Atmospheres and wind properties of non-spherical AGB stars

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. 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. Two different modelling approaches are used; the CO$^5$BOLD 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 $R\sim1-2R_\star$, which both modelling approaches simulate, are compared. Dynamical properties and luminosity variations derived from CO$^5$BOLD 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. The CO$^5$BOLD 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 CO$^5$BOLD-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 years.Comment: 13 pages, 12 figures, Accepted for publication in A&

Exploring wind-driving dust species in cool luminous giants III. Wind models for M-type AGB stars: dynamic and photometric properties

Stellar winds observed in asymptotic giant branch (AGB) stars are usually attributed to a combination of stellar pulsations and radiation pressure on dust. Shock waves triggered by pulsations propagate through the atmosphere, compressing the gas and lifting it to cooler regions, which create favourable conditions for grain growth. If sufficient radiative acceleration is exerted on the newly formed grains through absorption or scattering of stellar photons, an outflow can be triggered. Strong candidates for wind-driving dust species in M-type AGB stars are magnesium silicates (Mg$_2$SiO$_4$ and MgSiO$_3$). Such grains can form close to the stellar surface, they consist of abundant materials and, if they grow to sizes comparable to the wavelength of the stellar flux maximum, they experience strong acceleration by photon scattering. We use a frequency-dependent radiation-hydrodynamics code with a detailed description for the growth of Mg$_2$SiO$_4$ grains to calculate the first extensive set of time-dependent wind models for M-type AGB stars. The resulting wind properties, visual and near-IR photometry and mid-IR spectra are compared with observations.We show that the models can produce outflows for a wide range of stellar parameters. We also demonstrate that they reproduce observed mass-loss rates and wind velocities, as well as visual and near-IR photometry. However, the current models do not show the characteristic silicate features at 10 and 18 $\mu$m as a result of the cool temperature of Mg$_2$SiO$_4$ grains in the wind. Including a small amount of Fe in the grains further out in the circumstellar envelope will increase the grain temperature and result in pronounced silicate features, without significantly affecting the photometry in the visual and near-IR wavelength regions.Comment: 11 pages, 14 figure

Tomography of silicate dust around M-type AGB stars I. Diagnostics based on dynamical models

The heavy mass loss observed in evolved asymptotic giant branch stars is usually attributed to a two-step process: atmospheric levitation by pulsation-induced shock waves, followed by radiative acceleration of newly formed dust grains. Detailed wind models suggest that the outflows of M-type AGB stars may be triggered by photon scattering on Fe-free silicates with grain sizes of about 0.1 - 1 $\mu$m. Due to the low grain temperature, these Fe-free silicates can condense close to the star, but they do not produce the characteristic mid-IR features that are often observed in M-type AGB stars. However, it is probable that the silicate grains are gradually enriched with Fe as they move away from the star, to a degree where the grain temperature stays below the sublimation temperature, but is high enough to produce emission features. We investigate whether differences in grain temperature in the inner wind region, which are related to changes in the grain composition, can be detected with current interferometric techniques, in order to put constraints on the wind mechanism. To investigate this we use radial structures of the atmosphere and wind of an M-type AGB star, produced with the 1D radiation-hydrodynamical code DARWIN. The spectral energy distribution is found to be a poor indicator of different temperature profiles and therefore is not a good tool for distinguishing different scenarios of changing grain composition. However, spatially resolved interferometric observations have promising potential. They show signatures even for Fe-free silicates (found at 2-3 stellar radii), in contrast to the spectral energy distribution. Observations with baselines that probe spatial scales of about 4 stellar radii and beyond are suitable for tracing changes in grain composition, since this is where effects of Fe enrichment should be found.Comment: Accepted for publication in Section 8. Stellar atmospheres of Astronomy and Astrophysics. The official date of acceptance is 07/09/2017. 9 pages, 7 figures, 4 figures in appendi

An extensive grid of DARWIN models for M-type AGB stars I. Mass-loss rates and other properties of dust-driven winds

