The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - II. Horizontal and Temporal Averaging and Spectral Line Formation

We study the implications of averaging methods with different reference depth scales for 3D hydrodynamical model atmospheres computed with the Stagger-code. The temporally and spatially averaged (hereafter denoted as ) models are explored in the light of local thermodynamic equilibrium (LTE) spectral line formation by comparing spectrum calculations using full 3D atmosphere structures with those from averages. We explore methods for computing mean stratifications from the Stagger-grid time-dependent 3D radiative hydro- dynamical atmosphere models by considering four different reference depth scales (geometrical depth, column-mass density, and two optical depth scales). Furthermore, we investigate the influence of alternative averages (logarithmic or enforced hydrostatic equilibrium, flux-weighted temperatures). For the line formation we compute curves of growth for Fe i and Fe ii lines in LTE . The resulting stratifications for the four reference depth scales can be considerably different. We find typically that in the upper atmosphere and in the superadiabatic region just below the optical surface, where the temperature and density fluctuations are highest, the differences become considerable and increase for higher Teff, lower logg, and lower [Fe/H]. The differential comparison of spectral line formation shows distinctive differences depending on which model is applied. The averages over layers of constant column-mass density yield the best mean representation for LTE line formation, while the averages on layers at constant geometrical height are the least appropriate. Unexpectedly, the usually preferred averages over layers of constant optical depth are prone to the increasing interference of the reversed granulation towards higher effective temperature, in particular at low metallicity.Comment: Accepted for publication in A&A, 18 pages, 16 figure

On the effects of clouds and hazes in the atmospheres of hot Jupiters: semi-analytical temperature-pressure profiles

Motivated by the work of Guillot, we present a semi-analytical formalism for calculating the temperature-pressure profiles in hot Jovian atmospheres which includes the effects of clouds/hazes and collision-induced absorption. Using the dual-band approximation, we assume that stellar irradiation and thermal emission from the hot Jupiter occur at distinct wavelengths (‘shortwave' versus ‘longwave'). For a purely absorbing cloud/haze, we demonstrate its dual effect of cooling and warming the upper and lower atmosphere, respectively, which modifies, in a non-trivial manner, the condition for whether a temperature inversion is present in the upper atmosphere. The warming effect becomes more pronounced as the cloud/haze deck resides at greater depths. If it sits below the shortwave photosphere, the warming effect becomes either more subdued or ceases altogether. If shortwave scattering is present, its dual effect is to warm and cool the upper and lower atmospheres, respectively, thus counteracting the effects of enhanced longwave absorption by the cloud/haze. We make a tentative comparison of a four-parameter model to the temperature-pressure data points inferred from the observations of HD 189733b and estimate that its Bond albedo is approximately 10 per cent. Besides their utility in developing physical intuition, our semi-analytical models are a guide for the parameter space exploration of hot Jovian atmospheres via three-dimensional simulations of atmospheric circulatio

The elemental composition of the Sun I. The intermediate mass elements Na to Ca

The composition of the Sun is an essential piece of reference data for astronomy, cosmology, astroparticle, space and geo-physics. This article, dealing with the intermediate-mass elements Na to Ca, is the first in a series describing the comprehensive re-determination of the solar composition. In this series we severely scrutinise all ingredients of the analysis across all elements, to obtain the most accurate, homogeneous and reliable results possible. We employ a highly realistic 3D hydrodynamic solar photospheric model, which has successfully passed an arsenal of observational diagnostics. To quantify systematic errors, we repeat the analysis with three 1D hydrostatic model atmospheres (MARCS, MISS and Holweger & M\"{u}ller 1974) and a horizontally and temporally-averaged version of the 3D model ($\langle$3D$\rangle$). We account for departures from LTE wherever possible. We have scoured the literature for the best transition probabilities, partition functions, hyperfine and other data, and stringently checked all observed profiles for blends. Our final 3D+NLTE abundances are: $\log\epsilon_{\mathrm{Na}}=6.21\pm0.04$, $\log\epsilon_{\mathrm{Mg}}=7.59\pm0.04$, $\log\epsilon_{\mathrm{Al}}=6.43\pm0.04$, $\log\epsilon_{\mathrm{Si}}=7.51\pm0.03$, $\log\epsilon_{\mathrm{P}}=5.41\pm0.03$, $\log \epsilon_{\mathrm{S}}=7.13\pm0.03$, $\log\epsilon_{\mathrm{K}}=5.04\pm0.05$ and $\log\epsilon_{\mathrm{Ca}}=6.32\pm0.03$. The uncertainties include both statistical and systematic errors. Our results are systematically smaller than most previous ones with the 1D semi-empirical Holweger & M\"uller model. The $\langle$3D$\rangle$ model returns abundances very similar to the full 3D calculations. This analysis provides a complete description and a slight update of the Na to Ca results presented in Asplund, Grevesse, Sauval & Scott (arXiv:0909.0948), with full details of all lines and input data.Comment: 7 figures, 14 pages + 5 online-only pages of tables and an appendix. v2. Matches version accepted by A&

Three-dimensional surface convection simulations of metal-poor stars: The effect of scattering on the photospheric temperature stratification

