Testing Red Clump Models with the Asteroseismic Binary KIC 10841730

TL;DR

This paper presents the first detailed asteroseismic study of a binary where one star is a red clump (RC) and the other is a red giant branch (RGB) star, KIC 10841730, using a ~3000-day period to test RC modelling against the RGB benchmark. By modelling individual p-mode frequencies (via pi modes) and employing surface-correction schemes, the authors explore whether RC models can reproduce observed frequencies while honoring binary constraints on age and composition. They find that standard RC models struggle to fit the RC frequencies, but allowing an epsilon_p-like offset in the surface correction yields RC solutions with ages and masses broadly compatible with the RGB companion, albeit with caveats about the physical origin of the offset. The results imply that RC modelling uncertainties affect both g-mode period spacings and p-mode frequencies, emphasizing the value of asteroseismic binaries for validating and refining RC theories and the need for improved treatment of convective-core boundaries and surface effects. The study also highlights that the observed RC $\Delta\Pi_1$ can be smaller than model predictions, challenging simple overshoot prescriptions as a universal solution. Overall, KIC 10841730 demonstrates the potential of combining Delta Pi diagnostics with phase-offset diagnostics to constrain RC models and underlines the importance of refining RC theory for accurate stellar ages and masses in field and cluster populations.

Abstract

Binaries in which both stars are pulsating are rare but extremely valuable. We present the first study of an asteroseismic binary system consisting of a core helium-burning red clump (RC) star and a red giant branch (RGB) star. The Kepler target KIC 10841730 is a wide binary (period $2917 \pm 8$ d) that provides ideal conditions to test the accuracy of RC models. While prior studies of RC stars have revealed discrepancies in modelling the period spacings of mixed modes, other model parameters remain largely untested. We perform a detailed modelling analysis using individual mode frequencies and cover a large parameter space in mass, metallicity, He-abundance, mixing length, overshooting, and mass-loss, and we also explore different methods to correct for surface effects. We find two possible results for the red clump models. One solution requires introducing an unexpected offset of the phase shift in the red clump model, yielding an age consistent with the companion star and current masses of $1.01 \pm 0.06$ and $1.08 \pm 0.06$ M$_\odot$ for the RC and RGB star, respectively. Alternatively, we find that excluding the identification of two questionable radial modes resolves the phase-shift offset issue but results in a higher mass and thus a much younger age for the red clump star, contradicting the age obtained from its companion. We conclude that uncertainties in red clump models affect not only the g-mode period spacings but also the properties of the p modes. We show the power of asteroseismic binaries in validating and constraining stellar models and highlight the need for refining red-clump models.

Figures (13)

• Figure 1: Normalised light curve of KIC 10841730 for all available quarters Top: Uncorrected light curve with a zoom on the last dip generated by the overestimated smear correction. The red rectangle marks the zoomed-in area. Bottom: High-pass filtered light curve after we removed the dips and outliers.
• Figure 2: Consequences of the overestimated smear correction. Left: Cutout of the Kepler Full Frame Image (FFI) displaying KIC 10841730, marked by the red circle at the bottom, and the bright long-period variable V538 Lyr in the same pixel columns, which are highlighted by the thin red lines. Right: Normalised Kepler Simple Aperture Photometry (SAP) light curve for quarter 7 of V538 Lyr (top) and KIC 10841730 (bottom).
• Figure 3: Radial velocities of the absorption line centres of KIC 10841730. The green triangles and pink circles correspond to the points obtained with the HERMES and HDS spectra, respectively. The black line shows the Keplerian fit. For several measurements, the error bars are smaller than the symbol size and therefore not visible.
• Figure 4: Combined spectrum of KIC 10841730 observed with HERMES (top panel) and HDS (bottom panel) with the SPECTRUM fitted synthetic spectrum in red (see \ref{['sec:specFit']}).
• Figure 5: Power spectrum density (PSD) of KIC 10841730 displaying the different components of the fit. The grey and black lines represent the PSD before and after smoothing and rebinning. The pink dot-dashed lines correspond to the Gaussians of the solar-like oscillations, the two blue dashed lines are the super-Lorenzians, and the horizontal turquoise dashed line is the photon noise. The solid red line depicts the total fit, and the dotted red line is the background without the solar-like oscillations. The golden vertical lines mark the resulting $\nu_{\mathrm{max}}$ of both stars.