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Hans-Günter Ludwig

Publications and source records attributed to Hans-Günter Ludwig.

At least 19 recordsLinked to original sources

Kilogauss magnetic fields from simulations of small-scale dynamo action in the convective envelope of a white dwarf

About 20% of white dwarfs are observed to host large-scale magnetic fields, but the origin of white dwarf magnetism remains uncertain. Small-scale turbulent dynamos (SSDs), which efficiently generate magnetic fields in solar and stellar convection simulations, have so far been studied in white dwarfs only through equipartition arguments in one-dimensional models. We therefore investigate whether turbulent convection in white dwarf surface layers can sustain SSD action through local three-dimensional radiation-magnetohydrodynamics simulations of a DA white dwarf with a convective pure-hydrogen atmosphere, including the full convection zone together with the underlying overshoot and stably stratified layers. Starting from a weak seed field of 1 mG, the magnetic energy undergoes exponential amplification before saturating at a magnetic-to-kinetic energy density ratio of about 5.5% at the visible surface, demonstrating that SSD action naturally generates kG-strength magnetic fields in convective white dwarf atmospheres. The resulting magnetic field is characterised by a mixed-polarity small-scale structure, with kG field concentrations contributing about 14% of the total unsigned magnetic flux at the visible surface. Despite a rate of magnetic energy generation amounting to roughly one-seventh of the bolometric flux, no significant modification of the mean stratification is found. Although these fields remain spatially unresolved for observations, they may contribute to spectral line broadening, suggesting that small-scale magnetism in white dwarfs could be more widespread than currently inferred from observations.

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Evidence for elemental diffusion in the eclipsing binary star AI Phoenicis

AI Phe is an eclipsing binary star with an orbital period of 24.6 days for which the surface gravity and effective temperature are known from direct measurements to very high precision and accuracy. We have obtained high-quality spectroscopy of the K0IV star during the total eclipse of the F7V companion, and also obtained spectra with a very high signal-to-noise ratio for this star and its F7V companion using the spectral disentangling technique. We have used these spectra to measure the abundances of iron and magnesium for both stars. We compare the values of [Fe/H] and [Mg/H] for the F7V star and the K0IV star to stars in M67, an open cluster of similar age and metallicity to AI Phe. We find that our [Fe/H] and [Mg/H] measurements clearly show the signature of elemental diffusion in the F7V star. This suggests that AI Phe can be used to test models of single stars that include diffusion and mixing of elements.

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Solar photospheric spectrum microvariability III. Radial velocities and line profiles in magnetic active-region granulation

Finding low-mass planets around solar-type stars requires to understand the physical variability of the host star, which greatly exceeds the planet-induced radial-velocity modulation. Different solar photospheric absorption lines have slightly disparate responses to stellar activity, which should permit to disentangle wavelength shifts induced by exoplanets from those originating in stellar atmospheres. Changing area coverage of magnetic active-region granulation (faculae and plage) causes radial-velocity fluctuations of the disk-integrated solar spectrum, whose precise modeling requires active-region spectral line profiles. Hydrodynamic 3D modeling of granulation in magnetic fields extends previous non-magnetic studies, revealing different line profiles and altered convective velocity shifts. Different types of lines in the visual and near infrared are examined in synthetic hyper-high resolution spectra (R~900,000), comparing non-magnetic areas with those with strongly magnetic (240 mT = 2400 G) granulation. Magnetic fields inhibit convective motions, decrease the energy flow, produce more symmetric lines, and remove the common blueshift with its familiar C-shape bisectors. Unexpectedly, magnetic granulation displays convective redshifts. Their origin is traced to contributions from small areas, where hot and bright down-moving elements are created through shocks and adiabatic compression when rising gas is forced over into magnetically channeled downflows. Understanding line formation in also stellar active regions is needed to simulate full-disk spectra toward exoEarth detections. Detailed shapes of spectral lines carry significant information, suggesting that hyper-high spectral resolution may ultimately be required

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Solar photospheric spectrum microvariability

