8 Summary of the results

Four bolometric corrections were calibrated against three color indices for 375 carbon and Ba II giants and related objects. The mean relations are tabulated in the Appendix. They were selected by trial and error as the more efficient ones, and used to derive the bolometric magnitudes of 81 HIPPARCOS carbon stars and related objects. The coefficients $C_{\rm R}$ and $C_{\rm L}$ were defined, which are proportional to the true parallaxes, and are intended for statistical purposes. They allow to estimate unbiased mean photospheric radii and mean luminosities respectively. The relations between the photometric mean coefficient $\left < k \right >^{1/2}$ and the true parallax evaluated from HIPPARCOS astrometry (Knapik et al. 1998; Paper II) were studied and shown to be consistent with the existence of a range of photospheric radii for every photometric group. The data in Table $~\ref{pmin_max}$ illustrates the increase of the photospheric radius along the sequence of photometric groups from HC1 to HC5, and then from CV1 to CV6 (the extreme groups HC0 and CV7 are poorly-documented).

The above-described work completes the study of Paper I, and the resulting data can be found in Table 2 (only available at CDS), with 507 entries corresponding to the analyzed SEDs. This is a corrected, augmented and updated version of Table 10 of Paper I. Effective temperatures, interstellar (and eventually circumstellar) extinctions, classification in our photometric groups, bolometric magnitudes and comments are quoted there. For about 370 objects, absolute bolometric magnitudes estimated from true parallaxes are also given. This data base was essentially intended for statistical use. Mean data was provided for the various photometric groups (Table $~\ref{coef_gr}$), and then calculated for five variability classes and quoted in Table $~\ref{coef_cl}.$

The luminosity function (LF) of our sample of carbon giants (MW), was constructed and compared to the LFs of carbon stars in the Milky Way Bulge (MWB), LMC and SMC (Figs. $~\ref{lf1},$ $~\ref{lf2}$ and $~\ref{lf3}$). It displays two maxima which correspond to components of two distinct populations identified in Paper II. The HR diagram of nearly 370 Galactic carbon and BaII giants, and related objects was constructed (Fig. $~\ref{hr1}$), and explored. The localization of $^{99}\rm {Tc}$ stars within the (bright) CV-stars was then confirmed and discussed (Fig. $~\ref{hr2}$). On the contrary, $^{13}\rm {C}$-rich (J) stars were found nearly uniformly distributed.

A full discussion and conclusions will be given at the end of the companion article (Paper IV), attempting a synthesis of the results from Papers I, II, III and IV.

Acknowledgements

Valuable suggestions from the referee Dr. Maurizio Busso are gratefully acknowledged. We are especially indebted to him for having pointed out some weaknesses and misunderstandings withdrawn from the present account of predictions from theoretical models.