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

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6. Discussion

6.1. AGB stars

The AGB stars that we (re-)discovered have thick CSEs according to their large J-K and K-[12] colours. Le Sidaner & Le Bertre (1996) derive an empirical relation between the continuum [FORMULA] line optical depth [FORMULA] of an oxygen-rich CSE at 10 µm and its J-K colour:

[EQUATION]

Apart from the foreground star LI-LMC1821 and the object LI-LMC0530, the positive identifications between NIR and IRAS sources have J-K between 2.22 and more than 7.7 mag, indicating optical depths at 10 µm in the range 0.6-5 or more. All serendipitous detections have J-K [FORMULA] 2 mag, indicating small optical depths. Because we could not detect all stars in the J-band, the K-[12] colour is a better tool for studying the optical depth of the obscured AGB stars. Le Sidaner & Le Bertre (1996) derive an empirical relation between the optical depth of the CSE at 10 µm and the K-[12] colour:

[EQUATION]

Our obscured AGB stars would have optical depths between 0.6 and 45. Post-AGB stars would not satisfy both the J-K and K-[12] relations for the optical depth, as these two relations define a path in the K-[12] versus J-K diagram, that is unique to the obscured AGB stars:

[EQUATION]

It is clear from Fig. 11 that Le Sidaner & Le Bertre give a sequence for oxygen-rich obscured AGB stars which is reasonably consistent with our oxygen star sequence. We note that they corrected the IRAS 12 µm fluxes for the spectral slope, assuming blackbody temperatures between 300-2000 K. The colour correction factor then ranges between about 0.92 and 1.38 respectively. This makes their K-[12] colours change by -0.09 mag in the case of a 300 K blackbody, and 0.35 mag in the case of a 2000 K blackbody. As the stars with thick CSEs generally have the lower blackbody temperatures, the difference between the Le Sidaner & Le Bertre track and our oxygen star sequence in the K-[12] versus J-K diagram would only be appreciable at the smallest J-K, and only a few tenths of a magnitude at most.

[FIGURE] Fig. 11. K-[12] versus J-K colours according to our sequences for carbon (dotted) and oxygen (solid) obscured AGB stars, and according to the parameterisation of the optical depth at 10 µm by Le Sidaner & Le Bertre (1996, dashed). All are derived empirically. We adopt [12] [FORMULA], with [FORMULA] the flux density in Jy in the IRAS 12 µm band (IRAS Explanatory Supplement 1988)

The most luminous star in our sample has a bolometric magnitude [FORMULA] mag, a factor of two fainter than the theoretical AGB limit as derived from the Chandrasekhar limit for the core mass and the core mass-luminosity relation from Paczyski (1971). The mass-losing AGB star sample of paper II spanned the luminosity range between [FORMULA] and -7.2 mag. Our new sample consists of fainter stars on average, but with [FORMULA] mag our faintest star is not fainter than those of paper II.

Carbon stars are more numerous at fainter luminosities relative to oxygen stars. The two brightest stars have oxygen rich CSEs, but the brightest carbon star, with [FORMULA] mag, is not much fainter than these two oxygen stars. On the other hand, the faintest star is a carbon star, but the faintest oxygen star has the same [FORMULA] mag. Hence we conclude that we do not detect a luminosity regime in which the mass-losing AGB stars are exclusively either carbon stars or oxygen stars.

This could mean that luminous AGB stars are prevented from becoming carbon stars, starting from luminosities as low as [FORMULA] mag. Hot Bottom Burning (HBB) may be responsible for this, as the inner boundary of the convective mantles of the more massive AGB stars becomes sufficiently hot for CN processing to occur (Sugimoto 1971; Iben 1975; Scalo et al. 1975). The co-existence of oxygen and carbon stars over a large range of luminosity may be explained as a consequence of a spread in metallicity. Mass-losing oxygen stars would be metal poor and experience HBB at [FORMULA] mag, whereas mass-losing carbon stars would be more metal rich and not experience HBB at [FORMULA] mag. A thorough discussion of the luminosity distribution function and mass-loss rates of the mass-losing AGB stars in the LMC is postponed to the next paper in this series, in combination with the sample of paper II.

