Kelvin-Helmholtz timescale

A body's Kelvin-Helmholtz timescale (aka KH timescale, Kelvin-Helmholtz time, KH time or τ_KH and sometimes the term thermal timescale is taken to mean the same) is a simplified (back-of-the-envelope) calculation of the time a body could continue to shine as it does given its potential energy and kinetic energy (i.e., through the Kelvin-Helmholtz mechanism), but a variety of calculations are used:

• the time in which a body would radiate away its kinetic energy (thermal energy) given its current luminosity.
• similarly, the time it would radiate away its gravitational binding energy.
• similarly, the time it would radiate away its gravitational potential energy.
• the latter calculated for a sphere of uniform density.

 τKH = K/L = (-U/2)/L
or alternately:
 τKH = |U/L|
or treating the object as a uniform-density sphere:
 τKH = 3GM²/(5RL) ≈ GM² /(RL)

• τ_KH - Kelvin-Helmholtz timescale.
• L - luminosity (i.e., rate at which energy is emitted).
• U - object's gravitational potential energy.
• K - object's kinetic energy (of its particles, i.e., its thermal energy).
• G - gravitational constant.
• M - mass of the sphere.
• R - radius of the sphere.

These three formulae produce different values but are within the same order-of-magnitude, given the virial theorem. They ignore any luminosity variation over time.

I've also seen the term thermal timescale used regarding a different process.