3 How to explain the gap for observed O-rich LPVs

As seen in Sect. 2.1 the distribution of O-rich LPVs is clearly bimodal in the diagrams of Fig. 1, separating shell and no-shell stars. This gap may a priori be formed by several scenarios of the circumstellar shell formation, but one must not forget that the sample selection can also induce such an effect. Therefore, we must take both physics and sampling into account when examining the validity of the proposed hypotheses.

   
3.1 Several hypotheses

Figure 2: Distribution of the individual estimated K and 12 luminosities according to the assigned kinematical groups and to spectral types.

Figure 3: Distribution of the individual estimated K and 25 luminosities according to the assigned kinematical groups and to spectral types.

Our sample is composed of variable stars observed by HIPPARCOS, i.e., selected from criteria based on visual magnitude. As seen in Paper I, this selection effect is the most prominent in comparison with the other ones: availability of K magnitude and IRAS detection. A priori and with regard to the selection effects, we propose three possible explanations for the striking gap observed for O-rich LPVs in Figs. 1-3:

1.

During its evolution along the AGB, the star presents two stages of variability. Initially it is irregular or semi-regular of type b, then the pulsation stops and thereafter the star becomes variable for a second time as a semi-regular of type a or Mira and its circumstellar envelope grows;

2.

The first thermal pulses induce an irregular variability of the star. Thereafter, the pulsation becomes more regular and a significant mass loss is the source of the circumstellar envelope formation. Owing to the composition of the silicated envelope, the 12 and 25 (more 25 than 12) luminosities suddenly and strongly increase. After this rapid phase the evolution quietly continues;

3.

At the beginning of the thermal pulses the SRb or irregular variables slowly develop a circumstellar envelope that grows and becomes sufficiently thick to make the star undetectable in V magnitude. The envelope expands and becomes more transparent and thus the star becomes again visible in the visual magnitudes.

Obviously, reality may be more complex than these three proposed scenarios, and other explanations based on other results may be suggested. The following section is dedicated to the analysis of the three above proposed hypothesis.

Figure 4: Distribution of the individual estimated K, 12 and 25 luminosities and IRAS colors of Tc and S stars compared with O and C-rich LPVs.

   
3.2 Consequences of each hypothesis

First of all, the first hypothesis is not realistic. It has no convincing physical justification and no such behaviour is found in the models. We will thus discard it immediately.

The other two are plausible. Let us examine their coherence using Fig. 6, which shows the distributions of the individual estimated K absolute magnitudes and V-K indices from the V and K luminosities estimated for each group. Figure 6 also distinguishes the spectral types and the envelope thickness. A small number of stars assigned to the disk 1 or extended disk population have a 25-12 index close to 0. They are marked in the Fig. 6 as "simuf'' type points.

Figure 5: Distribution of the individual estimated K, 12 and 25 luminosities and IRAS colors of OH stars compared to O and C-rich LPVs.

Figure 6: Distribution of the individual estimated K luminosities and V-Kindices according to spectral types and indication of the envelope thickness by separating stars assigned to f group or with a 25-12 index close to 0 (simuf). Each figure corresponds to a kinematical group.

In the case of the third hypothesis, when the circumstellar envelope grows more luminous in K, higher values of V-K are initially found; then V-Kdecreases when the envelope expands. The star crosses back over the limit of visibility, being more luminous in K and with a larger V-K index.

In the case of the second hypothesis, the change in the infrared fluxes is rapid and there is no reason for a corresponding drastic change in K luminosity, but the absorption in V band suddenly increases. Thus, the stars belonging to the b group may be only visible (i.e. in our sample) from a more luminous lower limit in K than that of the f group. Briefly, in the second hypothesis, from one side to the other of the gap, the star has the same K luminosity but the K distribution of the sample after the gap can be truncated for faint values because of an increase in V-K. In the third hypothesis the gap corresponds to a time for which the star is invisible. Thereafter it is brighter in K.

