Linear and non-linear models for large-amplitude radial pulsation in faint blue stars (BLAPs)

The recent discovery of large-amplitude pulsations in faint blue stars (BLAPs) provides both challenges for stellar pulsation theory and opportunities to explore the late evolution of low-mass stars. This paper explores the radial-mode stability of stars across parameter space occupied by BLAPs. Models are constructed for homogeneous stellar envelopes and are agnostic of evolution. Linear non-adiabatic models demonstrate the major requirement for pulsations to be enrichment of iron and nickel in the driving zone to a few times the solar abundance. There is no constraint on mass. Non-linear models demonstrate that BLAP pulsations will be of large amplitude and will show strong shocks at minimum radius. A variety of light-curve shapes are found across the BLAP instability strip, accounting for the variety observed. Linearised period relations are derived from the non-linear models. The phase of maximum luminosity relative to minimum radius is correlated with effective temperature ($T_{\rm eff}$), preceding for cool stars and following for hot stars, and split if close to minimum radius. In both linear and non-linear cases, most models pulsate in the fundamental mode (F). First-overtone (1H) pulsations are excited on the low luminosity blue side of the instability region and become more prevalent at higher mass. The period ratio $P_{\rm 1H}/P_{\rm F}=0.81$ contrasts with the classical Cepheid value (0.70 - 0.75). The transition from F to 1H mode pulsations follows a period-mass relation; the F-mode pulsators adjacent to the transition show a reverse shock. At high $T_{\rm eff}$ some non-linear models show unstable overtone modes up to 5H and multi-mode behaviour. The linear and non-linear analyses concur on the red-edge of the instability region, but the non-linear blue edge is hotter.