Finding low-mass planets around solar-type stars requires to understand the physical variability of the host star, which greatly exceeds the planet-induced radial-velocity modulation. This project aims at analyzing - observationally and theoretically - the character and physical origins of fluctuations in solar photospheric absorption lines. Observationally, photospheric equivalent-width variations were measured in 1000 selected spectra from three years of HARPS-N data of the Sun-as-a-star, showing changes that largely shadow the chromospheric CaII H&K activity-cycle signal, but with much smaller amplitudes on sub-percent levels. Among iron lines, the greatest are for FeII in the blue, while the trends change sign among lines in the green MgI triplet and between Balmer lines. No variation was seen in the semi-forbidden MgI 457.1 nm. Theoretically, hydrodynamic 3D modeling of solar surface convection produced time sequences of synthetic high-resolution spectral atlases. Radial velocities averaged over small simulation areas jitter by some +-150 m/s, scaling to 2 m/s for the full solar disk on timescales of granular convection. Among different lines, jittering is in phase, but amplitudes differ by about one tenth of their values: greater for stronger and for ionized lines, decreasing at longer wavelengths.

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Granulation signatures in 3D hydrodynamical simulations: evaluating background model performance using a Bayesian nested sampling framework

Understanding the granulation background signal is of vital importance when interpreting the asteroseismic diagnostics of solar-like oscillators. Various descriptions exist in the literature for modelling the surface manifestation of convection, the choice of which affects our interpretations. We aim to evaluate the performance of and preference for various granulation background models for a suite of 3D hydrodynamical simulations of convection across the HR diagram, thereby expanding the number of simulations and coverage of parameter space for which such studies have been made. We take a statistical approach by considering the granulation in power density spectra of 3D simulations, where no biases or systematics of observational origin are present. To properly contrast the performance of the models, we develop a Bayesian nested sampling framework for model inference and comparison. This framework was extended to real stellar data using KIC 8006161 (Doris) and the Sun. We find that multi-component models are consistently preferred over a single-component model, with each tested multi-component model demonstrating merit in specific cases. This occurs for simulations with no magnetic activity, thus ruling out stellar faculae as the sole source of the second granulation component. Like a previous study, we find that a hybrid model with a single overall amplitude and two characteristic frequencies performs well for numerous simulations. Additionally, a tentative third granulation component beyond the value of $ν_\mathrm{max}$ is seen for some simulations, but its potential presence in observations requires further efforts. Studying the granulation signatures in these simulations paves the way to studying stars with accurate granulation models. This deeper understanding of the granulation signal may lead to complementary methods to existing algorithms for determining stellar parameters.

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Solar photospheric spectrum microvariability II. Observed relations to magnetic activity and radial-velocity modulation

Searches for small exoplanets around solar-type stars are limited by stellar physical variability. While chromospheric variability is well studied, observing, modeling. and understanding the much smaller fluctuations in photospheric spectral line strengths, shapes, and shifts is challenging. Extreme precision radial-velocity spectrometers now enable extreme precision stellar spectroscopy and time series of the Sun seen as a star permit monitoring of its photospheric variability. Fluctuations in their line strengths may well correlate with radial-velocity excursions and identify observable proxies for their monitoring. From three years of HARPS-N observations of the Sun-as-a-star, one thousand low-noise spectra are selected, and line absorption measured in Fe I, Fe II, Mg I, Mn I, H-alpha, H-beta, H-gamma, Na I, and the G-band. Their variations and likely atmospheric origins are examined, also with respect to simultaneously measured chromospheric emission and apparent radial velocity. Systematic line-strength variability is seen, largely shadowing the solar-cycle evolution of Ca II H & K emission, but with smaller amounts, typically on a sub-percent level. Among iron lines, greatest amplitudes are for Fe II in the blue, while the trends change sign among differently strong lines in the green Mg I triplet and between Balmer lines. Variations in the G-band core are greater than of the full G-band, in line with theoretical predictions. No variation is detected in the semi-forbidden Mg I 457.1 nm. Hyperfine split Mn I behaves largely similar to Fe I. For lines at longer wavelengths, telluric absorption limits the achievable precision. Microvariability in the solar photospheric spectrum thus displays systematic signatures among various features. These measure something different than the classical Ca II H & K index while still reflecting a strong influence from magnetic regions.

