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We update the capabilities of the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). The new auto_diff module implements automatic differentiation in MESA, an enabling capability that alleviates the need for hard-coded analytic expressions or finite-difference approximations. We significantly enhance the treatment of the growth and decay of convection in MESA with a new model for time-dependent convection, which is particularly important during late-stage nuclear burning in massive stars and electron-degenerate ignition events. We strengthen MESA’s implementation of the equation of state, and we quantify continued improvements to energy accounting and solver accuracy through a discussion of different energy equation features and enhancements. To improve the modeling of stars in MESA, we describe key updates to the treatment of stellar atmospheres, molecular opacities, Compton opacities, conductive opacities, element diffusion coefficients, and nuclear reaction rates. We introduce treatments of starspots, an important consideration for low-mass stars, and modifications for superadiabatic convection in radiation-dominated regions. We describe new approaches for increasing the efficiency of calculating monochromatic opacities and radiative levitation, and for increasing the efficiency of evolving the late stages of massive stars with a new operator-split nuclear burning mode. We close by discussing major updates to MESA’s software infrastructure that enhance source code development and community engagement.

As dark matter appears to comprise most of the Galactic mass, some of it may accumulate in the cores of stars, thereby making the Sun a laboratory for constraining various dark matter theories. We consider the effects on the solar structure arising from a general class of macroscopic dark matter candidates that include strange quark matter, compact dark objects, and others. We calibrate standard solar evolution models (i.e., models that reproduce the mass, luminosity, radius, and metallicity of the Sun at its present age) with variable compact dark core masses ranging from 10−8 to 10−2 M⊙ and assess their properties. We find that the weakest constraints come from solar neutrino flux measurements, which only rule out the most massive dark core comprising at least ∼1% of the total solar mass. The Sun’s acoustic oscillations impose stronger constraints, probing masses down to ∼10−5 M⊙. We find that a model with a 10−3 M⊙ dark core appears to improve the agreement with helioseismic observations. We nevertheless caution against interpreting this as evidence for dark matter in the solar interior, and suggest plausible effects that the dark core may instead be emulating. Finally, we show that future measurements of solar g-modes may constrain dark core masses down to 10−7 M⊙.

The first stars likely formed from pristine clouds, marking a transformative epoch after the dark ages by initiating reionization and synthesising the first heavy elements. Among these, low-mass Population III (Pop III) stars are of particular interest, as their long lifespans raise the possibility that some may survive to the present day in the Milky Way’s stellar halo or satellite dwarfs. As the first paper in a series, we present hydrodynamic evolutionary models for 0.7–1 M⊙ stars evolved up to the white dwarf phase, utilising the MESA software instrument. We systematically vary mass-loss efficiencies, convective transport, and overshooting prescriptions, thereby mapping (i) how uncertain physics influences nucleosynthetic yields; (ii) surface enrichment, including nitrogen-rich post-main-sequence stars arising from convective shell mergers; (iii) remnant properties, such as low-mass helium or carbon-oxygen white dwarfs (MWD ∼ 0.45−0.55 M⊙) and transient UV-bright phases; and (iv) potential observational signatures, including neutrino emission during shell mergers and helium flashes. These models establish a predictive framework for identifying surviving Pop III stars and their descendants, providing both evolutionary and observational constraints that were previously unexplored.

Low-mass stars from the first epoch of star formation may still persist in the Milky Way and its satellite dwarf galaxies today; however, their detection is confounded by surface pollution from interstellar accretion and internal mixing, which obscure their primordial composition and blur their distinction from second-generation stars. Asteroseismology offers a probe of the internal structure and evolutionary state of stars, and hence may aid in the search for primordial stars. In this second paper of the series, we present the first nonradial adiabatic pulsation analysis of low-mass, metal-free stellar models. We use a 0.85 M⊙ red giant as a case study and compare its seismic signatures with those of higher-metallicity models. At the same central hydrogen fractions, Population III (Pop III) main-sequence models display systematically higher r02 ≡ δν02/Δν ratio and lower Δν than metal-enriched analogues, a direct consequence of their larger internal sound speeds and steeper core-envelope stratification. To interpret the structural dependence during giant evolution, we introduce a composite asteroseismic diagnostic, ψ ≡ Δν/ΔΠ1, which traces how metallicity influences the balance between acoustic and buoyancy cavities through its imprint on opacity, core contraction, and mean molecular-weight gradients. Pop III models occupy a distinct locus in the ψ − ΔΠ1 plane due to their radiative interiors with lower mean densities and delayed development of core mean molecular weight gradients. We find that asteroseismology is a powerful diagnostic for identifying relic Pop III stars despite potentially polluted surfaces, providing a clear pathway for future searches of the Galaxy’s oldest surviving stars with upcoming surveys.

