Effective temperature is a term used in physics and astronomy to
quantify the temperature of an object by comparing its luminosity to that
of a black body.

A black body radiator will give off a certain amount of energy from its
surface per unit area per unit time (called the flux). The
Stefan-Boltzmann Law
states that the flux emitted by a black body is dependent *only* on
the temperature, according to

F_{total} = σ × (T_{effective})^{4}

If we know the size of an object we can compute the luminosity, which is
just the flux times the object's surface area. For a sphere,
the luminosity would be

L = 4 π R^{2} × F = 4 π R^{2} ×
σ T^{4}

So if we want to measure the temperature of a black body, we can solve this
relation for the effective temperature if we know the luminosity and the size
of the object.

The effective temperature is very important when solving
radiative transfer problems, particularly in stellar and planetary
atmospheres. The problem is that there are no *perfect* black
bodies in nature, though some objects come close. Any hot, dense object
(like the filament in a light bulb or an electric stove) is approximately
a black body. Stars are *almost* black bodies, though not quite.
The Sun is nearly a black body, and has an effective temperature of
5774 kelvins.

The concept of effective temperature doesn't make
much physical sense for nonthermal radiation sources. For those, we could
measure the brightness temperature, or else ignore the concept of
temperature altogether. For example, a synchrotron radiation source may
emit relativistic electrons, and we would
probably talk about the electrons' kinetic energy rather than their
temperature.

---

brightness temperature -- color temperature -- effective temperature

---

Sources:

*Radiative Processes In Astrophysics*, G. Rybicki and A. Lightman, Wiley
Interscience

Class lecture notes