Context: Three-dimensional (3D) radiative hydrodynamic model atmospheres of metal-poor late-type stars are characterized by cooler upper photospheric layers than their one-dimensional counterparts. This property of 3D model atmospheres can dramatically affect the determination of elemental abundances from temperature-sensitive spectral features, with profound consequences on galactic chemical evolution studies. Aims. We investigate whether the cool surface temperatures predicted by 3D model atmospheres of metal-poor stars can be ascribed to approximations in the treatment of scattering during the modelling phase. Methods. We use the Bifrost code to construct 3D model atmospheres of metal-poor stars and test three different ways to handle scattering in the radiative transfer equation. As a first approach, we solve iteratively the radiative transfer equation for the general case of a source function with a coherent scattering term, treating scattering in a correct and consistent way. As a second approach, we solve the radiative transfer equation in local thermodynamic equilibrium approximation, neglecting altogether the contribution of continuum scattering to extinction in the optically thin layers; this has been the default mode in our previous 3D modelling as well as in present Stagger-Code models. As our third and final approach, we treat continuum scattering as pure absorption everywhere, which is the standard case in the 3D modelling by the CO5BOLD collaboration. Results. For all simulations, we find that the second approach produces temperature structures with cool upper photospheric layers very similar to the case in which scattering is treated correctly. In contrast, treating scattering as pure absorption leads instead to significantly hotter and shallower temperature stratifications. The main differences in temperature structure between our published models computed with the Stagger- and Bifrost codes and those generated with the CO5BOLD code can be traced to the different treatments of scattering. Conclusions. Neglecting the contribution of continuum scattering to extinction in optically thin layers provides a good approximation to the full, iterative solution of the radiative transfer equation in metal-poor stellar surface convection simulations, and at a much lower computational cost. Our results also demonstrate that the cool temperature stratifications predicted for metal-poor late-type stars by previous models by our collaboration are not an artifact of the approximated treatment of scattering

On the effects of clouds and hazes in the atmospheres of hot Jupiters: semi-analytical temperature-pressure profiles

Motivated by the work of Guillot (2010), we present a semi-analytical formalism for calculating the temperature-pressure profiles in hot Jovian atmospheres which includes the effects of clouds/hazes and collision-induced absorption. Using the dual-band approximation, we assume that stellar irradiation and thermal emission from the hot Jupiter occur at distinct wavelengths ("shortwave" versus "longwave"). For a purely absorbing cloud/haze, we demonstrate its dual effect of cooling and warming the upper and lower atmosphere, respectively, which modifies, in a non-trivial manner, the condition for whether a temperature inversion is present in the upper atmosphere. The warming effect becomes more pronounced as the cloud/haze deck resides at greater depths. If it sits below the shortwave photosphere, the warming effect becomes either more subdued or ceases altogether. If shortwave scattering is present, its dual effect is to warm and cool the upper and lower atmosphere, respectively, thus counteracting the effects of enhanced longwave absorption by the cloud/haze. We make a tentative comparison of a 4-parameter model to the temperature-pressure data points inferred from the observations of HD 189733b and estimate that its Bond albedo is approximately 10%. Besides their utility in developing physical intuition, our semi-analytical models are a guide for the parameter space exploration of hot Jovian atmospheres via three-dimensional simulations of atmospheric circulation.Comment: Accepted by MNRAS. 18 pages, 8 figures. No changes made from last versio

COMPETITION POLICY WITH OPTIMALLY DIFFERENTIATED RULES INSTEAD OF “PER SE RULES VS RULE OF REASON”

Both in US antitrust and EU competition policy a development to a broader appli-cation of rule of reason instead of per se rules can be observed. In the European discussion the attempt to base competition policy on a more economic approach is mainly viewed as im-proving the economic analysis in the assessment of specific cases. In this paper it is shown from a general law and economics perspective that the application of rules instead of focus-sing on case-by-case analyses can have many advantages (less regulation costs, rent seeking and knowledge problems), although an additional differentiation of rules through a deeper assessment can also have advantages in regard to the reduction of decision errors of type I and II. After introducing the notion of a continuum of more or less differentiated rules, we show - based upon law and economics literature upon the optimal complexity of rules - in a simple model that a competition rule is optimally differentiated, if the marginal reduction of the sum of error costs (as the marginal benefit of differentiation) equals the marginal costs of differen-tiation. This model also allows for a more detailed analysis of the most important determi-nants of the optimal degree of rule-differentia¬tion. From this law and economics perspective, competition policy should consist mainly of (more or less differentiated) rules and should only rarely rely on case-by-case analysis. Therefore the main task of a more economic ap-proach is to use economics for the formulation of appropriate competition rules

Governance im Politikfeld Wirtschaftspolitik

This paper gives an overview of the topic "economic governance". This term is used in economics and neighboring social sciences as a generic term under which usually all activities are subsumed that are conducted by economic policymakers to 'steer' or 'control' the economic system, individual markets therein or certain economic actors (e.g., businesses, consumers). In addition to a more detailed clarification of the concept of "economic governance" and the presentation of actors and instruments of economic governance, the paper discusses why and in what situations economic governance is necessary. The latter issue is the subject of a continuing debate in politics, the public and the social sciences

Competitive Benchmarking: An IS Research Approach to Address Wicked Problems with Big Data and Analytics

Wicked problems like sustainable energy and financial market stability are societal challenges that arise from complex socio-technical systems in which numerous social, economic, political, and technical factors interact. Understanding and mitigating them requires research methods that scale beyond the traditional areas of inquiry of Information Systems (IS) “individuals, organizations, and markets” and that deliver solutions in addition to insights. We describe an approach to address these challenges through Competitive Benchmarking (CB), a novel research method that helps interdisciplinary research communities to tackle complex challenges of societal scale by using different types of data from a variety of sources such as usage data from customers, production patterns from producers, public policy and regulatory constraints, etc. for a given instantiation. Further, the CB platform generates data that can be used to improve operational strategies and judge the effectiveness of regulatory regimes and policies. We describe our experience applying CB to the sustainable energy challenge in the Power Trading Agent Competition (Power TAC) in which more than a dozen research groups from around the world jointly devise, benchmark, and improve IS-based solutions