Properties of carbon stars in the solar neighbourhood based on

Context. Stars evolving along the asymptotic giant branch (AGB) can become carbon rich in the final part of their evolution. The detailed description of their spectra has led to the definition of several spectral types: N, SC, J, and R. To date, differences among them have been partially established only on the basis of their chemical properties. Aims. An accurate determination of the luminosity function (LF) and kinematics together with their chemical properties is extremely important for testing the reliability of theoretical models and establishing on a solid basis the stellar population membership of the different carbon star types. Methods. Using Gaia Data Release 2 (Gaia DR2) astrometry, we determine the LF and kinematic properties of a sample of 210 carbon stars with different spectral types in the solar neighbourhood with measured parallaxes better than 20%. Their spatial distribution and velocity components are also derived. Furthermore, the use of the infrared Wesenheit function allows us to identify the different spectral types in a Gaia-2MASS diagram. Results. We find that the combined LF of N- and SC-type stars are consistent with a Gaussian distribution peaking at Mbol ∼ −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 Mbol ∼ −6.0 mag. This contrasts with the narrower LF derived in Galactic carbon Miras from previous studies. 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, although fainter in any case by several magnitudes than other carbon types. Part of these differences are due to systematically lower parallaxes measured by Gaia DR2 with respect to HIPPARCO