Properties of carbon stars in the Solar neighbourhood based on Gaia DR2
  astrometry
  We find that the combined LF of N- and SC-type stars are consistent with a
Gaussian distribution peaking at M_bol~ -5.2 mag. The resulting LF however
shows two tails at lower and higher luminosities more extended than those
previously found, indicating that AGB carbon stars with Solar metallicity may
reach M_bol~-6.0 mag. We find that J-type stars are about half a magnitude
fainter on average than N- and SC-type stars, while R-hot stars are half a
magnitude brighter than previously found. The Galactic spatial distribution and
velocity components of the N-, SC- and J-type stars are very similar, while
about 30 % of the R-hot stars in the sample are located at distances larger
than ~ 500 pc from the Galactic Plane, and show a significant drift with
respect to the local standard of rest. The LF derived for N- and SC-type in the
Solar neighbourhood fully agrees with the expected luminosity of stars of 1.5-3
M_o on the AGB. On a theoretical basis, the existence of an extended low
luminosity tail would require a contribution of extrinsic low mass carbon
stars, while the high luminosity one would imply that stars with mass up to ~5
Mo may become carbon star on the AGB. J-type stars not only differ
significantly in their chemical composition with respect to the N- and SC-types
but also in their LF, which reinforces the idea that these carbon stars belong
to a dvifferent type whose origin is still unknown. The derived luminosities of
R-hot stars make these stars unlikely to be in the red-clump as previously
claimed. On the other hand, the derived spatial distribution and kinematic
properties, together with their metallicity, indicate that most of the N-, SC-
and J-type stars belong to the thin disc population, while a significant
fraction of R-hot stars show characteristics compatible with the thick disc.
