1 Introduction

In a companion paper (Bergeat et al. 2002b, hereafter Paper III) a general introduction was provided to the subject of fundamental quantities (mass, luminosity, radius, effective temperature etc.) for carbon-rich giants, and diagrams in which their evolution can be traced. Following the HIPPARCOS mission (ESA 1997), associating astrometric data and radial velocities, spectral energy distributions (SEDs) and photometric classification, and angular diameters from lunar occultations and interferometry, our knowledge of those complex phases of stellar evolution considerably improved (Bergeat et al. 2001 hereafter Paper I; Bergeat et al. 2002a hereafter Paper II, and references therein). In Paper III, it was shown that the luminosity function (LF) of the Galactic carbon-rich giants in the Sun vicinity exhibit two maximas corresponding respectively to (faint) HC-objects of the thick disk contaminated by halo CH stars, and (bright) CV-members of the thin disk. The LF of the former giants appears similar to that of the Galactic bulge reinforcing the idea of a dynamical connection between Bulge and thick disk, while the LF of the latter seems similar to that of the Large Magellanic Cloud (LMC). The HR diagram of nearly 370 Galactic carbon and BaII giants, and related objects was constructed and discussed. The $\rm {^{99}Tc}$-rich stars were found to be (bright) CV-giants as expected, which is consistent with the third dredge-up (TDU) scenario. A similar result was already obtained for bright (intrinsic) S stars (Van Eck et al. 1998). The $\rm {^{13}C}$-rich objects (J-stars) are on the contrary nearly uniformly distributed within HC and CV-giants in the HR diagram. From comparison to predicted tracks for stellar evolution with various (Z) abundances in heavy elements, a range of initial masses of 0.8 up to $4~M_{\odot}$ was established for the majority of carbon-rich giants.

From periods of pulsation of long period variables (LPVs), the present masses can be estimated ("pulsation masses''). This requires identification in the observations of the various pulsation modes, and comparison of data to theoretical period-mass-radius (PMR) relations. Such a study has already been attempted for oxygen-rich LPVs or on samples including only a few carbon variables, making use of linear models (e.g. Barthès 1998 and references therein). Groenewegen & de Jong (1994) studied the pulsation modes of the LPVs in the LMC, including carbon-rich objects. They concluded that most of them should pulsate in the fundamental mode. The derived masses fall in the ranges of the low mass stars (LMS) and intermediate mass stars (IMS).

The pulsation mode of carbon LPVs is analyzed in the period-radius (PR) diagram (Sect. 2), and the multiperiodicity of part of the stars in our sample, is exploited to confirm the splitting of the PR-diagram into two portions for fundamental and (presumably first) overtone modes respectively. The (present) "pulsation'' masses are estimated (Sect. 3), applying the theoretical PMR-relations to the observed data. The results are displayed in a mass-luminosity diagram, where they are confronted to the prediction of stellar evolution calculations (Sect. 4). The carbon to oxygen abundance ratio (C/O) does exhibit distinct behaviors vs. effective temperature (Sect. 5), for three populations found in the Sun vicinity. The main results are finally summarized and discussed (Sect. 6), with special emphasis on luminosities, initial and present masses, evolutionary status, mean densities and surface gravities.