Testing the 3-equation Kuhfuss Convection Model using the Sun

Abstract

Simplified, one-dimensional models are necessary to model convection in the context of stellar evolution. By including the non-local effects of convection, turbulent convection models describe convection in a more physical way compared to mixing length theory, which is typically used in one-dimensional stellar evolution models. We recently showed that the 1-equation Kuhfuss turbulent convection model is not sufficient to model the solar convective envelope satisfactorily. Using the Sun as a benchmark, we test the physically more complete 3-equation Kuhfuss turbulent convection model. We calculate a solar calibrated model with the 3-equation Kuhfuss turbulent convection model using the one-dimensional stellar evolution code GARSTEC. We compare the predicted interior structure of the model with helioseismic measurements of the Sun. Furthermore, we investigate how the free parameters and the closure relations of the 3-equation model influence the results. We find that, with the 3-equation model, the temperature gradient at the inner boundary of the convective envelope is modelled more realistically compared to the mixing length theory or the 1-equation model. This also improves the agreement for the sound speed profile between the model and the Sun, and reduces the asteroseismic surface effect. However, close to the surface, the 3-equation model results in a layer having an unphysical, negative temperature gradient. This layer is connected to the closure relations used in the 3-equation model. Our results demonstrate the capabilities of turbulent convection models, and can serve as a next step towards an improved and more realistic modelling of convection in stellar evolution codes.

15 pages, 14 figures, accepted for publication in Astronomy & Astrophysics

References in corpus (43)

• The chemical composition of the Sun
• Low Temperature Opacities
• The chemical make-up of the Sun: A 2020 vision
• Modules for Experiments in Stellar Astrophysics (MESA): Time-Dependent Convection, Energy Conservation, Automatic Differentiation, and Infrastructure
• GYRE: An open-source stellar oscillation code based on a new Magnus Multiple Shooting Scheme
• ADIPLS -- the Aarhus adiabatic oscillation package
• Up-dated opacities from the Opacity Project
• Constraining solar abundances using helioseismology
• The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - I. Methods and General Properties
• Observational constraints on the origin of the elements. IV: The standard composition of the Sun
• CESAM: a free code for stellar evolution calculations
• Fresh insights on the structure of the solar core
• A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology
• The Correlation Between Mixing Length and Metallicity on the Giant Branch: Implications for Ages in the Gaia Era
• Solar structure and evolution
• The mass discrepancy in intermediate- and high-mass eclipsing binaries: the need for higher convective core masses
• Calibrating Convective properties of Solar-like Stars in the Kepler Field of View
• Not All Stars Are the Sun: Empirical Calibration of the Mixing Length for Metal-Poor Stars Using One-dimensional Stellar Evolution Models
• Investigating the Metallicity-Mixing Length Relation
• Stellar mixing length theory with entropy rain
• Calibration of the Mixing-Length Theory for Convective White Dwarf Envelopes
• Extended subadiabatic layer in simulations of overshooting convection
• Classically and Asteroseismically constrained 1D Stellar Evolution Models of $\alpha$ Centauri A and B using Empirical Mixing Length Calibrations
• On the surface physics affecting solar oscillation frequencies
• Benchmark stars for Gaia: fundamental properties of the Population II star HD140283 from interferometric, spectroscopic and photometric data
• MESA meets MURaM: Surface effects in main-sequence solar-like oscillators computed using three-dimensional radiation hydrodynamics simulations
• Effective temperatures of red giants in the APOKASC catalogue and the mixing length calibration in stellar models
• Convective boundary mixing in main-sequence stars: theory and empirical constraints
• Combining multiple structural inversions to constrain the Solar modelling problem
• Overshooting in simulations of compressible convection
• On the Red Giant Branch: Ambiguity in the Surface Boundary Condition Leads to ~100 K Uncertainty in Model Effective Temperatures
• Higher metal abundances do not solve the solar problem
• Sound-speed inversion of the Sun using a nonlocal statistical convection theory
• Solar $p$-mode damping rates: insight from a 3D hydrodynamical simulation
• Overcoming the structural surface effect with a realistic treatment of turbulent convection in 1D stellar models
• Stellar evolution models with overshooting based on 3-equation non-local theories, II. Main-sequence models of A- and B-type stars
• Stellar evolution models with overshooting based on 3-equation non-local theories I. Physical basis and the computation of the dissipation rate
• Multidimensional Simulations of Core Convection
• Testing the core overshooting mixing described by the turbulent convection model on the eclipsing binary star HY Vir
• Implications of a turbulent convection model for classical Cepheids
• Testing a non-local 1-equation turbulent convection model: A solar model
• Simulations of entropy rain-driven convection
• Third order correlations and skewness in convection. I. A new approach suitable for three-equation non-local models