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Astron. Astrophys. 325, 585-600 (1997)

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5. Bolometric luminosities

We calculate bolometric luminosities for the stars that we identified as the NIR counterparts of the IRAS point sources. The method for estimating the unobserved part of the spectral energy distribution is based on the average NIR colours for obscured AGB stars, and will be described in a forthcoming paper. The method for obtaining the integrated luminosity under the spectral energy distribution is described in paper II and originally in Whitelock et al. (1994). We adopted a distance modulus to the LMC of (m-M) [FORMULA] (Feast & Walker 1987). The results are tabulated in Table 4.

The cumulative luminosity distributions of the different classes of stars are presented in Fig. 10a. In principle we could derive the luminosity distribution by differentiation of the cumulative distribution function. In practice the errors would be huge because of the small number of stars. Instead, we apply Gaussian broadening by replacing each star with absolute bolometric magnitude [FORMULA] by

[EQUATION]

where [FORMULA] to normalise to unity per star. The FWHM of the star has thereby become 0.83 magnitude. Then we take the sum of the luminosity-broadened stars. A scientific motivation for applying the broadening to mass-losing AGB stars is that they are LPVs with bolometric amplitudes of about one magnitude but only observed at a single NIR epoch. The luminosity distributions are presented in Fig. 10b (line types are the same as in Fig. 10a). They represent the distribution over luminosity of the IRAS-detected AGB stars in the LMC, and they are likely to be incomplete, especially at the faint end. We assume that this does not seriously affect the relative distributions of the carbon and oxygen stars. The ratio of the number of carbon stars over the number of oxygen stars as a function of luminosity is derived by dividing the luminosity distribution function of the carbon stars by that of the oxygen stars (Fig. 10c). We have done this for the two extreme cases that all OC stars be carbon stars (dotted) or that all OC stars be oxygen stars (solid). The real luminosity relation of the fraction of carbon stars lies in between these two extremes.

[FIGURE] Fig. 10. a Cumulative distribution function of the stars over absolute bolometric magnitude: "oxygen" stars (solid), "oxygen or carbon" stars (dashed), "carbon" stars (dotted), all AGB stars (bold solid), and post-AGB candidates (dash-dotted). b Applying Gaussian broadening (see text), we derive the distribution functions N. c From this we derive the distribution function of the ratio of carbon to oxygen AGB stars for the two extreme cases of carbon star favoured (all OC stars are C stars; dotted) and oxygen star favoured (all OC stars are O stars; solid)
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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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