The Stagger-grid: A grid of 3D stellar atmosphere models - V. Fe line shapes, shifts and asymmetries

We present a theoretical study of the effects and signatures of realistic velocity field and atmospheric inhomogeneities associated with convective motions at the surface of cool late-type stars on the emergent profiles of iron spectral lines for a large range in stellar parameters. We compute 3D spectral line flux profiles under the assumption of local thermodynamic equilibrium (LTE) by employing state-of-the-art, time-dependent, 3D, radiative-hydrodynamical atmosphere models from the Stagger-grid. A set of 35 real unblended, optical FeI and FeII lines of varying excitation potential are considered. Additionally, fictitious Fe i and Fe ii lines (5000A and 0, 2, 4 eV) are used to construct general curves of growth and enable comparison of line profiles with the same line strength to illustrate systematical trends stemming from the intrinsic structural differences among 3D model atmospheres with different stellar parameters. Theoretical line shifts and bisectors are derived to analyze the shapes, shifts, and asymmetries imprinted in the full 3D line profiles emerging self-consistently from the convective simulations with velocity fields and atmospheric inhomogeneities. We find systematic variations in line strength, shift, width, and bisectors, that can be related to the respective physical conditions at the height of the line formation in the stellar atmospheric environment, in particular the amplitude of the vertical velocity field. Line shifts and asymmetries arise due to the presence of convective velocities and the granulation pattern that are ubiquitously found in observed stellar spectra of cool stars.Comment: 11 pages, 8 figures, 2 tables, submitted to A&

