Improved calibration of the radii of cool stars based on 3D simulations of convection: implications for the solar model

Abstract

Main sequence, solar-like stars (M < 1.5 Msun) have outer convective envelopes that are sufficiently thick to affect significantly their overall structure. The radii of these stars, in particular, are sensitive to the details of inefficient, super-adiabatic convection occurring in their outermost layers. The standard treatment of convection in stellar evolution models, based on the Mixing-Length Theory (MLT), provides only a very approximate description of convection in the super-adiabatic regime. Moreover, it contains a free parameter, alpha_MLT, whose standard calibration is based on the Sun, and is routinely applied to other stars ignoring the differences in their global parameters (e.g., effective temperature, gravity, chemical composition) and previous evolutionary history. In this paper, we present a calibration of alpha_MLT based on three-dimensional radiation-hydrodynamics (3D RHD) simulations of convection. The value of alpha_MLT is adjusted to match the specific entropy in the deep, adiabatic layers of the convective envelope to the corresponding value obtained from the 3D RHD simulations, as a function of the position of the star in the (log g, log T_eff) plane and its chemical composition. We have constructed a model of the present-day Sun using such entropy-based calibration. We find that its past luminosity evolution is not affected by the entropy calibration. The predicted solar radius, however, exceeds that of the standard model during the past several billion years, resulting in a lower surface temperature. This illustrative calculation also demonstrates the viability of the entropy approach for calibrating the radii of other late-type stars.

arXiv comment16 pages, 14 figures, accepted for publication in the Astrophysical Journal

References in corpus (66)

• emcee: The MCMC Hammer
• Accurate masses and radii of normal stars: modern results and applications
• Low Temperature Opacities
• Element Diffusion in the Solar Interior
• Helioseismology and Solar Abundances
• Evolution of low-mass star and brown dwarf eclipsing binaries
• A new Generation of Standard Solar Models
• Magnetic Inhibition of Convection and the Fundamental Properties of Low-Mass Stars. III. A Consistent 10 Myr Age for the Upper Scorpius OB Association
• The Habitability of Planets Orbiting M-dwarf Stars
• On the Correlation between the Magnetic Activity Levels, the Metallicities and the Radii of Low-Mass Stars
• The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - I. Methods and General Properties
• Stellar Models with Microscopic Diffusion and Rotational Mixing I: Application to the Sun
• YREC: The Yale Rotating Stellar Evolution Code
• The radius discrepancy in low mass stars: single vs. binaries
• Red Giant Branch stars: the theoretical framework
• Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length formulation
• Fresh insights on the structure of the solar core
• A Grid of 3D Stellar Atmosphere Models of Solar Metallicity: I. General Properties, Granulation and Atmospheric Expansion
• Magnetic Inhibition of Convection and the Fundamental Properties of Low-Mass Stars. I. Stars with a Radiative Core
• Elemental abundance differences in the 16 Cygni binary system: a signature of gas giant planet formation?
• The Stagger-grid: A grid of 3D stellar atmosphere models - III. The relation to mixing-length convection theory
• The Stagger-grid: A grid of 3D stellar atmosphere models - IV. Limb darkening coefficients
• Stellar Models with Microscopic Diffusion and Rotational Mixing II: Application to Open Clusters
• Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
• 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
• The Yale-Potsdam Stellar Isochrones (YaPSI)
• Older and Colder: The impact of starspots on pre-main sequence stellar evolution
• Reevaluating the Mass-Radius Relation for Low-Mass, Main Sequence Stars
• Stellar Diameters and Temperatures VI. High angular resolution measurements of the transiting exoplanet host stars HD 189733 and HD 209458 and implications for models of cool dwarfs
• Magnetic Inhibition of Convection and the Fundamental Properties of Low-Mass Stars. II. Fully Convective Main Sequence Stars
• Three carbon-enhanced metal-poor dwarf stars from the SDSS - Chemical abundances from CO^5BOLD 3D hydrodynamical model atmospheres
• Calibrating Convective properties of Solar-like Stars in the Kepler Field of View
• The Helium content and age of the Hyades: Constraints from five binary systems and Hipparcos parallaxes
• Correlation between lithium abundances and ages of solar twin stars
• Self-Consistent Magnetic Stellar Evolution Models of the Detached, Solar-Type Eclipsing Binary EF Aquarii
• The Mass Mixing Length in Convective Stellar Envelopes
• A Tale of Two Anomalies: Depletion, Dispersion, and the Connection Between the Stellar Lithium Spread and Inflated Radii on the Pre-Main Sequence
• Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations. I. $T(\tau )$-Relations
• Investigating the Metallicity-Mixing Length Relation
• Extended subadiabatic layer in simulations of overshooting convection
• Modelling Kepler Red Giants in Eclipsing Binaries:Calibrating the Mixing Length Parameter with Asteroseismology
• The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - II. Horizontal and Temporal Averaging and Spectral Line Formation
• Alive and well: a short review about standard solar models
• Convection Theory and Sub-photospheric Stratification
• Stellar models with mixing length and T(tau) relations calibrated on 3D convection simulations
• Effective temperatures of red giants in the APOKASC catalogue and the mixing length calibration in stellar models
• Stellar models with the ML2 theory of convection
• 3D hydrodynamical CO5BOLD model atmospheres of red giant stars: I. Atmospheric structure of a giant located near the RGB tip
• Stellar models with calibrated convection and temperature stratification from 3D hydrodynamics simulations
• Modelling the components of binaries in Hyades: The dependence of the mixing-length parameter on stellar mass
• Variation of Stellar Envelope Convection and Overshoot with Metallicity
• Surface convection and red giants radii measurements
• Hydrodynamical simulations of convection-related stellar micro-variability. II. The enigmatic granulation background of the COROT target HD49933
• Surface-effect corrections for the solar model
• Theoretical oscillation frequencies for solar-type dwarfs from stellar models with $⟨3\mathrm{D}⟩$-atmospheres
• The Radius and Entropy of a Magnetized, Rotating Fully-convective Star: Analysis With Depth-dependent Mixing Length Theories
• Dynamics of Turbulent Convection and Convective Overshoot in a Moderate Mass Star
• The Effect of Metallicity-Dependent T-tau Relations on Calibrated Stellar Models
• Simulating the outer layers of Procyon A: a comparison with the Sun
• Modelling fully convective stars in eclipsing binaries: KOI-126 and CM Draconis
• Entropy in adiabatic regions of convection simulations
• Helium-Abundance and Other Composition Effects on the Properties of Stellar Surface Convection in Solar-like Main-sequence Stars
• Evidence of radius inflation in stars approaching the slow-rotator sequence
• 3D stellar atmospheres for stellar structure models and asteroseismology
• The Dark Side of the Sun A Plea for a Next-Generation Opacity Calculation

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