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

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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.

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

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

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

[FIGURE] 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 [FORMULA]-value of each 12CN line is calculated as described in Paper I. The [FORMULA]-values of 13CN lines are reasonably assumed to be identical with those of the corresponding 12CN lines.

We determine [FORMULA] 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 [FORMULA], where [FORMULA] is a line intensity predicted using the weighting function method (e.g. Cayrel & Jugaku 1963). [FORMULA] can approximately be written in the form of [FORMULA], where [FORMULA] is the lower excitation potential (LEP) of a line, and [FORMULA] is a kind of weighted mean of the reciprocal excitation temperature in the line forming region. Paper II discusses the calculation of [FORMULA] 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, [FORMULA] ratio. The two curves for 12CN and 13CN are quite close to each other, demonstrating that [FORMULA] 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 [FORMULA]-values and LEP's.

[FIGURE] 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 [FORMULA]. 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 [FORMULA] 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 [FORMULA] 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 [FORMULA] 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 [FORMULA] 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.

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© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999
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