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Solar Photospheric Spectrum Microvariability I. Theoretical searches for proxies of radial-velocity jittering

Extreme precision radial-velocity spectrometers enable extreme precision stellar spectroscopy. Searches for low-mass exoplanets around solar-type stars are limited by the physical variability in stellar spectra, such as the short-term jittering of apparent radial velocities. To understand the physical origins of such jittering, the solar spectrum is assembled, as far as possible, from basic principles. Surface convection is modeled with time-dependent 3D hydrodynamics, followed by the computation of hyper-high resolution spectra during numerous instances of the simulation sequences. The behavior of different classes of photospheric absorption lines is monitored to identify commonalities or differences between different classes of lines: weak or strong, neutral or ionized, high- or low-excitation, atomic or molecular. For Fe I and Fe II lines, the radial-velocity jittering over the small simulation area typically amounts to +-150 m/s, scaling to about 2 m/s for the full solar disk. Most photospheric lines vary in phase but with different amplitudes among different classes of lines. Radial-velocity excursions are greater for stronger and for ionized lines, decreasing at longer wavelengths. The differences between various line-groups are about one order of magnitude less than the full jittering amplitudes. By matching very precisely measured radial velocities to the characteristic jittering patterns between different line-groups should enable to identify and to remove a significant component of the stellar noise originating in granulation. To verify the modeling toward such a filter, predictions of solar center-to-limb dependences of jittering amplitudes are presented for different classes of lines, testable with spatially resolving solar telescopes connected to existing radial-velocity instruments.

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Solar center-to-limb variation in Rossiter-McLaughlin and exoplanet transmission spectroscopy

Line profiles from spatially unresolved stellar observations consist of a superposition of local line profiles that result from observing the stellar atmosphere under specific viewing angles. Line profile variability caused by stellar magnetic activity or planetary transit selectively varies the weight and/or shape of profiles at individual surface positions. The effect is usually modeled with radiative transfer calculations because observations of spatially resolved stellar surfaces are not available. For the Sun, we recently obtained a broadband spectroscopic atlas of the solar center-to-limb variation (CLV). We use the atlas to study systematic differences between largely used radiative transfer calculations and solar observations. We concentrate on four strong lines useful for exoplanet transmission analysis, and we investigate the impact of CLV on transmission and Rossiter-McLaughlin (RM) curves. Solar models used to calculate synthetic spectra tend to underestimate line core depths but overestimate the effect of CLV. Our study shows that CLV can lead to significant systematic offsets in transmission curves and particularly in RM curves; transmission curves centered on individual lines are overestimated by up to a factor of two by the models, and simulations of RM curves yield amplitudes that are off by up to 5--10\,m\,s$^{-1}$ depending on the line. For the interpretation of transit observations, it is crucial for model spectra that accurately reproduce the solar CLV to become available which, for now, is the only calibration point available.

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First release of PLATO consortium stellar limb-darkening coefficients

We release the first grid of stellar limb-darkening coefficients (LDCs) and intensity profiles (IPs) computed by the consortium of the PLAnetary Transits and Oscillations of stars (PLATO), the next medium-class (M3) mission under development by the European Space Agency (ESA) to be launched in 2026. We have performed spectral synthesis with \texttt{TurboSpectrum} on a grid of \texttt{MARCS} model atmospheres. Finally, we adopted \texttt{ExoTETHyS} to convolve the high-resolution spectra ($R=2\times10^5$) with the state-of-the-art response functions for all the PLATO cameras, and computed the LDCs that best approximate the convolved IPs. In addition to the PLATO products, we provide new LDCs and IPs for the Kepler mission, based on the same grid of stellar atmospheric models and calculation procedures. The data can be downloaded from the following link: \url{https://doi.org/10.5281/zenodo.7339706}.

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Observational constraints on the origin of the elements. IV: The standard composition of the Sun

The chemical composition of the Sun is requested in the context of various studies in astrophysics, among them in the calculation of the standard solar models (SSMs), which describe the evolution of the Sun from the pre-main-sequence to its present age. In this work, we provide a critical re-analysis of the solar chemical abundances and corresponding SSMs. For the photospheric values, we employ new high-quality solar observational data collected with the IAG facility, state-of-the art non-equilibrium modelling, new oscillator strengths, and different atmospheric models, including the MARCS model, but also averages based on Stagger and CO5BOLD 3D radiation-hydrodynamics simulations of stellar convection. We perform new calculations of oscillator strengths for transitions in O I and N I. For O I - the critical element for the interior models - calculations are carried out using several independent methods. We find unprecedented agreement between the new estimates of transition probabilities, thus supporting our revised solar oxygen abundance. We also provide new estimates of the noble gas Ne abundance. We investigate our results in comparison with the previous estimates. We discuss the consistency of our photospheric measurements with meteoritic values taking into account systematic and correlated errors. Finally, we provide revised chemical abundances, leading to a new value of the solar photospheric present-day metallicity $Z/X = 0.0225$, and employ them in the calculations of the SSM. We find that the puzzling mismatch between the helioseismic constraints on the solar interior structure and the model is resolved with the new chemical composition.

