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Other quantities are also represented by their mean values that vary only with distance r from the stellar center. The chief aim is to determine the mean temperature gradient ∇(r ) in order to complete the model of the internal thermodynamic structure of the star. 24) 4πr 2 where L is the stellar luminosity. 25) [see Eq. 14)]. The mean gradient ∇ adjusts itself so that whatever part of the total flux F cannot be carried as radiative energy flux FR is carried by convection. 2 in Stix (1989) or to Chapter 6 in B¨ohm-Vitense (1989c).

If the corona is optically thin for the newly created photon, then that photon escapes (or is absorbed by the photosphere). Hence, in any spectral line or continuum, the number of emitted photons per unit volume is proportional to n e n y , where n e is the electron density and n y is the number density of the emitting ion. The ion density n y is connected with the proton density n p through the abundance of the element relative to hydrogen and the temperaturedependent population fraction of the element in the appropriate ionization stage.

The temperature gradient is found to be only slightly subadiabatic: ∇ − ∇ad −10−6 . Basic assumptions in the ML approach are not confirmed by the observed solar granulation and numerical simulations of the structure of the top layers of convective envelopes. 5 we discuss the resulting change in the picture of the patterns in stellar convective envelopes. 1 Radiative transfer and atmospheric structure For the description of a radiation field, the monochromatic specific intensity Iν (x, y, z, θ, φ, t) is the fundamental parameter.

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