3. The MK vs. log P diagram
3.1. The three samples
The periods adopted for Miras and SRs were taken from Kholopov et al. 1985 (GCVS) or from ESA (1997, vols. 11-12) for some improved data. The absolute magnitudes of Table 1 are plotted in Fig. 1a against the log of the period in days. The diagram obtained for carbon-rich LMC-stars is shown in Fig. 1b with similar scales. The ordinate is the dereddened apparent magnitude taken for carbon variables from Hughes & Wood (1990) and Groenewegen & Whitelock (1996), and 19 stars from Wood & Sebo (1996) (types not specified: shown with quots in Fig. 1). We found strong similarities and no marked differences between both diagrams. A few error bars are shown in Fig. 1a. The usual was kept for easy reference to published LMC data, despite the bias mentioned in Sect. 2. The sampling operated hereafter is found again in the diagram as well except possibly for 3 stars conservatively classified in Sample 3, i.e. not used in Sect. 4 analysis). A majority of Fig. 1b variables do concentrate in a clump where is increasing with increasing log P close to the PL relation (LMC Sample 1). This strip is widened by a "wave" of brighter stars (LMC Sample 2) in the region , while an upper limit (ul) is observed at longer periods. A few underluminous LPVs (LMC Sample 3) are noticed well below the PL relation. The same three samples are observed in Fig. 1a for galactic LPVs. The proportions found (72, 31 and 12 stars respectively) however differ from those in the LMC (190, 32 and 11 respectively). Substantial errors on parallaxes and statistical corrections can result in galactic LPVs scattered from the first sample in the latter two, and conversely of course. Doubtful classification is actually suspected for at least 11 stars located in transition regions: conservatively, they were quoted as 2: or 3: in Table 1. It is worth noting that for our 19 carbon Miras. None of them was found in Sample 2. It is known that, on the average, the carbon Miras have shallower light curves than their oxygen-rich counterparts. Longer periods are required for carbon LPVs to be classified as Miras since amplitudes and periods show a positive correlation. It has been argued that the LMC Sample 2 stars are overtones pulsators (Wood & Sebo 1996), while the other stars could be pulsating on the fundamental mode. Recently, van Leeuwen et al. (1997) provided modes identifications in a stellar radius vs. angular diagram (their Fig. 1): the values obtained for oxygen variables with measured angular diameters were compared to the predicted curves for the various modes. Assuming the latter lines hold for carbon variables with angular diameters (Dyck et al. 1996), our comparison points to overtones pulsation for stars in Sample 2 (Bergeat et al. 1997). These very preliminary conclusions play no role in Sect. 4 analysis.
3.2. Underluminous variables (UVs)
We have noted 12 (possibly) underluminous outliers (Sample 3) amongst the 115 stars (including 19 Miras) studied here, i.e. one tenth of the sample. The uncertainties in both periods and absolute magnitudes have to be taken into account before a firm conclusion could be reached on any individual star. In addition, the used expectations of true parallaxes by Knapik et al. (1997) are correct only in a statistical way. Despite the uncertainties, the existence of underluminous LPVs is thus confirmed, like C 2064 = RU Pup located about 3 mag. (i.e. 6 times the standard error) below the Sample 1 mean relation. This could also be the case of the Mira variable C 2165 = T Lyn but the gap is only two standard errors here. It is interesting to note that 4 stars out of 12 are Miras, two being CS-stars; also found the peculiar star C 1653 = BM Gem with strong emission which is presumably a carbon star with silicate dust in its circumstellar shell (e.g. Little-Marenin 1986). This latter star and 2 Miras are however only marginally underluminous. The faintest stars here are hardly explained with standard TP-AGB evolution (e.g. Straniero et al. 1997). We have also computed the velocities relative to sun making use of the HIPPARCOS proper motions and parallaxes, and of radial velocities observed from ground. Keeping off the exceptional 319 km/s of V Ari (which falls in Sample 2 close to Sample 1 ul) we obtained mean velocities of 30-40 km/s for the three samples. In addition, none of those stars seems to be metal deficient. Clearly, there is no marked population difference between the three samples. No significant difference between samples was found in terms of spectral types or color indices like J-K, or more generally making use of the CV-classification of Knapik & Bergeat (1997). Their mean bolometric magnitudes should significantly differ.
© European Southern Observatory (ESO) 1998
Online publication: March 30, 1998