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Spatially resolved spectroscopy across stellar surfaces. V. Observational prospects: Toward Earth-like exoplanet detection

Testing 3D hydrodynamic models of stellar atmospheres is feasible by retrieving spectral line shapes across stellar disks, using differential spectroscopy during exoplanet transits. From synthetic data at hyper-high spectral resolution, characteristic patterns for FeI and FeII lines were identified in Paper IV from 3D models spanning T=3964-6726K (spectral types approx. K8V-F3V). The observability of patterns among lines of different strength, excitation potential and ionization level are now examined, as observed at ordinary spectral resolutions and in the presence of noise. Time variability in 3D atmospheres induces changes in spectral-line parameters, some of which are correlated. An adequate calibration could identify proxies for the jitter in apparent radial velocity to enable adjustments to actual stellar radial motion. We also examined the center-to-limb temporal variability. Recovery of spatially resolved line profiles with fitted widths and depths is shown for various noise levels. Signals during exoplanet transit are simulated. In addition to Rossiter-McLaughlin type signatures in apparent radial velocity, analogous effects are shown for line depths and widths. From exoplanet transits, overall stellar line parameters of width, depth and wavelength position can be retrieved already with moderate efforts, but a very good signal-to-noise ratio is required to reveal the more subtle signatures between subgroups of spectral lines, where finer details of atmospheric structure are encoded. In a solar model, temporal variability shows correlations between jittering in apparent radial velocity and fluctuations in line depth. Since both fluctuations in line depth and jittering in wavelength can be measured from the ground, searches for low-mass exoplanets should explore these to adjust apparent radial velocities to actual stellar motion.

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Spatially resolved spectroscopy across stellar surfaces. IV. F, G, & K-stars: Synthetic 3D spectra at hyper-high resolution

High-precision stellar analyses require hydrodynamic 3D modeling. Such models predict changes across stellar disks of spectral line shapes, asymmetries, and wavelength shifts. For testing models in stars other than the Sun, spatially resolved observations are feasible from differential spectroscopy during exoplanet transits, retrieving spectra of stellar surface segments that successively become hidden behind the transiting planet, as shown in Papers I, II, and III. Synthetic high-resolution spectra over extended spectral regions are now available from 3D models. Similar to other ab initio simulations, these data contain patterns that have not been specifically modeled but may be revealed after analyses analogous to those of a large volume of observations. From five 3D models spanning T=3964-6726K (approx. spectral types K8V-F3V), synthetic spectra at hyper-high resolution (R>1,000,000) were analyzed. Selected FeI and FeII lines at various positions across stellar disks were searched for patterns between different lines in the same star and for similar lines between different stars. Such patterns are identified for representative photospheric lines of different strengths, excitation potential, and ionization level, encoding the hydrodynamic 3D structure. Line profiles and bisectors are shown for various stars at different positions across stellar disks. Absolute convective wavelength shifts are obtained as differences to 1D models, where such shifts do not occur. Observable relationships for line properties are retrieved from realistically complex synthetic spectra. Such patterns may also test very detailed 3D modeling, including non-LTE effects. While present results are obtained at hyper-high spectral resolution, the subsequent Paper V examines their practical observability at realistically lower resolutions, and in the presence of noise.

