### Kelvin-Helmholtz timescale

**(KH timescale, KH time, τ**_{KH}, 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 **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 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.

τ_{KH} = K/L = (-U/2)/L
or alternately:
τ_{KH} = U/L
or treating the object as a uniform-density sphere:
τ_{KH} = 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.

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

Index