Is there a unique asteroseismic interior model for the solar-like oscillating KIC 7747078?

TL;DR

The paper addresses whether a unique interior model exists for the solar-like subgiant KIC 7747078. It combines reference frequencies from helium ionisation glitches (ν_min0, ν_min1) with traditional seismic constraints (Δν, mixed-mode frequencies) and non-asteroseismic observables using MESA-based interior modelling, ADIPLS frequencies, and surface-correction schemes. Through extensive grid-search and χ² minimisation, incorporating different metallicities and nuclear-reaction-rate options (NACRE/JINA), the authors identify a unique solution with M ≈ 1.171 M☉, Z0 ≈ 0.0121, Y0 ≈ 0.2689, α ≈ 1.831, Z_s ≈ 0.0103, and an age around 5.15 Gyr, while Teff emerges as a model output (~5977–5993 K). They also demonstrate that including ν_min constraints and mixed-mode analysis with the astero module tightens the solution to a unique interior model, highlighting a pathway to resolving degeneracy for evolved solar-like stars and potentially enabling similar determinations for other Kepler Legacy targets.

Abstract

Asteroseismology provides a direct observational window into the structure and evolution of stars. While spectroscopic and photometric methods only provide information about the surface properties of stars, asteroseismology, through the analysis of oscillation frequencies, offers comprehensive information about the deep stellar interior as well as the surface. The scattering of effective temperature (Teff) determined from the spectrum and degeneracy in the Hertzsprung Russell diagram poses challenges in developing a unique interior model for a single star. Although observational asteroseismic data partially lift this degeneracy, the best model that meets all asteroseismic constraints is not obtained. Most models reported in the literature typically address the large separation Dnu constraint between oscillation frequencies, which is a critical issue, especially in post main sequence stars. Reference frequencies, influenced by helium ionisation zone induced glitches in oscillation frequencies, are instrumental in refining models. Using the high metallicity derived from the colors of the Kepler Legacy star KIC 7747078, we obtain the masses of models M as 1.208 Msun and 1.275 Msun using the reference frequencies and individual frequencies as constraints, respectively. By applying the chi2 method using these reference frequencies, Dnu, and surface metallicity determined from the spectrum, we develop a unique star model with a mass of 1.171 pm 0.019 Msun, a radius of 1.961 pm 0.011 Rsun, an effective temperature of 5993 K, an initial metallicity of 0.0121, and an age of 5.15 pm 0.29 Gyr. A significant advantage of this method is that Teff emerges as an output, not a constraint. The mixed mode oscillation frequencies of this model align well with the observations.

Figures (10)

• Figure 1: $\log{g}-T_{\rm eff}$ diagram. The filled yellow circles represent the values reported in the literature for KIC 7747078. Zero-age main-sequence (solid red line) and thermal-age main-sequence (solid black line) are plotted using the models constructed by employing the solar composition Yildiz2015.
• Figure 2: HR diagram. The diagram shows the evolutionary tracks of Models A, C and D. Although the models fit the same observation point, they have different evolutionary tracks. Models A, C and D are represented by solid circles in black, red and blue, respectively. The filled yellow circle indicates the observation point on the HR diagram for KIC 7747078.
• Figure 3: $\Delta\nu$ is plotted with respect to $\nu$. The filled yellow circle indicates the observational frequencies of KIC 7747078. The filled black, red and blue circles represent the adiabatic oscillation frequencies of Models A, C and D, respectively.
• Figure 4: Graph of $\Delta\nu$ versus $\nu$ for determining the reference frequencies $\nu_{\rm min1}$and ${\nu_{\rm min0}}$. The reference frequency $\nu_{\rm min1}$ is between $\nu_{\rm a}$ and $\nu_{\rm b}$. We plot two lines from the neighbourhood intervals. The intersection of these two lines gives us $\nu_{\rm min1}$. ${\nu_{\rm min0}}$ is around an observed frequency. The $\nu_{\rm min1}$ and $\nu_{\rm min0}$ values of the star are found to be 792.5 and 1039.3 ${\mu}$Hz, respectively.
• Figure 5: The upper panel shows the uncertainty ($\rm e_{\nu}$) of the observation frequencies of KIC 7727078 that is plotted with respect to $\nu_{\rm obs}$. The filled black triangles and the hollow red triangles represent the frequencies as reported by LiY2020 and Appo2012, respectively. The lower panel plots the fractional difference between the observational and model frequencies with respect to $\nu_{\rm obs}$. The graph shows the results obtained by six models. Model E provides the best agreement with the observational frequencies.