Regner Trampedach

Three-dimensional hydrodynamical simulations of surface convection in red giant stars: impact on spectral line formation and abundance analysis

We investigate the impact of 3D hydrodynamical model atmospheres of red giant stars at different metallicities on the formation of spectral lines of a number of ions and molecules. We carry out realistic 3D simulations of surface convection in red giant stars with varying stellar parameters. We use the simulations as time-dependent hydrodynamical model stellar atmospheres to compute atomic (Li, O, Na, Mg, Ca, Fe) and molecular (CH, NH, OH) spectral lines under the assumption of local thermodynamic equilibrium (LTE). We compare the line strengths computed in 3D with the results of analogous line formation calculations for 1D, hydrostatic, plane-parallel MARCS model atmospheres in order to estimate the impact of 3D models on the derivation of elemental abundances. The temperature and density inhomogeneities and correlated velocities in 3D models, as well as the differences between the 1D and mean 3D structures significantly affect the predicted line strengths. Under the assumption of LTE, the low atmospheric temperatures of very metal-poor 3D model atmospheres cause the lines from neutral species and molecules to appear stronger than in 1D. Therefore, elemental abundances derived from these lines using 3D models are significantly lower than according to 1D analyses. Differences between 3D and 1D abundances of C, N, and O derived from CH, NH, and OH weak low-excitation lines are found to be in the range -0.5 dex to -1.0 dex for the the red giant stars at [Fe/H]=-3 considered here. At this metallicity, large negative corrections (about -0.8 dex) are also found for weak low-excitation Fe I lines. We caution, however, that departures from LTE might be significant for these and other elements and comparable to the effects due to stellar granulation.The information about the chemical compositions of stars is encoded in their spectra. Accurate determinations of these compositions are crucial for our understanding of stellar nucleosynthesis and Galactic chemical evolution. The determination of elemental abundances in stars requires models for the stellar atmospheres and the processes of line formation. Nearly all spectroscopic analyses of late-type stars carried out today are based on one-dimensional (1D), hydrostatic model atmospheres and on the assumption of local thermodynamic equilibrium (LTE). This approach can lead to large systematic errors in the predicted stellar atmospheric structures and line-strengths, and, hence, in the derived stellar abundances. In this thesis, examples of departures from LTE and from hydrostatic equilibrium are explored. The effects of background line opacities (line-blocking) due to atomic lines on the statistical equilibrium of Fe are investigated in late-type stars. Accounting for this line opacity is important at solar metallicity, where line-blocking significantly reduces the rates of radiatively induced ionizations of Fe. On the contrary, the effects of line-blocking in metal-poor stars are insignificant. In metal-poor stars, the dominant uncertainty in the statistical equilibrium of Fe is the treatment of inelastic H+Fe collisions. Substantial departures of Fe abundances from LTE are found at low metallicities: about 0.3 dex with efficient H+Fe collisions and about 0.5 dex without. The impact of three-dimensional (3D) hydrodynamical model atmospheres on line formation in red giant stars is also investigated. Inhomogeneities and correlated velocity fields in 3D models and differences between the mean 3D stratifications and corresponding 1D model atmospheres can significantly affect the predicted line strengths and derived abundances, in particular at very low metallicities. In LTE, the differences between 3D and 1D abundances of C, N, and O derived from CH, NH, and OH weak low-excitation lines are in the range -0.5 dex to -1.0 dex at [Fe/H]=-3. Large negative corrections (about -0.8 dex) are also found in LTE for weak low-excitation neutral Fe lines. We also investigate the impact of 3D hydrodynamical model stellar atmospheres on the determination of elemental abundances in the carbon-rich, hyper iron-poor stars HE 0107-5240 and HE 1327-2326. The lower temperatures of the line-forming regions of the 3D models compared with 1D models cause changes in the predicted spectral line strengths. In particular we find the 3D abundances of C, N, and O to be lower by about -0.8 dex (or more) than estimated from a 1D analysis. The 3D abundance of Fe is decreased but only by -0.2 dex. Departures from LTE for Fe might actually be very large for these stars and dominate over the effects due to granulation.

