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

Understanding the internal structure of core helium burning (CHeB) stars is crucial for evaluating transport processes in nuclear-burning regions, constructing accurate stellar population models, and assessing nucleosynthesis processes that impact the chemical evolution of galaxies. While asteroseismic observations have recently enabled detailed probing of CHeB star interiors, seismic signatures related to structural variations at the boundary between the convective and radiative core, and chemical composition gradients within the radiative core remain underexplored. This paper investigates how such gradients affect the oscillation modes of low-mass CHeB stars, focusing on mixed dipole modes and uncoupled g-modes as diagnostic tools. Using semi-analytical models calibrated with the evolutionary codes $\texttt{BaSTI-IAC}$,$ \texttt{CLES}$, and $\texttt{MESA}$, we examine the impact of density discontinuities and associated structural glitches on mode period spacings. These codes span diverse physical prescriptions, allowing us to isolate robust features relevant for calibration. Our approach enables controlled glitch insertion while preserving a realistic representation of the star. Consistent with prior works, we find that structural glitches introduce periodic components in the period spacings, providing constraints on the location and amplitude of interior variations. We compare models with smooth and sharp transitions, demonstrating how glitch sharpness affects period spacing and mode trapping. Simulations based on four-year $\textit{Kepler}$ data show that our models yield oscillation frequencies closely matching observations. Ultimately, our results offer realistic predictions of how specific structural features affect the power spectral density, validating our theoretical framework and guiding future efforts to interpret glitch signatures in high-precision asteroseismic data.