Mean flow evolution of saturated forced shear flows in polytropic atmospheres

In stellar interiors shear flows play an important role in many physical processes. So far helioseismology provides only large-scale measurements, and so the small-scale dynamics remains insufficiently understood. To draw a connection between observations and threedimensional DNS of shear driven turbulence, we investigate horizontally averaged profiles of the numerically obtained mean state. We focus here on just one of the possible methods that can maintain a shear flow, namely the average relaxation method. We show that although some systems saturate by restoring linear marginal stability this is not a general trend. Finally, we discuss the reason that the results are more complex than expected

From Solar to Stellar Brightness Variations: The Effect of Metallicity

Context. Comparison studies of Sun-like stars with the Sun suggest an anomalously low photometric variability of the Sun compared to Sun-like stars with similar magnetic activity. Comprehensive understanding of stellar variability is needed, to find a physical reasoning for this observation. Aims. We investigate the effect of metallicity and effective temperature on the photometric brightness change of Sun-like stars seen at different inclinations. The considered range of fundamental stellar parameters is sufficiently small so the stars, investigated here, still count as Sun-like or even as solar twins. Methods. To model the brightness change of stars with solar magnetic activity, we extend a well established model of solar brightness variations, SATIRE (which stands for Spectral And Total Irradiance Reconstruction), which is based on solar spectra, to stars with different fundamental parameters. For that we calculate stellar spectra for different metallicities and effective temperature using the radiative transfer code ATLAS9. Results. We show that even a small change (e.g. within the observational error range) of metallicity or effective temperature significantly affects the photometric brightness change compared to the Sun. We find that for Sun-like stars, the amplitude of the brightness variations obtained for Str\"omgren (b + y)/2 reaches a local minimum for fundamental stellar parameters close to the solar metallicity and effective temperature. Moreover, our results show that the effect of inclination decreases for metallicity values greater than the solar metallicity. Overall, we find that an exact determination of fundamental stellar parameters is crucially important for understanding stellar brightness changes.Comment: 12 pages, 12 figures, accepted in A&

Shear instabilities in a fully compressible polytropic atmosphere

Shear flows have an important impact on the dynamics in an assortment of different astrophysical objects including accreditation discs and stellar interiors. Investigating shear flow instabilities in a polytropic atmosphere provides a fundamental understanding of the motion in stellar interiors where turbulent motions, mixing processes, as well as magnetic field generation takes place. Here, a linear stability analysis for a fully compressible fluid in a two-dimensional Cartesian geometry is carried out. Our study focuses on determining the critical Richardson number for different Mach numbers and the destabilising effects of high thermal diffusion. We find that there is a deviation of the predicted stability threshold for moderate Mach number flows along with a significant effect on the growth rate of the linear instability for small Peclet numbers. We show that in addition to a Kelvin-Helmholtz instability a Holmboe instability can appear and we discuss the implication of this in stellar interiors

Evolution and characteristics of forced shear flows in polytropic atmospheres: Large and small Péclet number regimes

Complex mixing and magnetic field generation occurs within stellar interiors particularly where there is a strong shear flow. To obtain a comprehensive understanding of these processes, it is necessary to study the complex dynamics of shear regions. Due to current observational limitations, it is necessary to investigate the inevitable small-scale dynamics via numerical calculations. Here, we examine direct numerical calculations of a local model of unstable shear flows in a compressible polytropic fluid primarily in a two-dimensional domain, where we focus on determining how key parameters affect the global properties and characteristics of the resulting saturated turbulent phase. We consider the effect of varying both the viscosity and the thermal diffusivity on the non-linear evolution. Moreover, our main focus is to understand the global properties of the saturated phase, in particular estimating for the first time the spread of the shear region from an initially hyperbolic tangent velocity profile. We find that the vertical extent of the mixing region in the saturated regime is generally determined by the initial Richardson number of the system. Further, the characteristic quantities of the turbulence, i.e. typical length-scale and the root-mean-square velocity are found to depend on both the Richardson number, and the thermal diffusivity. Finally, we present our findings of our investigation into saturated flows of a ‘secular’ shear instability in the low Péclet number regime with large Richardson numbers

