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At least 19 records

Photometric detection of internal gravity waves in upper main-sequence stars

Massive stars are predicted to excite internal gravity waves (IGWs) by turbulent core convection and from turbulent pressure fluctuations in their near-surface layers. These IGWs are extremely efficient at transporting angular momentum and chemical species within stellar interiors, but they remain largely unconstrained observationally. In this work, we aim to characterise the photometric detection of IGWs across a large number of O and early-B stars in the Hertzsprung–Russell diagram, and explain the ubiquitous detection of stochastic variability in the photospheres of massive stars. Furthermore, we combined high-precision time-series photometry from the NASA Transiting Exoplanet Survey Satellite with high-resolution ground-based spectroscopy of 70 stars with spectral types O and B to probe the relationship between the photometric signatures of IGWs and parameters such as spectroscopic mass, luminosity, and macroturbulence.

79 ASTRONOMY AND ASTROPHYSICS↗

RRab variables with identical light-curve shapes at different pulsation periods

In this paper, we report on the detection of RRab stars with quasi-identical-shape light curves but period differences as large as 0.05–0.21 d using the Galactic bulge data of the OGLE-IV survey. We have examined stars with shorter periods than the Oosterhoff I ridge of the bulge. These stars generally have smaller amplitudes and larger Fourier phase-differences than the typical bulge RRab stars have at the same period. Many of these ‘anomalous’ stars have good-quality light curves without any sign of the Blazhko modulation. Examining their Fourier parameters revealed that several of these stars show very similar light curve to the typical bulge RR Lyrae. We found hundreds of quasi-identical-shape light-curve pairs with different periods between the ‘anomalous’- and the ‘normal’-position RRab stars based on the OGLE I-band data. The OGLE V-band, and the archive VVV and MACHO surveys K s -, b- and r -band data of these stars were also checked for light-curve-shape similarity. Finally, 149 pairs with identical-shape light curves in each available photometric band were identified. Calculating the physical properties of the variables using empirical formulae, on average, −0.5 dex, −0.13 mag, 0.67, and 165 K differences between the [Fe/H], M V , R/R ⊙ , and T eff values of the members of the pairs are derived, being the short-period stars less metal-poor, fainter, smaller, and hotter than the long-period variables. To explain the existence of variables with different physical properties and pulsation periods but with identical-shape light curves is a challenging task for modelling.

79 ASTRONOMY AND ASTROPHYSICS↗

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗

Stellar loci IV. red giant stars

In the fourth paper of this series, we present the metallicity-dependent Sloan Digital Sky Survey (SDSS) stellar color loci of red giant stars, using a spectroscopic sample of red giants in the SDSS Stripe 82 region. The stars span a range of 0.55 – 1.2 mag in color g – i, –0.3 – –2.5 in metallicity [Fe/H], and have values of surface gravity log g smaller than 3.5 dex. As in the case of main-sequence (MS) stars, the intrinsic widths of loci of red giants are also found to be quite narrow, a few mmag at maximum. There are however systematic differences between the metallicity-dependent stellar loci of red giants and MS stars. The colors of red giants are less sensitive to metallicity than those of MS stars. With good photometry, photometric metallicities of red giants can be reliably determined by fitting the u – g, g – r, r – i, and i – z colors simultaneously to an accuracy of 0.2 – 0.25 dex, comparable to the precision achievable with low-resolution spectroscopy for a signal-to-noise ratio of 10. By comparing fitting results to the stellar loci of red giants and MS stars, we propose a new technique to discriminate between red giants and MS stars based on the SDSS photometry. The technique achieves completeness of ~70 per cent and efficiency of ~80 per cent in selecting metal-poor red giant stars of [Fe/H] ≤ –1.2. It thus provides an important tool to probe the structure and assemblage history of the Galactic halo using red giant stars.

