Astron. Astrophys. 319, 511-514 (1997)

3. Results and discussion

The results of simulating carbon star populations (the luminosity functions) are plotted in Fig.  3 for the initial heavy element abundance Z =0.002. The most significant result is a substantial extension of the carbon star luminosity towards lower luminosities in comparison with the TP-AGB carbon stars. The expected number of stars in these two stages is comparable. There are two reasons why the faint carbon stars in the MC have been discovered only recently: (a) they are apparently fainter in comparison to the TP-AGB stars, and (b) they have higher effective temperatures. The comparison between the theoretical luminosity function for E-AGB carbon stars, and the observational one for faint carbon stars in the SMC (Westerlund et al. 1995) is presented in Fig.  4. Both luminosity distributions are in qualitative agreement. The deficiency of the faintest stars in SMC, as compared to the theoretical prediction can be explained with the selection effect - the fainter the star, the more difficult it is to observe it.

Fig. 3. The theoretical luminosity functions of carbon stars with heavy element abundance . The coefficient in Reimers (1975) mass loss intensity law is: for and for . Solid line indicates TP-AGB stars, dashed line - E-AGB stars (the result of the evolution of close binaries). The sum over all bins is normalized to unity

Fig. 4. The luminosity functions of faint () carbon stars. Solid line indicates the results of observations (Westerlund et al. 1995), dashed line - the results of our calculations (, tenfold jump of mass-loss intensity for ). The sum over all bins is normalized to unity for each function

Fig. 5 presents the HR-diagram for the SMC carbon stars, also showing the theoretically calculated borders of regions occupied by the E-AGB and TP-AGB models. For comparison, besides these results obtained under assumptions described above, the border of E-AGB region according to detailed tables of stellar models (Fagotto et al. 1994) are also displayed (for the heavy element abundance Z =0.004). The positions of carbon stars are taken from Westerlund et al. (1991, 1995). All stars under consideration can be divided in two groups: (a) more luminous and with lower effective temperatures, (b) and fainter but with higher temperatures. The former correspond closely to the TP-AGB model region, and the latter - to the E-AGB region. The reasons of the relatively great scatter of the star positions on the HR diagram are the uncertainties due to the rather great observational errors for in , from which effective temperatures are derived (Westerlund et al. 1995), and the dependence of AGB tracks on the star's initial chemical composition.

Fig. 5. The position of SMC carbon stars on the HR diagram. Dots represent the data from Westerlund et al. (1991), crosses - from Westerlund et al. (1995). The solid line contours denote, according to our calculations, the regions occupied by the E-AGB stars (left region) and by the TP-AGB stars (right region). The calculations were performed assuming and a tenfold jump of mass loss intensity for . The dashed line contour denotes the E-AGB region according to calculations by Fagotto et al. (1994) for

Hence it is likely that N-type carbon stars in the MC belong to two different evolutionary phases: the hotter and on the average more faint ones - to the E-AGB phase, but cooler and more luminous - to the TP-AGB phase. The greater part of carbon stars from Table 1 of Westerlund et al. (1995), which are named "faint C stars", are E-AGB ones, although some of them are TP-AGB stars (for example, this appears possibly to be the case for stars No 324, 452, 818, 1011, 1018, 1032, and, with higher possibility, such faint ones as No 91 and 428).

One would expect that there may be carbon stars in MC clusters on both evolutionary stages, on the TP-AGB as well as on the E-AGB stages. It is possible to divide these stars on the basis of luminosity and effective temperature. There are only a few candidates of such clusters from the data of Westerlund et al. (1991), because there are the selection effect (relatively low luminosity and high effective temperatures of E-AGB stars), and the effect, mentioned in the paper by Frantsman and Pyleva (1995) (the strong dependence of E-AGB stars luminosity on the initial composition, as is shown in Fig. 2 of the above-mentioned paper). The clusters NGC 1783, 1846, 1978 may be noted as possible examples. However there is still some possibility that low luminosity carbon stars G6 in NGC 1783, LE 12 and AZ-11 in 1978 and FMB 16 in NGC 1846 are not members of these clusters and they may be field stars.

From the preceding, it may be seen that it is necessary to be very careful in identifying evolutionary stage of stars and trying to use the results of such identifications for interpretation of observations. Now there is an example of possible consequences of ignoring the fact that the AGB stage consists of two stages of evolution. It seems that Mould and Aaronson (1982) used the E-AGB stars in the age determination of several clusters, assuming that these stars are in the TP-AGB stage. For example, the upper limit of the age of the cluster NGC 1872 was determined as 5 Gyr. Assuming that the most luminous star in this cluster is on the E-AGB stage, in my paper (Frantsman 1988) it was estimated that the age of this cluster does not exceed 0.1 Gyr. And it was somewhat confirmed recently by a classical method, when the age was determined as 0.136 Gyr (Santos et al. 1995).

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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