Towards Accurate Asteroseismic Masses for Luminous Giants

TL;DR

The paper tackles systematic offsets in asteroseismic mass estimates for luminous red giants that arise when tying scaling relations to Gaia-based radii. It introduces a radius-centered correction controlled by a factor $f_R$, with an iterative update of $f_{\Delta\nu}$ and a nu-SVR model to predict $f_{\Delta\nu}$ from $\nu_{\max}$, stellar mass, and corrected metallicity. The adjusted correction reduces cross-scheme model sensitivity, significantly lowers mass and age discrepancies between lower and upper RGB in the $\alpha$-rich population (from $6.65\%$ to $1.72\%$ and from $-21.81\%$ to $-9.55\%$, respectively), and improves C/N-based diagnostics for the $\alpha$-poor population, enhancing the reliability of seismic masses for luminous giants. The work sets the stage for more accurate asteroseismic inferences with upcoming spectroscopic releases and space missions such as the Roman Space Telescope.

Abstract

Asteroseismology, the study of stellar oscillations, provides high-precision measurements of masses and ages for red giants. Scaling relations are a powerful tool for measuring fundamental stellar parameters, and the derived radii are in good agreement with fundamental data for low-luminosity giants. However, for luminous red giant branch (RGB) stars, there are clear systematic offsets. In APOKASC-3, the third joint spectroscopic and asteroseismic catalog for evolved stars in the Kepler fields, we tied asteroseismic radii to a reference system based on Gaia astrometry by introducing correction factors. This work proposes an alternative formulation of the correction scheme, which substantially reduces the sensitivity of the results to the technique used to infer mean density from frequency spacings. Compared to APOKASC-3, our adjusted correction scheme also reduces fractional discrepancies in median masses and ages of lower RGB and upper RGB within the $α$-rich population from $6.65\%$ to $1.72\%$ and from $-21.81\%$ to $-9.55\%$, respectively. For the $α$-poor population, the corrected mass scale leads to an improved agreement between theory and observation of the surface carbon-to-nitrogen abundance ratio, a significant diagnostic of the first dredge-up.

Figures (4)

• Figure 1: A comparison between different correction schemes for asteroseismic masses. All quantities are plotted as functions of $\nu_{\rm max}$, with the lower RGB shown on the left and the upper RGB shown on the right. The upper panel shows the published $f_{\Delta\nu}$ from APOKASC-3 for our sample. In the middle panel, we plot the ratio between the adjusted (see text) $f_{\Delta\nu}$ and the raw $f_{\Delta\nu}$. In the lower panel, we illustrate the net effect on the masses relative to the published APOKASC-3 values, which correspond to unity and are shown by the blue dashed line. The raw $f_R$ correction, holding $f_{\Delta\nu}$ fixed (so that the mass correction factor is simply $1 / f_R$), is shown by the green dash-dotted line. The adjusted $f_R$ correction, including feedback in the $f_{\Delta\nu}$ calculation, is shown by colored dots. Although it depends on both $\nu_{\rm max}$ and $M_{\rm seis}$, simple fitting results using Eq. (\ref{['eq:poly_fit']}) (ignoring mass dependence) are also shown by the orange solid curve. The fitting coefficients are tabulated in Table \ref{['tab:poly_coeffs']}.
• Figure 2: Consistency between lower RGB and upper RGB within the $\alpha$-rich population. The two columns study the consistency of asteroseismic masses and ages, respectively. The four rows correspond to four correction schemes; from top to bottom: APOKASC-3 without $\nu_{\rm max}$ correction, APOKASC-3 correction, raw $f_R$ correction, and adjusted $f_R$ correction. In each panel, we compare three combinations of models and weighting approaches: GARSTEC+Mosser (blue solid curves), GARSTEC+White (orange dashed curves), and Sharma+White (green dash-dotted curves). Rolling medians of masses and ages are shown as functions of $\nu_{\rm max}$; horizontal error bars (shaded regions) are median absolute deviations (MADs) multiplied by $k = 1/(\Phi^{-1}(3/4)) \approx 1.4826$, which converts MADs to standard deviations for normal distributions ($\Phi$ is the cumulative distribution function); overall medians are shown as vertical straight lines. For GARSTEC+Mosser, median masses and ages are tabulated in Table \ref{['tab:arich_medians']}.
• Figure 3: Scatter plots of asteroseismic age $\tau_{\rm seis}$ versus frequency of the maximum power $\nu_{\rm max}$. The $4439$ "Gold" sample stars are shown in blue, while the $1097$ "Silver" sample stars are shown in orange. The two columns present the $\alpha$-rich and $\alpha$-poor populations. The first two rows correspond to ages from APOKASC-3 Pinsonneault2025ApJS and our adjusted $f_R$ correction, respectively, and the last row shows the ratios between these two sets of age predictions. The age of the Universe ($\sim 13.8 \,{\rm Gyr}$) is shown as green dashed horizontal lines in the first two rows. All ages shown in this figure are based on GARSTEC Weiss2008ApSS models and the Mosser2012AA weighting approach.
• Figure 4: Impact on first dredge-up predictions for the $\alpha$-poor population. Each panel plots the difference between two versions of surface carbon-to-nitrogen abundance ratio changes $\Delta[{\rm C}/{\rm N}]$ (current minus birth) as a function of logarithmic seismic gravity. Upper panel: difference between post-FDU $\Delta[{\rm C}/{\rm N}]$ values predicted for corrected (adjusted $f_R$ correction; "New") and APOKASC-3 ("Old") asteroseismic masses. Note that the color-coding has been switched to corrected $M_{\rm seis}$. Lower panel: rolling medians of discrepancies between observed Roberts2024MNRAS and predicted $\Delta[{\rm C}/{\rm N}]$; vertical error bars (shaded regions) are MADs multiplied by $k \approx 1.4826$. The median trends using APOKASC-3 and corrected masses are shown as blue dashed and orange solid curves, respectively. In both panels, the end of FDU and the center of red giant branch bump are shown as green and brown bands, respectively. For both quantities, we use benchmark predictions from Cao2025ApJ; for the latter, we superimpose an observed zero-point shift of $0.1509 \,{\rm dex}$Cao2025ApJ.