# Effective temperature

 The articles Star Surface # Surface Temperature and Effective Temperature thematically overlap. Help me to better differentiate or merge the articles (→  instructions ) . To do this, take part in the relevant redundancy discussion . Please remove this module only after the redundancy has been completely processed and do not forget to include the relevant entry on the redundancy discussion page{{ Done | 1 = ~~~~}}to mark. McBayne ( discussion ) 10:21 p.m. , Jun 23, 2018 (CEST)

Spectral radiation density of our sun (effective temperature around 5780  K ) compared to that of a black body of the same size (labeling in English)

The effective temperature of a star is the temperature of its surface that a black body would have to have in order to shine with the same brightness per area . The effective temperature of an object deviates from the kinetically defined temperature, the less the spectrum of the object corresponds to that of a black body. ${\ displaystyle T _ {\ mathrm {eff}}}$ ${\ displaystyle {\ mathcal {F}} _ {\ mathrm {Bol}}}$

According to the Stefan-Boltzmann law, the following applies

${\ displaystyle {\ mathcal {F}} _ {\ mathrm {Bol}} = \ sigma \ cdot T _ {\ mathrm {eff}} ^ {4}}$

${\ displaystyle \ Leftrightarrow T _ {\ mathrm {eff}} = {\ sqrt [{4}] {\ frac {{\ mathcal {F}} _ {\ mathrm {Bol}}} {\ sigma}}}}$

with the Stefan-Boltzmann constant

${\ displaystyle \ sigma = 5 {,} 67 \, \ cdot \, 10 ^ {- 8} \, \ mathrm {W \, m ^ {- 2} K ^ {- 4}}}$

This gives the bolometric brightness to

{\ displaystyle {\ begin {alignedat} {2} L & = {\ frac {L} {A}} && \ cdot A \\ & = \ sigma T _ {\ mathrm {eff}} ^ {4} && \ cdot 4 \ pi R ^ {2} \ end {alignedat}}}

With

• the star's surface , where is the radius of the star.${\ displaystyle 4 \ pi R ^ {2}}$${\ displaystyle R}$

Since the stellar radius cannot be clearly defined, the optical density is used to calculate the effective temperature .

The effective temperature and the bolometric brightness are the two physical parameters with which a star can be classified in the Hertzsprung-Russell diagram .