The purpose of this work is to present an extensive grid of dynamical atmosphere and wind models for M-type AGB stars, covering a wide range of relevant stellar parameters. We used the DARWIN code, which includes frequency-dependent radiation-hydrodynamics and a time-dependent description of dust condensation and evaporation, to simulate the dynamical atmosphere. The wind-driving mechanism is photon scattering on submicron-sized Mg$_2$SiO$_4$ grains. The grid consists of $\sim4000$ models, with luminosities from $L_\star=890\,{\mathrm{L}}_\odot$ to $L_\star=40000\,{\mathrm{L}}_\odot$ and effective temperatures from 2200K to 3400K. For the first time different current stellar masses are explored with M-type DARWIN models, ranging from 0.75M$_\odot$ to 3M$_\odot$. The modelling results are radial atmospheric structures, dynamical properties such as mass-loss rates and wind velocities, and dust properties (e.g. grain sizes, dust-to-gas ratios, and degree of condensed Si). We find that the mass-loss rates of the models correlate strongly with luminosity. They also correlate with the ratio $L_*/M_*$: increasing $L_*/M_*$ by an order of magnitude increases the mass-loss rates by about three orders of magnitude, which may naturally create a superwind regime in evolution models. There is, however, no discernible trend of mass-loss rate with effective temperature, in contrast to what is found for C-type AGB stars. We also find that the mass-loss rates level off at luminosities higher than $\sim14000\,{\mathrm{L}}_\odot$, and consequently at pulsation periods longer than $\sim800$ days. The final grain radii range from 0.25 micron to 0.6 micron. The amount of condensed Si is typically between 10% and 40%, with gas-to-dust mass ratios between 500 and 4000.Comment: Accepted to A&A, 17 pages, 15 figure

Exploring wind-driving dust species in cool luminous giants II. Constraints from photometry of M-type AGB stars

The heavy mass loss observed in evolved asymptotic giant branch (AGB) stars is usually attributed to a two-stage process: atmospheric levitation by pulsation-induced shock waves, followed by radiative acceleration of newly formed dust grains. The dust transfers momentum to the surrounding gas through collisions and thereby triggers a general outflow. Radiation-hydrodynamical models of M-type AGB stars suggest that these winds can be driven by photon scattering -- in contrast to absorption -- on Fe-free silicate grains of sizes 0.1--1\,$\mu$m. In this paper we study photometric constraints for wind-driving dust species in M-type AGB stars, as part of an ongoing effort to identify likely candidates among the grain materials observed in circumstellar envelopes. To investigate the scenario of stellar winds driven by photon scattering on dust, and to explore how different optical and chemical properties of wind-driving dust species affect photometry we focus on two sets of dynamical models atmospheres: (i) models using a detailed description for the growth of Mg$_2$SiO$_4$ grains, taking into account both scattering and absorption cross-sections when calculating the radiative acceleration, and (ii) models using a parameterized dust description, constructed to represent different chemical and optical dust properties. By comparing synthetic photometry from these two sets of models to observations of M-type AGB stars we can provide constraints on the properties of wind-driving dust species. Photometry from wind models with a detailed description for the growth of Mg$_2$SiO$_4$ grains reproduces well both the values and the time-dependent behavior of observations of M-type AGB stars, providing further support for the scenario of winds driven by photon scattering on dust.Comment: Accepted for publication in A&A. 15 pages, 14 figure

Exploring wind-driving dust species in cool luminous giants I. Basic criteria and dynamical models of M-type AGB stars

This work is part of an ongoing effort aiming at identifying the actual wind-drivers among the dust species observed in circumstellar envelopes. In particular, we focus on the interplay between a strong stellar radiation field and the dust formation process. To identify critical properties of potential wind-driving dust species we use detailed radiation-hydrodynamical models which include a parameterized dust description, complemented by simple analytical estimates to help with the physical interpretation of the numerical results. The adopted dust description is constructed to mimic different chemical and optical dust properties in order to systematically study the effects of a realistic radiation field on the second stage of the mass loss mechanism. We see distinct trends in which combinations of optical and chemical dust properties are needed to trigger an outflow. Dust species with a low condensation temperature and a NIR absorption coefficient that decreases strongly with wavelength will not condense close enough to the stellar surface to be considered as potential wind-drivers. Our models confirm that metallic iron and Fe-bearing silicates are not viable as wind-drivers due to their near-infrared optical properties and resulting large condensation distances. TiO2 is also excluded as a wind-driver due to the low abundance of Ti. Other species, such a SiO2 and Al2O3, are less clear-cut cases due to uncertainties in the optical and chemical data and further work is needed. A strong candidate is Mg2SiO4 with grain sizes of 0.1-1 micron, where scattering contributes significantly to the radiative acceleration, as suggested by earlier theoretical work and supported by recent observations.Comment: 15 pages, 12 figure