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Horizontal spreading of planetary debris accreted by white dwarfs

White dwarfs with metal-polluted atmospheres have been studied widely in the context of the accretion of rocky debris from evolved planetary systems. One open question is the geometry of accretion and how material arrives and mixes in the white dwarf surface layers. Using the 3D radiation-hydrodynamics code CO$^5$BOLD, we present the first transport coefficients in degenerate star atmospheres which describe the advection-diffusion of a passive scalar across the surface-plane. We couple newly derived horizontal diffusion coefficients with previously published vertical diffusion coefficients to provide theoretical constraints on surface spreading of metals in white dwarfs. Our grid of 3D simulations probes the vast majority of the parameter space of convective white dwarfs, with pure-hydrogen atmospheres in the effective temperature range 6000-18000 K and pure-helium atmospheres in the range 12000-34000 K. Our results suggest that warm hydrogen-rich atmospheres (DA; $\gtrsim$13000 K) and helium-rich atmospheres (DB, DBA; $\gtrsim$30000 K) are unable to efficiently spread the accreted metals across their surface, regardless of the time dependence of accretion. This result may be at odds with the current non-detection of surface abundance variations at white dwarfs with debris discs. For cooler hydrogen- and helium-rich atmospheres, we predict a largely homogeneous distribution of metals across the surface within a vertical diffusion timescale. This is typically less than 0.1 per cent of disc lifetime estimates, a quantity which is revisited in this paper using the overshoot results. These results have relevance for studies of the bulk composition of evolved planetary systems and models of accretion disc physics.

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3D spectroscopic analysis of helium-line white dwarfs

In this paper, we present corrections to the spectroscopic parameters of DB and DBA white dwarfs with -10.0 < log(H/He) < -2.0, 7.5 < log(g) < 9.0 and 12000 K < T_eff < 34000 K, based on 282 3D atmospheric models calculated with the CO5BOLD radiation-hydrodynamics code. These corrections arise due to a better physical treatment of convective energy transport in 3D models when compared to the previously available 1D model atmospheres. By applying the corrections to an existing SDSS sample of DB and DBA white dwarfs, we find significant corrections both for the effective temperature and surface gravity. The 3D log(g) corrections are most significant for T_eff < 18000 K, reaching up to -0.20 dex at log(g) = 8.0. However, in this low effective temperature range, the surface gravity determined from the spectroscopic technique can also be significantly affected by the treatment of the neutral van der Waals line broadening of helium and by non-ideal effects due to the perturbation of helium by neutral atoms. Thus, by removing uncertainties due to 1D convection, our work showcases the need for improved description of microphysics for DB and DBA model atmospheres. Overall, we find that our 3D spectroscopic parameters for the SDSS sample are generally in agreement with Gaia DR2 absolute fluxes within 1-3σ for individual white dwarfs. By comparing our results to DA white dwarfs, we have determined that the precision and accuracy of DB/DBA atmospheric models are similar. For ease of user application of the correction functions, we provide an example Python code.

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The signature of granulation in a solar power spectrum as seen with CO$^5$BOLD

The granulation background seen in the power spectrum of a solar-like oscillator poses a serious challenge for extracting precise and detailed information about the stellar oscillations. Using a 3D hydrodynamical simulation of the Sun computed with CO$^5$BOLD, we investigate various background models to infer, using a Bayesian methodology, which one provides the best fit to the background in the simulated power spectrum. We find that the best fit is provided by an expression including the overall power level and two characteristic frequencies, one with an exponent of 2 and one with a free exponent taking on a value around 6. We assess the impact of the 3D hydro-code on this result by repeating the analysis with a simulation from Stagger and find that the main conclusion is unchanged. However, the details of the resulting best fits differ slightly between the two codes, but we explain this difference by studying the effect of the spatial resolution and the duration of the simulation on the fit. Additionally, we look into the impact of adding white noise to the simulated time series as a simple way to mimic a real star. We find that, as long as the noise level is not too low, the results are consistent with the no-noise case.

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Chemically peculiar A and F stars with enhanced s-process and iron-peak elements: stellar radiative acceleration at work

