arXiv subjects

P. E. Nissen

Publications and source records attributed to P. E. Nissen.

At least 19 recordsLinked to original sources

arXiv2026

Magnesium isotope ratios in Milky Way and dwarf galaxy stars

Under the assumption of hierarchical galaxy formation, dwarf galaxies are the closest existing analogues to the high-redshift protogalaxies that merged to form the Milky Way. These low-mass systems serve as unique laboratories for studying nucleosynthetic channels, given that the chemical compositions of their stars play a pivotal role in constraining their chemical enrichment history. To date, stellar abundances in dwarf galaxies have focused almost exclusively on elemental abundance ratios. While important, elemental abundances omit critical information about the isotopic composition. Here, we compute the Mg isotopic ratios of six accreted dwarf galaxy stars (low-alpha) and seven Milky Way stars (high-alpha) using a set of high-resolution (65000 < R < 160000) and high signal-to-noise ratio (S/N > 250) optical spectra. We show, for the first time, that at a given [Fe/H], stars born in a dwarf galaxy differ in their Mg isotopic ratios from stars born in the Milky Way. However, when comparing isotopic ratios at a given [Mg/H] rather than [Fe/H], a powerful diagnostic emerges that suggests nucleosynthesis processes are consistent across different stellar environments. This universality of Mg isotopic abundances provides additional dimensionality for chemical evolution models and helps to constrain massive-star nucleosynthesis across cosmic time.

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arXiv2025

The peculiar composition of the Sun is not related to giant planets

Highly-differential spectroscopic studies have revealed that the Sun is deficient in refractory elements relative to solar twins. To investigate the role of giant planets on this signature, we present a high precision abundance analysis of HARPS spectra for 50 F- and G-type stars spanning -0.4<[Fe/H]<+0.5. There are 29 stars in the sample which host planets of masses > 0.01 MJup. We derive abundances for 19 elements, and apply corrections to 14 of them for systematic errors associated with one dimensional (1D) model atmospheres, or the assumption of local thermodynamic equilibrium (LTE), or both. We find that, among the solar twins in our sample, the Sun is Li poor in comparison to other stars at similar age, in agreement to previous studies. The sample shows a variety of trends in elemental abundances as a function of condensation temperature. We find a strong correlation in these trends with [Fe/H], with a marginally-significant difference in the gradients for stars with and without giants planets detected, that increases after applying 3D and non-LTE corrections. Our overall results suggests that the peculiar composition of the Sun is primarily related to Galactic chemical evolution rather than the presence of giant planets.

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arXiv2024

A distinct halo population revealed from 3D non-LTE magnesium abundances

Magnesium is one of the important elements in stellar physics as an electron donor and in Galactic Archaeology as a discriminator of different stellar populations. However, previous studies of Mg I and Mg II lines in metal-poor benchmark stars have flagged problems with magnesium abundances inferred from one-dimensional (1D), hydrostatic models of stellar atmospheres, both with or without the local thermodynamic equilibrium (LTE) approximation. We here present 3D non-LTE calculations for magnesium in FG-type dwarfs, and provide corrections for 1D LTE abundances. The 3D non-LTE corrections reduce the ionisation imbalances in the benchmark metal-poor stars HD84937 and HD140283 from $-0.16$ dex and $-0.27$ dex in 1D LTE, to just $-0.02$ dex and $-0.09$ dex respectively. We then applied our abundance corrections to 1D LTE literature results for stars in the thin disc, thick disc, $α$-rich halo, and $α$-poor halo. We find that the 3D non-LTE results show a richer substructure in [Mg/Fe]-[Fe/H] in the $α$-poor halo, revealing two subpopulations at the metal-rich end. These two subpopulations are also separated in kinematics, supporting the astrophysical origin of the separation. While the more magnesium-poor subpopulation is likely to be debris from a massive accreted galaxy, Gaia-Enceladus, the other subpopulation may be related to a previous identified group of stars, called Eos. The presence of additional separation in [Mg/Fe] suggests that previous Mg abundance measurements may have been limited in the precision by the 1D and LTE approximations, highlighting the importance of 3D non-LTE modelling.

