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Astron. Astrophys. 317, 761-768 (1997)

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5. Luminosities and mass range

5.1. Mass as the origin of the scatter in the period-temperature relationship

The period-temperature (PT) relation is very scattered, and the error bars are not always large enough to explain this fact. The period does not depend only on temperature but on mass and metallicity too. Furthermore, there may be different relations depending whether the Miras pulsate mainly in the fundamental or the first harmonic.

Mira variables are supposed to obey to a period-luminosity (PL) relation (see, e.g., Feast et al. 1989). The PT and PL relations might be related with the help of a theoretical evolutionary track on AGB if some assumptions are made about masses and metallicities.

Different evolutionary tracks on the AGB described by [FORMULA] =f ([FORMULA], [FORMULA], Z) relations where [FORMULA] is the mass and Z is the metallicity have been considered: Lattanzio (1991), Vassiliadis & Wood (1993), Fox & Wood (1982) cited in Bessell et al. (1989b) and Barthès & Tuchman (1994 and private communication). The period-luminosity relations that are obtained if the temperature is replaced by the period from Eq. (2) are plotted in Fig. 6. All have been computed with [FORMULA] and [FORMULA] =1.5 [FORMULA].

[FIGURE] Fig. 6. Bolometric magnitude as a function of period for different theoretical evolutionary tracks on the AGB (with Z =0.02 and [FORMULA] =1.5 [FORMULA]) and using the period-temperature relation of Eq. (2). The solid line is the period-luminosity relation determined by Feast et al. (1989) for the LMC

On the same graph the period-luminosity relation observed by Feast et al. (1989) for the Miras of the Large Magellanic Cloud (a distance modulus of 18.47 has been adopted) has been plotted. Stars of the LMC are supposed to have a metallicity smaller than those of the Galaxy. Nevertheless, Whitelock et al. (1994) showed that a single PL relation is obeyed by Miras in the LMC, the Galactic globular clusters and the solar neighbourhood. They argue that there is no justification for making theoretical metallicity corrections to the observed PL relation. So, the choice to use the PL relation observed in the LMC without correction has been made here.

Some of the PL relations determined above (the ones calculated with Bessell et al. and Barthès & Tuchman tracks) have a slope similar to the relation observed by Feast et al. This is always the case even with another mass than 1.5 [FORMULA]. This suggests that the dispersion of masses may be introduced as the origin of the scatter in the period-temperature relationship.

We have made the following strong assumptions:
- the scatter of the PT relation is only due to dispersion of masses. The effect of metallicity which certainly exists is not taken into account
- there is a linear relation between [FORMULA] and mass, where [FORMULA] is the temperature of the Mira determined in Sect 4., and [FORMULA] is the temperature obtained with Eq. (2):

[EQUATION]

- the Miras follow the evolutionary track cited by Bessell et al. (for solar abundance):

[EQUATION]

The two free parameters [FORMULA] and [FORMULA] of the linear relation can be found by requiring a period-luminosity relation in agreement with the Feast et al. one. A mean mass [FORMULA] of 1.7 [FORMULA] and a minimum mass [FORMULA] (which corresponds to the smallest algebraic value of [FORMULA]) of 0.8 [FORMULA] give the following PL relation which is the best approximation in the range [FORMULA] =[2.0, 2.6]:

[EQUATION]

The PL relation of Feast et al. for oxygen-rich Miras of the LMC is:

[EQUATION]

The absolute bolometric magnitudes we obtained are thus very close to those given by the Feast et al. relation. With these parameters [FORMULA] and [FORMULA], the maximum mass of the sample is 2.6 [FORMULA]. The mass range so determined is not striking for oxygen Miras with period less than 550 days according to classical models.

5.2. Effect of metallicity

If, despite the results of Whitelock et al., thick disk and halo Miras follow different PL relations because of metallicity-as it is the case for Cepheids (Nemec et al. 1994)-, the absolute bolometric magnitudes determined previously are certainly not reliable for a large part of the sample. There is also an effect on the mass range.

For halo Miras, Eq. (5) is not adapted and another evolutionary track on the AGB for low-metallicity stars is needed. Such a track is given in Bessell et al. (1989b). Using that, we have computed new masses in the same way as described previously. We find low masses, which is not surprising for halo stars, but probably too low (the mean mass is 0.4 [FORMULA]). This may be due to an irrelevant period-temperature relationship. Indeed, if there is a different PT relation for each population (metal-poor and metal-rich Miras), Eq. (2) is certainly not suitable for halo stars, the less numerous population.

For thick disk Miras, Wood (1990), extrapolating results from pulsating theory, argues that the local stars are intrinsically fainter by 0.44 mag if the metal abundance of Miras in the LMC is taken to be 1/4 [FORMULA]. The necessary mass range to obtain a PL relation 0.44 fainter is 0.5 to 2.0 [FORMULA] with a mean mass [FORMULA] equal to 1.3 [FORMULA]. It is, however, difficult to quantify how much local Miras are really fainter than LMC Miras and the value of 0.44 mag is dependent on an assumption on pulsation mode (fundamental in this case).

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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