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Abstract Seismic structure inversions have been used to study the solar interior for decades. With the high-precision frequencies obtained using data from the Kepler mission, it has now become possible to study other solar-like oscillators using structure inversions, including both main-sequence and subgiant stars. Subgiant stars are particularly interesting because they exhibit modes of mixed acoustic-buoyancy nature, which provide the opportunity to probe the deeper region of stellar cores. This work examines whether the structure inversion techniques developed for the pure acoustic modes of the Sun and other main-sequence stars are still valid for mixed modes observed in subgiant stars. We construct two grids of models: one of main-sequence stars and one of early subgiant stars. Using these grids, we examine two different parts of the inversion procedure. First, we examine what we call the “kernel errors,” which measure how well the mode sensitivity functions can recover known frequency differences between two models. Second, we test how these kernel errors affect the ability of an inversion to infer known structure differences. On the main sequence, we find that reliable structure inversion results can be obtained across the entire range of masses and large frequency separations we consider. On the subgiant branch, however, the rapid evolution of mixed modes leads to large kernel errors and hence difficulty recovering known structure differences. Our tests show that using mixed modes to infer the structure of subgiant stars reliably will require improvements to current fitting approaches and modifications to the structure inversion techniques. 

Abstract Asteroseismic inferences of main-sequence solar-like oscillators often rely on best-fit models. However, these models cannot fully reproduce the observed mode frequencies, suggesting that the internal structure of the model does not fully match that of the star. Asteroseismic structure inversions provide a way to test the interior of our stellar models. Recently, structure inversion techniques were used to study 12 stars with radiative cores. In this work, we extend that analysis to 43 main-sequence stars with convective cores observed by Kepler to look for differences in the sound speed profiles in the inner 30% of the star by radius. For around half of our stars, the structure inversions show that our models reproduce the internal structure of the star, where the inversions are sensitive, within the observational uncertainties. For the stars where our inversions reveal significant differences, we find cases where our model sound speed is too high and cases where our model sound speed is too low. We use the star with the most significant differences to explore several changes to the physics of our model in an attempt to resolve the inferred differences. These changes include using a different overshoot prescription and including the effects of diffusion, gravitational settling, and radiative levitation. We find that the resulting changes to the model structure are too small to resolve the differences shown in our inversions. 

ABSTRACT High-precision light curves from space-based telescopes and precise astrometry from the Gaia satellite have revolutionized our ability to characterize exoplanet host stars. Asteroseismology has allowed for stellar parameters to be determined to remarkable precision, achieving age uncertainties as low as 10−20  per cent for Sun-like stars. We present an asteroseismic analysis of the naked-eye ($V = 5.78$), G4V star $$\nu ^2$$ Lupi (HD 136352), which hosts three small transiting planets with orbital periods of 11, 27, and 107 d. We used the latest 20-s cadence photometry data from the Transiting Exoplanet Survey Satellite (TESS) to extract stellar oscillations. Comparing these to stellar models, we find that the star has a mass of $$0.83^{+0.04}_{-0.03}$$ (ran) $$\pm 0.07$$ (sys) $$M_\odot$$, a radius of $$1.00^{+0.01}_{-0.02}$$ (ran) $$\pm 0.04$$ (sys) $$R_\odot$$, and an age of $$11.9^{+2.6}_{-1.6}$$ (ran) $$\pm 1.7$$ (sys) Gyr. We also confirm that the star is likely a member of the Galactic thick disc based on its Galactic velocities, consistent with the asteroseismic age. Based on the newly determined stellar parameters, we recalculate the planet parameters. The inner planet has a mass of $$4.55 \pm 0.40$$  $$M_{\oplus }$$ and a radius of $$1.57 \pm 0.04$$  $$R_{\oplus }$$, suggesting the planet is rocky and consisting primarily of silicates without an iron-rich core, consistent with its old age and significant alpha-element enhancement. The two outer planets have masses and radii of $$10.87 \pm 0.62$$  $$M_{\oplus }$$ and $$2.75 \pm 0.06$$  $$R_{\oplus }$$, and $$8.52 \pm 0.90$$  $$M_{\oplus }$$ and $$2.42 \pm 0.08$$  $$R_{\oplus }$$, respectively, suggesting both are sub-Neptune planets with a significant H–He atmosphere. 