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arXiv2023

Abundances of iron-peak elements in accreted and in situ born Galactic halo stars

Previous work on the abundances of C, O, Na, Mg, Si, Ca, Ti, Cr, Mn, Fe, Ni, Cu, and Zn in low-alpha (accreted) and high-alpha (in situ born) halo stars is extended to include the abundances of Sc, V, and Co, enabling us to study the nucleosynthesis of all iron-peak elements along with the lighter elements. The Sc, V, and Co abundances were determined from a 1D MARCS model-atmosphere analysis of equivalent widths of atomic lines in high signal-to-noise, high resolution spectra assuming local thermodynamic equilibrium (LTE). In addition, new 3D and/or non-LTE calculations were used to correct the 1D LTE abundances for several elements including consistent 3D non-LTE calculations for Mg. The two populations of accreted and in situ born stars are well separated in diagrams showing [Sc/Fe], [V/Fe], and [Co/Fe] as a function of [Fe/H]. The [X/Mg] versus [Mg/H] trends for high-alpha and low-alpha stars were used to determine the yields of core-collapse and Type Ia supernovae. The largest Type Ia contribution occurs for Cr, Mn, and Fe, whereas Cu is a pure core-collapse element. Sc, Ti, V, Co, Ni, and Zn represent intermediate cases. A comparison with yields calculated for supernova models shows poor agreement for the core-collapse yields. The Ia yields suggest that sub-Chandrasekhar-mass Type Ia supernovae provide a dominant contribution to the chemical evolution of the host galaxies of the low-alpha stars. A substructure in the abundances and kinematics of the low-alpha stars suggests that they arise from at least two different satellite accretion events, Gaia-Sausage-Enceladus and Thamnos.

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arXiv2022

3D non-LTE iron abundances in FG-type dwarfs

Spectroscopic measurements of iron abundances are prone to systematic modelling errors. We present 3D non-LTE calculations across 32 STAGGER-grid models with effective temperatures from 5000 K to 6500 K, surface gravities of 4.0 dex and 4.5 dex, and metallicities from $-$3 dex to 0 dex, and study the effects on 171 Fe I and 12 Fe II optical lines. In warm metal-poor stars, the 3D non-LTE abundances are up to 0.5 dex larger than 1D LTE abundances inferred from Fe I lines of intermediate excitation potential. In contrast, the 3D non-LTE abundances can be 0.2 dex smaller in cool metal-poor stars when using Fe I lines of low excitation potential. The corresponding abundance differences between 3D non-LTE and 1D non-LTE are generally less severe but can still reach $\pm$0.2 dex. For Fe II lines the 3D abundances range from up to 0.15 dex larger, to 0.10 dex smaller, than 1D abundances, with negligible departures from 3D LTE except for the warmest stars at the lowest metallicities. The results were used to correct 1D LTE abundances of the Sun and Procyon (HD 61421), and of the metal-poor stars HD 84937 and HD 140283, using an interpolation routine based on neural networks. The 3D non-LTE models achieve an improved ionisation balance in all four stars. In the two metal-poor stars, they remove excitation imbalances that amount to 250 K to 300 K errors in effective temperature. For Procyon, the 3D non-LTE models suggest [Fe/H] = 0.11 $\pm$ 0.03, which is significantly larger than literature values based on simpler models. We make the 3D non-LTE interpolation routine for FG-type dwarfs publicly available, in addition to 1D non-LTE departure coefficients for standard MARCS models of FGKM-type dwarfs and giants. These tools, together with an extended 3D LTE grid for Fe II from 2019, can help improve the accuracy of stellar parameter and iron abundance determinations for late-type stars.

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arXiv2021

G112-43/44: A metal-poor binary star with a unique chemical composition and kinematics like the Helmi streams

G112-43/44, alias BD+00_2058 A and B, is a metal-poor ([Fe/H] = -1.3) wide-orbit binary star with extreme kinematics. We use high-precision determinations of the chemical compositions of 94 metal-poor dwarf stars in the solar neighbourhood to compare abundance ratios for G112-43/44 with ratios for stars having similar metallicity taking into account the effect of deviations from local thermodynamic equilibrium on the derived abundances, and Gaia EDR3 data are used to compare the kinematics. The abundances of the two components of G112-43/44 agree within 0.05 dex for nearly all elements, but there is a hint of a correlation of the difference in [X/H] with elemental condensation temperature, which may be due to planet-star interactions. The Mg/Fe, Si/Fe, Ca/Fe, and Ti/Fe ratios of G112-43/44 agree with the corresponding ratios for accreted (Gaia-Enceladus) stars, but Mn/Fe, Ni/Fe, Cu/Fe, and Zn/Fe are significantly enhanced. The kinematics show that G112-43/44 belongs to the Helmi streams in the solar neighbourhood and in view of this, we discuss if the abundance peculiarities of G112-43/44 can be explained by chemical enrichment from supernovae events in the progenitor dwarf galaxy of the Helmi streams. Interestingly, yields calculated for a helium shell detonation Type Ia supernova model can explain the enhancement of Mn/Fe, Ni/Fe, Cu/Fe, and Zn/Fe in G112-43/44 and three other alpha-poor stars in the Galactic halo, one of which have Helmi streams kinematics. The helium shell detonation model predicts, however, also enhanced abundance ratios of Ca/Fe, Ti/Fe, and Cr/Fe in disagreement with the observed ratios.

