PX158 - F2 - luminosity-temperature-radius of stars

L_{*} = 4 π R_{*}^{2} σ T_{*}^{4}

the 'effective temperature', $T_{e f f}$ , is the mean temperature at the 'surface' of the star
- 'surface': when a star becomes optically thin, ie: photosphere
eg: what is $T_{e f f}$ for the sun?
$L_{⊙} = 3.83 \times 10^{26} W$
$R_{⊙} = 6.96 \times 10^{8} m$
$T_{e f f} = . . . \approx 5770 K$
eg: what is the luminosity of a white dwarf?
$T_{e f f, W D} = 25000 K$
$R_{W D} = 0.01 R_{⊙}$
$\begin{align*} L_{*} &= 4\,\pi\,R_{*}^{2}\, \sigma\,T_{*}^{4} \\ \frac{L}{L_{\odot}} &= \left(\frac{R}{R_{\odot}}\right)^{2}\left(\frac{T_{eff}}{T_{eff\odot}}\right)^{4} \\ &= (0.01)^{2}(4.3)^{4}L_{\odot} \\ \therefore L &\approx 0.034\,L_{\odot}$