6 Near-infared data

The near-infrared data from the DENIS survey allow to characterize the variables of our sample in more detail concerning their luminosity and chemical composition. Figure 9 shows the $K_{\rm S}/(J-K_{\rm S})$ diagram for the AGAPEROS variables. One can clearly see that the majority of the sources are located above the tip of the Red Giant Branch (hereafter RGB-tip) which is for the LMC about 12.0 mag in $K_{\rm S}$ (Cioni et al. 2000a). We find regular and semiregular variables which are below the RGB-tip. These objects have rather short periods (<100 days) and could be AGB stars in the early evolutionary phase (early-AGB phase) or variable stars on the red giant branch.

Carbon-rich objects are characterized by their red (J-K) and (I-J) colour compared to the oxygen-rich sequence (see Cioni et al. 1999). However, as noted by Loup et al. (2002) the colour-colour diagram is just a statistical tool to distinguish between oxygen-rich and carbon-rich objects. Figure 10 shows the $(I-J)_{\rm0}$ vs. $(J-K)_{\rm0}$ diagram. Obviously, the ratio of regular to semiregular variables is smaller for the oxygen-rich stars than for the carbon-rich objects. This suggests that the majority of the semiregular variables are less massive than Miras which prevents them from becoming carbon stars.

We do not find any significant difference in colours or luminosites between SRVs with one single period and SRVs with multiple periods.

Figure 9: Colour-magnitude diagram for DENIS/AGAPEROS stars. Regular variables are indicated by open squares, semiregular variables by filled triangles. The horizontal line indicates the tip of the red giant branch (RGB).

Figure 10: DENIS colour-colour diagram for AGAPEROS variables. The box indicates the approximate location of carbon-rich objects (see Loup et al. 2002). Regular variables and semiregular variables are indicated by open squares and filled triangles, respectively.

Figure 11: Log P vs. (I-J) relation for MACHO variables in Baade's window (Schultheis & Glass 2001) compared to AGAPEROS variables in the LMC. The open squares on the left panel indicate the SRVS, while the filled triangles the Mira variables. On the right panel, same symbols as in Fig. 10. The periods are given in days.

6.1 Colour-period diagrams

For the LMC bar, it is obvious from Fig. 11 that the AGAPEROS variables follow a tight $\log P$ vs. I-J relation. It is important to emphasize that the I magnitudes of DENIS correspond to a single epoch measurement and thus the $\log P$ vs. I-J diagram is affected by the scatter due to the amplitude variation of each source.

Relying on MACHO data in the Galactic Bulge, Schultheis & Glass (2001) demonstrated that semiregular variables in the Galactic Bulge show a noticeable scatter in I-J (3-4 mag) along the $\log P$ vs. I-J relation. The most significant difference between the Galactic Bulge and the LMC is the smaller range in I-J for the LMC ($\sim$2 mag) than for the Bulge ($\sim$4 mag). (see Fig. 11)

The I band for M stars is mostly affected by the strong TiO and VO molecular absorption (Turnshek et al. 1985; Lancon & Wood 2000). Schultheis et al. (1999) showed that lower metallicity is correlated with weaker TiO band intensities, corresponding to bluer I-J colours. The large scatter and the wide I-J range in the Galactic Bulge sample compared to the LMC might be explained by the wide spread in metallicity compared to the Magellanic Clouds. However, the difference in the I-J range between the Galactic Bulge ( $1 < (I-J)_{\rm0} < 5$) and the LMC ( $1 < (I-J)_{\rm0} < 3$) seems rather large. A more detailed quantitative analysis, using realistic model atmospheres of AGB stars (including metallic lines), is necessary to fully understand this systematic difference in the I-J colour between the Galactic Bulge and the LMC.

Figure 12 displays the J-K colours of the AGAPEROS variables as a function of their period. The majority of the SRVs appear to follow a different period-colour relation with a slope flatter than the regular variables. For comparison, we indicated in Fig. 12 the averaged colours of oxygen-rich Miras for the SgrI field (Glass et al. 1995). The majority of our long-period Miras ( $\log P > 250^{\rm d}$) follow the location of the oxygen-rich Miras in SgrI. The carbon rich objects (J-K > 1.6) seem to form a parallel sequence to the oxygen-rich Miras, while the long-period SRVs ( $P > 300^{\rm d}$) do show clearly another period-colour relation. These stars are located on the sequence D in Wood's diagram (see Wood et al. 1999 and discussion below) and are SRVs with multiple periods. A few long-period Miras also follow this sequence. However, the scatter in this diagram increases for $\log P > 2.3$ due to the contribution of the circumstellar dust shell arising from mass loss. Schultheis et al. (1999) and Schultheis & Glass (2001) obtain similar results for semiregular variables in the Galactic Bulge (see their Fig. 8).

6.2 K_S vs. log P diagram

In the Large Magellanic Cloud, the Miras and the SRVs seem to form distinct parallel sequences C,B,A which have been identified by Wood (2000) as pulsators in the fundamental, first and the next two higher overtones, respectively. Wood et al. (1999) showed by comparison of observed periods, luminosities and period ratios with theoretical models, that Miras are radial fundamental mode pulsators, while semiregular variables can be pulsating in the 1st, 2nd or 3rd overtone, or even the fundamental mode. The pulsation mode derived by Whitelock & Feast (2000) from diameter measurements of Miras in the Milky Way suggests first overtone pulsation for Miras. However, observations of radial velocity variations of Miras (e.g. Hinkle et al. 1982) clearly favour fundamental mode pulsation (Bessell et al. 1996).

Figure 12: $\log P$ vs. (J-K) relation for AGAPEROS variables in the LMC. The line indicates the average colours of SgrI Miras for various period groups (Glass et al. 1995). The symbols are the same as in Fig. 10.

In Fig. 13, we distinguish between semiregular variables with one period and those having a second or even third pulsational period. The location of our regular variables is consistent with the PL-relation from Feast et al. (1989) and Wood's sequence C corresponding to fundamental mode pulsation. However, a few regular variables are also found to be located on sequence B and A (first and second overtones according to Wood 2000). The majority of the SRVs follow Wood's sequence B although the scatter is rather large ($\sim$0.5 mag in $K_{\rm S}$ at a given period). The SRVs situated on sequence A show very low amplitudes (<0.5 mag in $R_{\rm EROS}$) and typically no secondary periods. While Cioni et al. (2001) found no objects on sequence A, we could clearly confirm the existence of this PL-sequence. On sequence B and C, we find both single periodic and multiperiodic objects. The occurrence of single or multiple periodic behaviour does not depend on the luminosity.

Several data points also mark sequence D of Wood (2000). The large scatter in this part of the K-$\log P$-diagram is due to the limited time window of our data set. We are therefore able to reproduce all four sequences found in the MACHO data. The PL-relation for SRVs found by Bedding & Zijlstra (1998) from local objects could not be confirmed with our data (see below).

Figure 13: $K_{\rm S}$ vs. $\log P$ diagram for AGAPEROS variables. The dashed line is the relationship suggested for local SRVs by Bedding & Zijlstra (1998). The dotted lines labelled A, B and C are eye fits to the sequence by Wood (2000). We use only the primary periods. Open squares show regular variables with one single period while regular variables with a second period are shown as open triangles. Semiregular variables with one single period are shown as filled squares while those with their second period are indicated as filled triangles. Sequence D of Wood (2000) lies on the right-hand side.