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arXiv2020

High-precision abundances of elements in solar-type stars. Evidence of two distinct sequences in abundance-age relations

HARPS spectra with signal-to-noise ratios S/N > 600 at 6000 A were analysed with MARCS model atmospheres to obtain 1D LTE abundances of C, O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Sr, and Y for 72 nearby solar-type stars with metallicities in the range -0.3 < [Fe/H] < +0.3 and ASTEC stellar models were used to determine stellar ages from effective temperatures, luminosities obtained via Gaia DR2 parallaxes, and heavy element abundances. The resulting age-metallicity distribution appears to consist of two distinct populations: a sequence of old stars with a steep rise of [Fe/H] to about +0.3 dex at an age of ~7 Gyr and a younger sequence with [Fe/H] increasing from -0.3 dex to about +0.2 dex over the last six Gyr. Furthermore, the trends of several abundance ratios, [O/Fe], [Na/Fe], [Ca/Fe], and [Ni/Fe], as a function of stellar age split into two corresponding sequences. The [Y/Mg]-age relation, on the other hand, shows no offset between the two age sequences and has no significant dependence on [Fe/H], but the components of a visual binary star, zeta Reticuli, have a large and puzzling deviation. The split of the age-metallicity distribution into two sequences may be interpreted as evidence of two episodes of accretion of gas onto the Galactic disk with a quenching of star formation in between. Some of the [X/Fe]-age relations support this scenario but other relations are not so easy to explain, which calls for a deeper study of systematic errors in the derived abundances as a function of [Fe/H], in particular 3D non-LTE effects.

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arXiv2019

Carbon, oxygen, and iron abundances in disk and halo stars. Implications of 3D non-LTE spectral line formation

The abundances of carbon, oxygen, and iron in late-type stars are important parameters in exoplanetary and stellar physics, as well as key tracers of stellar populations and Galactic chemical evolution. We carried out three-dimensional (3D) non-LTE radiative transfer calculations for CI and OI, and 3D LTE radiative transfer calculations for FeII, across the STAGGER-grid of 3D hydrodynamic model atmospheres. The absolute 3D non-LTE versus 1D LTE abundance corrections can be as severe as $-0.3$ dex for CI lines in low-metallicity F dwarfs, and $-0.6$ dex for OI lines in high-metallicity F dwarfs. The 3D LTE versus 1D LTE abundance corrections for FeII lines are less severe, typically less than $+0.15$ dex. We used the corrections in a re-analysis of carbon, oxygen, and iron in $187$ F and G dwarfs in the Galactic disk and halo. Applying the differential 3D non-LTE corrections to 1D LTE abundances visibly reduces the scatter in the abundance plots. The thick disk and high-$α$ halo population rise in carbon and oxygen with decreasing metallicity, and reach a maximum of [C/Fe]$\approx0.2$ and a plateau of [O/Fe]$\approx0.6$ at [Fe/H]$\approx-1.0$. The low-$α$ halo population is qualitatively similar, albeit offset towards lower metallicities and with larger scatter. Nevertheless, these populations overlap in the [C/O] versus [O/H] plane, decreasing to a plateau of [C/O]$\approx-0.6$ below [O/H]$\approx-1.0$. In the thin-disk, stars having confirmed planet detections tend to have higher values of C/O at given [O/H]; this potential signature of planet formation is only apparent after applying the abundance corrections to the 1D LTE results. Our grids of line-by-line abundance corrections are publicly available and can be readily used to improve the accuracy of spectroscopic analyses of late-type stars.

