The effective temperatures of carbon-rich stars

We evaluate effective temperatures of 390 carbon-rich stars. The interstellar extinction on their lines of sights was determined and circumstellar contributions derived. The intrinsic (dereddened) spectral energy distributions (SEDs) are classified into 14 photometric groups (HC i , CV j and SCV with $i=0$,5 and $j=1$,7). The new scale of effective temperatures proposed here is calibrated on the 54 angular diameters (measured on 52 stars) available at present from lunar occultations and interferometry. The brightness distribution on stellar discs and its influence on diameter evaluations are discussed. The effective temperatures directly deduced from those diameters correlate with the classification into photometric groups, despite the large error bars on diameters. The main parameter of our photometric classification is thus effective temperature . Our photometric $\left ^{1/2}$ coefficients are shown to be angular diameters on a relative scale for a given photometric group, (more precisely for a given effective temperature). The angular diameters are consistent with the photometric data previously shown to be consistent with the true parallaxes from HIPPARCOS observations (Knapik, et al. [CITE], Sect. 6). Provisional effective temperatures, as constrained by a successful comparison of dereddened SEDs from observations to model atmosphere predictions, are in good agreement with the values directly calculated from the observed angular diameters and with those deduced from five selected intrinsic color indices. These three approaches were used to calibrate a reference angular diameter $\Phi_{0}$ and the associated coefficient $C_{T_{\rm eff}}$. The effective temperature proposed for each star is the arithmetic mean of two estimates, one ("bolometric") from a reference integrated flux F 0 , the other ("spectral") from calibrated color indices which are representative of SED shapes. Effective temperatures for about 390 carbon stars are provided on this new homogeneous scale, together with values for some stars classified with oxygen-type SEDs with a total of 438 SEDs (410 stars) studied. Apparent bolometric magnitudes are given. Objects with strong infrared excesses and optically thick circumstellar dust shells are discussed separately. The new effective temperature scale is shown to be compatible and (statistically) consistent with the sample of direct values from the observed angular diameters. The effective temperatures are confirmed to be higher than the mean color temperatures (from 140 to 440 K). They are in good agreement with the published estimates from the infrared flux method for $T_{{\rm eff}}\ge 3170 {\rm K}$, while an increasing discrepancy is observed toward lower temperatures. As an illustration of the efficiency of the photometric classification and effective temperature scale, the C/O ratios and the Merrill-Sanford (M-S) band intensities are investigated. It is shown that the maximum value, mean value and dispersion of C/O increase along the photometric CV-sequence, i.e. with decreasing effective temperature. The M-S bands of ${\rm SiC_{2}}$ are shown to have a transition from "none"to "strong"at $T_{\rm eff}\simeq \left(2800\pm 150\right) {\rm K}$. Simultaneously, with decreasing effective temperature, the mean C/O ratio increases from 1.04 to 1.36, the transition in ${\rm SiC_{2}}$ strength occurring while $1.07\le {\rm C/O} \le 1.18$.