79 ASTRONOMY AND ASTROPHYSICS↗

A unified exploration of the chronology of the Galaxy

The Milky Way has distinct structural stellar components linked to its formation and subsequent evolution, but disentangling them is non-trivial. With the recent availability of high-quality data for a large numbers of stars in the Milky Way, it is a natural next step for research in the evolution of the Galaxy to perform automated explorations with unsupervised methods of the structures hidden in the combination of large-scale spectroscopic, astrometric, and asteroseismic data sets. We determine precise stellar properties for 21 076 red giants, mainly spanning 2–15 kpc in Galactocentric radii, making it the largest sample of red giants with measured asteroseismic ages available to date. We explore the nature of different stellar structures in the Galactic disc by using Gaussian mixture models as an unsupervised clustering method to find substructure in the combined chemical, kinematic, and age subspace. The best-fitting mixture model yields four distinct physical Galactic components in the stellar disc: the thin disc, the kinematically heated thin disc, the thick disc, and the stellar halo. We find hints of an age asymmetry between the Northern and Southern hemisphere, and we measure the vertical and radial age gradient of the Galactic disc using the asteroseismic ages extended to further distances than previous studies.

79 ASTRONOMY AND ASTROPHYSICS↗

The SDSS-HET Survey of Kepler Eclipsing Binaries. A Sample of Four Benchmark Binaries

The purpose of this work is to extend a sample of accurately modeled, benchmark-grade eclipsing binaries (EBs) with accurately determined masses and radii. We select four "well-behaved" Kepler binaries, KIC 2306740, KIC 4076952, KIC 5193386 and KIC 5288543, each with at least eight double-lined spectra from the Apache Point Observatory Galactic Evolution Experiment instrument that is part of the Sloan Digital Sky Surveys III and IV, and from the Hobby–Eberly High Resolution Spectrograph. We obtain masses and radii with uncertainties of 2.5% or less for all four systems. Three of these systems have orbital periods longer than 9 days, and thus populate an undersampled region of the parameter space for extremely well-characterized detached EBs. We compare the derived masses and radii against MESA MIST isochrones to determine the ages of the systems. All systems were found to be coeval, showing that the results are consistent across MESA MIST and PHOEBE .

79 ASTRONOMY AND ASTROPHYSICS↗

The stellar parameters and elemental abundances from low-resolution spectra – I. 1.2 million giants from LAMOST DR8

As a typical data-driven method, deep learning becomes a natural choice for analysing astronomical data. In this study, we built a deep convolutional neural network (NN) to estimate basic stellar parameters $T\rm {_{eff}}$, log g , metallicity ([M/H] and [Fe/H]) and [α/M] along with nine individual elemental abundances ([C/Fe], [N/Fe], [O/Fe], [Mg/Fe], [Al/Fe], [Si/Fe], [Ca/Fe], [Mn/Fe], and [Ni/Fe]). The NN is trained using common stars between the APOGEE survey and the LAMOST survey. We used low-resolution spectra from LAMOST survey as input, and measurements from APOGEE as labels. For stellar spectra with the signal-to-noise ratio in g band larger than 10 in the test set, the mean absolute error (MAE) is 29 K for $T\rm {_{eff}}$, 0.07 dex for log g , 0.03 dex for both [Fe/H] and [M/H], and 0.02 dex for [α/M]. The MAE of most elements is between 0.02 and 0.04 dex. The trained NN was applied to 1210 145 giants, including sub-giants, from LAMOST DR8 within the range of stellar parameters 3500 K < $T\rm {_{eff}}$ < 5500 K, 0.0 dex < log g < 4.0 dex, −2.5 dex < [Fe/H] < 0.5 dex. The distribution of our results in the chemical spaces is highly consistent with APOGEE labels and stellar parameters show consistency with external high-resolution measurements from GALAH. The results in this study allow us to further studies based on LAMOST data and deepen our understanding of the accretion and evolution history of the Milky Way. The electronic version of the value added catalog is available at http://www.lamost.org/dr8/v1.1/doc/vac.

