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Astron. Astrophys. 328, 211-218 (1997)

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4. Discussion

4.1. Metallicity and age

The isochrones in Fig. 2a indicate that the metallicity of the old population in the SDG is Z [FORMULA] 0.008. This is quite high, but within the uncertainties comparable with [Fe/H] = - 0.52 [FORMULA] 0.09 obtained by SL95 from a photometric study of a (V,V-I) CMD. This is in contrast with values [Fe/H] [FORMULA] - 0.7 obtained with different methods (IGI94, IGI95, Ibata et al. 1997, Fahlman et al. 1996, Mateo et al. 1995 & 1996, WIC96, Marconi et al. 1997).
SL95 found an indication of the possible existence of a [Fe/H] = - 1.3 (i.e. Z = 0.001) component in the dwarf galaxy. With such a metallicity the age of the carbon stars is somewhere between 1 and 10 Gyr, see Fig. 2b. Fig. 2a already shows that there is an old component with Z = 0.008 and an age around 10 Gyr. If there is a rather smooth age range present for Z = 0.001, then why are the younger stars absent among the RGB stars with Z = 0.008 ? Furthermore, why should the metallicity decreases towards younger age ? From a close box model one expects an increasing metallicity towards younger age. All together this does not favour a metallicity of Z = 0.001.

If on the other hand, the metallicity for the carbon stars is Z = 0.008 then we are apparently dealing with two different age populations. The carbon stars would in this case reflect a very recent star formation burst in this galaxy, while the major stellar population has an age [FORMULA] 10 Gyr. An almost zero metallicity enrichment is in agreement with the multiple starburst Carina dwarf spheroidal studied by Schmecker-Hane et al. (1996). A young age could be independently confirmed through the detection of Cepheids in the SDG. Mateo et al. (1995) report the possible detection of an anomalous Cepheid and suggest that the SDG might contain a considerable number of these stars.

Just as in this study, SL95 would not be able to distinguish from their CMD the difference between a very young Z = 0.008 population from an older Z = 0.001 population. So the present interpretation is not in contradiction with their results. An indication that we are indeed dealing with young stellar populations is present in the CMDs from Marconi et al. (1997). In Fig. 3 (i.e. Marconi's et al. Fig. 2) the 0.1 Gyr and 1.0 Gyr isochrones demonstrate clearly the presence of a young population above the main sequence turn-off of the old stellar population from the SDG. It is not clear though, why the two distinct age populations advocated above are not present in the CMDs analysed by Fahlman et al. (1996). Possibly the number of stars involved are too small to be conclusive and the analysis has to be repeated with a larger number of stars in the background of the globular clusters.

[FIGURE] Fig. 3a and b. CMD of SDG stars in field 1 from Marconi et al. (1997) with an overlay of Z = 0.008 isochrones of 0.1 Gyr (solid line) and 1 Gyr (dashed line) from Bertelli et al. (1994). The dashed line between (V,V-I) = (14 [FORMULA] 0,0 [FORMULA] 0) and (V,V-I) = (23 [FORMULA] 0, - 0 [FORMULA] 2) is the white dwarf cooling sequence from the 1 Gyr isochrone. An extinction of AV = 0 [FORMULA] 48 and a distance modulus of 17 [FORMULA] 02 (Mateo et al. 1995) have been adopted for the isochrones

From the considerations outlined above it is concluded that the metallicity of the SDG stars is Z [FORMULA] 0.008. The age of the ALRW91 carbon stars is with this metallicity younger than 1 Gyr. A second distinct population is present with an age around 10 Gyr.
If a star formation burst is related with a passage through the galactic disc then an age as young as 0.1 Gyr would confirm the assertion that the SDG already passed through the disc and is currently moving away from our Galaxy (Alcock et al. 1997, NS97). Fig. 4 indicates that this should indeed be the case. The absence of populations with intermediate ages separated by approximately 1 Gyr appears to rule out the orbital period suggested by Johnston et al. (1995), Velázquez & White (1995) and Ibata et al. (1997). Johnston et al. however pointed out that the existing observations were not sufficient to put limits on the orbit or initial state of the SDG.

