The Milky Way Halo in Action Space
  We analyse the structure of the local stellar halo of the Milky Way using
$\sim$ 60000 stars with full phase space coordinates extracted from the
SDSS--{\it Gaia} catalogue. We display stars in action space as a function of
metallicity in a realistic axisymmetric potential for the Milky Way Galaxy. The
metal-rich population is more distended towards high radial action $J_R$ as
compared to azimuthal or vertical action, $J_\phi$ or $J_z$. It has a mild
prograde rotation $(\langle v_\phi \rangle \approx 25$ km s$^{-1}$), is
radially anisotropic and highly flattened with axis ratio $q \approx 0.6 -
0.7$. The metal-poor population is more evenly distributed in all three
actions. It has larger prograde rotation $(\langle v_\phi \rangle \approx 50$
km s$^{-1}$), a mild radial anisotropy and a roundish morphology ($q\approx
0.9$). We identify two further components of the halo in action space. There is
a high energy, retrograde component that is only present in the metal-rich
stars. This is suggestive of an origin in a retrograde encounter, possibly the
one that created the stripped dwarf galaxy nucleus, $\omega$Centauri. Also
visible as a distinct entity in action space is a resonant component, which is
flattened and prograde. It extends over a range of metallicities down to [Fe/H]
$\approx -3$. It has a net outward radial velocity $\langle v_R \rangle \approx
12$ km s$^{-1}$ within the Solar circle at $|z| <3.5$ kpc. The existence of
resonant stars at such extremely low metallicities has not been seen before.
