Kelvin-Helmholtz timescale

PMS stars with M < 0.35 M0 have a simple structure - they are fully convective balls of gas all the way to the ZAMS. As the star contracts along its Hayashi track the core heats up, but the temperature gradient stays very close to adiabatic except in the surface layers. Li begins to burn in p, a reactions when the core temperature, Tc reaches c 3x 106 K and, because the reaction is so temperature sensitive (oc Tc16-19 at typical PMS densities) and convective mixing so very rapid, all the Li is burned in a small fraction of the Kelvin-Helmholtz timescale (see Fig. 1). 

Next, consider a star as a ball of hot gas which acts as reservoir of heat energy. How long would it take for this energy to radiate away if it were not replenished This is the thermal or Kelvin-Helmholtz timescale (Ik or tti,). If the total kinetic (thermal) energy of the star is E n, the timescale is approximately... 

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