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The promise of gyrochronology is that, given a star’s rotation period and mass, its age can be inferred. The reality of gyrochronology is complicated by effects other than ordinary magnetized braking that alter stellar rotation periods. In this work, we present an interpolation-based gyrochronology framework that reproduces the time- and mass-dependent spin-down rates implied by the latest open cluster data, while also matching the rate at which the dispersion in initial stellar rotation periods decreases as stars age. We validate our technique for stars with temperatures of 3800–6200 K and ages of 0.08–2.6 gigayears (Gyr), and use it to reexamine the empirical limits of gyrochronology. In line with previous work, we find that the uncertainty floor varies strongly with both stellar mass and age. For Sun-like stars (≈5800 K), the statistical age uncertainties improve monotonically from ±38% at 0.2 Gyr to ±12% at 2 Gyr, and are caused by the empirical scatter of the cluster rotation sequences combined with the rate of stellar spin-down. For low-mass K dwarfs (≈4200 K), the posteriors are highly asymmetric due to stalled spin-down, and ±1σ age uncertainties vary non-monotonically between 10% and 50% over the first few gigayears. High-mass K dwarfs (5000 K) older than ≈1.5 Gyr yield the most precise ages, with limiting uncertainties currently set by possible changes in the spin-down rate (12% systematic), the calibration of the absolute age scale (8% systematic), and the width of the slow sequence (4% statistical). An open-source implementation, gyro-interp, is available online at github.com/lgbouma/gyro-interp.

The absolute age of a simple stellar population is of fundamental interest for a wide range of applications but is difficult to measure in practice, as it requires an understanding of the uncertainties in a variety of stellar evolution processes as well as the uncertainty in the distance, reddening, and composition. As a result, most studies focus only on the relative age by assuming that stellar evolution calculations are accurate and using age determinations techniques that are relatively independent of distance and reddening. Here, we construct 20,000 sets of theoretical isochrones through Monte Carlo simulation using the Dartmouth Stellar Evolution Program to measure the absolute age of the globular cluster M92. For each model, we vary a range of input physics used in the stellar evolution models, including opacities, nuclear reaction rates, diffusion coefficients, atmospheric boundary conditions, helium abundance, and treatment of convection. We also explore variations in the distance and reddening as well as its overall metallicity and α enhancement. We generate simulated Hess diagrams around the main-sequence turn-off region from each set of isochrones and use a Voronoi binning method to fit the diagrams to Hubble Space Telescope Advanced Camera for Surveys data. We find the age of M92 to be 13.80 ± 0.75 Gyr. The 5.4% error in the absolute age is dominated by the uncertainty in the distance to M92 (∼80% of the error budget); of the remaining parameters, only the total metallicity, α element abundance, and treatment of helium diffusion contribute significantly to the total error.

A series of global major geological and biological events occurred during the Permian Period. Establishing a highresolution stratigraphic and temporal framework is essential to understand their cause-effect relationship. The official International timescale of the Permian System consists of three series (i.e., Cisuralian, Guadalupian and Lopingian in ascending order) and nine stages. In China, the Permian System is composed of three series (Chuanshanian, Yansingian and Lopingian) and eight stages, of which the subdivisions and definitions of the Chuanshanian and Yangsingian series are very different from the Cisuralian and Guadalupian series. The Permian Period spanned ∼47 Myr. Its base is defined by the First Appearance Datum (FAD) of the conodont Streptognathodus isolatus at Aidaralash, Kazakhstan with an interpolated absolute age 298.9±0.15 Ma at Usolka, southern Urals, Russia. Its top equals the base of the Triassic System and is defined by the FAD of the conodont Hindeodus parvus at Meishan D section, southeast China with an interpolated absolute age 251.902±0.024 Ma. Thirty-five conodont, 23 fusulinid, 17 radiolarian and 20 ammonoid zones are established for the Permian in China, of which the Guadalupian and Lopingian conodont zones have been served as the standard for international correlation. The Permian δ 13 C carb trend indicates that it is characterized by a rapid negative shift of 3–5‰ at the end of the Changhsingian, which can be used for global correlation of the end-Permian mass extinction interval, but δ 13 C carb records from all other intervals may have more or less suffered subsequent diagenetic alteration or represented regional or local signatures only. Permian δ 18 O{ainpatite} studies suggest that an icehouse stage dominated the time interval from the late Carboniferous to Kungurian (late Cisuralian). However, paleoclimate began to ameriolate during the late Kungurian and gradually shifted into a greenhouse-dominated stage during the Guadalupian. The Changhsingian was a relatively cool stage, followed by a globally-recognizable rapid temperature rise of 8–10°C at the very end of the Changhsingian. The 87 Sr/ 86 Sr ratio trend shows that their values at the beginning of the Permian were between 0.70800, then gradually decreased to the late Capitanian minimum 0.70680–0.70690, followed by a persistent increase until the end of the Permian with the value 0.70708. Magenetostratigraphy suggests two distinct stages separated by the Illawarra Reversal in the middle Wordian, of which the lower is the reverse polarity Kiaman Superchron and the upper is the mixed-polarity Illawarra Superchron. The end-Guadalupian (or pre-Lopingian) biological crisis occurred during the late Capitanian, when faunal changeovers of different fossil groups had different paces, but generally experienced a relatively long time from the Jinogondolella altudensis Zone until the earliest Wuchiapingian. The end-Permian mass extinction was a catastrophic event that is best constrained at the Meishan section, which occurred at 251.941±0.037 Ma and persisted no more than 61±48 kyr. After the major pulse at Bed 25, the extinction patterns are displayed differently in different sections. The global end-Guadalupian regression is manifested between the conodont Jinogondolella xuanhanensis and Clarkina dukouensis zones and the end-Changhsingian transgression began in the Hindeodus changxingensis-Clarkina zhejiangensis Zone. The Permian Period is also characterized by strong faunal provincialism in general, which resulted in difficulties in inter-continental and inter-regional correlation of both marine and terrestrial systems.

