The scale-free theory of stellar convection

Abstract

Context. A new, self-consistent, scale-free theory of stellar convection was recently developed (SFCT) in which velocities, dimensions, and energy fluxes carried by the convective elements are defined in a rest frame co-moving with the convective element itself. As the dynamics of the problem is formulated in a different framework with respect to the mixing length theory (MLT), the SFCT equations are sufficient to determine all the properties of stellar convection in accordance with the physics of the environment alone, with no need for the mixing length parameter (MLP). Subsequently, the SFCT was improved by introducing suitable boundary conditions at the surface of the external convective zones of the stars, and the first stellar models and evolutionary tracks on the Hertzsprung–Russell diagram were calculated. Aims. The SFCT received alternatively positive and negative attention that spurred us to reconsider the whole problem. In this work, we aim to re-examine the physical foundations and results of the SFCT, elucidate some misconceptions on its physical foundations, reply to reported criticisms, and present some recent improvements to the SFCT. Methods. The analysis was done using the same formalism of the previous studies, but novel arguments and demonstrations are added to better justify the controversial points, in particular the relaxation of instantaneous hydrostatic equilibrium between a convective element and the surrounding medium. Results. The main results include (i) a novel detailed discussion of the boundary conditions to ensure that the temperature gradients in the outermost regions of a star are adequate for analyses of stability or instability in asteroseismology; (ii) a quantitative comparison with the MLT; and, finally, (iii) the recovery of the MLT as a particular case of the SFCT, but also in this case with no need for the MLP. Conclusions. In conclusion, the SFCT is a step forward with respect to the classical MLT.