1 Introduction

LPVs are particularly interesting red giants for two main reasons. On the one hand, the brightest LPVs are luminous enough to be observed at large distances, providing information on the host galaxy (Van Loon et al. 1999a). On the other hand, although their precise ranges of masses and ages remain controversial, it is clear that they are large enough. Thus LPVs are very good tracers of the galactic history. Moreover the final evolution along the AGB, and peculiarly the carbon surface enrichment and the change of the envelope chemistry, is very complex. It depends on many factors (as convection, overshooting, internal chemical process, mass-loss, pulsation, etc.), the relative effects of which depend on the mass and metallicity, among other things.

In a previous paper (Mennessier et al. 2000), hereafter Paper I, HIPPARCOS astrometric data and multi-wavelength photometric measurements of a sample of 800 LPVs (semi-regular a and b, irregular L and Mira with O, S and C spectral types) were analyzed using the LM algorithm (Luri et al. 1996). V, K and IRAS 12 and 25 luminosities were calibrated. The LM algorithm classified the stars according to the galactic population (associated with the initial mass and metallicity of the stars) and to the circumstellar envelope thickness and expansion. Several groups were obtained in this classification:

• Bright disk (BD) and disk (disk 1 or D1) LPVs with bright and expanding envelopes;

• Not so young and massive disk population (disk 2 or D2) divided into two subgroups: one with a thin envelope (denoted f) and another one with a bright and expanding envelope (denoted b);

• Old disk (OD) population, showing a similar separation (b and f) according to envelope properties;

• Some LPVs were included in the extended disk (ED) population.

These groups were obtained by combining K and IRAS results.

From kinematic properties, the disk 1 population was found to be $1{-}4\times 10^9$ yr old, disk 2 population $4{-}8\times 10^9$ yr old and the old disk population older than $8\times 10^9$ yr, up to 10¹⁰ yr or even more. An extended disk was assumed to be composed of very old, metal-deficient stars.

The lower limits of the main sequence initial mass, ${\cal M}_{\rm ms}$, were estimated to be in the range $2{-}1.4~{\cal M}_{\odot}$, $1.4{-}1.15~{\cal M}_{\odot}$, and $1.15{-}1~{\cal M}_{\odot}$ for disk 1, disk 2 and old disk populations respectively. Moreover, in Paper I, statistical estimates were done to quantify how much groups and various variability and spectral types attract or repel each other.

Each star of the sample was assigned to a galactic population and its individual K and IRAS 12 and 25 absolute magnitudes were estimated. A table with these values is available in electronic form at CDS. They also are available in the ASTRID specialized database.

In this paper, we use the estimated individual stellar absolute magnitudes (K) together with properties of the circumstellar envelopes (deduced from IRAS absolute magnitudes) and the assigned galactic population to define an evolutive scenario of simultaneous stellar and circumstellar evolution of LPVs along the Asymptotic Giant Branch (AGB). We aimed to link the chemical evolution from O-rich to C-rich LPVs or OH emitters (through the intermediate states of S and/or Tc LPVs) and the stellar and circumstellar evolution, depending on the galactic population, i.e. on the initial mass, as discussed in Sect. 2.

In Sect. 3 we examine the first stages of O-rich LPVs and their correlation with initial mass. More precisely, we propose and critically study several possible explanations for the gap observed in the distribution of O-rich LPVs, separating those with and without a circumstellar shell.

Section 4 is dedicated to the brightest O and C-rich LPVs and points out candidates for peculiarities like Hot Bottom Burning (HBB). Special attention is given to the case of R Cen, a star in a He-shell flash.

Finally, a global stellar and circumstellar evolutive scenario is proposed in Sect. 5, which takes into account the differences between galactic populations and explains both chemical and variability-type changes.