The oscillation properties of the Blue Large Amplitude Pulsators (BLAPs): relative change rate of periods, excitations, and period relations

Abstract: \textbf{B}lue \textbf{L}arge \textbf{A}mplitude \textbf{P}ulsators (BLAPs) are a type of variable star that has been identified relatively recently. They are characterized by their large amplitude, high gravity, and long periods (2-75 minutes). Some BLAPs exhibit a rich helium abundance on their surfaces, while some of the others show rich hydrogen atmospheres. Up to date, both the mode identification and formation pathways of BLAPs remain subjects of ongoing debate. In this work, we gave an non-adiabatic pulsation analyses for low-order radial and non-radial dipole modes on a theoretical model grid to explore the characterist ics of BLAPs. The effects of element diffusion and radiative levitation are not taken into account our theoretical models. This because that these processes could lead to discrepancies in surface element abundance of the sdB or BLAP stars between theoretical models and observations. Based on the theoretical model grid, our analyses revealed that the radial fundamental modes align well with various observed properties of BLAPs, including the pulsation instability, the position of the excitable models on the HR diagram, surface element compositions, period ranges, and period changes. Our theoretical models also predicted a period-gravity ($\log g$) relation with a narrow distribution, while the observations exhibit a broader range. Furthermore, our findings indicate that the excitation of pulsation in BLAPs is primarily influenced by metal abundance. The thickness of the outer rich hydrogen envelope and the ratio of helium to hydrogen on the surface almost do not affect the pulsation instability.