The Mass Mixing Length in Convective Stellar Envelopes

The scale length over which convection mixes mass in a star can be calculated as the inverse of the vertical derivative of the unidirectional (up or down) mass flux. This is related to the mixing length in the mixing length theory of stellar convection. We give the ratio of mass mixing length to pressure scale height for a grid of 3D surface convection simulations, covering from 4300\,K to 6900\,K on the main-sequence, and up to giants at $\log g = 2.2$, all for solar composition. These simulations also confirm what is already known from solar simulations, that convection doesn't proceed by discrete convective elements, but rather as a continuous, slow, smooth, warm upflow and turbulent, entropy deficient, fast down drafts. This convective topology also results in mixing on a scale as that of the classic mixing length formulation, and is simply a consequence of mass conservation on flows in a stratified atmosphere.Comment: 14 pages, 6 figures, accepted for publication in Ap

In situ mineralogical-chemical analysis of Martian materials at landing/roving sites by active and passive remote sensing methods

Remote sensing of the Martian surface from the ground and from orbiting spacecraft has provided some first-order insight into the mineralogical-chemical composition and the weathering state of Martian surface materials. Much more detailed information can be gathered from performing such measurements in situ at the landing sites or from a rover in combination with analogous measurements from orbit. Measurements in the wavelength range of approximately 0.3 to 12.0 micrometers appear to be suitable to characterize much of the physical, mineralogical, petrological, and chemical properties of Martian surface materials and the weathering and other alteration processes that have acted on them. It is of particular importance to carry out measurements at the same time over a broad wavelength range since the reflectance signatures are caused by different effects and hence give different and complementing information. It appears particularly useful to employ a combination of active and passive methods because the use of active laser spectroscopy allows the obtaining of specific information on thermal infrared reflectance of surface materials. It seems to be evident that a spectrometric survey of Martian materials has to be focused on the analysis of altered and fresh mafic materials and rocks, water-bearing silicates, and possibly carbonates

Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations. I. T(τ)T(\tau)-Relations

Relations between temperature, T, and optical depth, tau, are often used for describing the photospheric transition from optically thick to optically thin in stellar structure models. We show that this is well justified, but also that currently used T(tau) relations are often inconsistent with their implementation. As an outer boundary condition on the system of stellar structure equations, T(tau) relations have an undue effect on the overall structure of stars. In this age of precision asteroseismology, we need to re-assess both the method for computing and for implementing T(tau) relations, and the assumptions they rest on. We develop a formulation for proper and consistent evaluation of T(tau) relations from arbitrary 1D or 3D stellar atmospheres, and for their implementation in stellar structure and evolution models. We extract radiative T(tau) relations, as described by our new formulation, from 3D simulations of convection in deep stellar atmospheres of late-type stars from dwarfs to giants. These simulations employ realistic opacities and equation of state, and account for line-blanketing. For comparison, we also extract T(tau) relations from 1D MARCS model atmospheres using the same formulation. T(tau)-relations from our grid of 3D convection simulations display a larger range of behaviours with surface gravity, compared with those of conventional theoretical 1D hydrostatic atmosphere models. Based on this, we recommend no longer to use scaled solar T(tau) relations. Files with T(tau) relations for our grid of simulations are made available to the community, together with routines for interpolating in this irregular grid. We also provide matching tables of atmospheric opacity, for consistent implementation in stellar structure models.Comment: 18 pages, 7 figures, 2 tables. Accepted for publication in MNRAS, 201

Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length formulation

We perform a calibration of the mixing length of convection in stellar structure models against realistic 3D radiation-coupled hydrodynamics (RHD) simulations of convection in stellar surface layers, determining the adiabat deep in convective stellar envelopes. The mixing-length parameter $\alpha$ is calibrated by matching averages of the 3D simulations to 1D stellar envelope models, ensuring identical atomic physics in the two cases. This is done for a previously published grid of solar-metallicity convection simulations, covering from 4200 K to 6900 K on the main sequence, and 4300-5000 K for giants with logg=2.2. Our calibration results in an $\alpha$ varying from 1.6 for the warmest dwarf, which is just cool enough to admit a convective envelope, and up to 2.05 for the coolest dwarfs in our grid. In between these is a triangular plateau of $\alpha$ ~ 1.76. The Sun is located on this plateau and has seen little change during its evolution so far. When stars ascend the giant branch, they largely do so along tracks of constant $\alpha$, with $\alpha$ decreasing with increasing mass.Comment: 22 pages, 15 figures, accepted for publication in MNRA

A Grid of 3D Stellar Atmosphere Models of Solar Metallicity: I. General Properties, Granulation and Atmospheric Expansion

