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Register a new userImprovements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations. I. $T(tau)$-Relations
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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.
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(abridged) The calculation of the thermal stratification in the superadiabatic layers of stellar models with convective envelopes is a long standing problem of stellar astrophysics, and has a major impact on predicted observational properties like radius and effective temperature. The Mixing Length Theory, almost universally used to model the superadiabatic convective layers, contains effectively one free parameter to be calibrated --alpha(ml)-- whose value controls the resulting effective temperature. Here we present the first self-consistent stellar evolution models calculated by employing the atmospheric temperature stratification, Rosseland opacities, and calibrated variable alpha(ml) (dependent on effective temperature and surface gravity) from a large suite of three-dimensional radiation hydrodynamics simulations of stellar convective envelopes and atmospheres for solar stellar composition (Trampedach et al. 2013). From our calculations (with the same composition of the radiation hydrodynamics simulations), we find that the effective temperatures of models with the hydro-calibrated variable alpha(ml) display only minor differences, by at most ~30-50 K, compared to models calculated at constant solar alpha(ml). The depth of the convective regions is essentially the same in both cases. We have also analyzed the role played by the hydro-calibrated T(tau) relationships in determining the evolution of the model effective temperatures, when compared to alternative T(tau) relationships often used in stellar model computations. The choice of the T(tau) can have a larger impact than the use of a variable alpha(ml) compared to a constant solar value. We found that the solar semi-empirical T(tau) by Vernazza et al. (1981) provides stellar model effective temperatures that agree quite well with the results with the hydro-calibrated relationships.
We analyse the effect on adiabatic stellar oscillation frequencies of replacing the near-surface layers in 1D stellar structure models with averaged 3D stellar surface convection simulations. The main difference is an expansion of the atmosphere by 3D convection, expected to explain a major part of the asteroseismic surface effect; a systematic overestimation of p-mode frequencies due to inadequate surface physics. We employ pairs of 1D stellar envelope models and 3D simulations from a previous calibration of the mixing-length parameter, alpha. That calibration constitutes the hitherto most consistent matching of 1D models to 3D simulations, ensuring that their differences are not spurious, but entirely due to the 3D nature of convection. The resulting frequency shift is identified as the structural part of the surface effect. The important, typically non-adiabatic, modal components of the surface effect are not included in the present analysis, but relegated to future papers. Evaluating the structural surface effect at the frequency of maximum mode amplitude, $ u_{rm max}$, we find shifts from $delta u$=-0.8 microHz for giants at $log g$=2.2 to -35 microHz for a ($T_{rm eff}=6901$ K, $log g$=4.29) dwarf. The fractional effect $delta u( u_{rm max})/ u_{rm max}$, ranges from -0.1% for a cool dwarf (4185 K, 4.74) to -6% for a warm giant (4962 K, 2.20).
We present the Stagger-grid, a comprehensive grid of time-dependent, 3D hydrodynamic model atmospheres for late-type stars with realistic treatment of radiative transfer, covering a wide range in stellar parameters. This grid of 3D models is intended for various applications like stellar spectroscopy, asteroseismology and the study of stellar convection. In this introductory paper, we describe the methods used for the computation of the grid and discuss the general properties of the 3D models as well as their temporal and spatial averages (<3D>). All our models were generated with the Stagger-code, using realistic input physics for the equation of state (EOS) and for continuous and line opacities. Our ~220 grid models range in Teff from 4000 to 7000K in steps of 500K, in log g from 1.5 to 5.0 in steps of 0.5 dex, and [Fe/H] from -4.0 to +0.5 in steps of 0.5 and 1.0 dex. We find a tight scaling relation between the vertical velocity and the surface entropy jump, which itself correlates with the constant entropy value of the adiabatic convection zone. The range in intensity contrast is enhanced at lower metallicity. The granule size correlates closely with the pressure scale height sampled at the depth of maximum velocity. We compare the <3D> models with widely applied 1D models, as well as with theoretical 1D hydrostatic models generated with the same EOS and opacity tables as the 3D models, in order to isolate the effects of using self-consistent and hydrodynamic modeling of convection, rather than the classical mixing length theory approach. For the first time, we are able to quantify systematically over a broad range of stellar parameters the uncertainties of 1D models arising from the simplified treatment of physics, in particular convective energy transport. In agreement with previous findings, we find that the differences can be significant, especially for metal-poor stars.
We present here the first stellar models on the Hertzsprung-Russell diagram (HRD), in which convection is treated according to the novel scale-free convection theory (SFC theory) by Pasetto et al. (2014). The aim is to compare the results of the new theory with those from the classical, calibrated mixing-length (ML) theory to examine differences and similarities. We integrate the equations describing the structure of the atmosphere from the stellar surface down to a few percent of the stellar mass using both ML theory and SFC theory. The key temperature over pressure gradients, the energy fluxes, and the extension of the convective zones are compared in both theories. The analysis is first made for the Sun and then extended to other stars of different mass and evolutionary stage. The results are adequate: the SFC theory yields convective zones, temperature gradients of the ambient and of the convective element, and energy fluxes that are very similar to those derived from the calibrated MT theory for main sequence stars. We conclude that the old scale dependent ML theory can now be replaced with a self-consistent scale-free theory able to predict correct results, one which is simpler and more physically grounded than the ML theory. Fundamentally, the SFC theory offers a deeper insight of the underlying physics than numerical simulations.
The impressive development of global numerical simulations of turbulent stellar interiors unveiled a variety of possible differential rotation (solar or anti-solar), meridional circulation (single or multi-cellular), and dynamo states (stable large scale toroidal field or periodically reversing magnetic fields). Various numerical schemes, based on the so-called anelastic set of equations, were used to obtain these results. It appears today mandatory to assess their robustness with respect to the details of the numerics, and in particular to the treatment of turbulent sub-grid scales. We report on an ongoing comparison between two global models, the ASH and EULAG codes. In EULAG the sub-grid scales are treated implicitly by the numerical scheme, while in ASH their effect is generally modelled by using enhanced dissipation coefficients. We characterize the sub-grid scales effect in a turbulent convection simulation with EULAG. We assess their effect at each resolved scale with a detailed energy budget. We derive equivalent eddy-diffusion coefficients and use the derived diffusivities in twin ASH numerical simulations. We find a good agreement between the large-scale flows developing in the two codes in the hydrodynamic regime, which encourages further investigation in the magnetohydrodynamic regime for various dynamo solutions.
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