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

TL;DR

The paper addresses the challenge of interpreting mixed-mode spectra in core helium-burning stars given uncertain core mixing by using updated Liège codes to model grids with $m_{He}=0.50\,M_\odot$, varying $XCO$ and $\alpha_{ov}$ at solar metallicity. It demonstrates that sharp chemical gradients and induced semi-convection markedly modify the Brunt–Väisälä frequency and the asymptotic period spacing $\Delta\Pi$, with overshoot changes largely compensated by semi-convective adjustments that keep the mixed-core size roughly constant. Consequently, evolutionary changes are modest, but seismic signatures are highly sensitive to these internal structure variations, highlighting the diagnostic power of asteroseismology for constraining core mixing. The findings offer a pathway to calibrate mixing processes near the convective core using detailed seismic constraints and point to future work on glitch smoothing, 3D mixing effects, and application to Kepler/TESS data for Galactic archaeology.

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.

Figures (15)

• Figure 1: Gradients profile as function of the mass fraction for a one solar mass CHeB star at solar metallicity and Y$_c$ = 0.90. The helium profile is put in parallel (black). The convective zone is in yellow, the overshooting layer in green and the sharp variation left by the He-flash in grey with XCO = 5%. The radiative gradient $\nabla_{rad}$ is in red and the adiabatic gradient $\nabla_{ad}$ in blue. The real gradient $\nabla$ is defined as following, $\nabla = \nabla_{ad}$ in the COS zone and $\nabla = \nabla_{rad}$ in the radiative zone. We focus on the central part of the star for showing purpose.
• Figure 2: Top panel: evolutionary track in the Hertzsprung–Russell diagram of the sequence of models from 1 M$_\odot$ to 1.5 M$_\odot$ stellar masses at fixed He-core mass. The markers indicate the state of central helium abundance studied Y$_c$ = 0.90,Y$_c$ = 0.40 and Y$_c$ = 0.10. Bottom panel: central temperature as a function of the central density in logarithmic scale of the corresponding set of masses.
• Figure 3: Top panel: diagram $\Delta \nu-\Delta \Pi$ of three models of different stellar mass. Each point correspond to a stage Y$_c$ in the evolution on the horizontal branch. The markers indicate the state of central helium abundance Y$_c$ = 0.90 ,Y$_c$ = 0.40, Y$_c$ = 0.10 and the appearance of the semi-convective layer. Bottom panel: diagram $\Delta \nu-\Delta \Pi$ of two models of different overshooting parameter $\alpha_{ov}$.
• Figure 4: Comparison of overshooting parameters $\alpha_{ov} = 0.50$ (top panel) and $\alpha_{ov} = 0.15$ (bottom panel) for 1 M$_\odot$ through the gradients and helium profiles as a function of the mass fraction at same age, in parallel to the helium profile (black). The convective zone is in yellow, the overshooting layer in green, the semi-convective zone in blue and the sharp variation left by the He-flash in grey. The radiative gradient $\nabla_{rad}$ is in red and the adiabatic gradient $\nabla_{ad}$ in blue. The real gradient $\nabla$ is defined as following, $\nabla = \nabla_{ad}$ in the COS zone and $\nabla = \nabla_{rad}$ in the radiative zone.
• Figure 5: Brunt-Väisälä frequency profile of two early models (Y$_c$ = 0.90) for 1 M$_\odot$ with different value of overshooting parameter, $\alpha_{ov}$ = 0.50 (blue) and $\alpha_{ov}$ = 0.15 (red). The vertical line indicates the fully mixed core boundary of each model.