A Uniform Asteroseismic Analysis of 22 Solar-type Stars Observed by Kepler

Asteroseismology with the Kepler space telescope is providing not only an improved characterization of exoplanets and their host stars, but also a new window on stellar structure and evolution for the large sample of solar-type stars in the field. We perform a uniform analysis of 22 of the brightest asteroseismic targets with the highest signal-to-noise ratio observed for 1 month each during the first year of the mission, and we quantify the precision and relative accuracy of asteroseismic determinations of the stellar radius, mass, and age that are possible using various methods. We present the properties of each star in the sample derived from an automated analysis of the individual oscillation frequencies and other observational constraints using the Asteroseismic Modeling Portal (AMP), and we compare them to the results of model-grid-based methods that fit the global oscillation properties. We find that fitting the individual frequencies typically yields asteroseismic radii and masses to ~1% precision, and ages to ~2.5% precision (respectively, 2, 5, and 8 times better than fitting the global oscillation properties). The absolute level of agreement between the results from different approaches is also encouraging, with model-grid-based methods yielding slightly smaller estimates of the radius and mass and slightly older values for the stellar age relative to AMP, which computes a large number of dedicated models for each star. The sample of targets for which this type of analysis is possible will grow as longer data sets are obtained during the remainder of the mission.

The Stagger-grid: A grid of 3D stellar atmosphere models - I. Methods and general properties

Aims. We present the Stagger-grid, a comprehensive grid of time-dependent, three-dimensional (3D), hydrodynamic model atmospheres for late-type stars with realistic treatment of rad iative transfer, covering a wide range in stellar parameter s. This grid of 3D models is intended for various applications besides studies of stellar convection and atmospheres per se, including stellar parameter determination, stellar spectroscopy and abundance analysis, asteroseismology, calibration of stellar evolution mo dels, interferometry, and extrasolar planet search. In this introductory paper, w e describe the methods we applied for the computation of the grid and discuss the general properties of the 3D models as well as of their temporal and spatial averages (here denotedh 3Di models). Methods. All our models were generated with the Stagger-code, using realistic input physics for the equation of sta te (EOS) and for continuous and line opacities. Our∼ 220 grid models range in effective temperature, Teff, from 4000 to 7000 K in steps of 500 K, in surface gravity, log g, from 1.5 to 5.0 in steps of 0.5 dex, and metallicity, [Fe/H], from−4.0 to +0.5 in steps of 0.5 and 1.0 dex. Results. We find a tight scaling relation between the vertical velocit y and the surface entropy jump, which itself correlates with the constant entropy value of the adiabatic convection zone. The range in intensity contrast is enhanced at lower metallici ty. The granule size correlates closely with the pressure scale height sampled at the depth of maximum velocity. We compare theh 3Di models with currently widely applied one-dimensional (1D) atmosphere models, as well as with theoretical 1D hydrostatic models generated with the same EOS and opacity tables as the 3D models, in order to isolate the effects of using self-consistent and hydrodynamic modeling of convection, rather than the classical mixing length theory (MLT) approach. For the first time, we are able to quantify s ystematically over a broad range of stellar parameters the uncertainties of 1D models arising from the simplified treatment of physics, in particular convective energy transport. In agreement with previous fin dings, we find that the di fferences can be rather significant, especially for metal-poor stars.

Granulation in red giants: observations by the Kepler mission and three-dimensional convection simulations

The granulation pattern that we observe on the surface of the Sun is due to hot plasma rising to the photosphere where it cools down and descends back into the interior at the edges of granules. This is the visible manifestation of convection taking place in the outer part of the solar convection zone. Because red giants have deeper convection zones than the Sun, we cannot a priori assume that their granulation is a scaled version of solar granulation. Until now, neither observations nor one-dimensional analytical convection models could put constraints on granulation in red giants. With asteroseismology, this study can now be performed. We analyze ~1000 red giants that have been observed by Kepler during 13 months. We fit the power spectra with Harvey-like profiles to retrieve the characteristics of the granulation (timescale τgran and power P gran). We search for a correlation between these parameters and the global acoustic-mode parameter (the position of maximum power, νmax) as well as with stellar parameters (mass, radius, surface gravity (log g), and effective temperature (T eff)). We show that τeffν–0.89 max and P granν–1.90 max, which is consistent with the theoretical predictions. We find that the granulation timescales of stars that belong to the red clump have similar values while the timescales of stars in the red giant branch are spread in a wider range. Finally, we show that realistic three-dimensional simulations of the surface convection in stars, spanning the (T eff, log g) range of our sample of red giants, match the Kepler observations well in terms of trends.

