Effective temperature

The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature when the body's emissivity curve (as a function of wavelength) is not known.

When the star's or planet's net emissivity in the relevant wavelength band is less than unity (less than that of a black body), the actual temperature of the body will be higher than the effective temperature. The net emissivity may be low due to surface or atmospheric properties, including greenhouse effect.

The effective temperature of a star is the temperature of a black body with the same luminosity per surface area (${\displaystyle {\mathcal {F}}_{\rm {Bol}}}$) as the star and is defined according to the Stefan–Boltzmann law ${\displaystyle {\mathcal {F}}_{\rm {Bol}}=\sigma T_{\rm {eff}}^{4}}$. Notice that the total (bolometric) luminosity of a star is then ${\displaystyle L=4\pi R^{2}\sigma T_{\rm {eff}}^{4}}$, where ${\displaystyle R}$ is the stellar radius. The definition of the stellar radius is obviously not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius that is defined by a certain value of the Rosseland optical depth (usually 1) within the stellar atmosphere. The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the Hertzsprung–Russell diagram. Both effective temperature and bolometric luminosity depend on the chemical composition of a star.

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