What is a "temperature distribution" in a stellar photosphere?

[AlphaCrucis]

TL;DR Summary

Explain what we mean by the term "temperature distribution" in the context of stellar photospheres.

What is a "temperature distribution" in the context of a stellar photosphere and How is the temperature distribution related to the effective temperature?

 

[Richard R Richard]

The effective temperature of the Sun's surface is about 5,600ºC. This data is important because the characteristics of the radiation emitted by a body are a function of its surface temperature.
A gas can be transparent, partially transparent, or opaque. Opacity is a measure of the transparency of a gas per unit length. If the opacity of a gas is very large, we cannot see very far through it.
When we look at the Sun, we see through the solar gas until the optical depth is very great and it becomes opaque. The base of the photosphere is defined as the level to which we can see directly at the center of the solar disk.
When we take pictures of the Sun, we find that the intensity of the light varies from the center of the disk towards the limbus. The regions near the edge are darker than the regions near the center, this phenomenon is called darkening in the limbus.

When we look at the center of the solar disk, that is, in the perpendicular direction, we can see up to the level that we have defined as the base of the photosphere, the deeper the solar gas is opaque. The radiation received therefore corresponds to this level, which compared to that of the black body corresponds to a temperature of 5780 K. When we observe at a point other than the center of the disk, the observation direction is no longer perpendicular, as we go towards the limbus we observe almost tangentially to disk. The gas becomes opaque at a level located above the base of the photosphere, at the same depth because it is an oblique line we see a higher level than when observing perpendicularly Solar gas when we observe near the limbus emits less radiation than near the center and comparing with a black body it corresponds to a lower temperature. Consequently we can deduce that the temperature of the photosphere increases as the radius decreases, in Physics it is said that there is a negative temperature gradient. In fact, the temperature decreases from the base of the photosphere (5780 K) to about 500 km above where its value is 4200 K, this limit corresponds to the lowest part of the chromosphere.
The temperature distribution is the mathematical representation of that gradient.

Sources: in Spanish
http://www.juntadeandalucia.es/aver...rio/250/289/html/antares/modulo4/m4_u103.html
http://edii.uclm.es/~arodenas/Solar...peratura efectiva de la,de la superficie del% 20 itself.