4. Relative mass-loss rates and dust-to-gas ratios
In determining mass-loss rates and dust-to-gas ratios in the MCs one can rely on the use of luminosities and eliminate from Eq. (1). Luminosities are difficult to measure for stars in the Milky Way, however, due to unknown distances and severe interstellar extinction. Often the Mira P-L relation is applied to infer distances to individual stars, but this relation possibly breaks down for stars whose stellar mantles have been significantly reduced due to mass loss (e.g. Blommaert et al. 1998; Wood et al. 1998; Wood 1998), or obscured AGB stars may fall on other, parallel sequences (Bedding & Zijlstra 1998; Wood 1999). For the Milky Way stars, L is eliminated from Eq. (1), leaving to be measured. Because has been measured for only a few LMC stars, Eq. (3) will be used for the remaining LMC stars to estimate from L (see Appendix B). Although these estimates are likely to be accurate within a few km s-1, the contribution of the uncertainty in is enlarged by a factor three in Eq. (5).
Eqs. (4) & (5) are used here to compare the combination of mass-loss rate and dust-to-gas ratio between the MCs and between the LMC and the Milky Way, respectively. If the mass-loss rate depends on luminosity but not on initial metallicity and if the luminosity distributions of the stars in these samples are identical - implying identical star formation histories - then the distributions over the combination of and are identical except for possible offsets due to different mean values for among the different samples. The stars within each of the samples are likely to cover a range in initial metallicities due to their different progenitor masses and hence different formation epochs. Similar star formation histories, however, are anticipated to result in similar distributions over initial metallicity, and it is therefore meaningful to assign a mean initial metallicity and a mean value for to each of the samples.
Eq. (4) is used to calculate the combination of mass-loss rate and dust-to-gas ratio from the optical depths and luminosities for the magellanic stars (Fig. 3). The stars with and mag are considered to be RSGs and obscured AGB stars, respectively (see van Loon et al. 1999b), except for the well-studied luminous obscured AGB star IRAS05298-6957 ( mag) and the weakly mass-losing RSG HV2700 ( mag). IRAS04498-6842 ( mag) was classified as an AGB star (Paper II), but here it is re-classified as a RSG (see also Paper IV). Fig. 4 shows the cumulative distributions (normalised to unity) of the obscured AGB stars in the LMC (solid) and SMC (dotted) over the value of . These do not include the few stars that have lower limits to their colours. The distributions for the subsamples of spectroscopically confirmed carbon stars and oxygen-rich (M-type) stars (van Loon et al. 1999b, and references therein; Groenewegen & Blommaert 1998) are boldfaced in Figs. 4a and b, respectively. Despite the small numbers for some of the sub-distributions, especially the M-type stars in the SMC, the shapes of the cumulative distributions are very similar. Both in the LMC and SMC the obscured M-type AGB stars and the obscured carbon stars have distributions that are coincident to a very high degree (Table 1). The only difference in the distributions is the systematic offset between those in the LMC compared to those in the SMC (Table 1). This offset is a result for the obscured AGB stars as a whole, a result for the obscured carbon stars, and consistent for the obscured M-type AGB stars (though not significant by itself).
Table 1. Mean and error in the mean of the values of for the distributions of obscured AGB stars in the LMC and SMC. Also the differences between the various (sub-)distributions are listed.
Eq. (5) is used to calculate the combination of mass-loss rate and dust-to-gas ratio from the optical depths and expansion velocities for the obscured AGB stars in the LMC and the Milky Way (Fig. 5). Only LMC stars for which periods are known from the literature (Wood et al. 1992; Wood 1998) are plotted. Stars in the different samples are not similarly distributed over P, with the LMC sample having an average pulsation period longer than that of the Milky Way sample, possibly due to selection effects or differences in the star formation histories. Hence the populations of stars in these samples may not be directly compared.
Two regimes of pulsation period will be focussed on: one for d, and another for d. The first group consists of stars that evolve beyond the optically bright Mira phase with moderate and into the obscured AGB phase (Jura 1986). The distribution of these stars in Fig. 5 suggests that they still increase in mass-loss rate and/or that they represent a large range in stellar masses. The second group consists of more evolved (or more massive) stars for which has become so high that they shed their mantles on a timescale much shorter than the nuclear burning timescale. Hence these stars stay at constant luminosity while their pulsation periods keep increasing as their mantles are steadily diminished. The lack of any clear correlation between and P in this part of Fig. 5 suggests that thereby the mass-loss rate remains essentially constant. Stars in the LMC sample are predominantly found in the second class of objects, whilst these kind of stars are very rare in the Galactic Centre sample due to their faintness in the K-band. M-type stars in the "Solar neighbourhood" sample of Groenewegen et al. (1998) populate both regimes rather evenly.
The relative distributions of mass-loss rates and dust-to-gas ratios are derived from Fig. 6 for the LMC (dotted), "Solar neighbourhood" (M-type; solid) and Galactic Centre (dashed), in the same way as before by estimating the relative offsets in of the normalised cumulative distributions. The sample of obscured AGB stars with d in the "Solar neighbourhood" (Groenewegen et al. 1998) is clearly inhomogeneous: (i) the distribution of obscured M-type AGB stars is much flatter than all other distributions, indicating a wide range of stellar parameters, and (ii) the distribution of obscured carbon stars is offset with respect to the distribution of obscured M-type AGB stars - a result (Table 2). This may reflect differences in age (initial stellar mass) and/or initial metallicity, as the sub-samples of obscured M-type AGB stars and obscured carbon stars in the Groenewegen et al. sample have been selected in a very different way. The distributions of the obscured M-type AGB stars and obscured carbon stars in the LMC sample are, again, indistinguishable (Table 2). The Galactic Centre sample is positively offset with respect to both the Groenewegen et al. sample ( result for d) and the LMC sample ( result).
Table 2. Mean and error in the mean of the values of for the distributions of obscured AGB stars in the LMC, in the Galactic Centre (GC), and in the "Solar neighbourhood" (Groen; excluding the point at d and a value of -2.7). Also the differences between the various (sub-)distributions are listed.
© European Southern Observatory (ESO) 2000
Online publication: January 31, 2000