At this stage neither hypotheses 2 nor 3 can be rejected. The data available are too scarce to decide between them. The reality may be a mixture of both, but as long as these two hypotheses are considered, it is obvious that the observed gap results from a circumstellar phenomenon. On the contrary, a discontinuity in the stellar evolution along the AGB can be excluded.

   
3.3 Differences according to the galactic populations

The (K, 12) and (K, 25) diagrams (Figs. 2 and 3) allow us to extend our analysis. They show the extent to which the evolution depends on the galactic population, i.e. on the initial mass and metallicity. We remark that the faint K luminosity truncation of the sample of stars with a thick envelope assigned to disk 2 population (D2b) is far lower than the one assigned to the old disk population (ODb). This difference between disk 2 and old disk populations favours the second hypothesis. Indeed such a difference is difficult to explain by an individual increase in K during the time of invisibility of the star assumed by the hypothesis 3. On the other hand, a less massive star has a less efficient mass loss with a formation of a less thick envelope and is thus less absorbed in the V band. Therefore, in the case of hypothesis 2, at a given K for a thin envelope star (f), old disk population LPVs have a larger probability than disk 2 population stars to be in our V-selected sample just after the circumstellar envelope formation.

The location of carbon stars also reinforces hypothesis 2. Indeed, a few C-rich LPVs have a 25-12 index close to zero but they cannot be stars just reaching the AGB. This is obvious when we examine the Fig. 1 except for the 4 carbon stars belonging to the disk 2 population fainter than -7 mag. However, if we consider these 4 stars as having evolved from O-rich LPVs belonging to the truncated faint part of the b distribution, everything is consistent.

   

Table 3: Individual K, 12 and 25 luminosities, with assigned crossing K (IRAS) group, spectral ( ${\rm O}={\rm O-rich}$, ${\rm C}={\rm C-rich}$ , ${\rm S}= {\rm S spectral}$ type star) and variability ( ${\rm M}={\rm Mira}$, ${\rm SR}={\rm semi}$ regular, ${\rm L}={\rm irregular}$) types, possible specificity ( ${\rm Tc}={\rm Technetium}$ star, ${\rm OH}={\rm OH}$ star, ${\rm BD}={\rm bright galactic disk star}$, ${\rm He}={\rm star}$ in He-shell flash) and IRAS spectrum.

HIP id	name		types	group	K	12	25	pec	IRAS sp.
13502	R	Hor	MO	ED	-8.40	-10.81	-11.49	Tc?
70339	RS	Lup	LC	ED	-8.96	-10.57	-11.20
77501	V	CrB	MC	ED	-8.82	-11.59	-12.06
1834	T	Cas	MO	D2b	-9.00	-11.37	-12.05		1 15
7139	IM	Cas	SROb	D1	-8.95	-11.43	-12.36	BD	1 15
7598	V539	Cas	LO	D1	-9.30	-11.50	-12.43	BD	1 16
12302	YZ	Per	SROb	D1	-8.83	-11.70	-12.91	BD	1 27
15530	UZ	Per	SROb	D1	-8.93	-11.04	-12.04		1 25
46502	Y	Vel	MO	D1	-9.01	-12.01	-12.79		1 23
69754	R	Cen	MO	D1	-9.60	-12.18	-12.79	BD,He	1 22
87668	V774	Sgr	LO	D1	-9.36	-12.85	-14.03		1 29
116705	SV	Cas	SROa	D1	-9.31	-11.74	-12.70		1 25
91389	X	Oph	MO	D1	-8.16	-11.11	-11.69	OH	1 15
32627	V613	Mon	SROb	D1	-8.60	-10.07	-10.31	BD
89980	V4028	Sgr	SROq	D1	-8.58	-9.80	-10.29	BD
65835	R	Hya	MS	D2b	-8.52	-11.04	-11.60	Tc, He
93820	R	Aql	MO	ODb	-7.31	-9.48	-10.49	OH, He