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Pulsation models for the 0.26M_sun star mimicking RR Lyrae pulsator. Model survey for the new class of variable stars

We present non-linear hydrodynamic pulsation models for OGLE-BLG-RRLYR-02792 - a 0.26M_sun pulsator, component of the eclipsing binary system, analysed recently by Pietrzynski et al. The star's light and radial velocity curves mimic that of classical RR Lyrae stars, except for the bump in the middle of the ascending branch of the radial velocity curve. We show that the bump is caused by the 2:1 resonance between the fundamental mode and the second overtone - the same mechanism that causes the Hertzsprung bump progression in classical Cepheids. The models allow to constrain the parameters of the star, in particular to estimate its absolute luminosity (approx 33L_sun) and effective temperature (approx 6970K, close to the blue edge of the instability strip). We conduct a model survey for the new class of low mass pulsators similar to OGLE-BLG-RRLYR-02792 - products of evolution in the binary systems. We compute a grid of models with masses corresponding to half (and less) of the typical mass of RR Lyrae variable, 0.20M_sun<=M<=0.30M_sun, and discuss the properties of the resulting light and radial velocity curves. Resonant bump progression is clear and may be used to distinguish such stars from classical RR Lyrae stars. We present the Fourier decomposition parameters for the modelled light and radial velocity curves. The expected values of the phi_31 Fourier phase for the light curves differ significantly from that observed in RR Lyrae stars, which is another discriminant of the new class.