6.2. Future searches for mass-losing AGB stars

We have been successful in detecting NIR counterparts in approximately two out of every three cases. Of these, approximately two out of every three cases turned out to be mass-losing AGB stars. Of these, approximately one out of every two cases was too faint to be detected in the J-band. Would it still be worthwhile to search for NIR counterparts of the remaining 37 IRAS sources? Current attempts to find NIR counterparts may in some cases already be limited by the ground-based NIR searches rather than by the IRAS mid-infrared detections. The ISO mission is expected to yield an extensive data base of new mid-infrared point sources. If ISO will detect bolometrically fainter stars exhibiting similar mass-loss rates to those of the obscured stars which are IRAS counterparts, then it will be difficult or impossible to detect their NIR counterparts with presently available ground-based instruments. However, if it turns out that (nearly) all of the new ISO detections have NIR counterparts, it will demonstrate that bolometrically fainter stars exhibit lower mass-loss rates.

6.3. Post-AGB stars

To investigate further the nature of the suspected post-AGB candidates in our sample, we have taken a closer look at the VHG-89 sample. They classify their post-AGB candidates into classes I, II, III, IV a, and IV b, based on the shape of the infrared spectral energy distribution. The higher the class, the more evolved the post-AGB object: class I is characterised by warm dust completely obscuring the underlying cool star, while in later classes the dust shell becomes detached, exposing the underlying, increasingly hotter star. They also argued that classes I and II result from more massive stars than the later classes. For each class of stars in the VHG-89 sample we have calculated the mean and standard deviation of the J-K, K-[12], and [12]-[25] colours. We drew boxes in the colour-colour diagrams, centred at the mean colours and having sides measuring two times the standard deviations of the colours. In this way we obtain a schematic picture of the positions of the VHG-89 classes in the colour-colour diagrams (Fig. 12). Indeed, the dust becomes cooler (larger [12]-[25] colour) and optically thinner (smaller J-K) with increasing class. The early classes with obscured stars generally have larger K-[12] and/or larger J-K than do the optically visible stars from class IV.

[FIGURE] Fig. 12. K-[12] colours versus [12]-[25] (a) and J-K (b) colours, and J-K colours versus [12]-[25] colours (c), for the VHG-89 sample of post-AGB stars. We follow their classification into classes I, II, III, IV a, and IV b. The boxes are derived from their data by calculating the mean and standard deviation for each colour, per object class. We adopt [12] [FORMULA] and [12]-[25] [FORMULA], with [FORMULA] and [FORMULA] the flux density in Jy in the IRAS 12 and 25 µm bands, respectively (IRAS Explanatory Supplement 1988). The Galactic AGB carbon star (dotted) and oxygen star (solid and dashed) sequences are as in Fig. 5

The LMC post-AGB star candidates could be identified with the VHG-89 classes II and III. The dust of the LMC stars may be warmer than that of similar stars in the Milky Way if the dust-to-gas ratio in CSEs of LMC stars is smaller, permitting stellar radiation to permeate farther out into the CSE, thus heating the dust to higher temperatures. Also the water abundance may be smaller in the LMC, causing the oxygen-rich CSEs to cool less efficiently. Similarly, lower CO and/or HCN abundances may cause warmer carbon-rich CSEs. This would result in somewhat smaller [12]-[25] in the LMC than in the Milky Way. The colours of the LMC post-AGB star candidates are indeed similar to the VHG-89 stars with relatively warm dust. The LMC post-AGB star candidates may have slightly smaller J-K colours because their CSEs are optically thinner due to the lower dust-to-gas ratio, but this could also be explained by selection effects: three of our newly identified IR stars with large K-[12] colours have lower limits to their J-K colours that would still permit them to be post-AGB candidates. On the other hand, the VHG-89 sample is constructed with a blue cut-off at [12]-[25] = 2 mag, selecting against the bluemost sources.