Theoretical stellar atmosphere models for cool stars

In kühlen Sternen wie der Sonne wird die nuklear erzeugte Energie aus dem Inneren an die Oberfläche transportiert. Diese kann dann in den freien Weltraum entfliehen, und so können wir das Sternenlicht letztlich beobachten. Die theoretische Modellierung des photosphärischen Übergangsbereiches – vom konvektiven zum radiativen Energietransport – ist aufgrund der inhärenten dreidimensionalen (3D) Natur der Konvektion und der komplexen, nicht-linearen und nicht-lokalen Interaktionen des Strahlungsfelds mit dem stellaren Plasma sehr anspruchsvoll. Theoretische Atmosphärenmodelle stellen die fundamentale Basis für die Untersuchung von Sternen dar, daher sind Astronomen für ihr Verständnis der Sterne auf diese letztlich angewiesen. Die üblicherweise verwendeten eindimensionalen (1D) Atmosphärenmodelle beinhalten verschiedene Vereinfachungen. Insbesondere wird die Konvektion für gewöhnlich mit der Mischungswegtheorie berechnet, trotz ihrer wohlbekannten Fehler, da derzeit keine deutlich besseren Alternativen vorhanden sind. Der einzige Ausweg, um dieses Problem zu überwinden ist, die zeitabhängigen, dreidimensionalen, hydrodynamischen Gleichungen, welche mit einem realistischen Strahlungstransport gekoppelt sind, zu lösen. Aufgrund der in den vergangenen Jahrzehnten rasch gestiegenen Rechenleistung wurden bedeutende Fortschritte mit Simulationen für 3D Strahlungshydrodynamik (RHD) von Atmosphären erzielt. Diese Modelle sind außerordentlich leistungsfähig, und besitzen eine enorme Vorhersagekraft, wie präzise Vergleiche mit Sonnenbeobachtungen wiederholt beweisen konnten. Ausgestattet mit diesen ausgereiften Methoden möchte ich als Ziel meiner Dissertation die drei folgenden Fragen näher untersuchen: Was sind die Eigenschaften der Atmosphären von kühlen Sternen? Welche Unterschiede sind zwischen den 1D und 3D Modellen vorhanden? Wie verändern sich die Vorhersagen für die Sternstrukturen und Spektrallinien? Um mich dieser Aufgabenstellung systematisch anzunehmen, habe ich das Stagger-Gitter berechnet. Das Stagger-Gitter ist ein umfangreiches Gitter aus 3D RHD Atmosphärenmodellen von kühlen Sternen, welches einen großen stellaren Parameterbereich abdeckt. In der vorliegenden Dissertation beschreibe ich die Methoden, welche angewendet wurden, um die vielen Atmosphärenmodelle zu berechnen. Zudem werden die allgemeinen Eigenschaften der resultierenden 3D Modelle, auch deren zeitliche und räumliche Mittelwerte detailliert dargestellt und diskutiert. Die Unterschiede zwischen den 1D und 3D Schichtungen, sowie die Details der stellaren Granulation (die Manifestation der Konvektion unterhalb der Sternoberfläche) werden ebenfalls umfangreich erläutert und beschrieben. Des Weiteren habe ich folgende Anwendungen für die 3D Atmosphärenmodelle untersucht: Berechnung theoretischer Spektrallinien, wichtig für die Bestimmung von Sternparametern, Spektroskopie und Häufigkeiten-Analyse; die sogenannte Randverdunkelung, notwendig für die Analyse interferometrischer Beobachtungen und Suche nach extrasolaren Planeten; und die Kalibrierung der Mischungsweglänge, womit 1D-Sternmodelle verbessert werden können. Die Qualität der hochauflösenden Beobachtungen hat inzwischen die der theoretischen 1D Atmosphärenmodelle aufgrund der technischen Entwicklungen in den vergangenen Jahren überschritten. Daher hat sich der Bedarf an besseren Simulationen für Atmosphärenmodelle erhöht. Durch die Bereitstellung eines umfangreichen Gitters aus 3D RHD Atmosphärenmodellen wurde dazu ein erheblicher Beitrag geleistet. Damit werden wir den Anforderungen an die Theorie für die derzeitigen und zukünftigen Beobachtungen gerecht werden, und können somit zu einem besseren Verständnis der kühlen Sterne beitragen.In cool stars, like the Sun, energy from the inside is transported to its surface by convection, which then can escape into space as radiation that we can observe. Modeling this photospheric transition region – from convective to radiative energy transport – is notoriously challenging due to the inherent three-dimensional (3D) nature of convection itself and the complex non-linear and non-local interaction of the radiation field with the stellar plasma. Astronomers rely on theoretical atmosphere models, which provide the fundamental basis to study and understand stars. The commonly employed one-dimensional (1D) atmosphere models make use of several simplifications, in particular, convection is usually treated with the mixing-length theory (MLT), despite its well-known wrongness simply due to the lack of a considerably improved alternative. Therefore, the only appropriate approach to overcome this issue, is to solve the time-dependent, 3D, hydrodynamic equations coupled a with the realistic treatment of radiative transfer. Due to the soaring computational power in the recent decades, significant progress has been established with the advent of 3D radiative hydrodynamic (RHD) atmosphere simulations. Nowadays, these perform exceedingly well and offer exceptional predictive potential as detailed comparisons with the Sun have repeatedly revealed. Equipped with this matured, powerful tool, I want to address the following three main questions as the aim of my thesis: What are the atmospheric properties of cool stars besides the Sun? Which differences are given between 1D and 3D models? How do the application-based predictions change? To attend to this matter in a systematical approach, I have computed the Stagger-grid, a comprehensive grid of 3D RHD model atmospheres of cool stars covering a wide range in stellar parameters. In this thesis I describe the methods I have applied for the computation of the grid models, and the general properties of the 3D models, as well as their temporal and spatial averages are presented and discussed in detail. Also, the differences between 1D and 3D stratifications are determined, and the details of stellar granulation, the manifestation of subsurface convection, is extensively depicted. Furthermore, I investigated with the Stagger-grid several applications for 3D atmosphere simulations including: spectral line profiles, important for stellar parameter determination, stellar spectroscopy and abundance analysis; limb darkening, necessary for interferometry and extrasolar planet search; and the calibration of the mixing length, which will improve stellar evolution models. The cumulative technical developments of high-resolution observations in the recent years have surpassed the standards of theoretical 1D atmosphere models, thereby, it has given rise to the enhanced demand of improved atmosphere simulations. By providing a comprehensive grid of 3D RHD atmosphere models to the astronomical community, a major contribution has been achieved to live up to the current and future high-precision observations, which ultimately will lead to a better understanding of cool stars

The Stagger-grid: A grid of 3D stellar atmosphere models - IV. Limb darkening coefficients

We compute the emergent stellar spectra from the UV to far infrared for different viewing angles using realistic 3D model atmospheres for a large range in stellar parameters to predict the stellar limb darkening. We have computed full 3D LTE synthetic spectra based on 3D radiative hydrodynamic atmosphere models from the Stagger-grid. From the resulting intensities at different wavelength, we derived coefficients for the standard limb darkening laws considering a number of often-used photometric filters. Furthermore, we calculated theoretical transit light curves, in order to quantify the differences between predictions by the widely used 1D model atmosphere and our 3D models. The 3D models are often found to predict steeper limb darkening compared to the 1D models, mainly due to the temperature stratifications and temperature gradients being different in the 3D models compared to those predicted with 1D models based on the mixing length theory description of convective energy transport. The resulting differences in the transit light curves are rather small; however, these can be significant for high-precision observations of extrasolar transits, and are able to lower the residuals from the fits with 1D limb darkening profiles. We advocate the use of the new limb darkening coefficients provided for the standard four-parameter non-linear power law, which can fit the limb darkening more accurately than other choices.Comment: Accepted for publication in A&A, 10 pages, 9 figures, 1 tabl

