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)

The title of this article is ambiguous. For further meanings see effective temperature

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 .