Kelvin–Helmholtz timescale

Remarks

It is the order of magnitude of the time for which the Kelvin–Helmholtz mechanism could supply the luminosity $L$, since the gravitational energy of the star is of order $G M^2 / R$. Some authors include a factor of order one, such as $3/5$ for a uniform ball or $1/2$ for the part of the energy that is radiated. Example: for the Sun, $G M^2 / R \approx 3.8 \times 10^{41} \, \mathrm{J}$ and $L \approx 3.8 \times 10^{26} \, \mathrm{W}$, so $t_{\mathrm{KH}} \approx 10^{15} \, \mathrm{s}$, about $3 \times 10^7$ years. Non-example: the free-fall time $(G \rho)^{-1/2}$, with $\rho$ the mean density, is a different time scale; for the Sun it is under an hour, much shorter than $t_{\mathrm{KH}}$.