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

ABSTRACT Asteroseismology provides a direct observational window into the structure and evolution of stars. While spectroscopic and photometric methods only offer information about the surface properties of stars, asteroseismology, through oscillation frequencies, provides comprehensive information about the deep stellar interior as well as the surface. The scattering of effective temperature ($T_{\rm eff}$) determined from the spectrum and degeneracy in the Hertzsprung–Russel 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 ($\Delta \nu$) constraint between oscillation frequencies, which is a critical issue, especially in post-main-sequence stars. Reference frequencies, influenced by helium ionization zone-induced glitches in oscillation frequencies, are instrumental in refining models. Using the high metallicity derived from the colours of the Kepler Legacy star KIC 7747078, we obtain the mass of models (M) as $1.208$ and $1.275\, \rm M_{\odot }$ using the reference frequencies and individual frequencies as constraints, respectively. By applying the $\chi ^2$ method using these reference frequencies, $\Delta \nu$, and surface metallicity determined from the spectrum, we develop a unique star model with a mass of $1.171 \pm 0.019\, \rm M_{\odot }$, a radius of $1.961 \pm 0.011\, \rm R_{\odot }$, 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 $T_{\rm eff}$ emerges as an output, not a constraint. The mixed-mode oscillation frequencies of this model align well with the observations.