Present grids of stellar atmosphere models are the workhorses in interpreting stellar observations, and determining their fundamental parameters. These models rely on greatly simplified models of convection, however, lending less predictive power to such models of late type stars. We present a grid of improved and more reliable stellar atmosphere models of late type stars, based on deep, 3D, convective, stellar atmosphere simulations. This grid is to be used in general for interpreting observations, and improve stellar and asteroseismic modeling. We solve the Navier Stokes equations in 3D and concurrent with the radiative transfer equation, for a range of atmospheric parameters, covering most of stellar evolution with convection at the surface. We emphasize use of the best available atomic physics for quantitative predictions and comparisons with observations. We present granulation size, convective expansion of the acoustic cavity, asymptotic adiabat, as function of atmospheric parameters. These and other results are also available in electronic form.Comment: 16 pages, 12 figures. Accepted for publication in ApJ, 201

Pay What You Want as a Marketing Strategy in Monopolistic and Competitive Markets

Pay What You Want (PWYW) can be an attractive marketing strategy to price discriminate between fair-minded and selfish customers, to fully penetrate a market without giving away the product for free, and to undercut competitors that use posted prices. We report on laboratory experiments that identify causal factors determining the willingness of buyers to pay voluntarily under PWYW. Furthermore, to see how competition affects the viability of PWYW, we implement markets in which a PWYW seller competes with a traditional seller. Finally, we endogenize the market structure and let sellers choose their pricing strategy. The experimental results show that outcome-based social preferences and strategic considerations to keep the seller in the market can explain why and how much buyers pay voluntarily to a PWYW seller. We find that PWYW can be viable in isolation, but it is less successful as a competitive strategy because it does not drive traditional posted-price sellers out of the market. Instead, the existence of a posted-price competitor reduces buyers’ payments and prevents the PWYW seller from fully penetrating the market. If given the choice, the majority of sellers opt for setting a posted price rather than a PWYW pricing. We discuss the implications of these results for the use of PWYW as a marketing strategy

Calibrating Convective properties of Solar-like Stars in the Kepler Field of View

Stellar models generally use simple parametrizations to treat convection. The most widely used parametrization is the so-called "Mixing Length Theory" where the convective eddy sizes are described using a single number, \alpha, the mixing-length parameter. This is a free parameter, and the general practice is to calibrate \alpha using the known properties of the Sun and apply that to all stars. Using data from NASA's Kepler mission we show that using the solar-calibrated \alpha is not always appropriate, and that in many cases it would lead to estimates of initial helium abundances that are lower than the primordial helium abundance. Kepler data allow us to calibrate \alpha for many other stars and we show that for the sample of stars we have studied, the mixing-length parameter is generally lower than the solar value. We studied the correlation between \alpha and stellar properties, and we find that \alpha increases with metallicity. We therefore conclude that results obtained by fitting stellar models or by using population-synthesis models constructed with solar values of \alpha are likely to have large systematic errors. Our results also confirm theoretical expectations that the mixing-length parameter should vary with stellar properties.Comment: 16 pages, 4 figures, accepted for publication in ApJ

Differentiation and identification of White Riesling clones by genetic markers

Three different marker systems were used to genotype 10 clones of the grapevine cultivar White Riesling. All clones could be differentiated by means of genetic polymorphism gained by RAPD, SSR or Inter-SSR markers. While RAPD profile lacks stability for an identificational approach, individual SSR and Inter-SSR alleles could be retrieved within samples of the same clone. The polymorphic DNA fragments confirm the genetic variability within a traditional grapevine cultivar and the reproducibility of some of these markers allows the identification of clones. Since SSR and Inter-SSR markers show high stability when comparing data from different laboratories these methods are appropriate to establish data bases for the characterization of clonal grapevine material

Highly variable Vitis microsatellite loci for the identification of Pinot Noir clones

Nineteen new microsatellite loci of Vitis were elaborated by following the procedure of tagging an SSRenriched library. Primers for these VRG markers were used for genotyping grapevines. Only the markers VRG 1, VRG 2, VRG 4, VRG 7, VRG 9, VRG 10, VRG 15 and VRG 16 show heterozygous alleles and Mendelian segregation. Other VRG loci such as VRG 5, VRG 6, VRG 11, VRG 12 VRG 13 and VRG 17 produce a multiallelic profile and some of them show distorted segregation. Variability of the VRG loci is rather high as compared to other grapevine SSR markers. Stable VRG markers such as VRG 16 can be useful for the identification of cultivars. Highly variable VRG microsatellites could be successfully applied to trace polymorphism within the variety Pinot Noir. Clones of Pinot Noir could be differentiated using these markers. By applying the PhyQuest program, a dendrogramm showing the genetic divergence within Pinot Noir clones was constructed.