Dynamics of mistuned radial turbine wheels

This paper presents investigations carried out at Holset into the dynamics of mistuned radial turbine wheels, including a literature review, a lumped parameter model, identification of the most responsive blade, distribution of the peak maximum order response and a method of mistiming identification

Modelling polarized light from dust shells surrounding asymptotic giant branch stars

Winds of asymptotic giant branch (AGB) stars are commonly assumed to be driven by radiative acceleration of dust grains. For M-type AGB stars, the nature of the wind-driving dust species has been a matter of intense debate. A proposed source of the radiation pressure triggering the outflows is photon scattering on Fe-free silicate grains. This wind-driving mechanism requires grain radii of about 0.1 - 1 micron in order to make the dust particles efficient at scattering radiation around the stellar flux maximum. Grain size is therefore an important parameter for understanding the physics behind the winds of M-type AGB stars. We seek to investigate the diagnostic potential of scattered polarized light for determining dust grain sizes. We have developed a new tool for computing synthetic images of scattered light in dust and gas shells around AGB stars, which can be applied to detailed models of dynamical atmospheres and dust-driven winds. We present maps of polarized light using dynamical models computed with the DARWIN code. The synthetic images clearly show that the intensity of the polarized light, the position of the inner edge of the dust shell, and the size of the dust grains near the inner edge are all changing with the luminosity phase. Non-spherical structures in the dust shells can also have an impact on the polarized light. We simulate this effect by combining different pulsation phases into a single 3D structure before computing synthetic images. An asymmetry of the circumstellar envelope can create a net polarization, which can be used as diagnostics for the grain size. The ratio between the size of the scattering particles and the observed wavelength determines at what wavelengths net polarization switches direction. If observed, this can be used to constrain average particle sizes.Comment: 9 page

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

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&

Dynamic atmospheres and winds of cool luminous giants, I. Al2_2O3_3 and silicate dust in the close vicinity of M-type AGB stars

High spatial resolution techniques have given valuable insights into the mass loss mechanism of AGB stars, which presumably involves a combination of atmospheric levitation by pulsation-induced shock waves and radiation pressure on dust. Observations indicate that Al$_2$O$_3$ condenses at distances of about 2 stellar radii or less, prior to the formation of silicates. Al$_2$O$_3$ grains are therefore prime candidates for producing the scattered light observed in the close vicinity of several M-type AGB stars, and they may be seed particles for the condensation of silicates at lower temperatures. We have constructed a new generation of Dynamic Atmosphere & Radiation-driven Wind models based on Implicit Numerics (DARWIN), including a time-dependent treatment of grain growth & evaporation for both Al$_2$O$_3$ and Fe-free silicates (Mg$_2$SiO$_4$). The equations describing these dust species are solved in the framework of a frequency-dependent radiation-hydrodynamical model for the atmosphere & wind structure, taking pulsation-induced shock waves and periodic luminosity variations into account. Condensation of Al$_2$O$_3$ at the close distances and in the high concentrations implied by observations requires high transparency of the grains in the visual and near-IR region to avoid destruction by radiative heating. For solar abundances, radiation pressure due to Al$_2$O$_3$ is too low to drive a wind. Nevertheless, this dust species may have indirect effects on mass loss. The formation of composite grains with an Al$_2$O$_3$ core and a silicate mantle can give grain growth a head start, increasing both mass loss rates and wind velocities. Furthermore, our experimental core-mantle grain models lead to variations of visual and near-IR colors during a pulsation cycle which are in excellent agreement with observations.Comment: Accepted for publication in Astronomy & Astrophysics (18 pages, 9 figures

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

Hard Body 2.0 The Construction of the Fitness Subject: An Analysis of Swedish Fitness Blogs

Through conducting a discourse analysis of Swedish fitness blogs, aided by the theoretical framework of Michel Foucault in terms of technologies of the self, and the concept of habitus as it is explained by Pierre Bourdieu, as well as a critical perspective concerning the morals of health, I’ve investigated how human beings engage and negotiate discourse and social structure through writing practices mediated through cyberspace. The results indicated that the fitness field is a field of possibilities, and that it is through agency that discourse and social structure come in to play, and thus it is through agency that different practices of appropriating fitness and health were displayed, signifying that the fitness subject is heterogeneously constructed

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