Understanding the ages of stars is crucial for unraveling the formation history and evolution of our Galaxy. Traditional methods for estimating stellar ages from spectroscopic data often struggle with providing appropriate uncertainty estimations and are severely constrained by the parameter space. In this work, we introduce a new approach using normalizing flows—a type of deep generative model—to estimate stellar ages for evolved stars with improved accuracy and robust uncertainty characterization. The model is trained on stellar masses for evolved stars derived from asteroseismology and predicts the relationship between the carbon and nitrogen abundances of a given star and its age. Unlike standard neural network techniques, normalizing flows enable the recovery of full likelihood distributions for individual stellar ages, offering a richer and more informative perspective on uncertainties. Our method yields age estimations for 378,720 evolved stars and achieves a typical absolute age uncertainty of approximately 2 Gyr. By intrinsically accounting for the coverage and density of the training data, our model ensures that the resulting uncertainties reflect both the inherent noise in the data and the completeness of the sampled parameter space. Applying this method to data from the fifth-generation Sloan Digital Sky Survey Milky Way Mapper, we have produced the largest stellar age catalog for evolved stars to date.

High-resolution Hubble Space Telescope optical observations have been used to analyze the stellar population and the structure of the poorly investigated bulge globular cluster NGC 6316. We constructed the first high-resolution reddening map in the cluster direction, which allowed us to correct the evolutionary sequences in the color–magnitude diagram (CMD) for the effects of differential reddening. A comparison between the CMDs of NGC 6316 and 47 Tucanae revealed strikingly similar stellar populations, with the two systems basically sharing the same turnoff, subgiant branch, and horizontal branch morphologies, indicating comparable ages. The red giant branch in NGC 6316 appears slightly bluer than in 47 Tucanae, suggesting a lower metal content. This has been confirmed by the isochrone fitting of the observed CMD, which provided us with updated values of the cluster age, distance, average color excess, and metallicity. We estimated an absolute age of 13.1 ± 0.5 Gyr, consistent with the age of 47 Tucanae, an average color excess E(B − V) = 0.64 ± 0.01, and a true distance modulus (m − M)0 = 15.27 ± 0.03 that sets the cluster distance at 11.3 kpc from the Sun. In addition, the photometric estimate of the cluster metallicity suggests [Fe/H] ≈ −0.9, which is ∼0.2 dex smaller than that of 47 Tucanae. We also determined the gravitational center and the density profile of the system from resolved stars. The latter is well reproduced by a King model. Our results confirm that NGC 6316 is another extremely old relic of the assembly history of the Galaxy.

Zircon U–Pb geochronology is a staple of crustal evolution studies and sedimentary provenance analysis. Constructing (detrital) U–Pb age spectra is straightforward for concordant 206Pb/238U and 207Pb/206Pb compositions. But unfortunately, many U–Pb datasets contain a significant proportion of discordant analyses. This paper investigates two decisions that must be made when analysing such discordant U–Pb data. First, the analyst must choose whether to use the 206Pb/238U or the 207Pb/206Pb date. The 206Pb/238U method is more precise for young samples, whereas the 207Pb/206Pb method is better suited for old samples. However there is no agreement which “cutoff” should be used to switch between the two. This subjective decision can be avoided by using single-grain concordia ages. These represent a kind of weighted mean between the 206Pb/238U and 207Pb/206Pb methods, which offers better precision than either of the latter two methods. A second subjective decision is how to define the discordance cutoff between “good” and “bad” data. Discordance is usually defined as (1) the relative age difference between the 206Pb/238U and 207Pb/206Pb dates. However, this paper shows that several other definitions are possible as well, including (2) the absolute age difference; (3) the common-Pb fraction according to the Stacey–Kramers mantle evolution model; (4) the p value of concordance; (5) the perpendicular log ratio (or “Aitchison”) distance to the concordia line; and (6) the log ratio distance to the maximum likelihood composition on the concordia line. Applying these six discordance filters to a 70 869-grain dataset of zircon U–Pb compositions reveals that (i) the relative age discordance filter tends to suppress the young age components in U–Pb age spectra, whilst inflating the older age components; (ii) the Stacey–Kramers discordance filter is more likely to reject old grains and less likely to reject young ones; (iii) the p-value-based discordance filter has the undesirable effect of biasing the results towards the least precise measurements; (iv) the log-ratio-based discordance filters are strictest for Proterozoic grains and more lenient for Phanerozoic and Archaean age components; (v) of all the methods, the log ratio distance to the concordia composition produces the best results, in the sense that it produces age spectra that most closely match those of the unfiltered data: it sharpens age spectra but does not change their shape. The popular relative age definition fares the worst according to this criterion. All the methods presented in this paper have been implemented in the IsoplotR toolbox for geochronology.

