The effective temperature is the star according to the Stefan Boltzmann law , corresponding to per unit surface area（ ）The temperature of a blackbody radiating the same brightness. Note that the total (thermal) luminosity of the star is , here Is the radius of the star. [2] The radius of a star is clearly defined, not directly observed. More precisely, the effective temperature is the temperature at the radius defined by Rossland's depth of light. The effective temperature and total luminosity are two necessary factors for placing stars in the Herot diagram Basic physical quantity The effective temperature and total luminosity actually depend on the chemical composition of the star. [3-4] The effective temperature of our sun is 5780K. In fact, the temperature of the star gradually decreases from the core to the atmosphere. The core temperature of the sun - the temperature of the solar center where nuclear fusion takes place - is about 15000000K.
The color index of stars shows that the stellar radiation from the very low temperature - in terms of star standards - is red M type stars mainly with infrared rays to blue high-temperature stars that emit a lot of ultraviolet rays. The effective temperature can show the heat energy radiated by each star per unit area. The surface from the warmest to the coldest is O B、A、F、G、K、 And M, which is known as star classification.
A red star may be a tiny red dwarf star with a small surface area and can only emit weak energy, or an expanding giant star or even a supergiant star, such as Antares (Antares) or Betelgeuse. Although the radiation energy per unit area of both stars is very low, they can emit huge energy because of their huge surface area. Stars with spectral types in the middle, such as the sun of moderate size or Capella of giant stars, can radiate more energy per unit area than red dwarfs or expanding supergiants, but still less than white or blue Vega or Rigel.
The effective temperature of the planet can be calculated by calculating the energy absorbed and the temperature T corresponding to the energy radiated by the black body.
In this case, the variables are distance D and luminosity L.
Assuming that the radiation of the star is isotropic and the distance between the planets is far enough, the energy absorbed by the planets is equal to the radius r of the planet disk, and the energy that can be intercepted when the star extends to the radius D. We also allow the planets to reflect some of the incoming energy and combine it into a parameter called albedo. An albedo of 1 means that all radiation is reflected, and an albedo of 0 means that all radiation is absorbed. The absorption capacity is expressed as follows:
Next, we will assume that the whole planet has the same temperature T, and the radiation of the planet is black body radiation. The type of planetary radiant energy can be expressed as:
These two equations are equal. After rearrangement, the effective temperature can be expressed as:
Notice that in the final equation, the radius of the planet no longer exists.
Jupiter's effective temperature is 112K, Pegasus 51b It is 1258K. However, the actual temperature is related to albedo, atmosphere and internal heat. From spectral analysis, the actual temperature of HD 209458b is 1130K, while the temperature of blackbody is 1359K. Jupiter's internal heat increases the actual temperature by 40 to 152 K. 
