Effective temperature

Definition

Let a body emit radiation with total bolometric flux $F > 0$ per unit area of its surface. This is the emitted power per unit area summed over all frequencies and directions. Let $\sigma$ be the Stefan–Boltzmann constant. The effective temperature of the body is the unique $T_{\text{eff}} > 0$ with $F = \sigma T_{\text{eff}}^4.$ For a spherical star of radius $R$ and luminosity $L$ , this means $L = 4\pi R^2 \sigma T_{\text{eff}}^4$ .

Remarks

Example: a black body at temperature $T$ emits $F = \sigma T^4$ by the Stefan–Boltzmann law, so its effective temperature is $T$ . Non-example: the temperature at the centre of the Sun, about $1.5 \times 10^7$ K, is not its effective temperature. The surface flux of the Sun corresponds to about $5772$ K. In the Eddington grey atmosphere, $T^4(\tau) = \frac{3}{4} T_{\text{eff}}^4 (\tau + \frac{2}{3})$ , so the local temperature equals $T_{\text{eff}}$ at optical depth $\tau = 2/3$ .

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Black body concept
Effective temperature definition

Tag	`YKYH24SSYH`
URI	`m2://YKYH24SSYH`
Kind	definition
Writing	W0 stub
MSC	85A25, 85A15, 80A21
Defines	Effective temperature
Uses	Black body
Changed	3 November 2026

Effective temperature

Definition

Remarks

Reading path

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