79 ASTRONOMY AND ASTROPHYSICS↗

A variational encoder–decoder approach to precise spectroscopic age estimation for large Galactic surveys

Constraints on the formation and evolution of the Milky Way Galaxy require multidimensional measurements of kinematics, abundances, and ages for a large population of stars. Ages for luminous giants, which can be seen to large distances, are an essential component of studies of the Milky Way, but they are traditionally very difficult to estimate precisely for a large data set and often require careful analysis on a star-by-star basis in asteroseismology. Because spectra are easier to obtain for large samples, being able to determine precise ages from spectra allows for large age samples to be constructed, but spectroscopic ages are often imprecise and contaminated by abundance correlations. Here we present an application of a variational encoder–decoder on cross-domain astronomical data to solve these issues. The model is trained on pairs of observations from APOGEE and Kepler of the same star in order to reduce the dimensionality of the APOGEE spectra in a latent space while removing abundance information. The low dimensional latent representation of these spectra can then be trained to predict age with just ∼1000 precise seismic ages. We demonstrate that this model produces more precise spectroscopic ages (∼ 22 per cent overall, ∼ 11 per cent for red-clump stars) than previous data-driven spectroscopic ages while being less contaminated by abundance information (in particular, our ages do not depend on [α/M]). We create a public age catalogue for the APOGEE DR17 data set and use it to map the age distribution and the age-[Fe/H]-[α/M] distribution across the radial range of the Galactic disc.

79 ASTRONOMY AND ASTROPHYSICS↗

The Gaia EDR3 view of Johnson-Kron-Cousins standard stars: the curated Landolt and Stetson collections

In the era of large surveys and space missions, it is necessary to rely on large samples of well-characterized stars for inter-calibrating and comparing measurements from different surveys and catalogues. Among the most employed photometric systems, the Johnson-Kron-Cousins has been used for decades and for a large amount of important datasets. Our goal is to profit from the Gaia EDR3 data, Gaia official cross-match algorithm, and Gaia -derived literature catalogues, to provide a well-characterized and clean sample of secondary standards in the Johnson-Kron-Cousins system, as well as a set of transformations between the main photometric systems and the Johnson-Kron-Cousins one. Using Gaia as a reference, as well as data from reddening maps, spectroscopic surveys, and variable stars monitoring surveys, we curated and characterized the widely used Landolt and Stetson collections of more than 200 000 secondary standards, employing classical as well as machine learning techniques. In particular, our atmospheric parameters agree significantly better with spectroscopic ones, compared to other machine learning catalogues. We also cross-matched the curated collections with the major photometric surveys to provide a comprehensive set of reliable measurements in the most widely adopted photometric systems. We provide a curated catalogue of secondary standards in the Johnson-Kron-Cousins system that are well-measured and as free as possible from variable and multiple sources. We characterize the collection in terms of astrophysical parameters, distance, reddening, and radial velocity. We provide a table with the magnitudes of the secondary standards in the most widely used photometric systems (ugriz, grizy, Gaia , HIPPARCOS, Tycho , 2MASS). We finally provide a set of 167 polynomial transformations, valid for dwarfs and giants, metal-poor and metal-rich stars, to transform UBVRI magnitudes in the above photometric systems and vice-versa.

79 ASTRONOMY AND ASTROPHYSICS↗

LAMOST Time-Domain survey: first results of four K2 plates

From Oct. 2019 to Apr. 2020, LAMOST performed a time-domain (TD) spectroscopic survey of four K2 plates with both low- and medium-resolution observations. The low-resolution spectroscopic survey acquired 282 exposures ( ≈ 46.6 h) over 25 nights, yielding a total of about 767 000 spectra, and the medium-resolution survey took 177 exposures ( ≈ 49.1 h) over 27 nights, collecting about 478 000 spectra. More than 70%/50% of low-resolution/medium-resolution spectra have signal-to-noise ratio higher than 10. We determine stellar parameters (e.g., T eff , log g, [Fe/H]) and radial velocity (RV) with different methods, including LASP, DD-Payne and SLAM. In general, these parameter estimations from different methods show good agreement, and the stellar parameter values are consistent with those of APOGEE. We use the Gaia DR2 RV values to calculate a median RV zero point (RVZP) for each spectrograph exposure by exposure, and the RVZP-corrected RVs agree well with the APOGEE data. The stellar evolutionary and spectroscopic masses are estimated based on the stellar parameters, multi-band magnitudes, distances and extinction values. Finally, we construct a binary catalog including about 2700 candidates by analyzing their light curves, fitting the RV data, calculating the binarity parameters from medium-resolution spectra and cross-matching the spatially resolved binary catalog from Gaia EDR3. In conclusion, the LAMOST TD survey is expected to represent a breakthrough in various scientific topics, such as binary systems, stellar activity, stellar pulsation, etc.