We present $\gtrsim 15,000$ metal-rich (${\rm [Fe/H]}>-0.2$dex) A and F stars whose surface abundances deviate strongly from Solar abundance ratios and cannot plausibly reflect their birth material composition. These stars are identified by their high [Ba/Fe] abundance ratios (${\rm [Ba/Fe]}>1.0$dex) in the LAMOST DR5 spectra analyzed by Xiang et al. (2019). They are almost exclusively main sequence and subgiant stars with $T_{\rm eff}\gtrsim6300$K. Their distribution in the Kiel diagram ($T_{\rm eff}$--$\log g$) traces a sharp border at low temperatures along a roughly fixed-mass trajectory (around $1.4M_\odot)$ that corresponds to an upper limit in convective envelope mass fraction of around $10^{-4}$. Most of these stars exhibit distinctly enhanced abundances of iron-peak elements (Cr, Mn, Fe, Ni) but depleted abundances of Mg and Ca. Rotational velocity measurements from GALAH DR2 show that the majority of these stars rotate slower than typical stars in an equivalent temperature range. These characteristics suggest that they are related to the so-called Am/Fm stars. Their abundance patterns are qualitatively consistent with the predictions of stellar evolution models that incorporate radiative acceleration, suggesting they are a consequence of stellar internal evolution particularly involving the competition between gravitational settling and radiative acceleration. These peculiar stars constitute 40% of the whole population of stars with mass above 1.5$M_\odot$, affirming that "peculiar" photospheric abundances due to stellar evolution effects are a ubiquitous phenomenon for these intermediate-mass stars. This large sample of Ba-enhanced chemically peculiar A/F stars with individual element abundances provides the statistics to test more stringently the mechanisms that alter the surface abundances in stars with radiative envelopes.

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A high-precision abundance analysis of the nuclear benchmark star HD 20

We present our chemical abundance investigation of the metal-poor ([Fe/H]=-1.60 dex), r-process-enriched ([Eu/Fe]=0.73 dex) halo star HD 20 using novel and archival high-resolution spectra at outstanding signal-to-noise ratios. By combining one of the first asteroseismic gravity measurements in the metal-poor regime from a TESS light curve with non-LTE analyses of iron lines, we derive a set of highly accurate and precise stellar parameters. These allow us to delineate a chemical pattern comprised of solid detections of 48 elements, including 28 neutron-capture elements, which establishes HD 20 among the few benchmark stars that have almost complete patterns with low systematic dependencies on the stellar parameters. Our light-element (Z<30) abundances are representative of other, similarly metal-poor stars in the Galactic halo with contributions from core-collapse supernovae of type II. A comparison to the scaled solar r-pattern shows that the lighter neutron-capture elements (37<Z<60) are poorly matched. In particular, we find imprints of the weak r-process acting at low metallicities. Nonetheless, by comparing our detailed abundances to the observed metal-poor star BD +17 3248, we find a persistent residual pattern that is indicative of enrichment contributions from the s-process. We show that mixing with material from predicted yields of massive, rotating AGB stars at low metallicity considerably improves the fit. Based on a solar ratio of heavy- to light-s elements -- at odds with model predictions for the i-process -- and a missing clear residual pattern with respect to other stars with claimed contributions from this process, we refute (strong) contributions from such astrophysical sites providing intermediate neutron densities. Finally, nuclear cosmochronology is used to tie our detection of the radioactive element Th to an age estimate for HD 20 of $11.0\pm3.8$ Gyr. [abridged]

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Spatially resolved spectroscopy across stellar surfaces. III. Photospheric Fe I lines across HD189733A (K1 V)

Spectroscopy across spatially resolved stellar surfaces reveals spectral line profiles free from rotational broadening, whose gradual changes from disk center toward the stellar limb reflect an atmospheric fine structure that is possible to model by 3-D hydrodynamics. Previous studies of photospheric spectral lines across stellar disks exist for the Sun and HD209458 (G0 V) and are now extended to the planet-hosting HD189733A to sample a cooler K-type star and explore the future potential of the method. During exoplanet transit, stellar surface portions successively become hidden and differential spectroscopy between various transit phases uncovers spectra of small surface segments temporarily hidden behind the planet. In Paper I, observable signatures were predicted quantitatively from hydrodynamic simulations. From observations of HD189733A with the ESO HARPS spectrometer at R=115,000, profiles for stronger and weaker Fe I lines are retrieved at several center-to-limb positions, reaching adequate S/N after averaging over numerous similar lines. Retrieved line profile widths and depths are compared to synthetic ones from models with parameters bracketing those of the target star and are found to be consistent with 3-D simulations. Center-to-limb changes strongly depend on the surface granulation structure and much greater line-width variation is predicted in hotter F-type stars with vigorous granulation than in cooler K-types. Such parameters, obtained from fits to full line profiles, are realistic to retrieve for brighter planet-hosting stars, while their hydrodynamic modeling offers previously unexplored diagnostics for stellar atmospheric fine structure and 3-D line formation. Precise modeling may be required in searches for Earth-analog exoplanets around K-type stars, whose more tranquil surface granulation and lower ensuing microvariability may enable such detections.

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