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Theory of Stellar Convection: Removing the Mixing-Length Parameter

by Cesare Chiosi (Dip. di Fisica e Astronomia, Univ. degli studi di Padova)

Dec 05, 2013 from 02:00 PM to 04:00 PM

Where Seminars' room, floor -1, via Ranzani 1

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Stellar convection is customarily described by the mixing-length theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to claim that the mixinglength parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in literature are hampered by this basic uncertainty. The aim of this study is to present a new theory of stellar convection 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 behaviour 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, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism 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. We obtain an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory are compared with those from the standard mixing-length paradigm with very satisfactory results.

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