Excitation of solar-like oscillations across the HR diagram

Aims. We extend semi-analytical computations of excitation rates for solar oscillation modes to those of other solar-like oscillating stars to compare them with recent observations Methods. Numerical 3D simulations of surface convective zones of several solar-type oscillating stars are used to characterize the turbulent spectra as well as to constrain the convective velocities and turbulent entropy fluctuations in the uppermost part of the convective zone of such stars. These constraints, coupled with a theoretical model for stochastic excitation, provide the rate P at which energy is injected into the p-modes by turbulent convection. These energy rates are compared with those derived directly from the 3D simulations. Results. The excitation rates obtained from the 3D simulations are systematically lower than those computed from the semi-analytical excitation model. We find that Pmax ,t heP maximum, scales as (L/M) s where s is the slope of the power law and L and M are the mass and luminosity of the 1D stellar model built consistently with the associated 3D simulation. The slope is found to depend significantly on the adopted form of χk, the eddy time-correlation; using a Lorentzian, χ L , results in s = 2.6, whereas a Gaussian, χ G ,g ivess = 3.1. Finally, values of Vmax, the maximum in the mode velocity, are estimated from the computed power laws for Pmax and we find that Vmax increases as (L/M) sv . Comparisons with the currently available ground-based observations show that the computations assuming a Lorentzian χk yield a slope, sv, closer to the observed one than the slope obtained when assuming a Gaussian. We show that the spatial resolution of the 3D simulations must be high enough to obtain accurate computed energy rates.

Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres - numerical methods and application to the quiet, non-magnetic, surface of a solar-type star

Aims. We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes and improved resolution of hydrodynamical structures. We apply the code to simulate the surface granulation in a solar-type star, ignoring magnetic fields, and investigate the importance of coherent scattering for the atmospheric structure. Methods. A scattering term is added to the radiative transfer equation, requiring an iterative computation of the radiation field. We use a short-characteristics-based Gauss-Seidel acceleration scheme to compute radiative flux divergences for the energy equation. The effects of coherent scattering are tested by comparing the temperature stratification of three 3D time-dependent hydrodynamical atmosphere models of a solar-type star: without scattering, with continuum scattering only, and with both continuum and line scattering. Results. We show that continuum scattering does not have a significant impact on the photospheric temperature structure for a star like the Sun. Including scattering in line-blanketing, however, leads to a decrease of temperatures by about 350 K below log10 τ5000 < −4. The effect is opposite to that of 1D hydrostatic models in radiative equilibrium, where scattering reduces the cooling effect of strong LTE lines in the higher layers of the photosphere. Coherent line scattering also changes the temperature distribution in the high atmosphere, where we observe stronger fluctuations compared to a treatment of lines as true absorbers.

Improvements to stellar structure models, based on a grid of 3D convection simulations – II. Calibrating the mixing-length formulation

ABSTRACT Weperformacalibrationofthemixinglengthofconvectioninstellarstructuremodelsagainstrealistic3Dradiation-coupledhydrodynamics(RHD)simulationsofconvectioninstellarsurfacelayers,determiningtheadiabatdeepinconvectivestellarenvelopes.The mixing-length parameter α is calibrated by matching averages of the3Dsimulationsto1Dstellarenvelopemodels,ensuringidenticalatomicphysicsinthetwocases.Thisisdoneforapreviouslypublishedgridofsolar-metallicityconvectionsimulations,coveringfrom4200Kto6900Konthemainsequence,and4300–5000Kforgiantswithlogg =2.2.Ourcalibrationresultsinanα varyingfrom1.6forthewarmestdwarf,whichisjustcoolenoughtoadmitaconvectiveenvelope,andupto2.05forthecoolestdwarfsinourgrid.Inbetweentheseisatriangularplateauofα ∼1.76.TheSunislocatedonthisplateauandhasseenlittlechangeduringitsevolutionsofar.Whenstarsascendthegiantbranch,theylargelydosoalongtracksofconstantα,withα decreasingwithincreasingmass.Key words: Stars:atmospheres–stars:evolution–convection 1 INTRODUCTIONDue to the lack of a better theory of convection in stars,the mixing-length theory (B¨ohm-Vitense 1958, MLT) hasbeen in use for more thanhalf a century.By far the largestpart of the solar convection zone is very close to adia-batic, and the stratification in the bulk of the convectionzone is therefore determined by the adiabatic gradient,∇

