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

Abstract

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.

arXiv comment18 pages, 7 figures, 2 tables. Accepted for publication in MNRAS, 2014

References in corpus (27)

• The chemical composition of the Sun
• Modules for Experiments in Stellar Astrophysics (MESA)
• A grid of MARCS model atmospheres for late-type stars I. Methods and general properties
• A large stellar evolution database for population synthesis studies. I. Scaled solar models and isochrones
• Low Temperature Opacities
• The NextGen Model Atmosphere grid for $3000\le \Teff \le 10000\K$
• The NextGen Model Atmosphere grid: II. Spherically symmetric model atmospheres for giant stars with effective temperatures between 3000 and 6800~K
• Heating of the Solar Chromosphere and Corona by Alfven Wave Turbulence
• Simulations of stellar convection with CO5BOLD
• Up-dated opacities from the Opacity Project
• New Solar Composition: The Problem With Solar Models Revisited
• An Ab Initio Approach to the Solar Coronal Heating Problem
• Helioseismological Implications of Recent Solar Abundance Determinations
• Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere
• The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - I. Methods and General Properties
• YREC: The Yale Rotating Stellar Evolution Code
• Spectroscopic Signatures of Convection in the Spectrum of Procyon. Fundamental Parameters and Iron Abundance
• 3D Hydrodynamical Simulations of Surface Convection in Red Giant Stars. Impact on spectral line formation and abundance analysis
• A Grid of 3D Stellar Atmosphere Models of Solar Metallicity: I. General Properties, Granulation and Atmospheric Expansion
• Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres
• The discrepancy between solar abundances and helioseismology
• Heavy Element Diffusion in Metal Poor Stars
• How realistic are solar model atmospheres?
• On the Use of Blanketed Atmospheres as Boundary Conditions for Stellar Evolutionary Models
• New extended atomic data in cool star model atmospheres - Using Kurucz's new iron data in MAFAGS-OS models
• The Effect of Metallicity-Dependent T-tau Relations on Calibrated Stellar Models
• Modeling the near-UV band of GK stars, Paper II: NLTE models

Cited by in corpus (53)

• Modules for Experiments in Stellar Astrophysics (MESA): Time-Dependent Convection, Energy Conservation, Automatic Differentiation, and Infrastructure
• Spectral Properties of Cool Stars: Extended Abundance Analysis of 1617 Planet Search Stars
• Standing on the shoulders of Dwarfs: the $Kepler$ asteroseismic LEGACY sample I - oscillation mode parameters
• Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length formulation
• Giant star seismology
• Properties of 42 Solar-type Kepler Targets from the Asteroseismic Modeling Portal
• RH 1.5D: a massively parallel code for multi-level radiative transfer with partial frequency redistribution and Zeeman polarisation
• Solar structure and evolution
• NGC 6819: testing the asteroseismic mass scale, mass loss, and evidence for products of non-standard evolution
• First Results From The Hertzsprung Song Telescope: Asteroseismology Of The G5 Subgiant Star {\Mu}Her
• Interaction Between Convection and Pulsation
• Characterizing solar-type stars from full-length Kepler data sets using the Asteroseismic Modeling Portal
• Numerical Simulations of Convective 3-Dimensional Red Supergiant Envelopes
• On the surface physics affecting solar oscillation frequencies
• Metallicity effect on stellar granulation detected from oscillating red giants in open clusters
• MESA meets MURaM: Surface effects in main-sequence solar-like oscillators computed using three-dimensional radiation hydrodynamics simulations
• Stellar models with mixing length and T(tau) relations calibrated on 3D convection simulations
• Stellar models with calibrated convection and temperature stratification from 3D hydrodynamics simulations
• The asteroseismic surface effect from a grid of 3D convection simulations. I. Frequency shifts from convective expansion of stellar atmospheres
• Coupling 1D stellar evolution with 3D-hydrodynamical simulations on-the-fly II: Stellar Evolution and Asteroseismic Applications
• Surface effects on the red giant branch
• Coupling 1D stellar evolution with 3D-hydrodynamical simulations on-the-fly I: A New Standard Solar Model
• Convective boundary mixing in low- and intermediate-mass stars I. Core properties from pressure-mode asteroseismology
• Calibration of the mixing-length parameter $\alpha$ for the MLT and FST models by matching with CO${}^5$BOLD models
• Tess asteroseismology of the known planet host star ${\lambda }^2$ Fornacis
• Surface-effect corrections for the solar model
• Theoretical uncertainties on the radius of low- and very-low mass stars
• Theoretical oscillation frequencies for solar-type dwarfs from stellar models with $⟨3\mathrm{D}⟩$-atmospheres
• Isochrone fitting to the open cluster M67 in the era of Gaia and improved model physics
• Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes
• Overcoming the structural surface effect with a realistic treatment of turbulent convection in 1D stellar models
• Convective Excitation and Damping of Solar-like Oscillations
• 3D Stagger model atmospheres with FreeEOS I. Exploring the impact of microphysics on the Sun
• Robust asteroseismic properties of the bright planet host HD 38529
• An asteroseismic age estimate of the open cluster NGC 6866 using Kepler and Gaia
• An extended and refined grid of 3D STAGGER model atmospheres. Processed snapshots for stellar spectroscopy
• Improved calibration of the radii of cool stars based on 3D simulations of convection: implications for the solar model
• Damping rates and frequency corrections of Kepler LEGACY stars
• An Expanded Set of Los Alamos OPLIB Tables in MESA: Type-1 Rosseland-mean Opacities and Solar Models
• Entropy in adiabatic regions of convection simulations
• Asteroseismic Study of Subgiants and Giants of the Open Cluster M67 using Kepler/K2: Expanded Sample and Precise Masses
• Critical Metallicity of Cool Supergiant Formation. I. Effects on Stellar Mass Loss and Feedback
• Bayesian inference of stellar parameters based on 1D stellar models coupled with 3D envelopes
• Does the ${\nu }_{\max }$ scaling relation depend on metallicity? Insights from 3D convection simulations
• Turbulent dynamo action and its effects on the mixing at the convective boundary of an idealized oxygen-burning shell
• A novel analytic atmospheric $T(\tau )$ relation for stellar models
• Theoretical predictions of surface light element abundances in protostellar and pre-Main Sequence phase
• Scaling of the asymptotic entropy jump in the superadiabatic layers of stellar atmospheres
• Modelling linewidths of Kepler red giants in NGC 6819
• Benchmarking the effective temperature scale of red giant branch stellar models: the case of the metal-poor halo giant HD 122563
• Improving 1D Stellar Models with 3D Atmospheres
• Calibrating damping rates with LEGACY linewidths
• Toward a Comprehensive Grid of Cepheid Models with MESA II. Impact of Physical and Numerical Assumptions on Elemental Abundances