Models of very-low-mass stars, brown dwarfs and exoplanets Allard, F.; Homeier, D.; Freytag, B.
Philosophical transactions - Royal Society. Mathematical, Physical and engineering sciences/Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences,
06/2012, Volume:
370, Issue:
1968
Journal Article
Peer reviewed
Open access
Within the next few years, GAIA and several instruments aiming to image extrasolar planets will be ready. In parallel, low-mass planets are being sought around red dwarfs, which offer more favourable ...conditions, for both radial velocity detection and transit studies, than solar-type stars. In this paper, the authors of a model atmosphere code that has allowed the detection of water vapour in the atmosphere of hot Jupiters review recent advances in modelling the stellar to substellar transition. The revised solar oxygen abundances and cloud model allow the photometric and spectroscopic properties of this transition to be reproduced for the first time. Also presented are highlight results of a model atmosphere grid for stars, brown dwarfs and extrasolar planets.
Context. Asymptotic giant branch (AGB) stars are characterised by complex stellar surface dynamics that affect the measurements and amplify the uncertainties on stellar parameters. The uncertainties ...in observed absolute magnitudes have been found to originate mainly from uncertainties in the parallaxes. The resulting motion of the stellar photocentre could have adverse effects on the parallax determination with Gaia. Aims. We explore the impact of the convection-related surface structure in AGBs on the photocentric variability. We quantify these effects to characterise the observed parallax errors and estimate fundamental stellar parameters and dynamical properties. Methods. We use three-dimensional (3D) radiative hydrodynamics simulations of convection with CO5BOLD and the post-processing radiative transfer code OPTIM3D to compute intensity maps in the Gaia G band 325–1030 nm. From those maps, we calculate the intensity-weighted mean of all emitting points tiling the visible stellar surface (i.e. the photocentre) and evaluate its motion as a function of time. We extract the parallax error from Gaia data-release 2 (DR2) for a sample of semi-regular variables in the solar neighbourhood and compare it to the synthetic predictions of photocentre displacements. Results. AGB stars show a complex surface morphology characterised by the presence of few large-scale long-lived convective cells accompanied by short-lived and small-scale structures. As a consequence, the position of the photocentre displays temporal excursions between 0.077 and 0.198 AU (≈5 to ≈11% of the corresponding stellar radius), depending on the simulation considered. We show that the convection-related variability accounts for a substantial part of the Gaia DR2 parallax error of our sample of semi-regular variables. Finally, we present evidence for a correlation between the mean photocentre displacement and the stellar fundamental parameters: surface gravity and pulsation. We suggest that parallax variations could be exploited quantitatively using appropriate radiation-hydrodynamics (RHD) simulations corresponding to the observed star.
Context. Observations of asymptotic giant branch (AGB) stars with increasing spatial resolution reveal new layers of complexity of atmospheric processes on a variety of scales. Aims. To analyze the ...physical mechanisms that cause asymmetries and surface structures in observed images, we use detailed 3D dynamical simulations of AGB stars; these simulations self-consistently describe convection and pulsations. Methods. We used the CO5BOLD radiation-hydrodynamics code to produce an exploratory grid of global "star-in-a-box" models of the outer convective envelope and the inner atmosphere of AGB stars to study convection, pulsations, and shock waves and their dependence on stellar and numerical parameters. Results. The model dynamics are governed by the interaction of long-lasting giant convection cells, short-lived surface granules, and strong, radial, fundamental-mode pulsations. Radial pulsations and shorter wavelength, traveling, acoustic waves induce shocks on various scales in the atmosphere. Convection, waves, and shocks all contribute to the dynamical pressure and, thus, to an increase of the stellar radius and to a levitation of material into layers where dust can form. Consequently, the resulting relation of pulsation period and stellar radius is shifted toward larger radii compared to that of non-linear 1D models. The dependence of pulsation period on luminosity agrees well with observed relations. The interaction of the pulsation mode with the non-stationary convective flow causes occasional amplitude changes and phase shifts. The regularity of the pulsations decreases with decreasing gravity as the relative size of convection cells increases. The model stars do not have a well-defined surface. Instead, the light is emitted from a very extended inhomogeneous atmosphere with a complex dynamic pattern of high-contrast features. Conclusions. Our models self-consistently describe convection, convectively generated acoustic noise, fundamental-mode radial pulsations, and atmospheric shocks of various scales, which give rise to complex changing structures in the atmospheres of AGB stars.
Context.
Despite being the best studied red supergiant star in our Galaxy, the physics behind the photometric variability and mass loss of Betelgeuse is poorly understood. Moreover, recently the star ...has experienced an unusual fading with its visual magnitude reaching a historical minimum. The nature of this event was investigated by several studies where mechanisms, such as episodic mass loss and the presence of dark spots in the photosphere, were invoked.
Aims.
