Improved Calibration of the Radii of Cool Stars Based on 3D Simulations of Convection: Implications for the Solar Model

Main-sequence, solar-like stars (M less than or similar to 1.5M(circle dot)) 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, superadiabatic 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 superadiabatic regime. Moreover, it contains a free parameter, (MLT)-M-alpha, 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 aMLT based on 3D radiation hydrodynamics (RHD) simulations of convection. The value of aMLT 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.