Multiple Current States of Two Phase-Coupled Superconducting Rings

The states of two phase-coupled superconducting rings have been investigated. Multiple current states have been revealed in the dependence of the critical current on the magnetic field. The performed calculations of the critical currents and energy states in a magnetic field have made it possible to interpret the experiment as the measurement of energy states into which the system comes with different probabilities because of the equilibrium and non-equilibrium noises upon the transition from the resistive state to the superconducting state during the measurement of the critical currentComment: 5 pages, 5 figure

Comparative Modelling of the Spectra of Cool Giants

Our ability to extract information from the spectra of stars depends on reliable models of stellar atmospheres and appropriate techniques for spectral synthesis. Various model codes and strategies for the analysis of stellar spectra are available today. We aim to compare the results of deriving stellar parameters using different atmosphere models and different analysis strategies. The focus is set on high-resolution spectroscopy of cool giant stars. Spectra representing four cool giant stars were made available to various groups and individuals working in the area of spectral synthesis, asking them to derive stellar parameters from the data provided. The results were discussed at a workshop in Vienna in 2010. Most of the major codes currently used in the astronomical community for analyses of stellar spectra were included in this experiment. We present the results from the different groups, as well as an additional experiment comparing the synthetic spectra produced by various codes for a given set of stellar parameters. Similarities and differences of the results are discussed. Several valid approaches to analyze a given spectrum of a star result in quite a wide range of solutions. The main causes for the differences in parameters derived by different groups seem to lie in the physical input data and in the details of the analysis method. This clearly shows how far from a definitive abundance analysis we still are.Comment: accepted for publication in A&A. This version includes also the online tables. Reference spectra will later be available via the CD

Constraining the thermally pulsing asymptotic giant branch phase with resolved stellar populations in the Small Magellanic Cloud

The thermally pulsing asymptotic giant branch (TP-AGB) experienced by low- and intermediate-mass stars is one of the most uncertain phases of stellar evolution and the models need to be calibrated with the aid of observations. To this purpose, we couple high-quality observations of resolved stars in the Small Magellanic Cloud (SMC) with detailed stellar population synthesis simulations computed with the TRILEGAL code. The strength of our approach relies on the detailed spatially resolved star formation history of the SMC, derived from the deep near-infrared photometry of the VISTA survey of the Magellanic Clouds, as well as on the capability to quickly and accurately explore a wide variety of parameters and effects with the COLIBRI code for the TP-AGB evolution. Adopting a well-characterized set of observations - star counts and luminosity functions - we set up a calibration cycle along which we iteratively change a few key parameters of the TP-AGB models until we eventually reach a good fit to the observations. Our work leads to identify two best-fitting models that mainly differ in the efficiencies of the third dredge-up and mass-loss in TP-AGB stars with initial masses larger than about 3 M⊙. On the basis of these calibrated models, we provide a full characterization of the TP-AGB stellar population in the SMC in terms of stellar parameters (initial masses, C/O ratios, carbon excess, mass-loss rates). Extensive tables of isochrones including these improved models are publicly available.This work is supported by the European Research Council (ERC) Consolidator Grant funding scheme (project STARKEY, G.A. n. 615604). We thank the entire VMC team for producing the spaceresolved SFH used in this work and J. Cummings and J. Kalirai for kindly providing us with their IFMR data. MRLC acknowledges funding from the ERC under the European Union’s Horizon 2020 research and innovation programme (G.A. n. 682115). Many thanks go to C. Maraston, S. Charlot, and G. Bruzual for providing us with their stellar population synthesis models