We aim to relate the atmospheric dynamics of Betelgeuse to its photometric variability, with the main focus on the dimming event.
Methods.
We used the tomographic method which allowed us to probe different depths in the stellar atmosphere and to recover the corresponding disk-averaged velocity field. The method was applied to a series of high-resolution HERMES observations of Betelgeuse. Variations in the velocity field were then compared with photometric and spectroscopic variations.
Results.
The tomographic method reveals that the succession of two shocks along our line-of-sight (in February 2018 and January 2019), the second one amplifying the effect of the first one, combined with underlying convection and/or outward motion present at this phase of the 400 d pulsation cycle, produced a rapid expansion of a portion of the atmosphere of Betelgeuse and an outflow between October 2019 and February 2020. This resulted in a sudden increase in molecular opacity in the cooler upper atmosphere of Betelgeuse and, thus, in the observed unusual decrease of the star’s brightness.
Context. Winds of asymptotic giant branch stars are assumed to be driven by radiation pressure on dust. Previously, this process has been modeled with detailed time-dependent simulations of ...atmospheres and winds assuming spherically symmetric flows. In such models kinetic energy is injected by a variable inner boundary (“piston”) simulating the effects of stellar pulsation. However, the dynamical processes in these atmospheres – convection and pulsations – are actually three-dimensional. Aims. We present and analyze first 3D radiation hydrodynamics simulations of the convective interior and the atmosphere of a typical AGB star. In particular, we check whether the piston description in the 1D wind models is compatible with the 3D results. Methods. We used two different RHD codes, one (CO5BOLD) to produce 3D models of the outer convective envelope and the inner atmosphere of an AGB star, the other to describe the atmosphere and the wind acceleration region, including dust formation and non-grey radiative transfer, but assuming spherically symmetric flows. From the movements of stellar surface layers in the 3D models, we derived a description for the variable inner boundary in the 1D models. Results. The 3D models show large convection cells and pulsations that give rise to roughly spherically expanding shock waves in the atmosphere, levitating material into regions which are cool enough to allow for dust formation. The atmospheric velocity fields have amplitudes and time scales close to the values that are necessary to start dust formation in the 1D wind models. Conclusions. The convection cells in the 3D simulations are so large that the associated shock fronts appear almost spherical, justifying the assumption of spherical symmetry and the use of a piston boundary condition in the context of wind models. Nevertheless, certain non-radial structures exist in the dust shell developing in the 3D simulations which should be detectable with current interferometric techniques.
In the last decade, the photospheric solar metallicity as determined from spectroscopy experienced a remarkable downward revision. Part of this effect can be attributed to an improvement of atomic ...data and the inclusion of NLTE computations, but also the use of hydrodynamical model atmospheres seemed to play a role. This “decrease” with time of the metallicity of the solar photosphere increased the disagreement with the results from helioseismology. With a CO
5
BOLD 3D model of the solar atmosphere, the CIFIST team at the Paris Observatory re-determined the photospheric solar abundances of several elements, among them C, N, and O. The spectroscopic abundances are obtained by fitting the equivalent width and/or the profile of observed spectral lines with synthetic spectra computed from the 3D model atmosphere. We conclude that the effects of granular fluctuations depend on the characteristics of the individual lines, but are found to be relevant only in a few particular cases. 3D effects are not responsible for the systematic lowering of the solar abundances in recent years. The solar metallicity resulting from this analysis is
Z
=0.0153,
Z
/
X
=0.0209.
Context.
High-precision photometry of exoplanet transits obtained with the
Kepler
satellite allows one to derive information on the center-to-limb variation (CLV) of the host stars. Recent analyses ...indicate a small but systematic discrepancy between observations and theoretical expectations based on detailed multidimensional model atmospheres. It has been hypothesized that the discrepancy is related to the neglect of magnetic fields in the models.
Aims.
Our goal is to test the above hypothesis for solar-like stars. We further intend to quantify the consequences for interferometry, and the possibility of extracting information at the level of stellar magnetic activity from the CLV.
Methods.
We constructed a sequence of multidimensional models including magnetic fields of varying strengths. We derived theoretical predictions on the CLV, taking into account factors like the observational passband, stellar sphericity, the methodology of the light curve analysis, and interstellar extinction.
Results.
The models predict a relative brightening of the stellar limb with increasing magnetic field strength, which qualitatively goes in the direction of reducing the mismatch between observation and theory. Quantitatively, however, the mismatch is not fully eliminated. Interstellar extinction on a level
A
V
≲ 1 mag has little impact on the CLV and is largely degenerate with the influence of magnetic fields. Global magnetic activity at field strengths ≲300 G influences interferometric radius measurements to ≲1%. We emphasize that our results refer to measurements taken in the
Kepler
passband.
Conclusions.
