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How can I make a black dwarf star?

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In response to a question about an asteroid filled with degenerate matter, Ender Look suggested that using matter from a black dwarf would be better than using matter from a white dwarf since black dwarfs are cooler. A typical white dwarf's temperature might be $\sim$10,000 K, which is way too high.

The problem is, it takes a long time to form a black dwarf. The distinction between a white dwarf and a black dwarf is somewhat arbitrary, partly because "black dwarf" is not a technical term. Some simply say that black dwarfs are white dwarfs that have cooled to the point where they no longer emit a substantial amount of visible light. According to that definition, we may already have some black dwarfs (e.g. the companion star to PSR J2222-0137). However, this corresponds to a temperature of about 2800 to 3000 K, which is still too high for the purposes of the original question about degenerate matter. Therefore, I need to define a black dwarf as a white dwarf that has cooled to about 1000 K or lower.

The problem is, this is going to take a really long time, and there may not be any black dwarfs this cool in the galaxy. This means that I'm willing to use artificial means to turn a regular white dwarf ($T\sim$10,000 K) into a black dwarf ($T\sim$1000 K). The civilization doing the transformation ranks as a Type II civilization on the Kardashev scale and has all the powers and technologies you would expect them to have (key exception: no FTL travel).

How can this Type II civilization turn a white dwarf into a black dwarf, within a reasonable timeframe (say, 100 to 1000 years)?

Other specifications:

  • We'll assume a mass of about 0.25 solar masses, and a radius of about 0.0038 solar radii (radius derived from a mass-radius relation, with Sirius B as a reference).
  • The white dwarf in question is alone, with no binary companion or planets.
  • There might be a handy interstellar cloud of gas in the region if needed.
  • Large-scale mass removal or addition is likely undesirable.
  • The object shouldn't merely appear black, so you can't paint it black, as it were.

I should add that What could be done to make a red dwarf become a blue dwarf, then a white dwarf and then finally a black dwarf in a short amount of time? does talk about this, but it seems like they're using a black dwarf that's extremely cool (more like 10 or 100 K). There are also some other differences:

  • Their civilization is a Type III civilization; I have a puny Type II one.
  • They're fine with FTL travel; I am certainly not.
  • They want to start with a red dwarf, meaning they have more control over the object. I'm starting from just a white dwarf.
  • I'm looking for a bit of a hotter black dwarf than they are, it seems.
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