[FIGURE] Fig. 4. The course of the Sagittarius dwarf galaxy projected on the [FORMULA] plane. The radial velocity of the galaxy indicates that it is moving away from us. Together with the indicated course this implies that the galaxy crossed quite recently the galactic disc. The position of the Sun is indicated by [FORMULA]

4.2. Are the `bulge' carbon stars on the TP-AGB?

In the current understanding of stellar evolution theory carbon stars are formed at the third dredge-up at the TP-AGB (thermally pulsing asymptotic giant branch) phase, in which the stellar surface is enriched with [FORMULA] C. Carbon stars cannot be formed before the TP-AGB phase. In the LMC the majority of the stars are located above the tip of the RGB (red giant branch), but they can be located [FORMULA] 1 [FORMULA] 0 below RGB tip for 20% - 30% of its interpulse period (see Marigo et al. 1996 a b and references cited therein).

At the distance of the SDG a considerable fraction of the ALRW91 carbon stars are located well below the tip of the RGB. Fig. 5 demonstrates that even if carbon stars can form directly after they enter the TP-AGB phase, the presence of a fraction of those carbon stars cannot be explained. These stars are likely formed through another mechanism not accounted for in the `standard theory' for the formation of carbon stars in the TP-AGB phase. The sequence of carbon stars parallel to the giant branch suggest that they are either RGB or early AGB stars. It apparently contradicts our theoretical understanding about the formation process of carbon stars.

[FIGURE] Fig. 5. Four solid lines are displayed for the LMC, indicating the start of the E-AGB, TP-AGB, the transition from M- to C-type stars and the end of the AGB evolution (see Marigo et al. 1996b for details). Above the dotted line carbon stars with masses in the range 1.2 - 3.0 M [FORMULA] have a 90% detection probability. M [FORMULA] is the initial mass of the carbon star. The dashed, horizontal line is the limiting magnitude for the SDG carbon stars and the dashed, vertical lines indicate the age range for the SDG stars (see Sect. 4.1) if Z [FORMULA] 0.008. The shaded area indicate the region in which the presence of carbon stars cannot be explained with a TP-AGB star, see Sect. 4.2

ALR88 suggested two possible scenarios. Westerlund et al. (1991) favoured the scenario where a very effective mixing occurs at an early phase on the ascend to the TP-AGB. Since this cannot be the case for even the faintest carbon stars related to the SDG, the scenario of mass transfer through binary evolution is favoured for the formation of the low luminosity carbon stars. The same scenario explains the observations of dwarf carbon stars (see Green 1997 and references cited therein).

In case of mass transfer through binary evolution, the primary star evolved through the TP-AGB phase and transferred a significant part of its [FORMULA] C enriched envelope to the secondary. The primary evolved away from the AGB and is a white dwarf now and the secondary is the presently observed carbon star. The fully convective envelope of stars at the RGB or AGB would dilute [FORMULA] C/ [FORMULA] C-ratio. The dilution is proportional to the time elapsed since the primary deposited part of its envelope on the secondary star. The dilution should increase towards larger distances from the galactic disc (see Figs. 1 and 4). The NaD equivalent width and the CN-line strength obtained from spectra for the carbon stars by Tyson & Rich (1991, see their Fig. 3) would support this assertion. For comparable envelope masses the dilution will be at least a factor 2. If the metallicity is about Z = 0.008 then the mass transfer should have occurred recently, indicating that the difference of the initial mass between the primary and secondary is very small. A metallicity of Z = 0.008 is in addition high enough to explain the strong NaD-features found present among the carbon stars.

