Beyond the Nyquist frequency: Asteroseismic catalog of undersampled Kepler late subgiants and early red giants

TL;DR

This work tackles the challenge of asteroseismology for undersampled Kepler targets, where many late subgiants and early red giants have oscillation frequencies near or above the Nyquist limit. It introduces PyA2Z, a pipeline that jointly classifies stars as sub-Nyquist, close-to-Nyquist, or super-Nyquist and retrieves global seismic parameters $\nu_{\max}$ and $\Delta\nu$ using PS2-based methods and echelle-diagram analysis, with careful treatment of apodization and mode mirroring. Applying this to 2,065 Kepler targets, the authors identify 285 super-Nyquist and 168 close-to-Nyquist stars, and derive masses, radii, and ages for a substantial subset when combined with APOGEE/Gaia data, yielding strong agreement with Gaia radii (within $0.9\%$) and consistent seismic mass scales to within $\sim 1.5\%$. The study shows that the timing of the first dredge-up broadly matches theoretical predictions but reveals discrepancies in depth and mass dependence, pointing to potential physics or abundance-scale calibration issues. Overall, PyA2Z expands the census of subgiant/early-giant asteroseismic stars and provides robust constraints on stellar evolution and dredge-up physics with implications for Galactic archaeology.

Abstract

Subgiants and early red giants are crucial for studying the first dredge-up, a key evolutionary phase where the convective envelope deepens, mixing previously interior-processed material and bringing it to the surface. Yet, very few have been seismically characterized with Kepler because their oscillation frequencies are close to the 30 minute sampling frequency of the mission. We developed a new method as part of the new PyA2Z code to identify super-Nyquist oscillators and infer their global seismic parameters, $ν_\mathrm{max}$ and large separation, $Δν$. Applying PyA2Z to 2 065 Kepler targets, we seismically characterize 285 super-Nyquist and 168 close-to-Nyquist stars with masses from 0.8 to 1.6 M$_\odot$. In combination with APOGEE spectroscopy, Gaia spectro-photometry, and stellar models, we derive stellar ages for the sample. There is good agreement between the predicted and actual positions of stars on the HR diagram (luminosity vs. effective temperature) as a function of mass and composition. While the timing of dredge-up is consistent with predictions, the magnitude and mass dependence show discrepancies with models, possibly due to uncertainties in model physics or calibration issues in observed abundance scales.

Figures (13)

• Figure 1: Power spectral density (PSD) of two simulated stars in units of signal-to-noise ratio (SNR) as a function of frequency. Panel (a): star with modes close to $\nu_{\mathrm{Nyq}}$ at the right edge of the frequency range. The true modes are in orange and the mirrored modes in black. Panel (b): star with super-Nyquist modes where only the folded modes are observed between $0$ µHz and $\nu_{\mathrm{Nyq}}$.
• Figure 2: PSD of the star KIC 8179973 and estimate of its background with a median filter.
• Figure 3: (a) PSD of the Kepler star KIC 8179973 on which a sliding box (shaded pink area) is taken to compute the PS2 (inset) with $\Gamma=2$ and filtered as explained in Section \ref{['numax']}. (b) The red line is the averaged filtered PS2 normalized to its maximum value as a function of the center of the sliding windows. The dashed black line is the Gaussian fit.
• Figure 4: (a) Synthesized PSD of the $\ell=0,2$ modes of a star with $\nu_{\mathrm{max}}=275\text{ µHz}$. The black modes are the true modes whereas the blue modes are those observed because of the undersampling: they are the black modes mirrored around $\nu_{\mathrm{Nyq}}$. Each box of width $\Delta\nu$ matches to one line of the echelle diagram shown in panel (b) along with its collapse in (c). In (b), the ridges due to the true modes are annotated in black whereas those annotated in blue are due to the shadow modes. In (c) the peaks due to the mirrored modes are marked with a blue vertical dashed line and the peaks due to the true modes are marked with a black vertical dotted line.
• Figure 5: One-to-one comparison of Gaia and asteroseimsic radius scales (top) and the fractional differences (bottom; with binned medians and uncertainties on the median). The two show excellent agreement (to within $0.9\%$ on average), which demonstrates the accuracy of the asteroseismic analysis here and of the asteroseismic radius scale in the subgiant regime.