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

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1. Introduction

Long-period variables of Mira type are excellent tracers of the history of the Galaxy as they mark with the other stars on the asymptotic giant branch a crucial stage in the evolution of stars with initial mass less than 8 [FORMULA]. But the use of them in this field is made difficult by the uncertainties that exist as regards values of fundamental parameters: only little is known about temperatures, masses, radius and luminosities. On one hand, observations in a long time range are necessary to study variations (a typical period is 300 days for a Mira and furthermore there are changes in light curves from one cycle to the other); on the other hand, a realistic model of the physical structure from the stellar core to the stellar surface does not exist up to now and will be difficult to construct due to the extreme complexity of these stars.

Indeed, Mira atmospheres are very extended: models have to take account of sphericity effects and, more problematically, the LTE hypothesis may be invalid. The atmosphere is cold ([FORMULA] 4000 K), which implies the apparition of a lot of lines of molecular bands: modeling requires a very large sum of molecular data among which some concerning important molecules are badly known. Moreover, these stars pulsate, and there does not yet exist a completely satisfactory theory explaining the real mechanism of pulsation. If it is now obvious that Miras are multi-pulsators, it is still unclear whether Miras pulsate mainly on fundamental or first harmonic, which has a great influence on the relationship between the fundamental physical parameters. Furthermore, there is a strong stellar wind with high mass-loss rates which could show irregular behaviour with time.

Some authors have nevertheless made important progress in some fields like theoretical models of pulsation (Fox & Wood 1985; Tuchman et al. 1993), dynamical models of atmospheres (Bowen 1988; Bessel et al. 1989) or models of late-type stellar photospheres (see Gustafsson & J[FORMULA]rgensen 1994 for a review).

In this paper, we have tried to determine some fundamental parameters from narrow-band photometry observations (Lockwood 1972) which were obtained during a period of more than two years and for nearly 300 Miras. From these photometric observations (described in Sect. 2) we have computed indices related to molecular band strengths of titanium oxide (TiO) and vanadiun oxide (VO) which are used as temperature indicators (Sect. 3). A period-temperature relation (Sect. 4) is determined which agrees well with a previous one (Glass & Feast 1982). The likely too simple way of explaining the scatter of this relation only by the distribution of mass is considered (Sect. 5) before luminosity and distance estimates are proposed for 165 Miras of the sample. These distances are compared with other estimates. The procedure allows us to check the reliability of our calibrations (Sect. 6).

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998