We compared the luminosities of the LMC post-AGB star candidates to those of the five R Coronae Borealis (RCB) stars known in the LMC (Alcock et al. 1996), which are also believed to be post-AGB stars, and to the luminosities of PNe in the LMC. The latter we took from Dopita & Meatheringham (1991), Zijlstra et al. (1994), and Dopita et al. (1997). For some of these PNe we know whether they result from an oxygen- or carbon-rich AGB star. The luminosity distributions are presented in Fig. 13. We note that we do not have complete samples of any of the type of objects shown. The distributions of the post-AGB star candidates are only shown down to [FORMULA] mag, since this is approximately the detection limit of the combined IRAS-IRAC2b search. The distributions of the post-AGB stars, RCB stars, and PNe are very similar, all dropping steeply from [FORMULA] to [FORMULA] mag. In fact, the only object more luminous than [FORMULA] mag is the unusual PN SMP-83 (Dopita et al. 1993).

[FIGURE] Fig. 13. a Cumulative distribution function of the LMC objects over absolute bolometric magnitude: post-AGB star candidates (dot-dashed), R Corona Borealis stars (dashed), oxygen-rich PNe (solid), carbon-rich PNe (dotted), and all PNe (including the PNe for which the C/O ratio is not known; bold solid). b The distribution functions derived in the same way as in Fig. 10. c The distribution function of the ratio of carbon-rich to oxygen-rich PNe

The PNe for which the C/O ratio is known can be used to derive the distributions of the oxygen- and carbon-rich PNe in the LMC, and their ratio (Fig. 13c). From this we conclude that the chemical composition of the PNe is consistent with the chemical composition of the present small sample of new mass-losing AGB stars.

We note that some of the PNe and two of the RCB stars in the LMC have been detected by IRAS at 12 µm at a level of [FORMULA] 0.1-0.2 Jy (Zijlstra et al. 1994; Moshir et al. 1992; Alcock et al. 1996), indicating that objects are capable of maintaining their 12 µm flux after they have left the AGB. Hence the fact that the LMC post-AGB star candidates are detected at 12 µm by IRAS does not necessarily imply their post-AGB age. Zijlstra et al. note that the IRAS detected LMC PNe have blue [12]-[25] colours, relative to Galactic PNe. They attribute this to selection effects. The LMC post-AGB star candidates also have blue [12]-[25] colours, relative to Galactic post-AGB star candidates. NIR-optical spectroscopy for the faint, obscured LMC post-AGB star candidates is difficult, but may be possible. If they are indeed post-AGB stars, their spectra are expected to be of intermediate type (A, F, G). However, this would not exclude the possibility that they are binary systems (e.g. Whitelock et al. 1995).

If we assume that, down to a certain lower bolometric luminosity limit we are equally incomplete for the currently available samples of mass-losing AGB stars (combining paper II with this paper), post-AGB stars, and PNe then we can, in principle, estimate their relative lifetimes. It is more difficult to do this compared to the AGB stars that have not been detected by IRAS, because many of them will still evolve significantly in bolometric luminosity. Comparing bolometric luminosity limited samples of IRAS detected and non-detected AGB stars therefore results in comparing different populations of stars, with different main-sequence masses. A synthetic evolution approach is needed to infer the AGB lifetimes for stars of different main-sequence masses (Groenewegen & de Jong 1994). The known PNe have been selected in a different way than the post-AGB and mass-losing AGB stars, because of the different observational properties of these objects. Hence it is not obvious that the currently known sample of PNe is equally incomplete as the currently known samples of post-AGB and mass-losing AGB stars. Amongst the IRAS point sources that remain to be searched for NIR counterparts, there may be a significant number of post-AGB and/or mass-losing AGB stars, in perhaps different relative numbers than those presently observed. There may also be none. Amongst the IRAS point sources that we could not identify with a NIR counterpart, there may be optically visible post-AGB stars, or not. The most we can say is that the currently available data suggest that the mass-losing AGB, post-AGB, and PN stages all have similar lifetimes, for a star with an AGB-tip bolometric luminosities between [FORMULA] and -6 mag, i.e. that has a progenitor mass in the range 2.5-4 [FORMULA] (Vassiliadis & Wood 1993). More massive stars seem to have post-AGB and PN lifetimes that are considerably shorter than their mass-losing AGB lifetimes.

