  Although the stellar halo accounts for just ~1% of the total stellar mass of
the Milky Way, the kinematics of halo stars encode valuable information about
the origins and evolution of our Galaxy. It has been shown that the high
transverse velocity stars in Gaia DR2 reveal a double sequence in the
Hertzsprung-Russell (HR) diagram, indicating a bifurcation in the local stellar
halo within 1 kpc. We fit these stars by updating the popular
Besan\c{c}on/Galaxia model, incorporating the latest observational results for
the stellar halo and an improved kinematic description for the thick-disk from
Sch\"onrich & Binney (2012). We are able to obtain a good match to the Gaia
data and provide new constraints on the properties of the Galactic disc and
stellar halo. In particular, we show that the kinematically defined thick disc
contribution to this high velocity tail is ~13%. We look in greater detail
using chemistry from LAMOST DR5, identifying a population of retrograde stars
with thick-disc chemistry. Our thick disc kinematic model cannot account for
this population and so we conclude there is likely to be a contribution from
heated or accreted stars in the Solar Neighbourhood. We also investigate
proposed dynamical substructures in this sample, concluding that they are
probably due to resonant orbits rather than accreted populations. Finally we
provide new insights on the nature of the two sequences and their relation with
past accretion events and the primordial Galactic disc.