Abstract Acoustic oscillations in stars are sensitive to stellar interiors¹. Frequency differences between overtone modes—large separations—probe stellar density², whereas differences between low-degree modes—small separations—probe the sound-speed gradient in the energy-generating core of main-sequence Sun-like stars³, and hence their ages. At later phases of stellar evolution, characterized by inert cores, small separations are believed to lose much of their power to probe deep interiors and become proportional to large separations^4,5. Here we present evidence of a rapidly evolving convective zone as stars evolve from the subgiant phase into red giants. By measuring acoustic oscillations in 27 stars from the open cluster M67, we observe deviations of proportionality between small and large separations, which are caused by the influence of the bottom of the convective envelope. These deviations become apparent as the convective envelope penetrates deep into the star during subgiant and red giant evolutions, eventually entering an ultradeep regime that leads to the red-giant-branch luminosity bump. The tight sequence of cluster stars, free of large spreads in ages and fundamental properties, is essential for revealing the connection between the observed small separations and the chemical discontinuities occurring at the bottom of the convective envelope. We use this sequence to show that combining large and small separations can improve estimations of the masses and ages of field stars well after the main sequence. 

Abstract On the main sequence, the asteroseismic small frequency separationδν₀₂between radial and quadrupolep-modes is customarily interpreted to be a direct diagnostic of internal structure. Such an interpretation is based on a well-known integral estimator relatingδν₀₂to a radially averaged sound-speed gradient. However, this estimator fails, catastrophically, when evaluated on structural models of red giants: their small separations must therefore be interpreted differently. We derive a single expression that both reduces to the classical estimator when applied to main-sequence stellar models and reproduces the qualitative features of the small separation for stellar models of very evolved red giants. This expression indicates that the small separations of red giants scale primarily with their global seismic properties as $\delta {\nu }_{02}\propto \Delta {\nu }^2/{\nu }_{\max }$, rather than being in any way sensitive to their internal structure. Departures from this asymptotic behavior, during the transition from the main-sequence to red giant regimes, have been recently reported in open-cluster Christensen–Dalsgaard (C-D) diagrams from K2 mission data. Investigating them in detail, we demonstrate that they occur when the convective envelope boundary passes a specific acoustic distance—roughly one-third of a wavelength at ${\nu }_{\max }$—from the center of the star, at which point radial modes become maximally sensitive to the position of the boundary. The shape of the corresponding features onϵ_pand C-D (orr₀₂) diagrams may be useful in constraining the nature of convective boundary mixing in the context of undershooting beneath a convective envelope. 

Abstract In the third APOKASC catalog, we present data for the complete sample of 15,808 evolved stars with APOGEE spectroscopic parameters and Kepler asteroseismology. We used 10 independent asteroseismic analysis techniques and anchor our system on fundamental radii derived from GaiaLand spectroscopicT_eff. We provide evolutionary state, asteroseismic surface gravity, mass, radius, age, and the data used to derive them for 12,418 stars. This includes 10,036 exceptionally precise measurements, with median fractional uncertainties in ${\nu }_{\max }$, Δν, mass, radius, and age of 0.6%, 0.6%, 3.8%, 1.8%, and 11.1%, respectively. We provide more limited data for 1624 additional stars that either have lower-quality data or are outside of our primary calibration domain. Using lower red giant branch (RGB) stars, we find a median age for the chemical thick disk of 9.14 ± 0.05(ran) ± 0.9(sys) Gyr with an age dispersion of 1.1 Gyr, consistent with our error model. We calibrate our red clump (RC) mass loss to derive an age consistent with the lower RGB and provide asymptotic GB and RGB ages for luminous stars. We also find a sharp upper-age boundary in the chemical thin disk. We find that scaling relations are precise and accurate on the lower RGB and RC, but they become more model dependent for more luminous giants and break down at the tip of the RGB. We recommend the use of multiple methods, calibration to a fundamental scale, and the use of stellar models to interpret frequency spacings. 