6.4. Thermal Pulse stars

The suspected secondary sequence in the K-[12] versus J-K diagram for Galactic oxygen stars does have some overlap with the VHG-89 stars, but the latter are mostly found having larger K-[12]. This can be partly due to larger optical depths of the CSEs of the VHG-89 stars, to the extent that the CSE becomes optically thick in the K-band, but it cannot explain the position of the VHG-89 class IV at small J-K. Probably the VHG-89 stars have more massive CSEs, yielding a larger 12 µm flux, but these CSEs are detached, yielding small column densities towards the star and hence small J-K. Consequently, stars at the secondary sequence are not expected to evolve directly into stars with larger K-[12]. If the stars from VHG-89 are post-AGB stars, then they are expected to have evolved from large J-K and K-[12], first getting smaller J-K before also getting smaller K-[12]. Hence the secondary sequence may be related to the VHG-89 class I only. The fact that we noticed a secondary sequence, rather than a gradient from the primary sequence into the VHG-89 areas of the K-[12] versus J-K diagram, suggests that the secondary sequence and perhaps the VHG-89 class I are not related to the VHG-89 post-AGB classes II -IV. We can explain them instead as stars that only temporarily stopped losing mass, possibly as a result of a Thermal Pulse (TP). They are then expected to return to the AGB and resume heavy mass loss (Zijlstra et al. 1992).

It is difficult to discern a TP star from a post-AGB star, since both experience the same phenomenon: the CSE becomes detached. But at least statistically there are differences to be expected, that can be observed in the near- and mid-IR: the K-[12] is expected to be statistically larger for a post-AGB star than for a TP star. There are three reasons for this. First, post-AGB stars shrink while maintaining the same bolometric luminosity, and therefore they must increase in effective temperature. This results in increased heating of the CSE, counteracting at least partly the cooling of the CSE as a result of its increasing distance to the star. TP stars do not change as much in effective temperature, and hence the detaching CSE of a TP star cools more rapidly than that of a post-AGB star. Second, as the effective temperature increases but not the bolometric luminosity, the star will become fainter in the K-band, increasing its K-[12] colour. Although TP stars may have decreased in bolometric luminosity, this is expected to be at most one magnitude (Vassiliadis & Wood 1993). Third, post-AGB stars are more evolved than TP stars. They have experienced mass loss for a longer time span, yielding more massive CSEs and consequently larger 12 µm fluxes.

LI-LMC0530 has too small a [12]-[25] colour for its K-[12] colour to be a normal post-AGB star candidate, relative to both the VHG-89 stars and the six LMC post-AGB star candidates discussed above. It is also much brighter in the K-band than the other LMC post-AGB star candidates, which suggests an optically thin CSE. Whitelock et al. (1995) found two stars in the South Galactic Cap that they explained as TP stars, because of their lack of variability. These two stars have J-K and [12]-[25] colours similar to those of LI-LMC0530, but their K-[12] colours are much smaller than that of LI-LMC0530, and even smaller than the secondary sequence in the K-[12] versus J-K diagram. In fact these Galactic TP star candidates are more similar to normal mass-losing AGB stars. This can be understood if they experienced one of their first TPs, before they had built up a massive CSE that yields a significant 12 µm excess. LI-LMC0530 seems to take an intermediate position between post-AGB stars and TP stars.

LI-LMC0530 is identified with the LPV SHV0510004-692755: an LPV with an I-band amplitude of 1.24 mag and a period of 169 days. Hughes & Wood (1990) give a spectral type of M6. It obeys the period-luminosity relation for the K-band magnitude perfectly, although bolometrically it is 4-5 times more luminous than the AGB stars that define the period-luminosity relation (Reid et al. 1995). LI-LMC0530 must have been a mass-losing AGB star in the past, because it has a large 12 µm excess. It may now be pulsating in a (high) overtone, and maybe it will resume Mira variability and mass loss. If it is a post-AGB star at present, then it must be in a very early post-AGB stage, because its effective temperature has not increased much. But in this case we would expect the star to be obscured by an optically thick CSE. This contradicts its small J-K, unless we invoke a highly aspherical shape of the CSE. We conclude that the nature of LI-LMC0530 is uncertain: it may be an early post-AGB star of class IV, or a star recovering from the effects of one of its last thermal pulses on the AGB. Alternatively, the measured flux at wavelengths shorter than [FORMULA] m may have been affected by the presence of another star in the line-of-sight.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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