Will white dwarfs cool down to blue, then yellow, then red?

[swampwiz]

AIUI, a white dwarf is a remnant from a star where the nuclear fusion process has exhausted since there is not enough pressure, etc., to continue to fuse heavier "metals" like carbon & oxygen, and that it is white because it is very hot, and thus relatively flat in the visible spectrum. It would seem then that eventually it will cool down to the temperature of regular stars that are blue, then on to white again, then yellow, then red before turning into a hot Jupiter and eventually a black dwarf.

 

[phyzguy]

Correct. You might try calculating how long it will take for a white dwarf to cool down to room temperature (300K), assuming that it is an ideal blackbody with a radius of the Earth and a mass of the sun.

 

[Ken G]

To do that, you will need to estimate the internal temperature, which is not so easy. You could take 10 million K as a kind of typical value, and use the current luminosity to get a cooling time, but in general it is not easy to connect the internal temperature to the surface temperature, you need a model of the heat conduction rate through the degenerate electrons (they are good conductors!). Note that the surface temperature, and luminosity, are set by the heat conduction rate, not the other way around. It will certainly be wrong to think the whole star shares its surface temperature, like some terribly oversimplified analyses do (e.g. http://www.ucolick.org/~mountain/AA...ong_does_it_take_for_a_white_dwarf_to_cool)-- that's going to be wrong by orders of magnitude.

A more detailed analysis of the cooling is given in http://adsbit.harvard.edu//full/1971IAUS...42...97V/0000099.000.html, where it shows that the luminosity scales like the interior temperature to the 3.5 power. That is strangely reminiscent of the Stefan-Boltzmann law for the surface temperature, but it's not due to radiation from the surface. Then to get the cooling law, one needs to start with the total thermal energy, which should be on the scale of the gravitational potential energy (though less, of course), and then assume the luminosity scales with the thermal energy to the 3.5 power to get the time dependence of the thermal energy. Setting the luminosity to be what it is now for some white dwarf of known age then fixes the constant of proportionality, and extrapolating forward gives you the future cooling of that particular white dwarf. (If you didn't know the ages of any white dwarfs, you'd have to use the constants from the theory, which is a lot more work!)

 

[Chronos]

Given, a white dwarf is the smoldering corpse of a small dead star, this is like asking how tall a 5 foot octogenarian may become.

 

[phyzguy]

Given, a white dwarf is the smoldering corpse of a small dead star, this is like asking how tall a 5 foot octogenarian may become.

Huh? You've lost me with your analogy.

 

[Chronos]

Dead stars evolve very differently than infant stars, so you the comparison between infants and octogenarians appears appropriate.

 

[Ken G]

It is important to understand white dwarf cooling though, because that provides a way to look into the past to understand the stellar population many billions of years ago. All you have left from that era are mostly white dwarfs and red dwarfs, and I think it's actually harder to backtrack the history of the red dwarfs because nothing changes all that much except their rotation rate, and that might depend on various factors. The white dwarf luminosity, on the other hand, changes quite a bit.

 

[stefan r]

...it is white because it is very hot, and thus relatively flat in the visible spectrum. ... blue, then on to white again, then yellow, then red ...

Not flat. Will be very blue then blue then white then yellow.

Black body radiation:

...Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature...

The atmosphere effects the perceived color.

... red dwarfs because nothing changes all that much except their rotation rate,...

The hydrogen to helium ratio should change.

 

[JMz]

The hydrogen to helium ratio should change.

Yes, but for red dwarfs, that effect is not significant over the whole life of the universe so far. We're dealing with stars whose lifetime is measured in trillions of years.

 

[Ken G]

Yes, and the small rate at which hydrogen turns to helium can get confused with other variables like metallicity, rotation, and magnetic fields, that it's probably pretty hard to pin down the age that way. White dwarf cooling is simple by comparison, so makes a better tool for looking far into the past.