Astron. Astrophys. 356, 301-307 (2000)

2. Radiative model

Quite generally, the radiative model should provide a relationship between the brightness intensity I and the temperature

In the photosphere, the Local Thermodynamic Equilibrium (LTE) is not too bad an assumption (Bray et al. 1984; Mihalas et al. 1984), so that the intensity emerging from the photosphere at frequency can be expressed as the blackbody source function, or Planck's function

which can be approximated at the optical wavelengths under concern by Wien's law

with the temperature constant (at the wavelength nm)

Expression (10) can be cast into the form

with (7) and

which clearly accounts for the contrast between the "cool" umbra at some 4000 K and the surrounding "hot" photosphere at 6000 K. Inversion of relation (12) yields

Let us here insist upon the fact that relation (14) provides a hint about the variations of temperature over the active region, which will be checked in Sect. 4 to be not so far from reality. Of course, the direct measurement of the pressure field remains the best way to provide reliable information (e.g. from the pressure broadening of spectral lines).

© European Southern Observatory (ESO) 2000

Online publication: March 28, 2000
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