Internal rotation of Milky Way dwarf spheroidal satellites with $Gaia$
  Early Data Release 3
  We present an analysis of the kinematics of 14 satellites of the Milky Way
(MW). We use proper motions (PMs) from the $Gaia$ Early Data Release 3 (EDR3)
and line-of-sight velocities ($v_{\mathrm{los}}$) available in the literature
to derive the systemic 3D motion of these systems. For six of them, namely the
Carina, Draco, Fornax, Sculptor, Sextans, and Ursa Minor dwarf spheroidal
galaxies (dSph), we study the internal kinematics projecting the stellar PMs
into radial, $V_R$ (expansion/contraction), and tangential, $V_T$ (rotation),
velocity components with respect to the centre of mass. We find significant
rotation in the Carina ($|V_T| = 9.6 \pm 4.5 \ {\rm{km \ s^{-1}}}\>$), Fornax
($|V_T| = 2.8 \pm 1.3 \ {\rm{km \ s^{-1}}}\>$), and Sculptor ($|V_T| = 3.0 \pm
1.0 \ {\rm{km \ s^{-1}}}\>$) dSphs. Besides the Sagittarius dSph, these are the
first measurements of internal rotation in the plane of the sky in the MW's
classical dSphs. All galaxies except Carina show $|V_T| / \sigma_v < 1$. We
find that slower rotators tend to show, on average, larger sky-projected
ellipticity (as expected for a sample with random viewing angles) and are
located at smaller Galactocentric distances (as expected for tidal stirring
scenarios in which rotation is transformed into random motions as satellites
sink into the parent halo). However, these trends are small and not
statistically significant, indicating that rotation has not played a dominant
role in shaping the 3D structure of these galaxies. Either tidal stirring had a
weak impact on the evolution of these systems or it perturbed them with similar
efficiency regardless of their current Galactocentric distance.
