Calibration of the mixing-length parameter $\alpha$ for the MLT and FST models by matching with CO${}^5$BOLD models

Abstract

The CoRoT and Kepler missions provided a wealth of high-quality data for solar-like oscillations. To make the best of such data for seismic inferences, we need theoretical models with precise near-surface structure, which has significant influence on solar-like oscillation frequencies. The mixing-length parameter, $\alpha$, is a key factor for the near-surface structure. In the convection formulations used in evolution codes, the $\alpha$ is a free parameter that needs to be properly specified. We calibrated $\alpha$ values by matching entropy profiles of 1D envelope models with those of 3D CO${}^5$BOLD models. For such calibration, previous works concentrated on the classical mixing-length theory (MLT). Here we also analyzed the full spectrum turbulence (FST) models. For the atmosphere part in the 1D models, we use the Eddington grey $T(\tau )$ relation and the one with the solar-calibrated Hopf-like function. For both the MLT and FST models with a mixing length $l=\alpha H_p$, calibrated $\alpha$ values increase with increasing $g$ or decreasing $T_{\mathrm{eff}}$. For the FST models, we also calibrated values of ${\alpha }^{\ast }$ defined as $l=r_{\mathrm{top}}-r+{\alpha }^{\ast }{H}_{p,\mathrm{top}}$. ${\alpha }^{\ast }$ is found to increase with $T_{\mathrm{eff}}$ and $g$. As for the correspondence to the 3D models, the solar Hopf-like function gives a photospheric-minimum entropy closer to a 3D model than the Eddington $T(\tau )$. The structure below the photosphere depends on the convection model. However, not a single convection model gives the best correspondence since the averaged 3D quantities are not necessarily related via an EOS. Although the FST models with $l=r_{\mathrm{top}}-r+{\alpha }^{\ast }{H}_{p,\mathrm{top}}$ are found to give the frequencies closest to the solar observed ones, a more appropriate treatment of the top part of the 1D convective envelope is necessary.

arXiv comment14 pages, 18 figures, accepted to Astronomy and Astrophysics

References in corpus (20)

• A grid of MARCS model atmospheres for late-type stars I. Methods and general properties
• Simulations of stellar convection with CO5BOLD
• Seismic diagnostics for transport of angular momentum in stars 1. Rotational splittings from the PMS to the RGB
• Stellar Turbulent Convection: A Selfconsistent Model
• Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere
• ASTEC -- the Aarhus STellar Evolution Code
• The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - I. Methods and General Properties
• Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length formulation
• A Grid of 3D Stellar Atmosphere Models of Solar Metallicity: I. General Properties, Granulation and Atmospheric Expansion
• The Stagger-grid: A grid of 3D stellar atmosphere models - III. The relation to mixing-length convection theory
• Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
• Surface-effect corrections for solar-like oscillations using 3D hydrodynamical simulations
• Definitive Sun-as-a-star p-mode frequencies: 23 years of BiSON observations
• Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations. I. $T(\tau )$-Relations
• Convection in the atmospheres and envelopes of Pre-Main Sequence stars
• 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
• Influence of local treatments of convection upon solar p mode excitation rates
• On the computation of eigenfrequencies for equilibrium models including turbulent pressure
• Radiation-hydrodynamics simulations of surface convection in low-mass stars: connections to stellar structure and asteroseismology

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