(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
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
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
Referenced by pages: