results
for Draco and Sculptor are (mu_W,mu_N)_Dra =
(-0.0562+/-0.0099,-0.1765+/-0.0100) mas/yr and (mu_W,mu_N)_Scl =
(-0.0296+/-0.0209,-0.1358 +/-0.0214) mas/yr. The implied Galactocentric
velocity vectors for Draco and Sculptor have radial and tangential components:
(V_rad,V_tan)_Dra = (-88.6,161.4) +/- (4.4,5.6) km/s; and (V_rad,V_tan)_Scl =
(72.6,200.2) +/- (1.3,10.8) km/s. We study the detailed orbital history of both
Draco and Sculptor via numerical orbit integrations. Orbital periods of Draco
and Sculptor are found to be 1-2 and 2-5 Gyrs, respectively, accounting for
uncertainties in the MW mass. We also study the influence of the Large
Magellanic Cloud (LMC) on the orbits of Draco and Sculptor. Overall, the
inclusion of the LMC increases the scatter in the orbital results. Based on our
calculations, Draco shows a rather wide range of orbital parameters depending
on the MW mass and inclusion/exclusion of the LMC, but Sculptor's orbit is very
well constrained with its most recent pericentric approach to the MW being
0.3-0.4 Gyr ago. Our new PMs imply that the orbital trajectories of both Draco
and Sculptor are confined within the Disk of Satellites (DoS), better so than
implied by earlier PM measurements, and likely rule out the possibility that
these two galaxies were accreted together as part of a tightly bound group.