Shear instabilities in stellar objects: linear stability and non-linear evolution

Shear flows have a significant impact on the dynamics in various astrophysical objects, including accretion discs and stellar interiors. Due to observational limitations the complex dynamics in stellar interiors that result in turbulent motions, mixing processes, and magnetic field generation, are not entirely understood. It is therefore necessary to investigate the inevitable small-scale dynamics via numerical calculations. In particular a thin region with strong shear at the base of the convection zone in the Sun, the tachocline, is believed to play an important role in the Sun's interior dynamics and magnetic field generation. Velocity measurements suggest a stable tachocline. However, helioseismology can only provide large-scale time-averaged measurements, so small scale turbulent motions can still be present. Therefore, studying the stability of shear flows and their non-linear evolution in a fully compressible polytropic atmosphere provides a fundamental understanding of potential motion in stellar interiors and is the main focus of this thesis. To commence the investigations a linear stability analysis of a stratified system in a two-dimensional Cartesian geometry is performed to study the effect of compressibility and thermal diffusivity on the stability threshold. In addition, this first investigation provides a reference for subsequent non-linear calculations. Focusing on a local model of unstable shear flows, direct numerical calculations are used to first compare numerical forcing methods to sustain a shear flow against viscous dissipation; and then to study the effect of key parameters on the saturated quasi-steady regime. Finally, magnetic fields are included and the full set of MHD equations is solved to study a potential kinematic dynamo in shear-driven turbulence

Evolution of forced shear flows in polytropic atmospheres: A comparison of forcing methods and energetics

Shear flows are ubiquitous in astrophysical objects including planetary and stellar interiors, where their dynamics can have significant impact on thermo-chemical processes. Investigating the complex dynamics of shear flows requires numerical calculations that provide a long time evolution of the system. To achieve a sufficiently long lifetime in a local numerical model the system has to be forced externally. However, at present, there exist several different forcing methods to sustain large-scale shear flows in local models. In this paper we examine and compare various methods used in the literature in order to resolve their respective applicability and limitations. These techniques are compared during the exponential growth phase of a shear flow instability, such as the Kelvin-Helmholtz (KH) instability, and some are examined during the subsequent non-linear evolution. A linear stability analysis provides reference for the growth rate of the most unstable modes in the system and a detailed analysis of the energetics provides a comprehensive understanding of the energy exchange during the system's evolution. Finally, we discuss the pros and cons of each forcing method and their relation with natural mechanisms generating shear flows

Vergleich der Anbaueignung verschiedender Ölpflanzenarten und -sorten für die Speiseölproduktion im Ökologischen Landbau

In Deutschland werden im Ökologischen Landbau trotz vorhandener Nachfrage nach Speiseöl fast keine Ölpflanzen angebaut. Zudem besteht ein Mangel an betriebseigenem pflanzlichen Protein. Im vorliegenden Vorhaben soll 2003 untersucht werden, welche Ölpflanzenart und -sorte hier eine sinnvolle Ergänzung bieten könnte: neben agronomischen Kenngrößen soll sie auch eine hochwertige Öl- und Eiweißqualität liefern. Es werden folgende Ölpflanzenarten getestet: Winterraps/-rübsen, Sonnenblumen, Leindotter, Saflor und Sojabohne. Anhand je zehn ausgewählter Sorten (bei Winterraps/-rübsen: 7+3) werden sie für den Ökologischen Landbau an fünf Standorten zunächst auf ihre Anbaueignung geprüft. Der Versuch wird auf folgenden Standorten angebaut: Kleinhohenheim, Sömmerda, Chorin, Müllheim und Oberer Lindenhof. Nachfolgend soll bei jeder der 50 Varianten eine Bewertung der relativen Vorzüglichkeit als Öl- und Eiweißlieferant gegeben werden. Es wird erwartet, daß praxisrelevante Empfehlungen für den Anbau geeigneter Ölpflanzen im Ökologischen Landbau resultieren, die praktikable Möglichkeiten für eine kombinierte Nutzung für eine Speiseölproduktion und den innerbetrieblichen Einsatz als Eiweißfuttermittel beinhalten