79 ASTRONOMY AND ASTROPHYSICS↗

Lyman alpha and Lyman continuum emission of Mg Ⅱ -selected star-forming galaxies

We present observations with the Cosmic Origins Spectrograph onboard the Hubble Space Telescope of seven compact low-mass star-forming galaxies at redshifts, z, in the range 0.3161–0.4276, with various O 3 Mg 2 = [O iii] λ5007/Mg ii λ2796+2803 and Mg 2 = Mg ii λ2796/Mg ii λ2803 emission-line ratios. We aim to study the dependence of leaking Lyman continuum (LyC) emission on the characteristics of Mg ii emission together with the dependencies on other indirect indicators of escaping ionizing radiation. LyC emission with escape fractions f esc (LyC) = 3.1–4.6 percent is detected in four galaxies, whereas only 1σ upper limits of f esc (LyC) in the remaining three galaxies were derived. A strong narrow Lyα emission line with two peaks separated by V sep ~ 298–592 km s -1 was observed in four galaxies with detected LyC emission and very weak Lyα emission is observed in galaxies with LyC non-detections. Our new data confirm the tight anticorrelation between f esc (LyC) and V sep found for previous low-redshift galaxy samples. V sep remains the best indirect indicator of LyC leakage among all considered indicators. It is found that escaping LyC emission is detected predominantly in galaxies with Mg 2 ≳ 1.3. A tendency of an increase of f esc (LyC) with increasing of both the O 3 Mg 2 and Mg 2 is possibly present. However, there is substantial scatter in these relations not allowing their use for reliable prediction of f esc (LyC).

79 ASTRONOMY AND ASTROPHYSICS↗

A spectrophotometric analysis of cool white dwarfs in the Gaia and pan-STARRS footprint

We present a spectrophotometric analysis of 2880 cool white dwarfs within 100 pc of the Sun and cooler than T eff ∼ 10 000 K, with grizy Pan-STARRS photometry and Gaia trigonometric parallaxes available. We also supplement our data sets with near-infrared JHK photometry, when available, which is shown to be essential for interpreting the coolest white dwarfs in our sample. We perform a detailed analysis of each individual object using state-of-the-art model atmospheres appropriate for each spectral type, including DA, DC, DQ, DZ, He-rich DA, and the so-called IR-faint white dwarfs. We discuss the temperature and mass distributions of each subsample, as well as revisit the spectral evolution of cool white dwarfs. We find little evidence in our sample for the transformation of a significant fraction of DA stars into He-atmosphere white dwarfs through the process of convective mixing between T eff = 10 000 and ∼6500 K, although the situation changes drastically in the range T eff = 6500–5500 K where the fraction of He-atmosphere white dwarfs reaches ∼45 per cent. However, we also provide strong evidence that at even cooler temperatures (T eff ≲ 5200 K), most DC white dwarfs have H atmospheres. We discuss a possible mechanism to account for this sudden transformation from He- to H-atmosphere white dwarfs involving the onset of crystallization and the occurrence of magnetism. Finally, we also argue that DQ, DZ, and DC white dwarfs may form a more homogeneous population than previously believed.

