Pulsation-induced atmospheric dynamics in M-type AGB stars. Effects on wind properties, photometric variations and near-IR CO line profiles

Wind-driving in asymptotic giant branch (AGB) stars is commonly attributed to a two-step process. First, matter in the stellar atmosphere is levitated by shock waves, induced by stellar pulsation, and second, this matter is accelerated by radiation pressure on dust, resulting in a wind. In dynamical atmosphere and wind models the effects of the stellar pulsation are often simulated by a simplistic prescription at the inner boundary. We test a sample of dynamical models for M-type AGB stars, for which we kept the stellar parameters fixed to values characteristic of a typical Mira variable but varied the inner boundary condition. The aim was to evaluate the effect on the resulting atmosphere structure and wind properties. The results of the models are compared to observed mass-loss rates and wind velocities, photometry, and radial velocity curves, and to results from 1D radial pulsation models. Dynamical atmosphere models are calculated, using the DARWIN code for different combinations of photospheric velocities and luminosity variations. The inner boundary is changed by introducing an offset between maximum expansion of the stellar surface and the luminosity and/or by using an asymmetric shape for the luminosity variation. Models that resulted in realistic wind velocities and mass-loss rates, when compared to observations, also produced realistic photometric variations. For the models to also reproduce the characteristic radial velocity curve present in Mira stars (derived from CO $\Delta v = 3$ lines), an overall phase shift of 0.2 between the maxima of the luminosity and radial variation had to be introduced. We find that a group of models with different boundary conditions (29 models, including the model with standard boundary conditions) results in realistic velocities and mass-loss rates, and in photometric variations

Dust-driven winds of AGB stars: The critical interplay of atmospheric shocks and luminosity variations

Winds of AGB stars are thought to be driven by a combination of pulsation-induced shock waves and radiation pressure on dust. In dynamic atmosphere and wind models, the stellar pulsation is often simulated by prescribing a simple sinusoidal variation in velocity and luminosity at the inner boundary of the model atmosphere. We experiment with different forms of the luminosity variation in order to assess the effects on the wind velocity and mass-loss rate, when progressing from the simple sinusoidal recipe towards more realistic descriptions. Using state-of-the-art dynamical models of C-rich AGB stars, a range of different asymmetric shapes of the luminosity variation and a range of phase shifts of the luminosity variation relative to the radial variation are tested. These tests are performed on two stellar atmosphere models. The first model has dust condensation and, as a consequence, a stellar wind is triggered, while the second model lacks both dust and wind. The first model with dust and stellar wind is very sensitive to moderate changes in the luminosity variation. There is a complex relationship between the luminosity minimum, and dust condensation: changing the phase corresponding to minimum luminosity can either increase or decrease mass-loss rate and wind velocity. The luminosity maximum dominates the radiative pressure on the dust, which in turn, is important for driving the wind. These effects of changed luminosity variation are coupled with the dust formation. In contrast there is very little change to the structure of the model without dust. Changing the luminosity variation, both by introducing a phase shift and by modifying the shape, influences wind velocity and the mass-loss rate. To improve wind models it would probably be desirable to extract boundary conditions from 3D dynamical interior models or stellar pulsation models.Comment: 11 pages, 13 figures, accepted for publication in A&

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

Requirements in feature algebra

Feature Algebra is intended to capture the commonalities of feature oriented software development (FOSD), such as introductions, refinements and quantification. It allows denoting systems composed of features by algebraic terms and transforming the systems by manipulating the terms using the laws of the algebra. The algebraic view abstracts from differences of minor importance and leads to more compact and effective reasoning. While the existing Feature Algebra covers most of the main aspects of FOSD, so far requirements have not been integrated into it. They naturally arise in connection with different aspects of feature orientation, such as feature elicitation, feature dependence, mutual feature exclusion and feature interaction. This paper presents a possibility for integrating requirements into Feature Algebra

Observing and modeling the dynamic atmosphere of the low mass-loss C-star R Sculptoris at high angular resolution

We study the circumstellar environment of the carbon-rich star R Scl using the near- and mid-infrared high spatial resolution observations from the ESO-VLTI instruments VINCI and MIDI. These observations aim at increasing our knowledge of the dynamic processes in play within the very close circumstellar environment where the mass loss of AGB stars is initiated. Data are interpreted using a self-consistent dynamic model. Interferometric observations do not show any significant variability effect at the 16 m baseline between phases 0.17 and 0.23 in the K band, and for both the 15 m baseline between phases 0.66 and 0.97 and the 31 m baseline between phases 0.90 and 0.97 in the N band. We find fairly good agreement between the dynamic model and the spectrophotometric data from 0.4 to 25 $\mu$m. The model agrees well with the time-dependent flux data at 8.5 $\mu$m, whereas it is too faint at 11.3 and 12.5 $\mu$m. The VINCI visibilities are reproduced well, meaning that the extension of the model is suitable in the K-band. In the mid-infrared, the model has the proper extension to reveal molecular structures of C2H2 and HCN located above the stellar photosphere. However, the windless model used is not able to reproduce the more extended and dense dusty environment. Among the different explanations for the discrepancy between the model and the measurements, the strong nonequilibrium process of dust formation is one of the most probable. The complete dynamic coupling of gas and dust and the approximation of grain opacities with the small-particle limit in the dynamic calculation could also contribute to the difference between the model and the data

