Hydrodynamic models for pulsating BL Herculis-type variables

Astronomy and Astrophysics – Astronomy

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A grid of hydrodynamic limit-cycle models is computed for pulsating BL Her variables with masses M = 0.55, 0.6, 0.65 M_solar, luminosities 106 <= Lbol /L_solar <= 169, and effective temperatures 5500 T_eff <= 7000 K. The OP tables are used to compute the opacity kappa R for the hydrogen and helium mass fractions X = 0.7 and Y = 0.299. Irrespective of the stellar mass, the pulsation instability in the first overtone is typical of stars with pulsation periods II < 1 day, while the radial pulsations for II > 1 day are attributable to the instability of the fundamental mode. Approximation formulas are derived which relate the pulsation constant Q to the mass-to-radius ratio (M/R) of the star. It is shown that alternating pulsations with variable amplitude may arise from the 2 II_0 = 3 II_1 resonance between the fundamental mode and the first overtone at certain mass-to-radius ratios. The pulsations of these stars are also characterized by good repetition of the pulsation motions, but only in an interval that cov- ers two cycles of the fundamental mode. The secondary bump, which is observed in the light and radial-velocity curves of BL Her stars with periods from 1.3 to 3 days, is associated with the pressure wave generated in the region of partial ionization of HeII at maximum compression of the stellar envelope.

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