The AMBRE project: The thick thin disk and thin thick disk of the Milky
  Way
  We analyze 494 main sequence turnoff and subgiant stars from the AMBRE:HARPS
survey. These stars have accurate astrometric information from
\textit{Gaia}/DR1, providing reliable age estimates with relative uncertainties
of $\pm1-2$ Gyr and allowing precise orbital determinations. The sample is
split based on chemistry into a low-[Mg/Fe] sequence, which are often
identified as thin disk stellar populations, and a high-[Mg/Fe] sequence, which
are often associated with the thick disk. We find that the high-[Mg/Fe]
chemical sequence has extended star formation for several Gyr and is coeval
with the oldest stars of the low-[Mg/Fe] chemical sequence: both the low- and
high-[Mg/Fe] sequences were forming stars at the same time. The high-[Mg/Fe]
stellar populations are only vertically extended for the oldest, most-metal
poor and highest [Mg/Fe] stars. When comparing vertical velocity dispersion for
both sequences, the high-[Mg/Fe] sequence has lower velocity dispersion than
the low-[Mg/Fe] sequence for stars of similar age. Identifying either group as
thin or thick disk based on chemistry is misleading. The stars belonging to the
high-[Mg/Fe] sequence have perigalacticons that originate in the inner disk,
while the perigalacticons of stars on the low-[Mg/Fe] sequence are generally
around the solar neighborhood. From the orbital properties of the stars, the
high-and low-[Mg/Fe] sequences are most likely a reflection of the chemical
enrichment history of the inner and outer disk populations; radial mixing
causes both populations to be observed in situ at the solar position. Based on
these results, we emphasize that it is important to be clear in defining what
populations are being referenced when using the terms thin and thick disk, and
that ideally the term thick disk should be reserved for purely geometric
definitions to avoid confusion and be consistent with definitions in external
galaxies.
