3 Classification of the variables

Classically, three types of variable red giants have been defined (General Catalogue of Variable Stars, GCVS, Kholopov et al. 1985-88): Mira-type variables show periodic large amplitude variations with time scales typically of the order of 200 to 500 days. Semiregular variables (SRVs) show a less regular behaviour and a smaller amplitude. A typical time scale of the variation can be found, but the light curve shows phases of irregularity as well. The GCVS has introduced a limiting amplitude of 2.5 mag to separate Miras and SRVs. While even within the GCVS this rule has not been strictly applied (see e.g. the SRV W Hya), several investigators used this simple criterion for classification (e.g. Alard et al. 2001; Cioni et al. 2001). The artificial nature of this division has been criticized already e.g. by Kerschbaum (1993). The third group of variables are the irregular variables. It is still not clear if such stars really exist or if these objects are simply not observed well enough to detect the same amount of periodicity as in the SRVs (e.g. Lebzelter et al. 1995).

In this work, we used a different approach to classify the light curves of the red giants in our sample. The classic classification system depends on whether a more-or-less constant period can be found and also depends on an arbitrary amplitude limit. Here we adopt a new scheme which is based on how well the light curve can be described by one or two periods only and where amplitude plays no role. In this way we are able to separate the two effects amplitude and regularity.

We based the classification on the regularity of the light curve on a visual comparison of the light change with a combination of up to three sine curves. To derive the periods, a Fourier analysis of the light curves (based on the program Period98 by Sperl 1998) has been applied. Semiregular and irregular light changes result in a large number of peaks of similar strength in the Fourier spectrum (Lebzelter 1999, see below). Therefore the periods used for the fit have been selected from peaks in the periodogram by visual inspection. The amplitudes of the peaks were the starting point for the selection of the periods. Naturally, this selection is influenced by aliases. Figure 2 shows the typical spectral window of our data that has been used to identify spurious peaks. The selected periods were always cross checked by a visual comparison with the light curve. For unclear cases a second Fourier analysis was made with the primary period subtracted.

As a first approach to this large amount of light curve data we made no attempt to fit every detail of the light curves but identified the major period(s) to roughly resemble the overall light change. A more detailed fitting, as it was done by e.g. Kerschbaum et al. (2001) for a small number of SRVs in the solar neighborhood, is planned. Finally, we stress that the total available baseline of the data set did not allow to derive periodicities on time scales longer than 900 days. The classification is based on three years of observation and represents the behaviour of each object over the 900-days window. Stars classified as irregular may show some periodicity on a longer time scale or during a different time interval. The amplitudes were estimated visually from the lightcurve.

We classified the light curves on the regularity and type of their light change into four groups:

• Regular: a constant cycle length is observed for the available measurements. Some of these objects show some amplitude variations or bumps in their light curves. This group includes also stars which show a second period, if the two periods allow a very good fit of the light curve. While this group will include almost all objects that classically would have been classified as Miras, possible small amplitude regular variables will be found in this class as well. We therefore did not use the name "Miras'' for this group. The only regular pulsators we did not include here were cepheids and obvious binaries, which have been classified as Other.
• Semiregular: the cycle length is variable, but some kind of periodicity is visible. The stars show up to three strong peaks in the Fourier spectrum. In some cases the light change can be fitted rather well with three or four periods.
• Irregular: these stars do not show any significant periodicity in their light change. Their light change occurs on time scales typical for AGB stars (i.e. a few 10 to a few 100 days). Typically, the Fourier spectrum shows a large number of peaks with similar strength.
• Other: this group includes stars with a large fraction of bad data points, stars that turned out to be constant (misidentification due to some erroneous data points), and stars with a luminosity variation atypical for long period variables (including a number of binaries). A large fraction of these objects have also no DENIS data.

Figure 1 shows a sample of regular, semiregular and irregular light curves. Note that our classification does not take into account the amplitude of the variation as in the GCVS classification. The examples were selected to represent the different expressions of variability found in the three groups. Among the regular variables, we included examples of amplitude variations (top left in Fig. 1), variables with two periods (top middle) and classical Mira variables (top right).

Naturally, this classification remains somewhat subjective. However, we made an attempt to check the homogeneity of our classification by using the Fourier spectra of the light curves. In Fig. 3, we plot the amplitude ratio of the strongest and the second strongest peak against the ratio of the second and the fifth strongest peak. The advantage of our sample is that all light curves have a similar sampling and therefore a similar spectral window. Examples for Fourier spectra and a spectral window are given in Figs. 4 and 2, respectively. A small number of stars has been excluded from this plot as their time coverage is not as good as for the majority of the sample.

Figure 2: Spectral window for the light curves used in this paper.

Figure 3: Ratio of the two strongest peaks of the Fourier amplitude spectrum versus the ratio of the second and fifth strongest peak. Open circles denote regular variables, filled boxes indicate semiregular variables and open triangles mark irregular variables. A few objects found at even higher ratios are not included in the plot.

Figure 4: Typical Fourier amplitude spectra for a regular, a semiregular and an irregular variable, respectively.

As mentioned above, a semiregular or irregular light curve typically results in a number of peaks of similar strength in the Fourier spectrum. Stars classified as regular have only one or two strong peaks in their Fourier spectrum. They should therefore be found on the right-hand side and the top side of Fig. 3. Stars with a single period are on the right, stars with a second period in the upper left region of the plot. Note that there is no correction for aliases in this approach. From the spectral window (Fig. 2) one would expect to find stars with a single period at a ratio a1/a2 of about 2.

For the regular variables the fifth strongest peak is typically already at the noise level and was used as a reference point. Note that we did not use more than three periods for each object in the following analysis. On the other hand, irregular variables should be found in the lower left corner of the plot. Semiregular stars are expected in between. Figure 3 shows this classification indicated by different symbols.

We observe that our classification criteria is coherent within our sample. However, for an individual object, Fig. 3 is not usable for classification as the borders between the three classes are not well defined.

For each star classified as regular, semiregular or irregular a typical amplitude of the light variation was determined. In the case of semiregular and irregular variables the light amplitude can change dramatically. In these cases, we used a mean value of the variation. As no standard Johnson filters have been used a direct comparison of the amplitude values found here and those given in the GCVS or the MACHO catalogue is not possible.