Among the most important and still unsolved issues concerning Long-Period Variable stars (LPV) are the modelling of their pulsation and even the mere identity of the predominant pulsation mode. Linear nonadiabatic (LNA) models are currently used on a wide scale for reasons of simplicity. Relying on LNA relations between the period and the fundamental parameters, and on dynamical models of the photospheric region, the pulsation mode of Mira stars is the fundamental according to the observed velocity amplitude (Hill & Willson 1979; Willson 1982; Bowen 1988; Wood 1990), and the first overtone according to the angular diameter estimates (Haniff et al. 1995; Van Leeuwen et al. 1997), pulsation accelerations (Tuchman 1991) and the PL distribution of globular cluster stars (Feast 1996). One study based on the periods and luminosities of LPVs of the Large Magellanic Cloud (LMC) concluded that Miras were pulsating in the fundamental mode and low-amplitude semi-regulars on the first or second overtone (Wood & Sebo 1996). However, another study, also taking into account a few Miras of the solar neighbourhood and various temperature estimates, supported the first overtone in a majority of Miras (Barthès 1998). Last, still relying on LNA models, Barthès & Tuchman (1994) and Barthès & Mattei (1997) found that the Fourier spectra of a few Miras were more easily explained than were the stars pulsating on the first overtone with the fundamental mode and other overtones also acting.
In fact, the large pulsation amplitude and the complexity of the chemistry and radiative transfer in the photospheric region make the mean effective temperature and radius very uncertain, even for nearby stars (Bessell et al. 1989a, 1996; Hofmann et al. 1998; Ya'ari & Tuchman 1998). The HIPPARCOS parallaxes, too, usually have large error bars, and they concern only about two dozen Miras.
Last, most of these studies suffered from a strong sampling bias, favouring periods longer than 250 days, especially those ranging from 300 to 400 days.
On the other hand, hydrodynamical models predict that, after thermal relaxation, Miras pulsate in the fundamental mode with a period either much shorter than (Ya'ari & Tuchman 1996, 1999) or very close to (Wood 1995; Bessell et al. 1996; Hofmann et al. 1998) the LNA period. These models mainly differ by their handling of the convective energy transport and of the equation of state, but they share the same unrealistic assumption: no wind and no extended circumstellar envelope at the outer boundary. As a consequence, the reliability of both the nonlinear and linear nonadiabatic pulsation models is uncertain, and the pulsation mode is still ambiguous.
An unfortunate result of these theoretical difficulties is that the present masses and metallicities of the LPVs have always been very uncertain. Indeed, no direct estimate of mass in binary systems has been possible up to now, and the chemistry and radiative transfer in the photospheric region are so complex that no reliable metallicity has been derived.
This paper mainly consists in exploiting the classification (based on kinematic and photometric criteria) and the period-luminosity-colour (PLC) distributions of the oxygen-rich LPVs of the solar neighbourhood, which were determined in Paper I of this series (Barthès et al. 1999). Its aims are to assess the pulsation models, and to identify the predominant mode and estimate the average mass and metallicity for each kinematic/photometric group.
The data sets are presented in Sect. 2. They include the results of Paper I, i.e. the periods, absorption-corrected absolute magnitudes and de-reddened colours of a sample of stars observed by HIPPARCOS, but also the de-biased distributions of the four kinematic/photometric groups to which they belong. LPVs found in the LMC and in various globular clusters are also included, with a view to calibrating the free parameters of the models.
Section 3 describes the pulsation models to which these data will be confronted: the linear nonadiabatic modelling code and the adopted temperature scale, i.e. colour-temperature-metallicity (CTZ) relations. Section 4 then explains the difficulties to be expected because of the physical approximations of the models, and also because of the nonlinear shape of the CTZ relations. We will be led to introduce some systematic correction parameters for the periods and colours.
These free parameters, together with the mixing length, are calibrated in Sect. 5 by confronting the models with the PLC distributions of the LPVs in the LMC and globular clusters. The so-calibrated models are then confronted with the PLC distribution of local stars in Sect. 6, and the pulsation mode, mass and metallicity are derived for each kinematic/photometric group. Finally, the stability and reliability of the results, as well as their consequences concerning the existing pulsation codes, are assessed in Sect. 7.
Copyright ESO 2001