Small-scale dynamo in cool main sequence stars. II. The effect of metallicity

All cool main sequence stars including our Sun are thought to have magnetic fields. Observations of the Sun revealed that even in quiet regions small-scale turbulent magnetic fields are present. Simulations further showed that such magnetic fields affect the subsurface and photospheric structure, and thus the radiative transfer and emergent flux. Since small-scale turbulent magnetic fields on other stars cannot be directly observed, it is imperative to study their effects on the near surface layers numerically. Until recently comprehensive three-dimensional simulations capturing the effect of small-scale turbulent magnetic fields only exists for the solar case. A series of investigations extending SSD simulations for other stars has been started. Here we aim to examine small-scale turbulent magnetic fields in stars of solar effective temperature but different metallicity. We investigate the properties of three-dimensional simulations of the magneto-convection in boxes covering the upper convection zone and photosphere carried out with the MURaM code for metallicity values of $\rm M/H = \{-1.0, 0.0, 0.5\}$ with and without a small-scale-dynamo. We find that small-scale turbulent magnetic fields enhanced by a small-scale turbulent dynamo noticeably affect the subsurface dynamics and significantly change the flow velocities in the photosphere. Moreover, significantly stronger magnetic field strengths are present in the convection zone for low metallicity. Whereas, at the optical surface the averaged vertical magnetic field ranges from 64G for M/H = 0.5 to 85G for M/H = -1.0.Comment: 13 pages, 18 figures, submitted to A&

Predictions of Astrometric Jitter for Sun-like Stars. II. Dependence on Inclination, Metallicity, and Active-Region Nesting

Ultra-precise astrometry from the Gaia mission is expected to lead to astrometric detections of more than 20,000 exoplanets in our Galaxy. One of the factors that could hamper such detections is the astrometric jitter caused by the magnetic activity of the planet host stars. In our previous study, we modeled astrometric jitter for the Sun observed equator-on. In this work, we generalize our model and calculate the photocenter jitter as it would be measured by the Gaia and Small-JASMINE missions for stars with solar rotation rate and effective temperature, but with various values of the inclination angle of the stellar rotation axis. In addition, we consider the effect of metallicity and of nesting of active regions (i.e. the tendency of active regions to emerge in the vicinity of each other). We find that, while the jitter of stars observed equator-on does not have any long-term trends and can be easily filtered out, the photocenters of stars observed out of their equatorial planes experience systematic shifts over the course of the activity cycle. Such trends allow the jitter to be detected with continuous measurements, in which case it can interfere with planet detectability. An increase in the metallicity is found to increase the jitter caused by stellar activity. Active-region nesting can further enhance the peak-to-peak amplitude of the photocenter jitter to a level that could be detected by Gaia.Comment: 24 pages, 20 figures in the main body and 4 in the appendix, accepted for publication in Ap

Can 1D radiative equilibrium models of faculae be used for calculating contamination of transmission spectra?

The reliable characterization of planetary atmospheres with transmission spectroscopy requires realistic modeling of stellar magnetic features, since features that are attributable to an exoplanet atmosphere could instead stem from the host star's magnetic activity. Current retrieval algorithms for analysing transmission spectra rely on intensity contrasts of magnetic features from 1D radiative-convective models. However, magnetic features, especially faculae, are not fully captured by such simplified models. Here we investigate how well such 1D models can reproduce 3D facular contrasts, taking a G2V star as an example. We employ the well established radiative magnetohydrodynamic code MURaM to obtain three-dimensional simulations of the magneto-convection and photosphere harboring a local small-scale-dynamo. Simulations without additional vertical magnetic fields are taken to describe the quiet solar regions, while simulations with initially 100 G, 200 G and 300 G vertical magnetic fields are used to represent different magnetic activity levels. Subsequently, the spectra emergent from the MURaM cubes are calculated with the MPS-ATLAS radiative transfer code. We find that the wavelength dependence of facular contrast from 1D radiative-convective models cannot reproduce facular contrasts obtained from 3D modeling. This has far reaching consequences for exoplanet characterization using transmission spectroscopy, where accurate knowledge of the host star is essential for unbiased inferences of the planetary atmospheric properties.Comment: 7 pages, 2 figures, submitted to APJ