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arXiv2019

Carbon and oxygen in metal-poor halo stars

Carbon and oxygen are key tracers of the Galactic chemical evolution; in particular, a reported upturn in [C/O] towards decreasing [O/H] in metal-poor halo stars could be a signature of nucleosynthesis by massive Population III stars. We reanalyse carbon, oxygen, and iron abundances in thirty-nine metal-poor turn-off stars. For the first time, we take into account three-dimensional (3D) hydrodynamic effects together with departures from local thermodynamic equilibrium (LTE) when determining both the stellar parameters and the elemental abundances, by deriving effective temperatures from 3D non-LTE H$β$ profiles, surface gravities from Gaia parallaxes, iron abundances from 3D LTE Feii equivalent widths, and carbon and oxygen abundances from 3D non-LTE Ci and Oi equivalent widths. We find that [C/Fe] stays flat with [Fe/H], whereas [O/Fe] increases linearly up to $0.75$ dex with decreasing [Fe/H] down to $-3.0$ dex. As such [C/O] monotonically decreases towards decreasing [O/H], in contrast to previous findings, mainly by virtue of less severe non-LTE effects for Oi at low [Fe/H] with our improved calculations.

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arXiv2018

Confirming chemical clocks: asteroseismic age dissection of the Milky Way disk(s)

Investigations of the origin and evolution of the Milky Way disk have long relied on chemical and kinematic identification of its components to reconstruct our Galactic past. Difficulties in determining precise stellar ages have restricted most studies to small samples, normally confined to the solar neighbourhood. Here we break this impasse with the help of asteroseismic inference and perform a chronology of the evolution of the disk throughout the age of the Galaxy. We chemically dissect the Milky Way disk population using a sample of red giant stars spanning out to 2~kpc in the solar annulus observed by the {\it Kepler} satellite, with the added dimension of asteroseismic ages. Our results reveal a clear difference in age between the low- and high-$α$ populations, which also show distinct velocity dispersions in the $V$ and $W$ components. We find no tight correlation between age and metallicity nor [$α$/Fe] for the high-$α$ disk stars. Our results indicate that this component formed over a period of more than 2~Gyr with a wide range of [M/H] and [$α$/Fe] independent of time. Our findings show that the kinematic properties of young $α$-rich stars are consistent with the rest of the high-$α$ population and different from the low-$α$ stars of similar age, rendering support to their origin being old stars that went through a mass transfer or stellar merger event, making them appear younger, instead of migration of truly young stars formed close to the Galactic bar.

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arXiv2017

High-precision abundances of elements in Kepler LEGACY stars. Verification of trends with stellar age

HARPS-N spectra with S/N > 250 and MARCS model atmospheres were used to derive abundances of C, O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Zn, and Y in ten stars from the Kepler LEGACY sample (including the binary pair 16 Cyg A and B) selected to have metallicities in the range -0.15 < [Fe/H] < +0.15 and ages between 1 and 7 Gyr. Stellar gravities were obtained from seismic data and effective temperatures were determined by comparing non-LTE iron abundances derived from FeI and FeII lines. Available non-LTE corrections were also applied when deriving abundances of the other elements. The results support the [X/Fe]-age relations previously found for solar twins. [Mg/Fe], [Al/Fe], and [Zn/Fe] decrease by ~0.1 dex over the lifetime of the Galactic thin disk due to delayed contribution of iron from Type Ia supernovae relative to prompt production of Mg, Al, and Zn in Type II supernovae. [Y/Mg] and [Y/Al], on the other hand, increase by ~0.3 dex, which can be explained by an increasing contribution of s-process elements from low-mass AGB stars as time goes on. The trends of [C/Fe] and [O/Fe] are more complicated due to variations of the ratio between refractory and volatile elements among stars of similar age. Two stars with about the same age as the Sun show very different trends of [X/H] as a function of elemental condensation temperature Tc and for 16 Cyg, the two components have an abundance difference, which increases with Tc. These anomalies may be connected to planet-star interactions.

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arXiv2017

The [Y/Mg] clock works for evolved solar metallicity stars

Previously [Y/Mg] has been proven to be an age indicator for solar twins. Here, we investigate if this relation also holds for helium-core-burning stars of solar metallicity. High resolution and high signal-to-noise ratio (S/N) spectroscopic data of stars in the helium-core-burning phase have been obtained with the FIES spectrograph on the NOT 2.56m telescope and the HIRES spectrograph on the Keck I 10 m telescope. They have been analyzed to determine the chemical abundances of four open clusters with close to solar metallicity; NGC 6811, NGC 6819, M67 and NGC 188. The abundances are derived from equivalent widths of spectral lines using ATLAS9 model atmospheres with parameters determined from the excitation and ionization balance of Fe lines. Results from asteroseismology and binary studies were used as priors on the atmospheric parameters, where especially the $\log g$ is determined to much higher precision than what is possible with spectroscopy. It is confirmed that the four open clusters are close to solar metallicity and they follow the [Y/Mg] vs. age trend previously found for solar twins. The [Y/Mg] vs. age clock also works for giant stars in the helium-core burning phase, which vastly increases the possibilities to estimate the age of stars not only in the solar neighborhood, but in large parts of the Galaxy, due to the brighter nature of evolved stars compared to dwarfs.