The ~70 km-diameter Yarrabubba impact structure in Western Australia is regarded as among Earth’s oldest, but has hitherto lacked precise age constraints. Here we present U-Pb ages for impact21 driven shock recrystallised accessory minerals. Shock-recrystallised monazite yields a precise impact age of 2229 ± 5 Ma, coeval with shock-reset zircon. This result establishes Yarrabubba as the oldest recognized meteorite impact structure on Earth, extending the terrestrial cratering record back >200 million years. The age of Yarrabubba coincides, within uncertainty, with temporal constraint for the youngest Palaeoproterozoic glacial deposits, the Rietfontein diamictite in South Africa. Numerical impact simulations indicate that a 70 km-diameter crater into a continental glacier could release between 8.7x1013 to 5.0x1015 kg of H2O vapour instantaneously into the atmosphere. These results provide new estimates of impact-produced H2O vapour abundances for models investigating termination of the Paleoproterozoic glaciations, and highlight the possible role of impact cratering in modifying Earth’s climate.

What factors influence whether a lineage can successfully transition into a new biome, and why have some biome shifts been more frequent than others? To orient this line of research we develop a conceptual framework in which the likelihood of a biome shift is a function of ( a ) exposure to contrasting environments over time, ( b ) the evolutionary accessibility of relevant adaptations, and ( c ) changing biotic interactions. We evaluate the literature on biome shifts in plants in relation to a set of hypotheses on the size, connectedness, and absolute age of biomes, as well as on the adaptability of particular lineages and ecological interactions over time. We also critique the phylogenetic inference of past biomes and a \"global\" model-based approach to biome evolution. More robust generalizations about biome shifts will require detailed studies of well-sampled and well-resolved clades, accounting for changes in the relevant abiotic and biotic factors through time.

The origin of hot Jupiters is the oldest problem in exoplanet astrophysics. Hot Jupiters formed in situ or via disk migration should be in place just a few million years after the formation of their host stars. On the other hand, hot Jupiters formed via eccentricity excitation and tidal damping as a result of planet–planet scattering or Kozai–Lidov oscillations may take 1 Gyr or more to arrive at their observed locations. We propose that the relative ages of hot Jupiters inside, near, and outside the bias-corrected peak of the observed hot Jupiter period distribution can be used to distinguish between these possibilities. Though the lack of precise and accurate age inferences for isolated hot Jupiter host stars makes this test difficult to implement, comparisons between the Galactic velocity dispersions of the hot Jupiter subpopulations enable this investigation. To transform relative age offsets into absolute age offsets, we calibrate the monotonically increasing solar neighborhood age–velocity dispersion relation using an all-sky sample of subgiants with precise ages and a metallicity distribution matched to that of hot Jupiter hosts. We find that the inside-peak and near-peak subpopulations are older than the outside-peak subpopulation, with the inside-peak subpopulation slightly older than the near-peak subpopulation. We conclude that at least 40% but not more than 70% of the hot Jupiter population must have formed via a late-time, peak-populating process like high-eccentricity migration that typically occurs more than 1.5 Gyr after system formation.

Globular clusters (GCs) provide statistically significant coeval populations of stars spanning various evolutionary stages, allowing robust constraints on stellar evolution model parameters and ages. We analyze eight old Milky Way GCs with metallicities between [Fe/H] = −2.31 and −0.77 by comparing theoretical isochrone sets from the Dartmouth Stellar Evolution Program to Hubble Space Telescope (HST) observations. The theoretical isochrones include uncertainties introduced by 21 stellar evolution parameters such as convective mixing, opacity, diffusion, and nuclear reactions, capturing much of the quantifiable physics used in our code. For each isochrone, we construct simulated color–magnitude diagrams (CMDs) near the main-sequence turnoff region and apply two full-CMD-fitting methods to fit HST Advanced Camera for Surveys data across a range of distances and reddening and measure the absolute age of each GC from the resulting posterior distribution, which accounts for uncertainties in the stellar models, observations, and fitting method. The resulting best-fitting absolute ages range from ≈11.5 to 13.5 Gyr, with a typical error of 0.5–0.75 Gyr; the data show a clear trend toward older ages at lower metallicities. Notably, distance and reddening account for over 50% of the uncertainty in age determination in each case, with metallicity, α abundance, mixing length, and helium diffusion being the most important stellar physics parameters for the error budget. We also provide an absolute age–metallicity relation for Milky Way GCs.