Radiative Equilibrium

radiative equilibrium [′rād·ē‚ād·iv ‚ē·kwə′lib·rē·əm]

(astrophysics)

The energy transfer through a star by radiation, absorption, and reradiation at a rate such that each section of the star is maintained at the appropriate temperature.

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Radiative Equilibrium 

in the atmospheres of stars, the state of the stellar atmosphere for which energy transfer in the atmosphere is carried out by radiation, with each element of volume of the atmosphere radiating as much energy as it absorbs. The radiation-equilibrium hypothesis is valid for most stars since the other types of energy transfer (convection and conduction) play a lesser role in stellar atmospheres.

The determination of the physical conditions in the atmosphere for which there is radiative equilibrium reduces to the joint solution of the equations of radiative transfer and radiative equilibrium. These equations are supplemented by the equation of mechanical equilibrium of the atmosphere under the effect of the force of attraction and the forces of gas pressure and the pressure of light. Thermodynamic equilibrium for the intrinsic temperature at each point is also assumed. The solution of these equations has made it possible to determine the radiation field and the variation in density and temperature with height in a star’s atmosphere. In particular, the energy distribution in the continuous spectrum of a star is found in this way. By comparing the energy distribution in the spectrum calculated using this method with the observed distribution, we can verify the validity of the assumed theory.

In the theoretical determination of the line spectra of stars, we take into account in the radiative-equilibrium equation the redistribution of radiation over frequencies within the spectral line. The theory makes it possible to determine the profile of the spectral line and the equivalent width of the line, that is, the width of the adjacent segment of the continuous spectrum for which the energy is equal to the total energy absorbed in the line. Of great importance is the dependence of the equivalent width on the number of absorbing atoms (called the growth curve), by means of which it is possible to determine the chemical composition of stellar atmospheres. Line profiles may be used to determine effects such as stellar rotation and the presence of magnetic fields in stellar atmospheres. The study of stars having bright lines in the spectra is of particular importance in the theory of radiative equilibrium. These spectra appear in envelopes ejected by different nova-like variables (such as novae and type Be stars).

REFERENCES

Sobolev, V. V. Kurs teoreticheskoi astrofiziki. Moscow, 1967.
Ivanov, V. V. Perenos izlucheniia i spektry nebesnykh tel. Moscow, 1969.

V. V. SOBOLEV