The Stagger-grid: A grid of 3D stellar atmosphere models III. The relation to mixing length convection theory

Aims. We investigate the relation between 1D atmosphere models that rely on the mixing length theory and models based on full 3D radiative hydrodynamic (RHD) calculations to describe convection in the envelopes of late-type stars. Methods. The adiabatic entropy value of the deep convection zone, sbot, and the entropy jump, Δs, determined from the 3D RHD models, were matched with the mixing length parameter, αMLT, from 1D hydrostatic atmosphere models with identical microphysics (opacities and equation-of-state). We also derived the mass mixing length parameter, αm, and the vertical correlation length of the vertical velocity, C vz, vz , directly from the 3D hydrodynamical simulations of stellar subsurface convection. Results. The calibrated mixing length parameter for the Sun is α MLT (sbot) = 1.98. For different stellar parameters, αMLT varies systematically in the range of 1.7−2.4. In particular, αMLT decreases towards higher effective temperature, lower surface gravity and higher metallicity. We find equivalent results for α MLT (Δs). In addition, we find a tight correlation between the mixing length parameter and the inverse entropy jump. We derive an analytical expression from the hydrodynamic mean-field equations that motivates the relation to the mass mixing length parameter, αm, and find that it qualitatively shows a similar variation with stellar parameter (between 1.6 and 2.4) with the solar value of α m = 1.83. The vertical correlation length scaled with the pressure scale height yields 1.71 for the Sun, but only displays a small systematic variation with stellar parameters, the correlation length slightly increases with Teff. Conclusions. We derive mixing length parameters for various stellar parameters that can be used to replace a constant value. Within any convective envelope, αm and related quantities vary strongly. Our results will help to replace a constant αMLT

The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - II. Horizontal and Temporal Averaging and Spectral Line Formation

We study the implications of averaging methods with different reference depth scales for 3D hydrodynamical model atmospheres computed with the Stagger-code. The temporally and spatially averaged (hereafter denoted as ) models are explored in the light of local thermodynamic equilibrium (LTE) spectral line formation by comparing spectrum calculations using full 3D atmosphere structures with those from averages. We explore methods for computing mean stratifications from the Stagger-grid time-dependent 3D radiative hydro- dynamical atmosphere models by considering four different reference depth scales (geometrical depth, column-mass density, and two optical depth scales). Furthermore, we investigate the influence of alternative averages (logarithmic or enforced hydrostatic equilibrium, flux-weighted temperatures). For the line formation we compute curves of growth for Fe i and Fe ii lines in LTE . The resulting stratifications for the four reference depth scales can be considerably different. We find typically that in the upper atmosphere and in the superadiabatic region just below the optical surface, where the temperature and density fluctuations are highest, the differences become considerable and increase for higher Teff, lower logg, and lower [Fe/H]. The differential comparison of spectral line formation shows distinctive differences depending on which model is applied. The averages over layers of constant column-mass density yield the best mean representation for LTE line formation, while the averages on layers at constant geometrical height are the least appropriate. Unexpectedly, the usually preferred averages over layers of constant optical depth are prone to the increasing interference of the reversed granulation towards higher effective temperature, in particular at low metallicity.Comment: Accepted for publication in A&A, 18 pages, 16 figure

The STAGGER-grid: A grid of 3D stellar atmosphere models IV. Limb darkening coefficients

Aims. We compute the emergent stellar spectra from the UV to far infrared for different viewing angles using realistic 3D model atmospheres for a large range in stellar parameters to predict the stellar limb darkening. Methods. We have computed full 3D LTE synthetic spectra based on 3D radiative hydrodynamic atmosphere models from the Stagger-grid in the ranges: Teff from 4000 to 7000 K, log g from 1.5 to 5.0, and [Fe/H], from −4.0 to +0.5. From the resulting intensities, we derived coefficients for the standard limb darkening laws considering a number of often-used photometric filters. Furthermore, we calculated theoretical transit light curves, in order to quantify the differences between predictions by the widely used 1D model atmosphere and our 3D models. Results. The 3D models are often found to predict steeper darkening towards the limb compared to the 1D models, mainly due to the temperature stratifications and temperature gradients being different in the 3D models compared to those predicted with 1D models based on the mixing length theory description of convective energy transport. The resulting differences in the transit light curves are rather small; however, these can be significant for high-precision observations of extrasolar transits, and are able to lower the residuals from the fits with 1D limb darkening profiles. Conclusions. We advocate the use of the new limb darkening coefficients provided for the standard four-parameter non-linear power law, which can fit the limb darkening more accurately than other choices