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arXiv2017

Sun-like stars unlike the Sun: Clues for chemical anomalies of cool stars

We present a summary of the splinter session "Sun-like stars unlike the Sun" that was held on 09 June 2016 as part of the Cool Stars 19 conference (Uppsala, Sweden). We discussed the main limitations (in the theory and observations) in the derivation of very precise stellar parameters and chemical abundances of Sun-like stars. We outlined and discussed the most important and most debated processes that can produce chemical peculiarities in solar-type stars. Finally, in an open discussion between all the participants we tried to identify new pathways and prospects towards future solutions of the currently open questions.

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arXiv2017

Sc and neutron-capture abundances in Galactic low- and high-alpha field halo stars

We determine relative abundance ratios for the neutron-capture elements Zr, La, Ce, Nd, and Eu for a sample of 27 Galactic dwarf stars with -1.5 < [Fe/H] <-0.8. We also measure the iron-peak element Sc. These stars separate into three populations (low- and high-alpha halo and thick-disc stars) based on the [alpha/Fe] abundance ratio and their kinematics as discovered by Nissen & Schuster. We find differences between the low- and high-alpha groups in the abundance ratios of [Sc/Fe], [Zr/Fe], [La/Zr], [Y/Eu], and [Ba/Eu] when including Y and Ba from Nissen & Schuster. For all ratios except [La/Zr], the low-alpha stars have a lower abundance compared to the high-alpha stars. The low-alpha stars display the same abundance patterns of high [Ba/Y] and low [Y/Eu] as observed in present-day dwarf spheroidal galaxies, although with smaller abundance differences, when compared to the high-alpha stars. These distinct chemical patterns have been attributed to differences in the star formation rate between the two populations and the contribution of low-metallicity, low-mass asymptotic giant branch (AGB) stars to the low-alpha population. By comparing the low-alpha population with AGB stellar models, we place constraints on the mass range of the AGB stars.

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arXiv2016

High-precision abundances of Sc, Mn, Cu, and Ba in solar twins. Trends of element ratios with stellar age

A previous study of correlations between element abundance ratios, [X/Fe], and ages of solar twin stars is extended to include Sc, Mn, Cu, and Ba. HARPS spectra with S/N > 600 are used to derive very precise (+/- 0.01 dex) differential abundances, and stellar ages with internal errors less than 1 Gyr are obtained by interpolation in the logg - Teff diagram between isochrones calculated with the Aarhus Stellar Evolution Code. For stars younger than 6 Gyr, [X/Fe] is tightly correlated with stellar age for all elements. For ages between 6 and 9 Gyr, the [X/Fe] - age correlations break down and the stars split up into two groups having respectively high and low [X/Fe] for the odd-Z elements. It is concluded that while stars in the solar neighborhood younger than about 6 Gyr were formed from interstellar gas with a smooth chemical evolution, older stars have originated from regions enriched by supernovae with different neutron excesses. Furthermore, the correlations between abundance ratios and stellar age suggest that: i) Sc is made in Type II supernovae along with the alpha-capture elements, ii) the Type II to Ia SNe yield ratio is about the same for Mn and Fe, iii) Cu is mainly made by the weak s-process in massive stars, iv) the Ba/Y yield ratio for AGB stars increases with decreasing stellar mass, v) [Y/Mg] and [Y/Al] can be used as "chemical clocks" when determining ages of solar metallicity stars.

