Parametric models of core-helium-burning stars: structural glitches near the core

Understanding the internal structure of core-helium-burning (CHeB) stars is essential for evaluating transport processes in regions where nuclear reactions occur, developing accurate models of stellar populations, and assessing nucleosynthesis processes that impact the chemical evolution of galaxies. Until recently, detailed insights into the innermost layers of these stars were limited. However, advancements in asteroseismic observations have allowed for exploration of their stratification more thoroughly. Despite this progress, in CHeB stars the seismic signatures associated with structural variations at the boundary between the convective and radiative core, as well as the chemical composition gradients within the radiative core, have been relatively underexplored. This paper aims to fill that gap by investigating how these gradients influence the oscillation modes of low-mass CHeB stars. Specifically, we focus on mixed dipole modes and uncoupled g-modes as effective probes of stellar interiors. Using semi-analytical models calibrated with the evolutionary codes BaSTI-IAC, CLES, and MESA, we explored the influence of density discontinuities and their associated structural glitches on the period spacings of these oscillation modes. These codes were chosen for their distinct physical prescriptions, and they allowed us to identify common relevant features for calibration purposes. Moreover, this approach enabled us to control the type of glitch introduced while maintaining a realistic representation of the star. As expected from previous studies, our results indicate that these glitches manifest as distinct periodic components in the period spacings, which can be used to infer the position and amplitude of the structural variations inside CHeB stars. Furthermore, we compared models with smooth transitions to those with sharp discontinuities, highlighting the differences in period spacing and mode trapping, which permitted us to infer the sharpness of the glitches. Additionally, we conducted simulations based on four-year-long Kepler observations. These simulations demonstrate that our models predict oscillation frequencies closely resembling the observed data. Ultimately, our models enable realistic predictions of how each sharp structural variation impacts the observed power spectral density. This alignment not only validates our theoretical approach but also suggests promising directions for interpreting glitch signatures in high-quality asteroseismic data.