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.

Primordial black holes (PBHs) in the asteroid mass window from 10−16 M ⊙ to 10−10 M ⊙ are currently a popular dark matter candidate. If they exist, some stars would capture them upon formation, and they would slowly accrete the star over gigayears. Such Hawking stars—stars with a central PBH—provide a novel channel for the formation of both sub-Chandrasekhar-mass black holes and red straggler stars. Here we report on stellar evolution models that extend our previous work to Hawking stars with masses between 0.5 and 1.4 M ⊙. We explore three accretion schemes, and find that a wide range of PBHs in the asteroid mass window can robustly accrete stars as small as 1 M ⊙ within the age of the Universe. This mechanism of producing subsolar-mass black holes is highly dependent on the assumed accretion physics and stellar metallicity. Lower-metallicity stars are generally accreted more rapidly, suggesting that it may be more likely for sub-Chandrasekhar-mass Hawking stars formed in the early Universe, such as those in ultrafaint dwarf (UFD) galaxies, to transmute their star into a sub-Chandrasekhar-mass black hole within a Hubble time. We present a stellar population synthesis of a Draco II–like UFD galaxy containing Hawking stars and show that the number of red stragglers they produce can qualitatively match the observed population for black hole seed masses around 10−11 M ⊙ and under the assumption that they accrete with high radiative efficiency.

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.

We extend the time-dependent convection (TDC) treatment in MESA by introducing eddy-viscous dissipation. This software change brings MESA-TDC into closer alignment with the radial stellar pulsation (RSP) framework of the MESA-RSP module. We demonstrate that the inclusion of the eddy viscosity in hydrodynamic stellar models remains stable on evolutionary timescales. We then present the first self-consistent integration of large-amplitude, nonlinear classical Cepheid pulsations directly within a MESA-star evolutionary run, demonstrating that the TDC formalism implemented in MESA-star and the MESA-RSP module are physically identical. Starting from a 6 M⊙ blue-loop stellar evolution model, we demonstrate evolving the entire stellar model through pulsations as well as pausing the evolution, excising the core, and remeshing the envelope to match the grid used by MESA-RSP. We compare the pulsation properties (e.g., period, light and radius curves, and growth rate) with a matched MESA-RSP run, and find reasonable agreement between the two modules. This unified approach eliminates the reliance on separate postprocessing workflows and enables fully coupled evolution–pulsation simulations. This approach enables future studies of stellar pulsations with the inclusion of composition gradients, mass loss, or rotation. It also enables future studies of the ϵ mechanism as well as providing a physical source of viscosity for other science cases explored using MESA’s hydrodynamics solver. We have integrated these modifications into the MESA-star module, enabling open-source use by the community.

Hawking proposed that the Sun may harbor a primordial black hole (BH) whose accretion supplies some of the solar luminosity. Such an object would have formed within the first 1 s after the Big Bang with the mass of a moon or an asteroid. These light BHs are a candidate solution to the dark matter problem, and could grow to become stellar-mass BHs if captured by stars. Here we compute the evolution of stars having such a BH at their center. We find that such objects can be surprisingly long-lived, with the lightest BHs having no influence over stellar evolution, while more massive ones consume the star over time to produce a range of observable consequences. Models of the Sun born about a BH whose mass has since grown to approximately 10−6 M ⊙ are compatible with current observations. In this scenario, the Sun would first dim to half its current luminosity over a span of 100 Myr as the accretion starts to generate enough energy to quench nuclear reactions. The Sun would then expand into a fully convective star, where it would shine luminously for potentially several gigayears with an enriched surface helium abundance, first as a sub-subgiant star, and later as a red straggler, before becoming a subsolar-mass BH. We also present results for a range of stellar masses and metallicities. The unique internal structures of stars harboring BHs may make it possible for asteroseismology to discover them, should they exist. We conclude with a list of open problems and predictions.

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 1.15 M ⊙. 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.