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Astron. Astrophys. 337, L29-L33 (1998)

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4. The nonlinear double mode solution

In Table 1 the parameters of the nonlinear double mode solution are summarised. A comparison with observed period and amplitude ratios of both, globular clusters and the four known double mode RR Lyrae stars in the Galactic field is given in Fig. 4. Concerning the amplitude ratios it is important to note that we compare theoretical bolometric ratios with observed ratios meassured in different photometric systems. In order to estimate the deviations we calculate a detailed frequency-dependent radiative transfer by solving the static radiative transfer equation on the dynamical structure of the model. The radiative opacities are taken from Kurucz (1993) and the computed amplitude ratios for the Johnson UBV system are given in Table 2. It turns out that the relative deviations are below 5% indicating that in contrast to the amplitudes the amplitude ratios are only weakely dependent on the photometric system.


[TABLE]

Table 1. Parameters of the double mode solution at 6820 K. All quantities are mean values over the whole computation and the second line gives the corresponding standard deviations.



[TABLE]

Table 2. Comparison of the bolometric amplitude ratio with U, B and V ratios calculated by a detailed radiative transfer. The second line refers to the relative deviations with respect to the bolometric values. In order to provide a simple consistency check for the radiative transfer the last column corresponds to the bolometric amplitude ratio calculated by integration over the whole frequency range.


Fig. 3A shows the bolometric light curve of the double mode model. The bolometric amplitude corresponds to [FORMULA] and the luminosity variation over consecutive cycles presents the typical beat shape. The light curves phased according to the fundamental and first overtone periods are depicted in Fig. 3D and 3E, respectively. Fig. 3B refers to the fundamental mode light curve after removal of the first overtone and Fig. 3C to the same but for the first overtone, again phased according to the corresponding mode. We want to emphasize the bump close to the maximum light in Fig. 3C and E which is common both in observed and theoretical RRc light curves (e.g. Lub 1977, Feuchtinger & Dorfi 1994, Bono et al. 1997). The Fourier analysis of the light curve is listed in Table 3 and shows that only the fundamental and first overtone frequencies and corresponding linear combinations are present.

[FIGURE] Fig. 3. Bolometric lightcurves of the nonlinear RR Lyrae double mode model. Each point depicts one time level of the numerical computation. See text for details.

[FIGURE] Fig. 4. Period a and amplitude b ratios of the double mode model in comparison with observed double mode stars in the galactic field (from Garcia-Melendo & Clement, 1997), M15 (from Cox et al. 1983), M68 (Walker 1994, Clement et al. 1993) and IC 4499 (Walker & Nemec, 1996).


[TABLE]

Table 3. Fourier analysis (first 6 frequencies) of the light curve given in Fig. 3A


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© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998
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