The elemental composition of the Sun I. The intermediate mass elements Na to Ca

The chemical composition of the Sun is an essential piece of reference data for astronomy, cosmology, astroparticle, space and geophysics: elemental abundances of essentially all astronomical objects are referenced to the solar composition, and basically every process involving the Sun depends on its composition. This article, dealing with the intermediate-mass elements Na to Ca, is the first in a series describing the comprehensive re-determination of the solar composition. In this series we severely scrutinise all ingredients of the analysis across all elements, to obtain the most accurate, homogeneous and reliable results possible. We employ a highly realistic 3D hydrodynamic model of the solar photosphere, which has successfully passed an arsenal of observational diagnostics. For comparison, and to quantify remaining systematic errors, we repeat the analysis using three different 1D hydrostatic model atmospheres (marcs, miss and Holweger & Muller 1974, Sol. Phys., 39, 19) and a horizontally and temporally-averaged version of the 3D model (〈3D〉). We account for departures from local thermodynamic equilibrium (LTE) wherever possible. We have scoured the literature for the best possible input data, carefully assessing transition probabilities, hyperfine splitting, partition functions and other data for inclusion in the analysis. We have put the lines we use through a very stringent quality check in terms of their observed profiles and atomic data, and discarded all that we suspect to be blended. Our final recommended 3D+NLTE abundances are: log e = 6:21 ± 0:04, log e = 7:59 ± 0:04, log e = 6:43 ± 0:04, log e = 7:51 ± 0:03, log e = 5:41 ± 0:03, log e = 7:13 ± 0:03, log e = 5:04 ± 0:05 and log e = 6:32 ± 0:03. The uncertainties include both statistical and systematic errors. Our results are systematically smaller than most previous ones with the 1D semi-empirical Holweger & Muller model, whereas the 〈3D〉 model returns abundances very similar to the full 3D calculations. This analysis provides a complete description and a slight update of the results presented in Asplund et al. (2009, ARA&A, 47, 481) for Na to Ca, and includes full details of all lines and input data used.

A GRID OF THREE-DIMENSIONAL STELLAR ATMOSPHERE MODELS OF SOLAR METALLICITY. I. GENERAL PROPERTIES, GRANULATION, AND ATMOSPHERIC EXPANSION

Present grids of stellar atmosphere models are the workhorses in interpreting stellar observations and determining their fundamental parameters. These models rely on greatly simplified models of convection, however, lending less predictive power to such models of late-type stars. We present a grid of improved and more reliable stellar atmosphere models of late-type stars, based on deep, three-dimensional (3D), convective, stellar atmosphere simulations. This grid is to be used in general for interpreting observations and improving stellar and asteroseismic modeling. We solve the Navier Stokes equations in 3D and concurrent with the radiative transfer equation, for a range of atmospheric parameters, covering most of stellar evolution with convection at the surface. We emphasize the use of the best available atomic physics for quantitative predictions and comparisons with observations. We present granulation size, convective expansion of the acoustic cavity, and asymptotic adiabat as functions of atmospheric parameters.

THE MASS MIXING LENGTH IN CONVECTIVE STELLAR ENVELOPES

The scale length over which convection mixes mass in a star can be calculated as the inverse of the vertical derivative of the unidirectional (up or down) mass flux. This is related to the mixing length in the mixing length theory of stellar convection. We give the ratio of mass mixing length to pressure scale height for a grid of three-dimensional surface convection simulations, covering from 4300 K to 6900 K on the main sequence, and up to giants at log g = 2.2, all for solar composition. These simulations also confirm what is already known from solar simulations that convection does not proceed by discrete convective elements, but rather as a continuous, slow, smooth, warm upflow and turbulent, entropy deficient, fast down drafts. This convective topology also results in mixing on a scale comparable to the classic mixing length formulation, and is simply a consequence of mass conservation on flows in a stratified atmosphere.