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4 Fundamental stellar parameters

If the spectra of this paper are to be used in association with population synthesis models, it is necessary to relate them to fundamental stellar parameters such as initial mass, initial metallicity and evolutionary status. Ideally, one should derive these parameters for each individual object and compute an energy-weighted mean spectrum to be used at one particular point of one particular AGB evolution track. As discussed by Lançon (1999), this currently isn't practical, be it only because it requires light curves and a full phase coverage for each star. Lançon et al. (1999) have adopted a different procedure based on averages inside apparent temperature bins instead of mean spectra of individual objects. The underlying assumptions and the required calibration of the resulting population synthesis predictions will be discussed in detail elsewhere (Mouhcine et al., in preparation). It remains useful to investigate the nature of the stars observed for this paper, because it will allow us to reevaluate the two procedures once more stellar and extragalactic data becomes available. Optically visible Miras are observed to lie on a rather narrow period-luminosity (PL) relation (Feast et al. 1989; Hughes & Wood 1990) with little or no metallicity dependance. Even the effects of the O-rich to C-rich transition are small (Groenewegen & Whitelock 1996). A main result of the 5 year photometric survey of LMC stars by the MACHO consortium was the demonstration that large amplitude variables and a significant fraction of the semi-regular variables with V amplitudes larger than 1 mag are fundamental mode pulsators (Wood et al. 1999). Vassiliadis & Wood (1993) combined a theoretical fundamental mode period-mass-radius relation with stellar evolution models to compute the evolutionary tracks of TPAGB stars in the PL diagram. Assuming that the stars of our programme lie on the mean Mira PL relation, we have used these tracks to estimate the stellar initial masses. The PL evolution of a TPAGB star depends on metallicity: at a given luminosity and for a given initial mass, a metal rich star will have a lower effective temperature due to higher opacities and a smaller mass due to enhanced mass loss, two effects that combine to lengthen the pulsation period. Table 8 lists the initial masses derived assuming either LMC or solar metallicity.


Table 8: Indicative initial masses for variable stars, sorted by period, with the assumption of either LMC (lower value) or solar metallicity (higher value). Fundamental mode pulsation is assumed; overtone pulsation leads to higher masses (see text)
Star vartype $\delta$V P M Notes
SY Vel SRb 1.30 63.0 $\leq 0.94$ O
S Cen SR 1.5 65 $\leq 0.94$ C
ET Vir SRb 0.20 80.0 $\leq 0.94$ O
T Cen SRa 3.50 90.4 $\leq 0.94$ P
BD Hya SRa 1.80 117.4 $\sim 0.94$ P
Z Aql M 6.60 129.2 $\sim 0.94$  
S Phe SRb 2.00 141.0 0.94-1  
S Car M 5.40 149.5 0.94-1.1 P
KV Car SRb 0.80 150.0 0.94-1.1 O
T Cae SR 1.80 156 0.94-1.1 C
U Crt M 4.0 169.0 0.94-1.2  
AO Cen M 1.90 189.0 0.95-1.3  
S Lib M 5.50 192.9 0.95-1.3 P
RY Cra M 1.90 195.0 0.95-1.3 P
RS Hor M 5.20 202.9 0.96-1.3 P
RS Lib M 6.0 217.6 0.97-1.3 R
SW Hya M 3.20 218.8 1-1.4  
R Cir SRb 1.90 222.0 1-1.4  
SV Tel M 3.00 225.5 1-1.5 P
V 603 Cen M 2.30 253.0 1-1.6  
UZ Hya M 5.70 261.0 1.1-1.7  
R Phe M 6.90 269.3 1.1-1.7  
RZ Car M 6.2 272.8 1.1-1.7  
V Oph M 4.3 297.2 1.25-1.9 C
Z Lib M 3.60 298.6 1.25-1.9  
Y Hya SRb 3.70 302.8 1.25-1.9 C
R Leo M 6.9 312.0 1.3-1.95  
R Cha M 6.7 334.6 1.5-2.1  
CM Car M 2.50 335.0 1.5-2.1  
RS Hya M 5.20 338.6 1.5-2.1 R
EV Car SRb 1.40 347.0 1.55-2.2  
DX Ser SRa 2.00 360.0 1.65-2.25  
R Cnc M 5.6 361.7 1.65-2.25  
X Men M 3.60 380.0 1.8-2.4 R
SV Lib M 1.30 402.7 2-2.5  
BH Cru M 2.8 520.0 2.2-2.6 C
RU Pup SRb 1.90 425 2.2-2.65 C
R Lep M 6.20 427.1 2.3-2.7 C, IR
WW Sco M 4.1 431.0 2.3-2.7 R
CL Car SRc 2.50 513.0 3.3-3.7 S
WX Psc M >2.5 645 >5  
AFGL 1686 M >2.5 700: >5 IR

Notes to Table 8:
O: overtone pulsator? C: carbon rich star. P: metal poor?
R: metal rich? IR: IRAS source. S: supergiant.

In Sect. 3.4, potentially metal poor or metal rich stars have been identified. Due to the global chemical evolution of the solar neighbourhood, a general correlation between age and metallicty exists: with the above assumption of a single mode of pulsation, stars with short periods have low initial masses and are thus likely to be metal poor (the smaller of the mass estimates of Table 8 is more appropriate), while stars with long periods are more massive, thus younger and more metal rich (i.e. the larger of the mass estimates applies).

On the other hand, a subsample of the small amplitude, short period LPVs may be overtone pulsators. Surveys show that additional PL sequences run parallel to the Mira sequence on the high luminosity side, consistent with overtone pulsation (Bedding & Zijlstra 1998; Wood et al. 1999). These sequences are populated with semi-regular variables, mostly with V band amplitudes smaller than $\sim$1 magnitude and periods shorter than 200 days. Higher initial masses (and an earlier evolutionary status) would result from the use of the corresponding PL relations. The only stars this may reasonably apply to in our sample are ET Vir, SY Vel and KV Car. As an example, the 150 day period of KV Car would suggest an initial mass of the order of $2~M_{\odot}$ if overtone pulsation applied, instead of about $1~M_{\odot}$ in the case of the fundamental mode assumption. The resulting high luminosity might then explain the relatively strong CO bands of KV Car noted in Sect. 3.2.

The longest period variables of the sample are IRAS sources, i.e. they are loosing mass at superwind rates and lie on the long period side of the mean PL relation of optically visible Miras. At this stage of evolution, the periods increase rapidly and the tracks run horizontally in the PL diagram for all initial masses. The spectra of the IRAS sources thus probably correspond to late stages of stars slightly less massive than indicated in Table 8.

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