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The observation of an unprecedented number of solar-like oscillating subgiant (SG) stars by the Kepler and TESS missions is crucial for the asteroseismic characterization of these stars, stellar population studies, and the study of stellar evolution theories. Owing to these missions, the fundamental parameters of the solar-like oscillating stars are precisely calculated from the evolution codes using the observed oscillation frequencies. Herein, we considered four solar-like oscillating SG stars. We obtained the fundamental parameters of the SG stars by constructing interior models using asteroseismic and non-asteroseismic observed parameters. The interior models of the four SG stars are constructed using the Modules for Experiments in Stellar Astrophysics code to effectively determine the fundamental properties. Using this method, the four solar-like oscillating SG stars are found to have masses and radii within the ranges of 1.16–1.75 M⊙ and 2.26–3.17 R⊙, respectively. The estimation accuracy of the typical asteroseismic radius, mass, and age is increased by fitting the observed and model reference frequencies. The typical uncertainties of the mass and radius are 3–4 |${{\ \rm per\ cent}}$| and 1–2 |${{\ \rm per\ cent}}$|⁠ , respectively. Furthermore, the observed l  = 1 frequencies, which showed a mixed mode for the first time, were also fitted to the models. Information regarding the gravity and density of the helium core was obtained by examining the mixed modes. Moreover, new asteroseismic methods for determining the age of SG stars are developed for the first time in this study. [ABSTRACT FROM AUTHOR]

When main-sequence stars expand into red giants, they are expected to engulf close-in planets 1-5 . Until now, the absence of planets with short orbital periods around post-expansion, core-helium-burning red giants 6-8 has been interpreted as evidence that short-period planets around Sun-like stars do not survive the giant expansion phase of their host stars 9 . Here we present the discovery that the giant planet 8 Ursae Minoris b 10 orbits a core-helium-burning red giant. At a distance of only 0.5 AU from its host star, the planet would have been engulfed by its host star, which is predicted by standard single-star evolution to have previously expanded to a radius of 0.7 AU. Given the brief lifetime of helium-burning giants, the nearly circular orbit of the planet is challenging to reconcile with scenarios in which the planet survives by having a distant orbit initially. Instead, the planet may have avoided engulfment through a stellar merger that either altered the evolution of the host star or produced 8 Ursae Minoris b as a second-generation planet 11 . This system shows that core-helium-burning red giants can harbour close planets and provides evidence for the role of non-canonical stellar evolution in the extended survival of late-stage exoplanetary systems., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)