79 ASTRONOMY AND ASTROPHYSICS↗

Decoding the age–chemical structure of the Milky Way disc: an application of copulas and elicitable maps

In the Milky Way, the distribution of stars in the [α/Fe] versus [Fe/H] and [Fe/H] versus age planes holds essential information about the history of star formation, accretion, and dynamical evolution of the Galactic disc. We investigate these planes by applying novel statistical methods called copulas and elicitable maps to the ages and abundances of red giants in the Apache Point Observatory Galactic Evolution Experiment survey. We find that the high- and low-α disc stars have a clean separation in copula space and use this to provide an automated separation of the α sequences using a purely statistical approach. This separation reveals that the high-α disc ends at the same [α/Fe] and age at high [Fe/H] as the low-[Fe/H] start of the low-α disc, thus supporting a sequential formation scenario for the high- and low-α discs. We then combine copulas with elicitable maps to precisely obtain the correlation between stellar age τ and metallicity [Fe/H] conditional on Galactocentric radius R and height z in the range 0 < R < 20 kpc and |z| < 2 kpc. The resulting trends in the age–metallicity correlation with radius, height, and [α/Fe] demonstrate a ≈0 correlation wherever kinematically cold orbits dominate, while the naively expected negative correlation is present where kinematically hot orbits dominate. This is consistent with the effects of spiral-driven radial migration, which must be strong enough to completely flatten the age–metallicity structure of the low-α disc.

79 ASTRONOMY AND ASTROPHYSICS↗

Exogeological inferences from white dwarf pollutants: the impact of stellar physics

Many white dwarfs have accreted material from their own planetary systems. These objects can be used to infer the composition of exoplanetary material and identify evidence for key geological processes. However, the white dwarf atmospheric physics distorts the inferred material composition away from the true composition, mainly through differential atomic diffusion of the accreted metals. Correcting for this effect is essential, but is dependent on various physical assumptions associated with the white dwarf itself. We first focus on the effect of assumptions related to convective overshoot and thermohaline mixing on the atomic diffusion time-scales. For white dwarfs with H-dominated atmospheres between 12000 K and 18000 K⁠, we find that including a complete treatment of convective overshoot decreases the inferred Fe and O abundances in accreted material. For these white dwarfs, we also find that including thermohaline mixing decreases Fe and O abundances. For He-dominated systems, the effect of convective overshoot is comparatively minor. We then explore the overall effect of other physical assumptions by comparing publicly available grids of diffusion time-scales. We find that the choice of model grid can have a large impact for white dwarfs with He-dominated atmospheres, notably on the inferred core to mantle ratio of accreted material. We identify several systems for which the geological interpretation is robust against these systematics. We also present a ‘discrepancy metric’ which can be used to estimate the potential impact of changing the stellar physics without requiring detailed modelling.

Astronomy and AstroPhysics↗

Fundamental effective temperature measurements for eclipsing binary stars – IV. Selection of new benchmark stars and first results for HD 22064

I describe the selection and initial characterization of 20 eclipsing binary stars that are suitable for calibration and testing of stellar models and data analysis algorithms used by the PLATO mission and spectroscopic surveys. The binary stars selected are F-/G-type dwarf stars with M-type dwarf companions that contribute less than 2 per cent of the flux at optical wavelengths. The light curves typically show well-defined total eclipses with very little variability between the eclipses. I have used near-infrared spectra obtained by the APOGEE survey to measure the spectroscopic orbit for both stars in HD 22064. Combined with an analysis of the TESS light curve, I derive the following masses and radii: M 1 = 1.35 ± 0.03M ⊙ , M 2 = 0.58 ± 0.01M ⊙ , R 1 = 1.554 ± 0.014R ⊙ , R 2 = 0.595 ± 0.008R ⊙ . Using R 1 and the parallax from Gaia EDR3, I find that the primary star’s angular diameter is θ = 0.1035 ± 0.0009 mas. The apparent bolometric flux of the primary star is ${\mathcal {F}}_{{\oplus },0} = (7.51\pm 0.09)\times 10^{-9}$ erg cm -2 s -1 . Hence, this F2V star has an effective temperature $T_{\rm eff,1} = 6763{\rm \, K} \pm 39{\rm \, K}$. HD 22064 is an ideal benchmark star that can be used for ‘end-to-end’ tests of the stellar parameters measured by large-scale spectroscopic surveys or stellar parameters derived from asteroseismology with PLATO. The techniques described here for HD 22064 can be applied to the other eclipsing binaries in the sample in order to create an all-sky network of such benchmark stars.

