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### Kelvin-Helmholtz timescale

(KH timescale, KH time, τKH, Kelvin-Helmholtz time, thermal timescale)
(time that would radiate away a body's heat energy given its luminosity)

A body's Kelvin-Helmholtz timescale (aka KH timescale, Kelvin-Helmholtz time, KH time or τKH 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 varying definitions are used:

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

These are within the same order-of-magnitude, given the virial theorem. They do not take into account any luminosity variation.

``` 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)
```
• τKH - 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.

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

(astrophysics,luminosity,timescale)
Further reading:
http://en.wikipedia.org/wiki/Thermal_time_scale

Referenced by pages:
Kelvin-Helmholtz mechanism

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