McClure (1984) showed that CH-stars are binaries, some of them are long-period systems. Suntzeff et al. (1993) argue that the CH-stars in the LMC, with Mbol ranging from - 5 [FORMULA] 3 to - 6 [FORMULA] 5, have an age near 0.1 Gyr. Some of the CH-stars could well be the predecessors of the SDG carbon stars. If L199 is a CH star and the four giant stars observed by WIC96 are related to the SDG they have Mbol [FORMULA] 6 [FORMULA] 5. A binary nature of those stars would strongly support the evolution scenario outlined above.

In Fig. 6 the near-infrared photometry of the `bulge' carbon stars are compared with the photometry for the obtained for a sample of SMC carbon stars (Westerlund et al. 1995). For the SMC carbon stars we adopted (m-M)0 = 18 [FORMULA] 9 and E(B-V) = 0 [FORMULA] 09 (Westerlund 1997). Westerlund et al. (1991, 1993, 1995) noted that the most luminous `bulge' and SMC carbon stars have comparable C2 and CN values, whereas the fainter `bulge' stars are more similar to the main bulk of faint SMC carbon stars. This result is not surprising anymore if, as argued in this paper, the `bulge' carbon stars are indeed related to the SDG. Fig. 6 indicates that the former `bulge' carbon stars have luminosities almost comparable to the SMC carbon stars. The ALRW91 carbon stars form a parallel sequence with the SMC stars. As argued in Sect. 4.1 the ALRW91 carbon stars likely have a metallicity Z [FORMULA] 0.008, while the SMC carbon stars are expected to be metal poorer. The SMC sequence ought to be bluer than the SDG sequence, if the carbon stars have a similar age. This however is not the case and the carbon stars therefore do not originate from a population with a similar age. The colours of both sequences can be explained when the SMC carbon stars evolved from an older stellar population.

[FIGURE] Fig. 6. A comparison between the `bulge' carbon stars (symbols as in Fig. 2) if located in the SDG and the SMC carbon stars (Westerlund et al. 1995; filled dots)

4.3. Are there more SDG carbon stars?

It is an important issue to check if more carbon stars from the dwarf galaxy can be found in other fields. From NS97 a crude estimate of about 1/2 is found for the ratio of LPVs versus the RR Lyrae stars of Bailey type ab. About one out of six LPVs could be a carbon star. This is however a lower limit, because the sample from NS97 is biased towards the brighter stars. The observations were mainly limited due to the instrumental setup and the telescope size and no reliable data was obtained for some of the fainter, suspected carbon stars in the sample.

About 29 more carbon stars with M [FORMULA] - 6 [FORMULA] 5 might be found among the long period variables in the DUO (Disc Unseen Objects; see Alard 1996 and references cited therein), MACHO (Massive Astrophysical Compact Halo Objects; see references in Alcock 1997), and even the OGLE (see references in Paczyski et al. 1994) databases. However, considerably more candidate carbon might be present among the stars with - 6 [FORMULA] 5 [FORMULA] - 4 [FORMULA] 0. Extrapolating the carbon star PK-relation from GW96 indicates that if some of these stars are variables, they might be found among the variables with periods in the range from 40 - 130 days. An additional result would be a significant increase of the number of LPVs related to the SDG.

Another way to estimate the expected number of carbon stars for the SDG is through the fuel consumption theorem (see Renzini & Buzzoni 1983,1986 for details). For a population of young stars we have the relation: [FORMULA], where [FORMULA] (Mateo et al. 1996; [FORMULA]) and [FORMULA]. About 100 carbon stars are thus expected. The number is a lower limit, because the full extent of the SDG has not been taken into account and the bolometric luminosity has therefore been underestimated. Moreover, the duration over which carbon stars can be observed is prolonged through mass transfer from binary evolution. All together the expected number of SDG carbon stars might be about 10 times larger than hitherto found.

