Testing the entropy calibration of the radii of cool stars: models of α Centauri A and B

Abstract

Abstract We present models of α Centauri A and B implementing an entropy calibration of the mixing-length parameter αMLT, recently developed and successfully applied to the Sun (Spada et al. 2018, ApJ, 869, 135). In this technique the value of αMLT in the 1D stellar evolution code is calibrated to match the adiabatic specific entropy derived from 3D radiation-hydrodynamics simulations of stellar convective envelopes, whose effective temperature, surface gravity, and metallicity are selected consistently along the evolutionary track. The customary treatment of convection in stellar evolution models relies on a constant, solar-calibrated αMLT. There is, however, mounting evidence that this procedure does not reproduce the observed radii of cool stars satisfactorily. For instance, modelling α Cen A and B requires an ad-hoc tuning of αMLT to distinct, non-solar values. The entropy-calibrated models of α Cen A and B reproduce their observed radii within $1\%$ (or better) without externally adjusted parameters. The fit is of comparable quality to that of models with freely adjusted αMLT for α Cen B (within 1 σ), while it is less satisfactory for α Cen A (within ≈2.5 σ). This level of accuracy is consistent with the intrinsic uncertainties of the method. Our results demonstrate the capability of the entropy calibration method to produce stellar models with radii accurate within $1\%$. This is especially relevant in characterising exoplanet-host stars and their planetary systems accurately.