Planet transit and stellar granulation detection with interferometry

Aims. We used realistic three-dimensional (3D) radiative hydrodynamical (RHD) simulations from the Stagger-grid and synthetic images computed with the radiative transfer code Optim3D to provide interferometric observables to extract the signature of stellar granulation and transiting planets. Methods. We computed intensity maps from RHD simulations for twelve interferometric instruments covering wavelengths ranging from optical to infrared. The stellar surface asymmetries in the brightness distribution mostly affect closure phases. We compared the closure phases of the system star with a transiting planet and the star alone and considered the impact of magnetic spots constructing a hypothetical starspots image. Results. All the simulations show departure from the axisymmetric case at all wavelengths. We presented two possible targets (Beta Com and Procyon) and found that departures up to 16 deg can be detected on the 3rd lobe and higher. In particular, MIRC is the most appropriate instrument because it combines good UV coverage and long baselines. Moreover, we explored the impact of convection on interferometric planet signature for three prototypes of planets. It is possible to disentangle the signature of the planet at particular wavelengths (either in the infrared or in the optical) by comparing the closure phases of the star at difference phases of the planetary transit. Conclusions. The detection and characterisation of planets must be based on a comprehensive knowledge of the host star; this includes the detailed study of the stellar surface convection with interferometric techniques. In this context, RHD simulations are crucial to reach this aim. We emphasize that interferometric observations should be pushed at high spatial frequencies by accumulating observations on closure phases at short and long baselines.Comment: accepted in Astronomy and Astrophysics, 13 pages. Some figures have reduced resolution to decrease the size of the output file. Please contact [email protected] to have the high resolution version of the pape

The lithium isotopic ratio in very metal-poor stars

Context. Un-evolved, very metal-poor stars are the most important tracers of the cosmic abundance of lithium in the early universe. Combining the standard Big Bang nucleosynthesis model with Galactic production through cosmic ray spallation, these stars

Planet transit and stellar granulation detection with interferometry: Using the three-dimensional stellar atmosphere S tagger -grid simulations

Context. Stellar activity and, in particular, convection-related surface structures, potentially cause bias in planet detection and characterisation. In the latter, interferometry can help disentangle the signal of the transiting planet. Aims. We used realistic three-dimensional (3D) radiative hydrodynamical (RHD) simulations from the Stagger-grid and synthetic images computed with the radiative transfer code Optim3D to provide interferometric observables to extract the signature of stellar granulation and transiting planets. Methods. We computed intensity maps from RHD simulations and produced synthetic stellar disk images as a nearby observer would see, thereby accounting for the centre-to-limb variations. We did this for twelve interferometric instruments covering wavelengths ranging from optical to infrared. We chose an arbitrary date and arbitrary star with coordinates, and this ensures observability throughout the night. This optimisation of observability allows for a broad coverage of spatial frequencies. The stellar surface asymmetries in the brightness distribution mostly affect closure phases, because of either convection-related structures or a faint companion. We then computed closure phases for all images and compared the system star with a transiting planet and the star alone. We considered the impact of magnetic spots with the construction of a hypothetical starspot image and compared the resulting closure phases with the system star that has a transiting planet. Results. We analysed the impact of convection at different wavelengths. All the simulation depart from the axisymmetric case (closure phases not equal to 0 or ± π) at all wavelengths. The levels of asymmetry and inhomogeneity of stellar disk images reach high values with stronger effects from the 3rd visibility lobe on. We present two possible targets (Beta Com and Procyon) either in the visible or in the infrared and find that departures up to 16° can be detected on the 3rd lobe and higher. In particular, MIRC is the most appropriate instrument because it combines good UV coverage and long baselines. Moreover, we explored the impact of convection on interferometric planet signature for three prototypes of planets with sizes corresponding to one hot Jupiter, one hot Neptune, and a terrestrial planet. The signature of the transiting planet in the closure phase is mixed with the signal due to the convection-related surface structures, but it is possible to disentangle it at particular wavelengths (either in the infrared or in the optical) by comparing the closure phases of the star at difference phases of the planetary transit. It must be noted that starspots caused by the magnetic field may pollute the granulation and the transiting planet signals. However, it is possible to differentiate the transiting planet signal because the time scale of a planet crossing the stellar disk is much smaller than the typical rotational modulation of a star. Conclusions. Detection and characterisation of planets must be based on a comprehensive knowledge of the host star, and this includes the detailed study of the stellar surface convection with interferometric techniques. In this context, RHD simulations are crucial for this aim. We emphasise that interferometric observations should be pushed at high spatial frequencies by accumulating observations on closure phases at short and long baselines