Abstract
Stellar convection is usually described by the mixing-length theory, which makes use of the mixing-length scale factor to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is proportional to the local pressure scale height of the star, and the proportionality factor (i.e. mixing-length parameter) is determined by comparing the stellar models to some calibrator, i.e. the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and all evolutionary phases and because of this, all stellar models in the literature are hampered by this basic uncertainty.In a recent paper [1] we presented a new theory that does not require the mixing length parameter. Our self-consistent analytical formulation of stellar convection determines all the properties of stellar convection as a function of the physical behavior of the convective elements themselves and the surrounding medium. The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations expressed in a non-inertial reference frame co-moving with the convective elements. The motion of stellar convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism.The predictions of the new theory are compared with those from the standard mixing-length paradigm with positive results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.
Highlights
The transfer of energy by convection is of paramount importance in all the stars
The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations expressed in a noninertial reference frame co-moving with the convective elements
In the same plot we show the predictions of the mixing-length theory (MLT) with Λm = 1.65
Summary
The transfer of energy by convection is of paramount importance in all the stars. High-mass stars, roughly for masses M > 1.3M contain fully convective cores, all stars M ∈ [0.1, 100] M have outer convective envelopes, and stars smaller in mass than M < 0.3M are fully convective. A satisfactory treatment of stellar convection in stars is still open to debate and a self-consistent treatment of the physics of convective energy transfer is still missing. The most successful theory dealing with the external convection is the mixing-length theory (MLT) developed long ago by [2] and [3]. In the following we will refer to this theory as the scale-free convection (SFC) theory. In this approach the authors obtained a solution for the equations governing stellar atmospheres that self-consistently predict the energy transport, luminosities, radii and effective temperatures all along the evolutionary sequence of a star
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