Glitch analysis and asteroseismic modelling of subgiant $μ$ Herculis: confirming and interpreting the $Γ_1$ peak as the helium glitch

Abstract

The measurements of pressure-mode and mixed-mode oscillation frequencies in subgiant stars offer a unique opportunity to probe their internal structures -- from the surface to the deep interior -- and to precisely determine their global properties. We have conducted a detailed asteroseismic analysis of the benchmark subgiant $μ$ Herculis using eight seasons of radial velocity observations from the SONG-Tenerife, and have determined its mass, radius, age, and surface helium abundance to be $1.105_{-0.024}^{+0.058}$ M$_\odot$, $1.709_{-0.015}^{+0.030}$ R$_\odot$, $8.4_{-0.1}^{+0.4}$ Gyr, and $0.242^{+0.006}_{-0.021}$, respectively. We have demonstrated that simultaneously fitting the helium glitch properties, oscillation frequencies, and spectroscopic observables yields a more accurate inference of the surface helium abundance and hence stellar age. A significant discrepancy between the observed extent of the helium ionization zone and that predicted by stellar models is identified and examined, underscoring potential limitations in the current modelling of stellar interiors. Our analysis confirms that the helium glitch originates from the region between the two stages of helium ionisation, i.e. from the $Γ_1$ peak, rather than from the second helium ionisation zone itself. Within the conventional formalism, this implies that the glitch analysis characterises the region located between the two helium ionisation zones.

Figures (15)

• Figure 1: Acoustic glitch signatures (sum of both the helium and the base of convective envelope) as a function of frequency for $\mu$ Herculis. The circles and diamonds with errorbar represent the observed radial and quadrupole mode frequencies, respectively. The solid curve is the best fit to the data. The dotted horizontal line marks the zero level.
• Figure 2: The distributions of helium glitch parameters obtained from Monte Carlo simulations with 10,000 realisations of the observed frequencies of $\mu$ Herculis. The top left, top right, bottom left, and bottom right panels show distributions for the average amplitude, acoustic width of the helium ionisation zone, its acoustic depth, and the phase, respectively. The vertical black line in each panel shows the median of the distribution. The horizontal line in the bottom left panel shows the range of acoustic depth explored for finding the global minimum.
• Figure 3: Convective-core mass as a function of large frequency separation for 10 evolutionary tracks uniformly sampled in the mass range $M \in [1.05, 1.20]$$M_\odot$ and initial metallicity range $[{\rm Fe}/{\rm H}]_i \in [0.14, 0.42]$ dex. The curves represent different tracks with their $M$ and $[{\rm Fe}/{\rm H}]_i$ given in the legend. The initial helium abundance and the mixing length parameter for all the tracks are $0.29$ and $1.85$, respectively. The tracks begin from the zero-age main sequence (ZAMS) and terminate when $\Delta\nu = 60~\mu\mathrm{Hz}$. The dashed vertical line marks the observed large frequency separation of $\mu$ Herculis.
• Figure 4: Frequency differences between two consecutive models ("older model" $-$ "younger model") along an evolutionary track, selected such that their large frequency separation approximates the corresponding observed value of $\mu$ Herculis, plotted as a function of radial order. The track is evolved with stellar mass, initial metallicity, initial helium abundance, and mixing-length parameter of $1.125$$M_{\odot}$, $0.28$ dex, $0.29$, and $1.85$, respectively. As shown in the legend, the orange circles, green stars, and black diamonds represent the frequency differences for modes with $\ell = 0$, $\ell = 1$, and $\ell = 2$, respectively. The dashed horizontal line marks the zero difference.
• Figure 5: Comparison of the observed and best-fitting model frequencies in an échelle diagram. The filled, cyan diamonds, squares, and triangles represent the observed oscillation modes with harmonic degrees $\ell = 0$, $\ell = 1$, and $\ell = 2$, respectively. The corresponding empty, red and blue symbols represent oscillation frequencies of the best-fitting models M1 and M2 obtained from fitting approaches Fit1 and Fit2, respectively (see the text). The model symbol sizes are scaled inversely with their normalized mode inertias.