The presence of magnetic activity appears to be a plausible explanation for the present discrepancy between observation and theory. The still-present partial mismatch needs to be understood. To this end, we point to improvements in modeling and wishes for more observational data of active stars, including spectral information.
Context. It has been proposed that convection in red supergiant (RSG) stars produces large-scale granules causing observable surface inhomogeneities. This convection is also extremely vigorous and is ...suspected to be one of the main causes of mass-loss in RSGs. It should thus be understood in detail. Evidence has accumulated of asymmetries in the photospheres of RSGs, but detailed studies of granulation are still lacking. Interferometric observations provide an innovative way of addressing this question, but they are still often interpreted using smooth symmetrical limb-darkened intensity distributions, or simple, spotted, ad hoc models. Aims. We explore the impact of the granulation on visibility curves and closure phases using the radiative transfer code OPTIM3D. We simultaneously assess how 3D simulations of convection in RSG with CO5BOLD can be tested by comparing with these observations. Methods. We use 3D radiative hydrodynamical (RHD) simulations of convection to compute intensity maps at various wavelengths and time, from which we derive interferometric visibility amplitudes and phases. We study their behaviour with time, position angle, and wavelength, and compare them to observations of the RSG α Ori. Results. We provide average limb-darkening coefficients for RSGs. We describe the prospects for the detection and characterization of granulation (i.e., contrast, size) on RSGs. We demonstrate that our RHD simulations provide an excellent fit to existing interferometric observations of α Ori, in contrast to limb darkened disks. This confirms the existence of large convective cells on the surface of Betelgeuse.
Context. The wind-driving mechanism of asymptotic giant branch (AGB) stars is commonly attributed to a two-step process: first, gas in the stellar atmosphere is levitated by shockwaves caused by ...stellar pulsation, then accelerated outwards by radiative pressure on newly formed dust, inducing a wind. Dynamical modelling of such winds usually assumes a spherically symmetric star. Aims. We explore the potential consequences of complex stellar surface structures, as predicted by three-dimensional (3D) star-in-a-box modelling of M-type AGB stars, on the resulting wind properties with the aim to improve the current wind models. Methods. Two different modelling approaches are used; the CO5BOLD 3D star-in-a-box code to simulate the convective, pulsating interior and lower atmosphere of the star, and the DARWIN one-dimensional (1D) code to describe the dynamical atmosphere where the wind is accelerated. The gas dynamics of the inner atmosphere region at distances of R ∼ 1−2 R⋆, which both modelling approaches simulate, are compared. Dynamical properties and luminosity variations derived from CO5BOLD interior models are used as input for the inner boundary in DARWIN wind models in order to emulate the effects of giant convection cells and pulsation, and explore their influence on the dynamical properties. Results. The CO5BOLD models are inherently anisotropic, with non-uniform shock fronts and varying luminosity amplitudes, in contrast to the spherically symmetrical DARWIN wind models. DARWIN wind models with CO5BOLD-derived inner boundary conditions produced wind velocities and mass-loss rates comparable to the standard DARWIN models, however the winds show large density variations on time-scales of 10–20 yr. Conclusions. The method outlined in this paper derives pulsation properties from the 3D star-in-a-box CO5BOLD models, to be used in the DARWIN models. If the current grid of CO5BOLD models is extended, it will be possible to construct extensive DARWIN grids with inner boundary conditions derived from 3D interior modelling of convection and pulsation, and avoid the free parameters of the current approach.
High-resolution images of the solar surface show a granulation pattern of hot rising and cooler downward-sinking material – the top of the deep-reaching solar convection zone. Convection plays a role ...for the thermal structure of the solar interior and the dynamo acting there, for the stratification of the photosphere, where most of the visible light is emitted, as well as for the energy budget of the spectacular processes in the chromosphere and corona. Convective stellar atmospheres can be modeled by numerically solving the coupled equations of (magneto)hydrodynamics and non-local radiation transport in the presence of a gravity field. The CO5BOLD code described in this article is designed for so-called “realistic” simulations that take into account the detailed microphysics under the conditions in solar or stellar surface layers (equation-of-state and optical properties of the matter). These simulations indeed deserve the label “realistic” because they reproduce the various observables very well – with only minor differences between different implementations. The agreement with observations has improved over time and the simulations are now well-established and have been performed for a number of stars. Still, severe challenges are encountered when it comes to extending these simulations to include ideally the entire star or substellar object: the strong stratification leads to completely different conditions in the interior, the photosphere, and the corona. Simulations have to cover spatial scales from the sub-granular level to the stellar diameter and time scales from photospheric wave travel times to stellar rotation or dynamo cycle periods. Various non-equilibrium processes have to be taken into account. Last but not least, realistic simulations are based on detailed microphysics and depend on the quality of the input data, which can be the actual accuracy limiter. This article provides an overview of the physical problem and the numerical solution and the capabilities of CO5BOLD, illustrated with a number of applications.
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