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Astron. Astrophys. 345, 233-243 (1999)

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4. Determination of effective temperatures

To determine the effective temperature of each star, we apply the InfraRed Flux Method (IRFM, Blackwell et al. 1980). We also applied it to the determination of the effective temperatures of N- and SC-type carbon stars in Paper I. The effective temperature can be determined by the ratio of observed bolometric flux ([FORMULA]) to infrared flux, once the ratio is calibrated by model atmospheres. The [FORMULA]-band (3.7 µm) flux is employed as infrared flux, because this band region is least disturbed by molecular absorption in the spectra of carbon stars. Molecular absorption features are dependent on other parameters such as chemical composition, surface gravity, and micro-turbulent velocity as well as effective temperature. However, by using the [FORMULA]-band flux, we can determine effective temperatures as independently of those parameters as possible. The calibration of the ratio [FORMULA] is shown in Fig. 2, where the ratios are calculated with the model atmospheres with C/O = 1.1, 1.3, and 2.0. As we mentioned in the previous section, we adopt the T[FORMULA] - [FORMULA] relation calculated with C/O = 1.3.

[FIGURE] Fig. 2. The calibration of [FORMULA] against T[FORMULA] with different C/O ratios. The filled squares, triangles, and circles correspond to the models with C/O = 1.1, 1.3, and 2.0, respectively

Though the [FORMULA]-band is relatively free from molecular absorption lines, one concern is the effect of the 3 µm absorption due to HCN and C2H2. The effect of this absorption feature is corrected in the empirical way mentioned in Paper I. But the 3 µm absorption is located almost at the edge of the response function of the [FORMULA] filter, thus its effect on the observed [FORMULA]-band flux is minor. As discussed in Paper I, other molecular absorption features such as [FORMULA] bands of HCN and [FORMULA] bands of C2H2 at 3.7 µm are unlikely to have any serious effects on the observed [FORMULA]-band flux. Regarding the CS first overtone bands at 3.9 µm, Aoki et al. (1998) have recently analyzed the spectra acquired with the Infrared Space Observatory (ISO), and have identified strong CS absorption in 3 SC stars. But they also reveal that the CS absorption is very weak in N-type carbon stars. Probably this is also the case for J-type carbon stars. In fact, the spectrum of the J-type carbon star Y CVn obtained by Goebel et al. (1980) does not show any strong absorption at 3.9 µm. Therefore, it is also unlikely that the determination of the effective temperatures of J-type stars is affected by the CS absorption.

Photometric data from U or B-band throughout to L or [FORMULA]-band are available in the literature (Mendoza & Johnson 1965, Noguchi et al. 1981, and Walker 1979) for four of our program stars: RY Dra, BM Gem, HD75021, and VX And. The photometric data are de-reddened, using [FORMULA] estimated based on the works by Sharov (1964) and by FitzGerald (1968). Then the bolometric fluxes are obtained by integrating the monochromatic fluxes throughout the relevant spectral region. With the bolometric fluxes and infrared fluxes evaluated in this way, we determine the effective temperatures, using the T[FORMULA] - [FORMULA] relation. The effective temperatures determined in this way are indicated by asterisks(*) in the third and seventh columns of Table 3. The uncertainty of T[FORMULA] is about 5%, or about 150 K for T[FORMULA] = 3000 K. The detail of the origins of the uncertainty is discussed in Paper I.


Table 3. Effective temperatures and [FORMULA] ratios

Concerning the stars for which photometric data throughout the whole spectral region are not available, we determine the effective temperatures by the use of the [FORMULA] - T[FORMULA] relation. Dr. K. Noguchi kindly obtained the photometric data of [FORMULA] and [FORMULA]-bands of our program stars, except for those available in the literature (Noguchi et al. 1981, Noguchi et al. 1995). In Fig. 3, we plot the effective temperatures of the four stars, determined directly with the IRFM, against [FORMULA]. The effective temperatures of N- and SC-type carbon stars, which were determined directly with the IRFM in Paper I, are also plotted. The effective temperatures of the four J-type carbon stars (filled circles) seem to be marginally higher than those of N- and SC-type carbon stars (open squares and open triangles, respectively) with the same [FORMULA] color. However, given the accuracies of T[FORMULA] , it seems safer to use the [FORMULA] - T[FORMULA] relation based on all the three types of carbon stars than to use that based on only four J-type carbon stars. Thus, we derive the [FORMULA] - T[FORMULA] relation by the linear least square fit, including all the three types of carbon stars, and determine effective temperatures for the rest of our program stars. The effective temperatures determined are summarized in the third and seventh columns of Table 3. The uncertainties of the effective temperatures determined from the [FORMULA] - T[FORMULA] relation are about 200 K, as discussed in Paper I.

[FIGURE] Fig. 3. [FORMULA] - T[FORMULA] relation based on the effective temperatures determined with the IRFM. The filled circles represent the J-type carbon stars. The N- and SC-type carbon stars analyzed in Paper I are represented by the open squares and the open triangles, respectively

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© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999