4 Calibrations of the LPVs population

The LM method was applied four times, as described in Sect. 3, once for each photometric bandpass: V - results already presented in Mennessier et al. (1997b) -, K, 12 and 25 - in the present paper. In principle, one could assign a joint luminosity distribution to two or more bandpass magnitudes simultaneously, and the LM method would separate the sample into stellar groups consistent with all the photometric measurements together. This option, however, requires a perfectly well known relationship between the different magnitudes in order to define a joint distribution function as realistic as possible for all the band passes. The correlation between the near-infrared (K) and IRAS infrared properties presently cannot be well modeled and very likely has a non-unique form depending on the stellar and circumstellar evolutive stage along the AGB. Thus, we decided not to couple the photometric band passes and to calibrate each luminosity separately. Furthermore, bandpasses are related to different physical processes and can provide separate interesting information: V is greatly affected by absorption molecular lines, K reflects the stellar emission, and IRAS bandpasses depend on the nature and density of grains in the circumstellar envelope.

The LM method is simultaneously sensitive to kinematics and luminosity and thus the number of significant discriminating groups depends on both these characteristics and is not necessarily the same for the different bandpass analyses. Furthermore, the samples used are not the same, and this can also affect the number of discriminated groups.

Six distinct groups are identified in the V magnitudes, three in K and four in each of the two IRAS magnitudes. Those are successively analyzed in terms of the classical galactic populations. Although the number of groups is found to be different for each analysis, the groups present similarities in their kinematical composition and with respect to the galactic populations (see Sect. 6).

   
4.1 The V band

An analysis of the six groups identified in the V band has been presented in Mennessier et al. (1997b). In order to compare these results with the ones obtained for infrared calibrations, the main results are summarized here. Table 1 reviews the estimated mean parameters for the analysis corresponding to the V luminosity at the phase of maximum light. The LPVs are found to belong to all galactic populations from disk to very extended disk. We wish to emphasize three points:

• LPVs belonging to the bright disk population (BD) have a mean luminosity of M_V=-3.6 and Z₀=104 pc, while the corresponding values for the disk population (D) are M_V=-1.0 and Z₀=126 pc. Among LPVs belonging to BD population there are probably stars at the upper limit of the AGB or even at the first step of the post-AGB state.

• the main group (44%) has an estimated scale height of Z₀=249 pc. Its kinematics is typical of the old disk population.

• a few LPVs (less than 2%) belong to the extreme extended disk (ED), with Z₀ greater than 1200 pc and a very large Schwarzschild ellipsoid velocity distribution. This most probably indicates a birth of those stars early in the evolution of our Galaxy. Those stars should thus be a metal-deficient disk population (see 6.2). This is consistent with the bright luminosity found (M_V=-2.8).

 

 

Table 1: V calibration: estimated parameters of the different groups and percentage of the sample into each of them.

Group	BD	D	OD1	OD2	TD	ED
MV	-3.6	-1.0	-1.2	-0.2	-1.2	-2.8
$\sigma_{M_V}$	1.4	0.8	0.2	1.0	0.5	1.2
U0	-10	-6	-44	-1	-34	-61
V0	-11	-6	-35	-21	-84	-235
W0	-13	-6	-6	-10	-19	-20
$\sigma_{U_0}$	13	24	28	37	77	188
$\sigma_{V_0}$	14	14	25	23	29	126
$\sigma_{W_0}$	9	9	22	23	65	72
Z0	104	126	217	249	409	1227
$\%$	8	25	13	44	8	2

   
4.2 The K band

Only three groups are identified in the K band. From their kinematics and spatial distribution, given in Table 2, they can be interpreted as the galactic disk (D), old disk (OD) and extended disk (ED) populations. They are similar to the four main groups identified in the V band (Sect. 4.1), except that the disk and a part of the old disk population seem to be mixed.

In a previous analysis of a sample restricted to O-rich Miras (Alvarez et al. 1997), only two groups were found. One corresponded to the extended disk population, with a percentage of 17, in agreement with our result i.e. $18/142=13\%$ of O-rich Miras belonging to the ED group (see Table 7). The other group mixed disk and old disk populations. In the present paper, a more numerous sample allows a more refined separation of the kinematic populations.

 

 

Table 2: K calibration: estimated parameters of the different groups and percentage of the LPVs population in each of them.

	Group D		Group OD		Group ED
	est.	$\sigma$	est.	$\sigma$	est.	$\sigma$
K0	-6.1	0.4	-6.0	0.7	-5.3	0.8
$\sigma_K$	1.1	0.3	0.7	0.4	1.4	0.5
U0	-7	10	-17	27	-21	14
$\sigma_U$	29	9	45	16	111	11
V0	-12	8	-36	25	-123	12
$\sigma_V$	16	5	27	11	69	18
W0	-9	6	-6	9	-20	19
$\sigma_W$	12	3	26	13	90	25
Z0	184	44	268	85	782	313
$\%$	60		35		5

 

 

Table 3: 12 calibration: estimated parameters of the different groups and percentage of the LPVs population in each of them.

	Group D		Group ODb		Group ODf		Group ED
	est.	$\sigma$	est.	$\sigma$	est.	$\sigma$	est.	$\sigma$
120	-6.4	0.3	-8.0	0.4	-6.4	0.5	-6.2	1.0
$\sigma_{12}$	1.7	0.1	1.2	0.2	0.6	0.4	1.6	0.2
U0	-6	9	-12	5	-10	9	-30	37
$\sigma_U$	22	6	35	8	39	6	106	45
V0	-7	8	-26	7	-24	8	-97	54
$\sigma_V$	12	5	26	11	22	6	65	64
W0	-9	4	-9	5	-8	5	-2	44
$\sigma_W$	9	8	21	8	21	7	75	29
Z0	161	55	258	56	256	79	1065	724
$\%$	29		32		29		10

 

 

Table 4: 25 calibration: estimated parameters of the different groups and percentage of the LPVs population in each of them.

	Group D		Group ODb		Group ODf		Group ED
	est.	$\sigma$	est.	$\sigma$	est.	$\sigma$	est.	$\sigma$
250	-7.1	0.5	-8.6	0.4	-6.5	0.3	-6.8	0.8
$\sigma_{25}$	1.7	0.1	1.2	0.2	0.6	0.4	1.6	0.5
U0	-6	6	-10	4	-10	7	-39	48
$\sigma_U$	21	8	36	10	38	6	111	33
V0	-6	4	-26	7	-22	6	-99	63
$\sigma_V$	13	4	27	9	22	5	69	23
W0	-10	4	-9	5	-8	4	1	42
$\sigma_W$	11	7	21	8	20	4	75	37
Z0	158	43	277	34	270	107	1610	1180
$\%$	28		32		30		10

   
4.3 The IRAS bands

The four LPV groups identified in the IRAS 12 and 25 bands are given in Tables 3 and 4, respectively. They are similar to those identified in the K band (Table 2), except that the old disk group is further divided into "bright'' (ODb) and "faint'' (ODf) subgroups. Let us remember here that the method allows us to distinguish groups with similar mean kinematics but different luminosities (ODb and ODf) or groups with a similar luminosity distribution but different kinematics (D and ED for instance). Moreover, it is important to remark that D, ODb and ED have, on average, a similar color index 25-12 = -0.6 mag corresponding to a thick circumstellar envelope, while ODf has a mean index of 0.1 mag that suggests that the majority of the stars in this last group have thin envelopes.

Let us finally point out that the kinematic parameters ( U₀,V₀,W₀) associated with each of the four groups are very similar for both the 12 and 25 calibrations.