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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 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. 

Three-dimensional bioprinting has emerged as a promising tool for spatially patterning cells to fabricate models of human tissue. Here, we present an engineered bioink material designed to have viscoelastic mechanical behavior, similar to that of living tissue. This viscoelastic bioink is cross-linked through dynamic covalent bonds, a reversible bond type that allows for cellular remodeling over time. Viscoelastic materials are challenging to use as inks, as one must tune the kinetics of the dynamic cross-links to allow for both extrudability and long-term stability. We overcome this challenge through the use of small molecule catalysts and competitors that temporarily modulate the cross-linking kinetics and degree of network formation. These inks were then used to print a model of breast cancer cell invasion, where the inclusion of dynamic cross-links was found to be required for the formation of invasive protrusions. Together, we demonstrate the power of engineered, dynamic bioinks to recapitulate the native cellular microenvironment for disease modeling.