2 The sample of LPV stars

   
2.1 Data

In order to benefit from the accurate astrometric data made available by the HIPPARCOS satellite, we use in our study the sample of all LPV stars observed on this mission, i.e. the LPVs brighter than 12.5 mag in Vduring more than 80% of their variability cycle. The sample is composed of about 900 stars which are either of type M (O-rich), C (C-rich) or S (O/C $\mathbin{\;\raise1pt\hbox{$<$ }\kern-8pt\lower3pt\hbox{$\sim$ }\;}$1). They include Mira, SR (of both type a and b) and L variables.

Astrometric data is taken exclusively from the HIPPARCOS Catalogue (Perryman et al. 1997) to provide a homogeneous data set. Radial velocities are taken from the HIPPARCOS Input Catalogue (HIC; Turon et al. 1992).

Photometric data are gathered from various sources. V magnitudes (m_V) are taken from the HIC. They correspond to the magnitudes given in the General Catalogue of Variable Stars (GCVS; Kholopov et al. 1985), corrected as described in the HIC volumes to obtain mean magnitudes at the maxima of light. K magnitudes (m_K) are taken from the Catalogue of Infrared Observations (Gezari et al. 1996), and include the large set of JHKL measurements of LPVs by Catchpole et al. (1979) and the measurements by Fouqué et al. (1992), Guglielmo et al. (1993), Groenewegen et al. (1993), Whitelock et al. (1994), Fluks et al. (1994), Kerschbaum & Hron (1994), Kerschbaum (1995) and Kerschbaum et al. (1996). Infrared magnitudes are derived from the F₁₂ and F₂₅ fluxes measured at 12 and 25 micrometers respectively by the infrared astronomy satellite (IRAS). We use

$$% m_{12} = 3.63 - 2.5\times \log F_{12}$$ (1)

and

$$m_{25} = 2.07 -2.5\times \log F_{25},$$ (2)

as given in the IRAS-PSC catalog (vol. 1, Sect. VI.C.2). One should note that not all authors use this definition for the infrared magnitudes m₁₂ and m₂₅. The color index m₂₅-m₁₂ used by Van der Veen and Habing (1988), for instance, is higher than the one deduced from Eqs. (1) and (2) by 1.56 mag.

Among the ${\sim}900$ stars of our sample, the number of stars for which V, K and IRAS infrared magnitudes are available amounts to 882, 652 and 793, respectively, with 608 stars having both K and IRAS magnitudes.

Finally, variability and spectral types are taken from the GCVS.

   
2.2 Selection effects

The main selection bias in our sample comes from the HIPPARCOS magnitude limit V<12.5 mag (see Sect. 2.1). This selection is well determined and thus easy to take into account in the statistical analysis.

Figure 1: Distribution of the GCVS LPVs according to apparent visual magnitude at maximum luminosity and IRAS color index. Stars observed by HIPPARCOS are indicated.

The characteristics of LPVs cause another bias related to the magnitude limit of the sample. LPV stars are evolved red giants, often characterized by the formation of dust around them. The presence of a dusty circumstellar envelope affects the stellar spectrum by reducing their visible light. As a result, obscured LPVs are under-represented in our sample, because the HIPPARCOS selection was done on the basis of the visible magnitude. The importance of this bias can be estimated by comparing the number of stars included in the HIC with the number recorded in the GCVS. This comparison is shown in Fig. 1 as a function of the V magnitude m_Vand the color index m₂₅-m₁₂, where we consider all LPVs of the GCVS for which either the visual (m_V) or the photographic ($m_{\rm P}$) magnitude at maximum is given, and assuming $m_{\rm P} - m_V =1.8$ as the mean value for LPVs. All stars from the HIC, represented by filled circles in Fig. 1, are found to have m_V > 12.5, as expected (the very few exceptions being most probably due to the fact that the assumed $m_{\rm P} - m_V =1.8$ relation does not apply to them). Figure 1 also shows that the number of stars included in the HIC (relative to the number of stars recorded in the GCVS, represented by filled and open circles in Fig. 1) decreases with increasing circumstellar envelope thickness (i.e. decreasing m₂₅-m₁₂ index). This bias is further discussed in Sect. 5.2.3.

It must be noted that the GCVS itself is, of course, not exhaustive, and is certainly biased at the expense of the reddest stars. OH-IR stars, for example, are not well represented in the GCVS sample. For these reasons, a statistical method which can take into account all these biases is necessary for our analysis. This method is described in the next section.