When the sun becomes a white dwarf why will it take SO long to cool off?

On 2006-08-19, Jonathan Thornburg -- remove -animal to reply wrote:
Ok, let's work out what determines the lifetime of a star:
To within a factor of two ot so (we're neglecting all time dependence),
the lifetime is just the ratio of the internal (thermal) energy in the
star, to the luminosity (energy radiated per unit time):

That's not true for the Sun, though, because the nuclear reactions at the
core effectively replenish the thermal energy. A thermal timescale for the
sun is closer to 10^7 years than its lifetime (10^10 years or so).

* Finally, sun-as-white-dwarf will be somewhat hotter than sun-now,
and thus radiate more energy per square meter of surface area per
unit time. I'm rusty enough on my stellar astrophysics that I no
longer recall the typical surface temperatures of *old* white dwarfs,
but I'll make a SWAG of a factor of 3 hotter than the sun, i.e. 80
times more radiated energy per square meter of surface area per
unit time.

The white dwarf cools as it radiates, though... Looking at the model I have
to hand, after ~ a Hubble time the white dwarf that the sun forms will have
a surface temperature of ~6000K; roughly the same as the Sun today.

I agree with your basic point though; the white dwarf is small so its
luminosity is small, and as it cools it radiates more slowly.

Cheers,

Ross