[Paper Review] Asteroseismology of red giants

J. Christensen‐Dalsgaard|arXiv (Cornell University)|Jun 29, 2011

Stellar, planetary, and galactic studies5 references7 citations

TL;DR

This paper presents a theoretical framework for asteroseismology of red giants using gravity-mode period spacing, showing that the presence of central helium fusion causes a distinct jump in period spacing due to changes in the buoyancy frequency and core structure. The analysis explains observed differences between red-giant branch and red-clump stars via modeling of buoyancy frequency profiles and adiabatic pulsation codes, enabling core diagnostics from space-based data.

ABSTRACT

Red-giant stars are emerging as one of the most interesting areas of space asteroseismology. Even a relatively basic analysis leads to the determination of the global parameters of the stars, such as their mass and radius, and the very extensive space-based data now available for a large number of stars allow detailed investigation of the deep interiors of red giants, including distinguishing between stars that do and do not have helium fusion in the core, on the basis of periods of gravity waves partially trapped in the core. Here I review the theoretical background for these new developments and provide a simple explanation for the effect on the period spacing of central helium fusion.

Motivation & Objective

• To explain the observed difference in period spacing between red-giant branch and red-clump stars using theoretical modeling of stellar interiors.
• To investigate how central helium fusion alters the buoyancy frequency profile and thus the period spacing of gravity modes in red giants.
• To demonstrate that period spacing can serve as a diagnostic tool for core properties, including convective core formation and composition changes during helium burning.
• To provide a theoretical basis for interpreting space-based asteroseismic data from CoRoT and Kepler missions on red giants.
• To clarify the role of adiabatic pulsation codes and model resolution in capturing core oscillation features in evolved stars.

Proposed method

• Modeling red-giant evolution using the Aarhus Stellar Evolution Code (ASTEC) with standard equations of state, opacities, and nuclear reaction rates.
• Computing adiabatic oscillation frequencies with the Aarhus adiabatic pulsation code ADIPLS, using a refined radial mesh to resolve core structure.
• Analyzing period spacing ΔΠ₁ via the integral of 1/N(r) over log r, where N(r) is the buoyancy frequency.
• Comparing models with and without central helium burning to isolate the effect of core convection and composition changes on period spacing.
• Using the relation ΔΠ₁ ≈ 2π ∫ (1/N(r)) d(log r) to link observable period spacing to core structure and buoyancy frequency profiles.
• Visualizing buoyancy frequency evolution across evolutionary tracks to explain observed jumps in period spacing during helium ignition and core burning.

Experimental results

Research questions

• RQ1 How does central helium fusion affect the period spacing of gravity modes in red giants?
• RQ2 Why do red-giant branch stars and red-clump stars exhibit distinct period spacing values in asteroseismic data?
• RQ3 What role does the buoyancy frequency profile play in determining the period spacing of g modes in evolved stars?
• RQ4 Can period spacing be used as a reliable diagnostic for core properties such as convection and composition in red giants?
• RQ5 How do changes in core structure during helium ignition and burning alter the observable asteroseismic signatures?

Key findings

• The period spacing ΔΠ₁ increases significantly when a red giant transitions from hydrogen-shell burning to central helium burning, due to the formation of a convective core that suppresses the buoyancy frequency integral.
• The jump in ΔΠ₁ during helium ignition is linked to a structural change in the core, including the onset of convection and composition changes, as shown in the 2.5 M☉ evolution track.
• The period spacing remains relatively stable during the red-giant branch phase, with only minor variations due to core contraction and electron degeneracy effects.
• The observed difference in period spacing between red-giant branch and red-clump stars is primarily caused by the presence of a convective core in helium-burning stars, which reduces the effective integral in the period spacing formula.
• The buoyancy frequency profile, particularly in the core, is the dominant factor controlling period spacing, and its variation provides a sensitive probe of internal structure.
• The model results explain the key observational findings of Bedding et al. (2011), showing that period spacing can distinguish between stars with and without central helium fusion.