79 ASTRONOMY AND ASTROPHYSICS↗

The impact of composition choices on solar evolution: age, helio- and asteroseismology, and neutrinos

ABSTRACT The Sun is the most studied and well-known star, and as such, solar fundamental parameters are often used to bridge gaps in the knowledge of other stars, when these are required for modelling. However, the two most powerful and precise independent methodologies currently available to infer the internal solar structure are in disagreement. We aim to show the potential impact of composition choices in the overall evolution of a star, using the Sun as example. To this effect, we create two Standard Solar Models and a comparison model using different combinations of metallicity and relative element abundances and compare evolutionary, helioseismic, and neutrino-related properties for each. We report differences in age for models calibrated to the same point on the HR diagram, in red giant branch, of more than 1 Gyr, and found that the current precision level of asteroseismic measurements is enough to differentiate these models, which would exhibit differences in period spacing of 1.30–2.58 per cent. Additionally, we show that the measurement of neutrino fluxes from the carbon–nitrogen–oxygen cycle with a precision of around 17 per cent, which could be achieved by the next generation of solar neutrino experiments, could help resolve the stellar abundance problem.

Capelo, Diogo↗

A Quantum-mechanical Treatment of Electron Broadening in Strong Magnetic Fields

Abstract Spectral line-shape fitting is an extremely useful tool in determining the gravity of white dwarf stars. This method is so far limited to nonmagnetic white dwarfs largely because the theory of line broadening in high magnetic fields is not as complete as in the nonmagnetic case. Current Stark+Zeeman models treat plasma particles classically and ignore the motion of the nucleus. We develop the formalism for a quantum-mechanical treatment of the perturbing electrons and include the nuclear motion as part of the broadening and explore their relative importance. The conditions we explore are those found in white dwarf and neutron star atmospheres. We find that, contrary to previous studies, the quantized perturbing electrons create more broadening than perturbers on a straight-path trajectory. Additionally, the quantization of the plasma electrons gives rise to resonances away from the line center. The nuclear motion creates an additional electric field, which also leads to an increase in line broadening; however, this effect in neutron star atmospheres is not as large as previously estimated. This suggests that neutron star spectral lines are sensitive to density and that their mass and radius can be obtained from spectral line fitting, which would help constrain the neutron star equation of state.

79 ASTRONOMY AND ASTROPHYSICS↗

SDSS-IV MaStar: [α/Fe] for the MaNGA Stellar Library from synthetic model spectra

ABSTRACT We calculate the α-enhancement ratio [α/Fe] for the Mapping Nearby Galaxies at APO (MaNGA) Stellar Library (MaStar) while also fitting for the fundamental atmospheric parameters effective temperature, surface gravity, and metallicity – Teff, log g, [Fe/H]. This approach builds upon a previous catalogue of stellar parameters, whereby only the fundamental atmospheric parameters are fit with solar-scaled models. Here, we use the same Markov Chain Monte Carlo method with the additional free parameter [α/Fe]. Using the full spectral fitting code pPXF, we are able to fit multiple lines sensitive to [α/Fe] for a more robust measurement. Quality flags based on the convergence of the sampler, errors in [α/Fe] and a cut in the χ2 of the model fit are used to clean the final catalogue, returning 17 214 spectra and values in the range of −0.25 < [α/Fe] < 0.48. Comparing our calculated [α/Fe] with literature values reveals a degeneracy in cool stars with log g ≥ ∼4; this comparison is then used to create an alternative and calibrated parameter set. We also plot the final catalogue in an [Fe/H] versus [α/Fe] diagram and recover the expected result of increasing [α/Fe] with decreasing [Fe/H] for Milky Way disc-halo stars. We apply our method to a subsample of spectra of uniform resolution and higher signal to noise that finds that our results are independent of this higher signal to noise. In the context of stellar population models, we are able to cover a parameter space for the creation of intermediate to old age models at solar-scaled [α/Fe], high [Fe/H] and enhanced [α/Fe], low [Fe/H].

79 ASTRONOMY AND ASTROPHYSICS↗