"Radium" wrote in news:1156103700.335569.172140
@i3g2000cwc.googlegroups.com:


Brian Tung wrote:
Radium wrote:
I've read about the sun's life cycle. Apparently, when the sun becomes
a white dwarf, it will take at least a trillion years to completely
cool off. Why such a long time?

Because at that point, the Sun will still have a lot of heat left, but
it will be radiating it much slower than it does now.

A white dwarf is the hot exposed core of the progenitor star. As such,
it contains most of the heat that was in the star at the time that it
died. But the white dwarf radiates heat much slower than it did when
the star was alive, simply because its surface area is so much smaller.

The Sun as a white dwarf will be, let's say, 100 times smaller (by
diameter) than it is now, meaning it will be 10,000 times smaller by
area. To be sure, it will initially be quite hot, perhaps four times
hotter (in kelvins) than it is now, so it'll radiate tens of times more
energy per unit area than it does now. Still, that means that its
overall rate of radiation (and therefore rate of cooling) will be
several hundreds of times slower than it is now.

That factor will only increase as the Sun cools down, and the rate at
which it radiates off into space slows down. It will approach the cold
of interstellar space only very slowly at the end.

--
Brian Tung
The Astronomy Corner at http://astro.isi.edu/
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When the sun become a black dwarf, will it ever get a chance to cool to
around 70 Fahrenheit? Or will it likely form another star before?


You can do the calculation yourself. Knowing the surface area of the dwarf,
the specific heat of degenerate matter made of carbon and oxygen combined
with the Stefan-Boltzmann law. i.e radiated power goes as the fourth power
of temperature. That is good enough as a first approximation anyway. BTW,
if a black dwarf manages to accumulate additional mass through accretion
then it runs into a small problem once it reaches about 1.4 Solar masses.
At that point, the pressure caused by the object's own gravity, can no
longer be resisted by electron degeneracy pressure. This means that the
dwarf starts to collapse but now all that Carbon and Oxygen is then
available as fuel. Kablooooie. Type 1a supernova.

Klazmon.