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arXiv2015

Non-LTE analysis of copper abundances for the two distinct halo populations in the solar neighborhood

Two distinct halo populations were found in the solar neighborhood by a series of works. They can be clearly separated by [alpha\Fe] and several other elemental abundance ratios including [Cu/Fe]. Very recently, a non-local thermodynamic equilibrium (non-LTE) study revealed that relatively large departures exist between LTE and non-LTE results in copper abundance analysis. We aim to derive the copper abundances for the stars from the sample of Nissen et al (2010) with both LTE and non-LTE calculations. Based on our results, we study the non-LTE effects of copper and investigate whether the high-alpha population can still be distinguished from the low-alpha population in the non-LTE [Cu/Fe] results. Our differential abundance ratios are derived from the high-resolution spectra collected from VLT/UVES and NOT/FIES spectrographs. Applying the MAFAGS opacity sampling atmospheric models and spectrum synthesis method, we derive the non-LTE copper abundances based on the new atomic model with current atomic data obtained from both laboratory and theoretical calculations. The copper abundances determined from non-LTE calculations are increased by 0.01 to 0.2 dex depending on the stellar parameters compared with the LTE results. The non-LTE [Cu/Fe] trend is much flatter than the LTE one in the metallicity range -1.6<[Fe/H]<-0.8. Taking non-LTE effects into consideration, the high- and low-alpha stars still show distinguishable copper abundances, which appear even more clear in a diagram of non-LTE [Cu/Fe] versus [Fe/H]. The non-LTE effects are strong for copper, especially in metal-poor stars. Our results confirmed that there are two distinct halo populations in the solar neighborhood. The dichotomy in copper abundance is a peculiar feature of each population, suggesting that they formed in different environments and evolved obeying diverse scenarios.

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arXiv2015

Ages and fundamental properties of Kepler exoplanet host stars from asteroseismology

We present a study of 33 {\it Kepler} planet-candidate host stars for which asteroseismic observations have sufficiently high signal-to-noise ratio to allow extraction of individual pulsation frequencies. We implement a new Bayesian scheme that is flexible in its input to process individual oscillation frequencies, combinations of them, and average asteroseismic parameters, and derive robust fundamental properties for these targets. Applying this scheme to grids of evolutionary models yields stellar properties with median statistical uncertainties of 1.2\% (radius), 1.7\% (density), 3.3\% (mass), 4.4\% (distance), and 14\% (age), making this the exoplanet host-star sample with the most precise and uniformly determined fundamental parameters to date. We assess the systematics from changes in the solar abundances and mixing-length parameter, showing that they are smaller than the statistical errors. We also determine the stellar properties with three other fitting algorithms and explore the systematics arising from using different evolution and pulsation codes, resulting in 1\% in density and radius, and 2\% and 7\% in mass and age, respectively. We confirm previous findings of the initial helium abundance being a source of systematics comparable to our statistical uncertainties, and discuss future prospects for constraining this parameter by combining asteroseismology and data from space missions. Finally we compare our derived properties with those obtained using the global average asteroseismic observables along with effective temperature and metallicity, finding an excellent level of agreement. Owing to selection effects, our results show that the majority of the high signal-to-noise ratio asteroseismic {\it Kepler} host stars are older than the Sun.

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arXiv2014

Three Ancient Halo Subgiants: Precise Parallaxes, Compositions, Ages, and Implications for Globular Clusters

The most accurate ages for the oldest stars are those obtained for nearby halo subgiants, because they depend almost entirely on just the measured parallaxes and absolute oxygen abundances. In this study, we have used the Fine Guidance Sensors on the Hubble Space Telescope to determine trigonometric parallaxes, with precisions of 2.1% or better, for the Population II subgiants HD 84937, HD 132475, and HD 140283. High quality spectra have been used to derive their surface abundances of O, Fe, Mg, Si, and Ca, which are assumed to be 0.1-0.15 dex less than their initial abundances due to the effects of diffusion. Comparisons of isochrones with the three subgiants on the $(\log\,T_{\rm eff}, M_V)$-diagram yielded ages of $12.08 \pm 0.14, 12.56 \pm 0.46$, and $14.27 \pm 0.38$ Gyr for HD 84937, HD 132475, and HD 140283, in turn, where each error bar includes only the parallax uncertainty. The total uncertainty is estimated to be $\sim\pm 0.8$ Gyr (larger in the case of the near-turnoff star HD 84937). Although the age of HD 140283 is greater than the age of the universe as inferred from the cosmic microwave background by $\sim$ 0.4-0.5 Gyr, this discrepancy is at a level of $< 1\,σ$. Nevertheless, the first Population II stars apparently formed very soon after the Big Bang. (Stellar models that neglect diffusive processes seem to be ruled out as they would predict that HD 140283 is $\sim 1.5$ Gyr older than the universe.) The halo field subgiants appear to be older than globular clusters of similar metallicities: if distances close to those implied by the RR Lyrae standard candle are assumed, M92 and M5 are younger than HD 140283 and HD 132475 by $\sim 1.5$ and $\sim 1.0$ Gyr, respectively.

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