Thick disk and old disk carbon-rich giants in the Sun vicinity

Making use of the HIPPARCOS data and refining a previous study of the space distribution of the carbon-rich giant stars located in the vicinity of the Sun (Paper I), we fully investigate their space distributions and space velocities on the basis of our photometric grouping (CVi i.e. carbon variable stars with $i=1$ to 7; HCj i.e. hot carbon stars with $j=0$ to 5). As expected, the CH stars (a subset of the HC stars delineated on the grounds of spectroscopic criteria) need to be considered separately. We also used groupings according to variability classes. The various biases affecting the use of the data are taken into account as far as possible. The mean distance to the Galactic plane of the faint $\left(\left\ge-3.5\right)$ HC-stars amounts to 0.5 kpc compared to 0.15 kpc for the bright $\left(\left\le-3.5\right)$ CV-stars. Exponentially decreasing distributions are fit with distance scales of $0.95\pm0.06$ kpc and 0.19 kpc respectively, and a normalization factor of 5.2% to 7.3% for the former component, compatible with a thick disk and thin disk respectively. Projected surface densities on the Plane are given with a total of about $76\,\rm{kpc}^{-2}$, including 6% of CH stars and at least 18% for the other HC-stars (namely the HC'-sample). While halo-type velocities are found for CH stars with a substantial drift of $-112\,\rm{km\,s^{-1}}$, the solar reflex velocities and residual-velocity dispersions for the HC'-sample are about twice those of the CV-sample, close to thick disk and thin disk values respectively. In summary, we identify the HC-sample as a component of the thick disk contaminated by the CH stars which are a spheroidal contribution, and possibly by CV-stars at HC5. As expected, the CV-sample is a component of the old (thin) disk, dated from AVR, $\left(3 \pm 1 \right) \rm{Gyr}$ on average, but with a likely spread from a few $10^{8}\, \rm{Myr}$ up to $8{-}12 \, \rm{Gyr}.$ While the former (HC) represents very old low mass stars (initial masses less than $1.15~{M_{\odot}}$ but subject to mass-loss), the latter (CV) are younger stars with higher initial masses on average (up to a few solar masses). The high frequency of HC'-stars rules out models requiring rare events. Better modeling of mixing events in low mass stars on the RGB and AGB could help. Less dragged up carbon is needed to transform the low-mass stars with a low O/H ratio into carbon giants