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

5. Analysis

Figs. 4a-d show four examples of the observed spectra. A glance of the figures reveals that the spectra are heavily line-blanketed by the absorption due to ¹²CN together with the strong absorption due to ¹³CN. The spectra shown in the figures are normalized by the fictitious continuum level, which is drawn so that it should travel through the highest point in the region observed and assumed to be constant over the region. In fact, the change of flux level predicted by the blackbody of 3000 K is 3% over 230 Å, and therefore, this assumption is reasonable.

Fig. 4a. The observed spectrum of HD 75021. The lines used in the analysis are indicated by the filled circles

Fig. 4b. The observed spectrum of VX And. See also the legend to Fig. 4a

Fig. 4c. The observed spectrum of EU And. See also the legend to Fig. 4a

Fig. 4d. The observed spectrum of Y CVn. See also the legend to Fig. 4a

The line positions of the ¹²CN red system are given in Davis & Phillips (1963). For ¹³CN, Wyller (1966) analyzed (2,0) and (3,1) bands of the red system and listed the positions of 437 lines. The lines of ¹³CN are located at the wavelengths by about 40 Å longer than the corresponding lines of ¹²CN due to the isotope effect. The -value of each ¹²CN line is calculated as described in Paper I. The -values of ¹³CN lines are reasonably assumed to be identical with those of the corresponding ¹²CN lines.

We determine ratios using the iso-intensity method. For lines due to ¹²CN and ¹³CN, the logarithms of central depths normalized by the fictitious continuum level are plotted against , where is a line intensity predicted using the weighting function method (e.g. Cayrel & Jugaku 1963). can approximately be written in the form of , where is the lower excitation potential (LEP) of a line, and is a kind of weighted mean of the reciprocal excitation temperature in the line forming region. Paper II discusses the calculation of and the effects of model atmospheres on it in detail, and we will not repeat them here. Fig. 5 shows examples of the iso-intensity method. The horizontal shift between the two curves for ¹²CN and ¹³CN gives the ratio of the abundance of ¹²CN to that of ¹³CN, namely, ratio. The two curves for ¹²CN and ¹³CN are quite close to each other, demonstrating that ratios in J-type carbon stars are very low. As Fig. 5 shows, we selected about 10 lines of ¹²CN and 2 lines of ¹³CN which are expected not to have their central depths affected by the adjacent lines. However, only several lines could be found for the stars whose spectra show very strong ¹³CN lines. Some lines are blended with other lines of the same isotopic species at almost the same wavelength. We used such lines, if the blending lines are weak enough, considering their -values and LEP's.

Fig. 5a-d. Examples of the iso-intensity method applied to J-type carbon stars. The ordinates are the logarithms of central depths normalized by the fictitious continuum level, while the abscissas are . See also the text. a  HD 75021. b  VX And. c  EU And. d  Y CVn

It is very difficult to determine the true continuum level in such heavily line-blanketed spectra as shown in Figs. 4a-d. It should be kept in mind, however, that ratios are derived from the horizontal shifts between the two curves of ¹²CN and ¹³CN, namely, the ratios are determined basically from the lines of ¹²CN and ¹³CN with the same intensity. In other words, the absolute values of central depths, which should be measured with respect to the true continuum, do not matter. The point is that the central depths measured with respect to the fictitious continuum level is a kind of measure of line intensities, and that they serve to recognize that the lines of ¹²CN and ¹³CN are of iso -intensity. Thus, the resulting ratios are not affected by the location of the fictitious continuum level, as long as it is assumed to be constant over the region observed. The spectral synthesis method, which is often used in the analyses of complicated spectra, is not applied in the present work. In fact, such analyses cannot be justified unless a spectral range wide enough to reach some points of the true continuum is used, since synthetic spectra are usually normalized by the true continuum.

The uncertainties of the resulting ratios amount to about 20%. For several stars, the uncertainties are much larger, about 50%. The internal errors, which result from the scattering of the lines plotted in the curves-of-growth, dominate the total errors. The effect of changing model parameters is quite minor. An increase or decrease in the effective temperature by 200 K leads to no noticeable change in the resulting ratios. The adoption of the models with C/O = 1.1 and 2.0, instead of C/O = 1.3, neither gives any noticeable changes.

© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999
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