On Feb 11, 5:01=A0am, sigidu...@[EMAIL PROTECTED]
wrote:
> The cooler they get, the slower they cool, so there are more
> (relatively) cool ones around than hot bright ones.
You are making the assumption that the population of white dwarfs in
in steady state. That might not be a good assumption. The current
population of the various luminosities would depend on the past
production rates, as well as how long the population has aged... & for
tiny white dwarfs, they cool off so slowly that the population isn't
near equilibrium yet. In short, i think empirically there's more hot
than not - thus why they are called "WHITE dwarfs"
> A white dwarf with a temperature similar to the Sun would be about
> 1/10,000 as bright
I'm not sure there are a lot of these around. Given the current age of
the universe (young, compared to white dwarf cooling times), the very
oldest white dwarfs might be a few thousand K... but you won't find
any very old white dwarfs to begin with, because early star formation
was biased towards very large stars (that don't leave white dwarfs).
> Presumably a planet in the habitable zone
> would be tidally locked.
Maybe. Tidal locking time depends on the primary's mass (& of course
distance), but not on the primary's diameter*. What's critically
unknown here is the Q factor of your hypothetical world, or how fast
it dissipates tidal energy. Very roughly, you can get an estimate of
the tidal locking distance from:
a =3D 0.104 ( (k2/Q) T P M^2 / rho )^(1/6)
where:
a =3D tidal locking limit in [AU] (anything closer is likely locked)
k2/Q =3D the 2nd order Love # divided by the Quality factor, both
dimensionless
T =3D age of system (in [yr])
P =3D initial rotational period (in [hr])
M =3D central (primary) mass (in solar m*****, [Ms])
rho =3D density of the planet (in [kg/m^3])
For our solar system, for instance, a 5000 kg/m^3 Mercury-like body
(k2/Q =3D 0.0025, very very roughly), anything inside of 0.58 [AU]
should be tidally locked... as we see in the Solar System.
>=A0We can make the dwarf quite a lot brighter, but... lots of
> hard UV and X-rays.
Assuming you can get a habitable planet to reform around the white
dwarf, I think this is the biggest issue. You have to wait a long
time... a *very* long time... until the dwarf cools enough so that the
much greater UV flux isn't likely to be a show stopper.
--
Brian Davis
*note: changes in the planets *orbit* due to tides induced on the
primary are a different matter, they do depend on the primary's
diameter. But the diameter of the primary doesn't play a roll in tidal
braking of the *rotation* of the planet.
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