4.4. What about the RR Lyrae stars?

A significant amount of RR Lyrae stars have been found and have been used to constrain the distance towards the SDG, see Sect. 2.2. As mentioned in Sect. 1.3 the distance of the LPVs is consistent with the RR Lyrae found in the same field (NS97). The LPVs likely have an age comparable to the age of the carbon stars and a metallicity of Z [FORMULA] 0.008.
The metallicity of the RR Lyrae stars are expected to be considerably smaller, say between Z = 0.0004 - 0.001. The GB stars from the parent population appears to be absent in Fig. 2a. This could be due to a bias in the selection of the GB stars, confusion of an old, metal-poor population with the GB from a 0.1 - 1.0 Gyr population with Z = 0.008, or the parent population of the RR Lyrae stars has a metallicity close to Z = 0.008. In addition, it is not clear how the SDG RR Lyrae stars are related to, or even might originated from the four globular clusters located at the SDG distance (Da Costa & Armandroff 1995).
The present situation is rather confusing. It is not clear at all what the actual metallicity of the parent population of the SDG RR Lyrae stars is. A thorough analysis of deep CMDs, similar to those from Marconi et al. (1997), with a significant number of stars near the main sequence turn-off is required to determine the age and metallicity of the oldest population in the SDG.

4.5. A twist of fate?

4.5.1. Radial velocities

The radial velocities of the `bulge' carbon stars would provide an independent verification of the photometric analysis presented here, concerning membership of the SDG. Tyson & Rich (1991) determined the radial velocities for 33 stars from the ALRW91 sample. Their radial velocities would support only for a small number of stars the suggestion that the ALRW91 carbon stars are actually located in the SDG, while the majority of the stars are moving towards us and could be Bulge members.

The spectroscopic results related to the CN-line strength and the NaD equivalent width would support membership to the SDG combined with a binary evolution scenario for these stars. Membership of the Bulge does not make sense, because there is in that case no trace of a predecessor, i.e. a brighter population of carbon stars (see Azzopardi 1994, Fig. 2). One could argue that an independent verification of the radial velocities, with a zeropoint based on other stars than the one template star ROA 153 used by Tyson & Rich (1991), might shed some light on the present contradictory results.
However, if both the photometric and spectroscopic analysis are correct then the ALRW91 carbon stars are related to the SDG. Some stars move away from us in the same direction as the SDG, while others move towards us, away from the SDG. This does not necessarily imply that we observe the ongoing disruption of the SDG. It is not clear if an encounter of the SDG with the galactic disc could result in the bifurcation of the radial velocity distribution for stars formed or located in the tidal tail. The numerical simulations from Johnston et al. (1995, their Fig. 10c and 10d) do show that the stars from a 1 Gyr old, tidal stream have a different radial velocity when observed at about 10o further along the orbit. But the presence of a moving group is not obvious, since its velocity distribution is not easily distinguished from halo or bulge stars.

4.5.2. Completeness limits

An intriguing point is that in the LMC carbon stars have not been identified with M [FORMULA] - 6 [FORMULA] 5, while they are found in some dwarf spheroidal galaxies. The majority of the carbon stars were found from green or near-IR grism surveys (see Azzopardi et al. 1985b and references cited therein). It is not unlikely that the limiting magnitude mentioned above mark the completeness boundary due to heavily crowding. More carbon stars might be present, but they have not yet been identified. If they are variable, then the databases from the various microlensing projects (see contributions in Ferlet et al. 1997) will prove to be an important and valuable asset. A massive spectroscopic study combined with a near-IR photometry of the LPVs might reveal the carbon stars below the completeness boundary of the grism survey. Finding faint carbon stars in the LMC would provide a significant contribution to understand the origin of the low luminosity SDG carbon stars.

As an aside it is interesting that the colours of the ALRW91 & the SDG carbon stars have comparable colours with those found in other dwarf spheroidals. The question rises if this implies that they have comparable age and metallicities. If this is the case: a) where are the LPVs, and b) how would that change the star formation and chemical evolution history ? As shown in Fig. 2b the blue giant branch sequence does not necessarily imply only an old, metal-poor population which is indistinguishable from a young, metal-richer giant branch.

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Online publication: March 24, 1998