- a) EFFECTIVE TEMPERATURE ®given by Stefan-Boltzmann eqn.
b) EXCITATION TEMPERATURE ®given by Boltzmann eqn.
c) IONIZATION TEMPERATURE ®given by Saha eqn.
d) KINETIC TEMPERATURE ®given by Maxwell-Boltzmann eqn (most probable speed).
e) COLOR TEMPERATURE ®(fit continuum to Plank's fn.)
The temperature can be determined by broadband photometry, via color indices (B-V, V-R, etc.). Note that B-V is a good Teff indicator for A stars, but not for M stars.
B) IN PERFECT THERMAL EQUILIBRIUM (TE), ALL OF THESE TEMPERATURES ARE EQUAL
- a) A BLACKBODY IS AN EXAMPLE OF TE
In the case of a BB, the absorption of a photon occurs at same rate as the emission of the same kind of photon.
C) LOCAL THERMODYNAMIC EQUILIBRIUM (LTE)
- a) A STAR IS NOT IN PERFECT TE
In a star, there is a net outward flow of energy, which means that there must be a temperature gradient. If there is a temperature gradient, then obviously the star is not in TE (strictly speaking).
b) WHEN A SINGLE TEMPERTURE CAN BE ASSUMED, EVEN IF TE DOES NOT STRICTLY HOLD ...
If the distance over which the temperature changes significantly is LARGE, compared to the distances travelled by particles and photons between collisions (called the mean free path, or mfp), then an idealized single temperature may be used.