Abstract Some physical processes that occur during a star's main-sequence evolution also affect its post-main-sequence evolution. It is well known that stars with masses above approximately 1.1M_⊙have well-mixed convective cores on the main sequence; however, the structure of the star in the neighborhood of the convective core regions is currently underconstrained. We use asteroseismology to study the properties of the stellar core, in particular convective boundary mixing through convective overshoot, in such intermediate-mass stars. These core regions are poorly constrained by the acoustic (p) mode oscillations observed for cool main-sequence stars. Consequently, we seek fossil signatures of main-sequence core properties during the subgiant and early first-ascent red giant phases of evolution. During these stages of stellar evolution, modes of mixed character that sample the deep interior can be observed. These modes sample the parts of the stars that are affected by the main-sequence structure of these regions. We model the global and near-core properties of 62 subgiant and early first-ascent red giant branch stars observed by theKepler, K2, and TESS space missions. We find that the effective overshoot parameter,α_ov,eff, increases fromM= 1.0M_⊙toM= 1.2M_⊙before flattening out, although we note that the relationship betweenα_ov,effand mass will depend on the incorporated modeling choices of internal physics and nuclear reaction network. We also situate these results within existing studies of main-sequence convective core boundaries. 

Abstract The theoretical oscillation frequencies of even the best asteroseismic models of solar-like oscillators show significant differences from observed oscillation frequencies. Structure inversions seek to use these frequency differences to infer the underlying differences in stellar structure. While used extensively to study the Sun, structure inversion results for other stars have so far been limited. Applying sound speed inversions to more stars allows us to probe stellar theory over a larger range of conditions, as well as look for overall patterns that may hint at deficits in our current understanding. To that end, we present structure inversion results for 12 main-sequence solar-type stars with masses between 1 and 1.15M_⊙. Our inversions are able to infer differences in the isothermal sound speed in the innermost 30% by radius of our target stars. In half of our target stars, the structure of our best-fit model fully agrees with the observations. In the remainder, the inversions reveal significant differences between the sound speed profile of the star and that of the model. We find five stars where the sound speed in the core of our stellar models is too low and one star showing the opposite behavior. For the two stars in which our inversions reveal the most significant differences, we examine whether changing the microphysics of our models improves them and find that changes to nuclear reaction rates or core opacities can reduce, but do not fully resolve, the differences. 

Abstract The consistently low activity level of the old solar analog 51 Peg not only facilitated the discovery of the first hot Jupiter, but also led to the suggestion that the star could be experiencing a magnetic grand minimum. However, the 50 yr time series showing minimal chromospheric variability could also be associated with the onset of weakened magnetic braking (WMB), where sufficiently slow rotation disrupts cycling activity and the production of large-scale magnetic fields by the stellar dynamo, thereby shrinking the Alfvén radius and inhibiting the efficient loss of angular momentum to magnetized stellar winds. In this Letter, we evaluate the magnetic evolutionary state of 51 Peg by estimating its wind braking torque. We use new spectropolarimetric measurements from the Large Binocular Telescope to reconstruct the large-scale magnetic morphology, we reanalyze archival X-ray measurements to estimate the mass-loss rate, and we detect solar-like oscillations in photometry from the Transiting Exoplanet Survey Satellite, yielding precise stellar properties from asteroseismology. Our estimate of the wind braking torque for 51 Peg clearly places it in the WMB regime, driven by changes in the mass-loss rate and the magnetic field strength and morphology that substantially exceed theoretical expectations. Although our revised stellar properties have minimal consequences for the characterization of the exoplanet, they have interesting implications for the current space weather environment of the system. 

Abstract Asteroseismology has been used extensively in recent years to study the interior structure and physical processes of main-sequence stars. We consider prospects for using pressure modes (p-modes) near the frequency of maximum oscillation power to probe the structure of the near-core layers of main-sequence stars with convective cores by constructing stellar model tracks. Within our mass range of interest, the inner turning point of p-modes as determined by the Jeffreys–Wentzel–Kramers–Brillouin (JWKB) approximation evolves in two distinct phases during the main sequence, implying a sudden loss of near-core sensitivity during the discontinuous transition between the two phases. However, we also employ non-JWKB asymptotic analysis to derive a contrasting set of expressions for the effects that these structural properties will have on the mode frequencies, which do not encode any such transition. We show analytically that a sufficiently near-core perturbation to the stellar structure results in nonoscillatory, degree-dependent perturbations to the star’s oscillation mode frequencies, contrasting with the case of an outer glitch. We also demonstrate numerically that these near-core acoustic glitches exhibit strong angular degree dependence, even at low degree, agreeing with the non-JWKB analysis, rather than the degree-independent oscillations that emerge from JWKB analyses. These properties have important implications for using p-modes to study near-core mixing processes for intermediate-mass stars on the main sequence, as well as for the interpretation of near-center acoustic glitches in other astrophysical configurations, such as red giants.