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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. 

Context: Modeling of the stars in the red clump (RC), that is, core helium-burning stars that have gone through a He flash, is challenging because of the uncertainties associated with the physical processes in their core and during the helium flash. By probing the internal stellar structure, asteroseismology allows us to constrain the core properties of RC stars and eventually, to improve our understanding of this evolutionary phase. Aims: We aim to quantify the impact on the seismic properties of the RC stars of the two main core modeling uncertainties: core boundary mixing, and helium-burning nuclear reaction rates. Methods: Using the MESA stellar evolution code, we computed models with different core boundary mixing as well as different 3α and 12C(alpha, gamma)16O nuclear reaction rates. We investigated the impact of these parameters on the period spacing ΔΠ, which is a probe of the region around the core. Results: We find that different core boundary mixing schemes yield significantly different period spacings, with differences of 30 s between the maximum ΔΠ value computed with semiconvection and maximal overshoot. We show that an increased rate of 12C(alpha, gamma)16O lengthens the core helium-burning phase, which extends the range of ΔΠ covered by the models during their evolution. This results in a difference of 10 s between the models computed with a nominal rate and a rate multiplied by 2, which exceeds the observational uncertainties. The effect of changing the 3α reaction rate is comparatively small. Conclusions. The core boundary mixing is the main source of uncertainty in the seismic modeling of RC stars. Moreover, the effect of the 12C(alpha, gamma)16O is non-negligible, even though it is difficult to distinguish from the effect of the mixing. This degeneracy could be seen more frequently in the future in the new seismic data from the PLATO mission and through theoretical constraints from numerical simulations. 

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 solar-type subgiantβHyi has long been studied as an old analog of the Sun. Although the rotation period has never been measured directly, it was estimated to be near 27 days. As a Southern Hemisphere target, it was not monitored by long-term stellar activity surveys, but archival International Ultraviolet Explorer data revealed a 12 yr activity cycle. Previous ground-based asteroseismology suggested that the star is slightly more massive and substantially larger and older than the Sun, so the similarity of both the rotation rate and the activity cycle period to solar values is perplexing. We use two months of precise time-series photometry from the Transiting Exoplanet Survey Satellite to detect solar-like oscillations inβHyi and determine the fundamental stellar properties from asteroseismic modeling. We also obtain a direct measurement of the rotation period, which was previously estimated from an ultraviolet activity–rotation relation. We then use rotational evolution modeling to predict the rotation period expected from either standard spin-down or weakened magnetic braking (WMB). We conclude that the rotation period ofβHyi is consistent with WMB and that changes in stellar structure on the subgiant branch can reinvigorate the large-scale dynamo and briefly sustain magnetic activity cycles. Our results support the existence of a “born-again” dynamo in evolved subgiants—previously suggested to explain the cycle in 94 Aqr Aa—which can best be understood within the WMB scenario. 

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 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. 

Abstract Stellar spin down is a critical yet poorly understood component of stellar evolution. In particular, results from the Kepler Mission imply that mature age, solar-type stars have inefficient magnetic braking, resulting in a stalled spin-down rate. However, a large number of precise asteroseismic ages are needed for mature (≥3 Gyr) stars in order to probe the regime where traditional and stalled spin-down models differ. In this paper, we present a new asteroseismic benchmark star for gyrochronology discovered using reprocessed Kepler short cadence data. KIC 11029516 (Papayu) is a bright (Kp= 9.6 mag) solar-type star with a well-measured rotation period (21.1 ± 0.8 days) from spot modulation using 4 yr of Kepler long-cadence data. We combine asteroseismology and spectroscopy to obtainT_eff= 5888 ± 100 K, [Fe/H] = 0.30 ± 0.06 dex,M= 1.24 ± 0.05M_⊙,R= 1.34 ± 0.02R_⊙, and age of 4.0 ± 0.4 Gyr, making Papayu one of the most similar stars to the Sun in terms of temperature and radius with an asteroseismic age and a rotation period measured from spot modulation. We find that Papayu sits at the transition of where traditional and weakened spin-down models diverge. A comparison with stars of similar zero-age main-sequence temperatures supports previous findings that weakened spin-down models are required to explain the ages and rotation periods of old solar-type stars. 

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 We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.