tokens: low-order radial modes may be simultaneously excited (their fig.3) andbeat pulsation is, thus, possible. The linear pulsation models disprove this scenario as well. We have computed a grid of models with masses in the 0.20.4M range, with luminosities in the 2070L range and metallicity range the same as considered in Fig. 10 (other model parameters are the same as in Smolec etal. 2016 ). We note that little is known about the expected physical parameters of BEPs, as only one object has been observed so far (see, however, Karczmarek etal. 2017 ). The range of the physical parameters given above is motivated by the model study by Smolec etal. ( 2013 ) and assumes that model periods are not far from those observed in RR Lyr stars. The models assume an homogeneous envelope with chemical composition the same as in RR Lyr-type models. For the 0.2M and 0.3M models, the periods of the unstable radial modes are significantly longer than those observed for our stars. The period ratios for the 0.4M models are plotted in Fig. 11 . The models have longer periods and higher period ratios, and are far from the region in which double-periodic stars reside. Clearly, the discussed stars are not fundamental and first-overtone double-mode radial pulsators, at least, not if we assume their physical parameters are close to those expected for RR Lyr stars or BEPs (which mimic RR Lyr stars). Other combinations of radial modes also do not fit the discussed group. Figure 11. As Fig. 10 , but for BEP models of 0.4M . The different colours correspond to different metallicities, as indicated in the top panel of Fig. 10 . We note that simple triangular light curve shape is characteristic for fundamental-mode HADS stars. The Fourier parameters of these stars are similar as well (see fig.8 and figs47 in Poretti 2001 , note that the cosine convention is adopted in that paper). The periods of these stars are typically below 0.2d, however, while for our stars they are longer than 0.28d. The period ratios in the radial multi-mode HADS stars are also vastly different, see e.g. fig.10 in Pietrukowicz etal. ( 2013 ). Assuming that the dominant variability does correspond to the radial fundamental mode (the large amplitude and non-linear light curve shape make this hypothesis most plausible), the additional variability may correspond to the non-radial pulsation mode. Low-degree modes may be excited in RR Lyr models (Van Hoolst, Dziembowski Kawaler 1998 ; Dziembowski Cassisi 1999 ), preferentially in the vicinity of the radial modes. Although the frequency spectrum of such modes is very dense, their growth rates do display a local maximum close to the position of the radial modes. In particular, for 1 modes, the growth rates approach that of the radial first-overtone mode and their frequency is higher than the radial first-overtone frequency [see, e.g. fig.1 in Van Hoolst etal. ( 1998 ) or fig.1 in Dziembowski ( 2016 )]. This would lead to period ratios a bit lower than observed for
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O