The Kelvin-Helmholtz Timescale
The Sun contains a great deal of gravitational potential energy. You can
compute the amount of this energy: it is given by the expression
Eg = GM2/R
Suppose the Sun were not in equilibrium: there were no forces opposing
gravitational collapse. In order for the collapse to proceed, the pressure
supporting the Sun against collapse, provided by the hot gas, would have to
be lost. As the gas radiates its energy away, pressure support
would decrease, and the Sun would contract. But the release of gravitational
potential energy would reheat the Sun (at a slightly smaller radius).
The Sun would slowly contract, radiating away all of its gravitational
potential energy. If it does so at its present luminosity, the time it
takes to radiate away its energy is given by the total energy divided by
the rate the energy is lost (which is the luminosity). This time,
tKH = GM2/RL
is called the Kelvin-Helmholtz Time. It is the time neded to radiate away
a significant fraction of the thermal energy of a star. For today's Sun,
this timescale is about 30 million years.
Consequences of the Kelvin-Helmholtz Timescale
The Kelvin-Helmholtz Timescale sets the time for
- protostars to collapse to the main sequence
- main sequence stars to evolve into giants
Note that if the Sun were to cease burning nuclear fuel now, it
would continue to shine for tens of millions of years.