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The radii of planets serve as significant constraints for their internal structure. Despite the complexity of planetary internal structure compared to stars, substantial advancements have been made in this field. The most critical uncertainties stem from the chemical composition and equation of state of planetary material. Using the MESA code, we construct rotating and non-rotating interior models for Jupiter and Saturn and sought to align these models to the observed radii. Rotation exerts a significant influence on their structures, distorting planetary, and stellar structures in distinct ways. Regarding gas planets' structure, two pivotal uncertain parameters depend on a possible separation between hydrogen and helium in the protosolar disc gas due to unequal evaporation between these two gases. In an extreme scenario where only hydrogen is lost and no heavy elements or helium are lost, Jupiter and Saturn would have a core mass of zero. However, this approach fails to yield a solution for Uranus and Neptune. Instead, our models indicate that hydrogen and helium were likely lost together during the protosolar disc phase, resulting in core masses of approximately 40, 25, 14, and 12 M⊕ for Jupiter, Saturn, Neptune, and Uranus, respectively. These findings are highly compatible with the observed mass–radius relationship of exoplanets, as well as the seismic and Juno data for Jupiter's near-surface temperature. [ABSTRACT FROM AUTHOR]

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]

Context. The Transiting Exoplanet Survey Satellite (TESS) is observing bright known planet-host stars across almost the entire sky. These stars have been subject to extensive ground-based observations, providing a large number of radial velocity measurements. Aims. The objective of this work is to use the new TESS photometric observations to characterize the star λ2 Fornacis, and following this to update the parameters of the orbiting planet λ2 For b. Methods. We measured the frequencies of the p-mode oscillations in λ2 For, and in combination with non-seismic parameters estimated the stellar fundamental properties using stellar models. Using the revised stellar properties and a time series of archival radial velocities from the UCLES, HIRES and HARPS instruments spanning almost 20 years, we refit the orbit of λ2 For b and searched the residual radial velocities for remaining variability. Results. We find that λ2 For has a mass of 1.16 ± 0.03 M⊙ and a radius of 1.63 ± 0.04 R⊙, with an age of 6.3 ± 0.9 Gyr. This and the updated radial velocity measurements suggest a mass of λ2 For b of 16.8−1.3+1.2M⊕ 16. 8 − 1.3 + 1.2 M ⊕ $ 16.8^{+1.2}_{-1.3}\,{{M}_\oplus} $ , which is ∼5M⊕ less than literature estimates. We also detect an additional periodicity at 33 days in the radial velocity measurements, which is likely due to the rotation of the host star. Conclusions. While previous literature estimates of the properties of λ2 For are ambiguous, the asteroseismic measurements place the star firmly at the early stage of its subgiant evolutionary phase. Typically only short time series of photometric data are available from TESS, but by using asteroseismology it is still possible to provide tight constraints on the properties of bright stars that until now have only been observed from the ground. This prompts a reexamination of archival radial velocity data that have been accumulated in the past few decades in order to update the characteristics of the planet hosting systems observed by TESS for which asteroseismology is possible. [ABSTRACT FROM AUTHOR]

Low amplitude is the defining characteristic of solar-like oscillations. The space projects Kepler and CoRoT give us a great opportunity to successfully detect such oscillations in numerous targets. Achievements of asteroseismology depend on new discoveries of connections between the oscillation frequencies and stellar properties. In the previous studies, the frequency of the maximum amplitude and the large separation between frequencies were used for this purpose. In the present study, we confirm that the large separation between the frequencies has two minima at two different frequency values. These are the signatures of the He ii ionization zone, and as such have very strong diagnostic potential. We relate these minima to fundamental stellar properties such as mass, radius, luminosity, age and mass of convective zone. For mass, the relation is simply based on the ratio of the frequency of minimum Δν to the frequency of maximum amplitude. These frequency comparisons can be very precisely computed, and thus the mass and radius of a solar-like oscillating star can be determined to high precision. We also develop a new asteroseismic diagram which predicts structural and evolutionary properties of stars with such data. We derive expressions for mass, radius, effective temperature, luminosity and age in terms of purely asteroseismic quantities. For solar-like oscillating stars, we now will have five very important asteroseismic tools (two frequencies of minimum Δν, the frequency of maximum amplitude, and the large and small separations between the oscillation frequencies) to decipher properties of stellar interior astrophysics. [ABSTRACT FROM AUTHOR]