2 Mass luminosity relation

With the help of relations (6) and the OGLE data we therefore obtain a period, a luminosity and a $T_{\rm {ef f}}$ for each fundamental and for each overtone Cepheid. These quantities are sufficient to compute the masses with the help of a stellar model builder and linear pulsation code, since P₀=P₀(L, M, ${T_{\rm {ef f}} },$ X, Z) and $P_1=P_1(L, M, {T_{\rm {ef f}} }, X, Z)$.

For the computation of the SMC and LMC Cepheid models we have adopted the respective compositions X=0.726, Z=0.004 and X=0.716, Z=0.01. We have used OPAL opacities (Iglesias & Rogers 1996) merged with the low temperature ones of Alexander & Ferguson (1994). Turbulent convection has been treated as described in Yecko et al. (1998). The convective parameters were chosen as in Kolláth et al. (2001), although, the precise values of these parameters will have very little effect on the periods.

In Fig. 1 we present the M-L diagrams obtained from our Cepheid model calculations that use the observational constraints, A in the left panel, and B in the right panel. Fig. 2 displays the results for choice (C). The fundamental Cepheids are represented as dots and the overtone Cepheids as open circles. To guide the eye and for later reference we have also shown the M-Lrelations of Girardi et al. (2000) for the Cepheids on the second crossing of the instability strip.

Four features stand out immediately. First, the three choices give very similar M-L distributions, especially in slope and scatter, but choice (A) has a zero point that is in substantial disagreement with the evolutionary calculations. Second, the observations indicate a curved mass-luminosity relation. Third, the average M-L for the fundamental Cepheids agrees with that of the overtones. Fourth, there is a huge scatter whose nature needs to be addressed, because the Cepheids form a homogeneous group, and one would expect all of them to fall on a very tight M-L line.