On 11 veebr, 19:39, Brian Davis <brda...@[EMAIL PROTECTED]
> wrote:
> On Feb 11, 5:01 am, 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).
>
There are plenty of main sequence orange dwarfs in globular clusters.
As for nearby "white" dwarfs, Procyon B is just about 7500 K, and it
is considerably younger than Sun.
> > 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 = 0.104 ( (k2/Q) T P M^2 / rho )^(1/6)
> where:
> a = tidal locking limit in [AU] (anything closer is likely locked)
> k2/Q = the 2nd order Love # divided by the Quality factor, both
> dimensionless
> T = age of system (in [yr])
> P = initial rotational period (in [hr])
> M = central (primary) mass (in solar masses, [Ms])
> rho = density of the planet (in [kg/m^3])
>
This is excessively complicated, in my opinion.
Simply drop the distance and central mass from the equation, and
express the tidal locking limit in terms of orbital period.
This leaves the variables of 2nd order Love #, Quality factor, initial
rotational period and density of the planet.
> For our solar system, for instance, a 5000 kg/m^3 Mercury-like body
> (k2/Q = 0.0025, very very roughly), anything inside of 0.58 [AU]
> should be tidally locked... as we see in the Solar System.
>
> > We 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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