Detailed theoretical analysis of core Helium-burning stars: Mixed mode patterns I. Impact of the He-flash discontinuity and of induced semi-convection

Abstract

Space missions like CoRoT, Kepler, and TESS have made asteroseismology a powerful probe of stellar interiors. Red giants are key targets thanks to their rich mixed-mode oscillation spectra, which reveal properties of both core and envelope. However, current models of core helium-burning red giants still fail to fully reproduce observed oscillation patterns, largely due to uncertainties in mixing processes such as overshooting and semi-convection. This motivates the need for better seismic constraints to refine stellar models. We investigate how internal structural features shape asteroseismic signatures in core helium-burning stars, focusing on the links between seismic properties and internal chemical profiles. Using an updated version of the Liege stellar evolution code and its adiabatic oscillation code, we compute and analyse mixed-mode patterns for a range of stellar models. Our results show that sharp chemical gradients and central overshooting strongly influence the mixed-mode spectra. Changes in overshooting modify the extent of the semi-convective region, altering the local Brunt-Vaisala frequency and thus the observed period spacing. Variations in overshooting are compensated by shifts in semi-convective layers, keeping the total mixed-core size nearly constant across models. As a result, stellar evolution is only mildly affected, while the seismic signatures, especially the Brunt-Vaisala frequency profile, are highly sensitive to these internal adjustments.

12 pages, 15 figures. Version of the manuscript before the language editor

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