Abundance analysis for long period variables. Velocity effects studied with O-rich dynamic model atmospheres

(abbreviated) Measuring the surface abundances of AGB stars is an important tool for studying the effects of nucleosynthesis and mixing in the interior of low- to intermediate mass stars during their final evolutionary phases. The atmospheres of AGB stars can be strongly affected by stellar pulsation and the development of a stellar wind, though, and the abundance determination of these objects should therefore be based on dynamic model atmospheres. We investigate the effects of stellar pulsation and mass loss on the appearance of selected spectral features (line profiles, line intensities) and on the derived elemental abundances by performing a systematic comparison of hydrostatic and dynamic model atmospheres. High-resolution synthetic spectra in the near infrared range were calculated based on two dynamic model atmospheres (at various phases during the pulsation cycle) as well as a grid of hydrostatic COMARCS models. Equivalent widths of a selection of atomic and molecular lines were derived in both cases and compared with each other. In the case of the dynamic models, the equivalent widths of all investigated features vary over the pulsation cycle. A consistent reproduction of the derived variations with a set of hydrostatic models is not possible, but several individual phases and spectral features can be reproduced well with the help of specific hydrostatic atmospheric models. In addition, we show that the variations in equivalent width that we found on the basis of the adopted dynamic model atmospheres agree qualitatively with observational results for the Mira R Cas over its light cycle. The findings of our modelling form a starting point to deal with the problem of abundance determination in strongly dynamic AGB stars (i.e., long-period variables).Comment: 13 pages, 22 figures, accepted for publication in A&

Interferometric properties of pulsating C-rich AGB stars I. Intensity profiles and uniform disc diameters of dynamic model atmospheres

We present the first theoretical study on center-to-limb variation (CLV) properties and relative radius interpretation for narrow and broad-band filters, on the basis of a set of dynamic model atmospheres of C-rich AGB stars. We computed visibility profiles and the equivalent uniform disc radii (UD-radii) in order to investigate the dependence of these quantities upon the wavelength and pulsation phase. After an accurate morphological analysis of the visibility and intensity profiles determined in narrow and broad-band filter, we fitted our visibility profiles with a UD function simulating the observational approach. UD-radii have been computed using three different fitting-methods to investigate the influence of the sampling of the visibility profile: single point, two points and least square method. The intensity and visibility profiles of models characterized by mass loss show a behaviour very different from a UD. We found that UD-radii are wavelength dependent and this dependence is stronger if mass loss is present. Strong opacity contributions from C2H2 affect all radius measurements at 3 micron and in the N-band, resulting in higher values for the UD-radii. The predicted behaviour of UD-radii versus phase is complicated in the case of models with mass loss, while the radial changes are almost sinusoidal for the models without mass loss. Compared to the M-type stars, for the C-stars no windows for measuring the pure continuum are available.Comment: 13 pages, 9 figures, accepted for publication in A&

Atmospheric dynamics in carbon-rich Miras. I. Model atmospheres and synthetic line profiles

Atmospheres of evolved AGB stars are heavily affected by pulsation, dust formation and mass loss, and they can become very extended. Time series of observed high-resolution spectra proved to be a useful tool to study atmospheric dynamics throughout the outer layers of these pulsating red giants. Originating at various depths, different molecular spectral lines observed in the near-infrared can be used to probe gas velocities there for different phases during the lightcycle. Dynamic model atmospheres are needed to represent the complicated structures of Mira variables properly. An important aspect which should be reproduced by the models is the variation of line profiles due to the influence of gas velocities. Based on a dynamic model, synthetic spectra (containing CO and CN lines) were calculated, using an LTE radiative transfer code that includes velocity effects. It is shown that profiles of lines that sample different depths qualitatively reproduce the behaviour expected from observations.Comment: accepted by A&A, 12 pages, 9 figure

Atmospheric dynamics in carbon-rich Miras. II. Models meet observations

Originating in different depths of the very extended atmospheres of AGB stars, various molecular spectral lines observable in the near-infrared show diverse behaviours and can be used to probe atmospheric dynamics throughout the outer layers of these pulsating red giants. In Nowotny et al. (2005, Paper I) time series of synthetic high-resolution spectra were presented, computed from a dynamic model atmosphere for a typical carbon-rich Mira. In this work, line profile shapes, their variations during the lightcycle and radial velocities derived from wavelength shifts are analyzed and compared with results from observed FTS spectra of the C-rich Mira S Cep and other Miras. It is found that the global velocity structure of the model is in qualitative agreement with observations. Radial velocities of molecular lines sampling different layers behave comparably, although some differences are apparant concerning absolute values. A correction factor of p=1.36 between measured RVs and actual gas velocities is derived for CO dv=3 lines. It is shown that dynamic model atmospheres are capable of reproducing Mira spectra without introducing an additional ''static layer'' proposed by several authors.Comment: accepted by A&A, 12 pages, 10 figure